Collaborative and Individual Learning in Teaching [1 ed.] 9781617281525, 9781608768899

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Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved. Collaborative and Individual Learning in Teaching, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved. Collaborative and Individual Learning in Teaching, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

EDUCATION IN A COMPETITIVE AND GLOBALIZING WORLD SERIES

COLLABORATIVE AND INDIVIDUAL LEARNING IN TEACHING: A TRAJECTORY TO EXPERTISE IN Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

PEDAGOGICAL REASONING

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EDUCATION IN A COMPETITIVE AND GLOBALIZING WORLD SERIES Success in Mathematics Education Caroline B. Baumann 2009. ISBN: 978-1-60692-299-6 Mentoring: Program Development, Relationships and Outcomes Michael I. Keel (Editor) 2009. ISBN: 978-1-60692-287-3

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Mentoring: Program Development, Relationships and Outcomes Michael I. Keel (Editor) 2009. ISBN: 978-1-60876-727-4 (Online Book) Motivation in Education Desmond H. Elsworth (Editor) 2009. ISBN: 978-1-60692-234-7 Evaluating Online Learning: Challenges and Strategies for Success Arthur T. Weston (Editor) 2009. ISBN: 978-1-60741-107-9 Enhancing Prospects of LongerTerm Sustainability of CrossCultural INSET Initiatives in China Chunmei Yan 2009. ISBN: 978-1-60741-615-9

Reading at Risk: A Survey of Literary Reading in America Rainer D. Ivanov 2009. ISBN: 978-1-60692-582-9 Reading: Assessment, Comprehension and Teaching Nancy H. Salas and Donna D. Peyton (Editors) 2009. ISBN: 978-1-60692-615-4 Reading: Assessment, Comprehension and Teaching Nancy H. Salas and Donna D. Peyton (Editors) 2009. ISBN: 978-1-60876-543-0 (Online Book) Multimedia in Education and Special Education Onan Demir and Cari Celik 2009. ISBN: 978-1-60741-073-7 Rural Education in the 21st Century Christine M.E. Frisiras (Editor) 2009. ISBN: 978-1-60692-966-7 Nutrition Education and Change Beatra F. Realine (Editor) 2009. ISBN: 978-1-60692-983-4

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The Reading Literacy of U.S. Fourth-Grade Students in an International Context Justin Baer, Stéphane Baldi, Kaylin Ayotte,Patricia J. Gree and Daniel McGrath 2009. ISBN: 978-1-60741-138-3 Teacher Qualifications and Kindergartners’ Achievements Cassandra M. Guarino, Laura S. Hamilton, J.R. Lockwood, Amy H. Rathbun and Elvira Germino Hausken 2009. ISBN: 978-1-60741-180-2

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PCK and Teaching Innovations Syh-Jong Jang 2009. ISBN: 978-1-60741-147-5 IT- Based Project Change Management System Faisal Manzoor Arain and Low Sui Pheng 2009. ISBN: 978-1-60741-148-2 Learning in the Network Society and the Digitized School Rune Krumsvik (Editor) 2009. ISBN: 978-1-60741-172-7 Effects of Family Literacy Interventions on Children's Acquisition of Reading Ana Carolina Pena (Editor) 2009. ISBN: 978-1-60741-236-6

Approaches to Early Childhood and Elementary Education Francis Wardle 2009. ISBN: 978-1-60741-643-2

Academic Administration: A Quest for Better Management and Leadership in Higher Education Sheying Chen (Editor) 2009. ISBN: 978-1-60741-732-3 Recent Trends in Education Borislav Kuzmanović and Adelina Cuevas (Editors) 2009. ISBN: 978-1-60741-795-8 Expanding Teaching and Learning Horizons in Economic Education Franklin G. Mixon, Jr. and Richard J. Cebula 2009. ISBN: 978-1-60741-971-6 New Research in Education: Adult, Medical and Vocational Edmondo Balistrieri and Giustino DeNino (Editors) 2009. ISBN: 978-1-60741-873-3

Disadvantaged Students and Crisis in Faith-Based Urban Schools Thomas G. Wilson 2010. ISBN: 978-1-60741-535-0 Delving into Diversity: An International Exploration of Issues of Diversity in Education Vanessa Green and Sue Cherrington (Editors) 2010. ISBN: 978-1-60876-361-0

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Developments in Higher Education Mary Lee Albertson (Editor) 2010. ISBN: 978-1-60876-113-5 The Process of Change in Education: Moving from Descriptive to Prescriptive Research Baruch Offir 2010. ISBN: 978-1-60741-451-3

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Career Development Hjalmar Ohlsson and Hanne Borg (Editors) 2010. ISBN: 978-1-60741-464-3 Adopting Blended Learning for Collaborative Work in Higher Education Alan Hogarth 2010. ISBN: 978-1-60876-260-6 Special Education in the 21st Century MaryAnn T. Burton (Editor) 2010. ISBN: 978-1-60741-556-5 Challenges of Quality Education in Sub-Saharan African Countries Daniel Namusonge Sifuna and Nobuhide Sawamura 2010. ISBN: 978-1-60741-509-1

Collaborative Learning: Methodology, Types of Interactions and Techniques Edda Luzzatto and Giordano DiMarco (Editors) 2010. ISBN: 978-1-60876-076-3 Handbook of Lifelong Learning Developments Margaret P. Caltone (Editor) 2010. ISBN: 978-1-60876-177-7 Virtual Worlds: Controversies at the Frontier of Education Kieron Sheehy, Rebecca Ferguson and Gill Clough (Editors) 2010. ISBN: 978-1-60876-261-3 Health Education: Challenges, Issues and Impact André Fortier and Sophie Turcotte (Editors) 2010. ISBN: 978-1-60876-568-3 Reading in 2010: A Comprehensive Review of a Changing Field Michael F. Shaughnessy (Editor) 2010. ISBN: 978-1-60876-659-8 Becoming an Innovative Teacher Educator: Designing and Developing a Successful Hybrid Course Qiuyun Lin 2010. ISBN: 978-1-60876-465-5

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Sexuality Education Kelly N. Stanton (Editor) 2010. ISBN: 978-1-60692-153-1 Sexuality Education and Attitudes Jovan Stanovic and Milo Lalic (Editors) 2010. ISBN: 978-1-60741-662-3

National Financial Literacy Strategy Toma P. Hendriks (Editor) 2010. ISBN: 978-1-60741-827-6 Collaborative and Individual Learning in Teaching Julien Mercie, Caroline Girard, Monique Brodeur and Line Laplante 2010. ISBN: 978-1-60876-889-9

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What Content-Area Teachers Should Know About Adolescent Literacy National Institute for Literacy 2010. ISBN: 978-1-60741-137-6

Educational Change Aden D. Henshall and Bruce C. Fontanez (Editors) 2010. ISBN: 978-1-60876-389-4

Collaborative and Individual Learning in Teaching, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved. Collaborative and Individual Learning in Teaching, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

EDUCATION IN A COMPETITIVE AND GLOBALIZING WORLD SERIES

COLLABORATIVE AND INDIVIDUAL LEARNING IN TEACHING: A

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

TRAJECTORY TO EXPERTISE IN PEDAGOGICAL REASONING

JULIEN MERCIER CAROLINE GIRARD MONIQUE BRODEUR AND

LINE LAPLANTE

Nova Science Publishers, Inc. New York

Collaborative and Individual Learning in Teaching, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Collaborative and individual learning in teaching / Julien Mercie ... [et al.]. p. cm. Includes index. ISBN:(eBook) 1. Action research in education. 2. Teachers--Psychology. 3. Group work in education. 4. Cognitive learning. 5. Cognition. I. Mercie, Julien. LB1028.24.C657 2009 370.15'2--dc22 2009050473

Published by Nova Science Publishers, Inc.  New York

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CONTENTS

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Preface

vii

Chapter 1

Introduction to Teacher Cognition

1

Chapter 2

Foundations for the Study of Teacher Cognition: A Cognitive Modeling Perspective

11

Chapter 3

A Cognitive Model of Pedagogical Reasoning

21

Chapter 4

A Study of Collaborative Pedagogical Reasoning

45

Chapter 5

A Study of Individual Pedagogical Reasoning

69

Chapter 6

Outcomes of the Two Studies

79

Chapter 7

The Added Value of Collaboration in Learning and Performance: Cognitive and Social Cognitive Modeling as a Rationale and Strategy for Empirical Investigations

87

An Essay on the Nature and Structure of Teacher Knowledge

97

Epilogue: From a Research Agenda to Contributions to Teacher Education on a Trajectory to Expertise in Pedagogical Reasoning

113

Chapter 8 Chapter 9

References

117

Index

129

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PREFACE The theory and empirical studies reported herein are part of the first phase of the Pedagogical Reasoning Project, a research program that began in 2006. In hope of improving teacher education and teacher professional development, the main outcome of the first phase of the project is a theory accounting for aspects of teachers’ cognition in terms of problem-solving processes, knowledge and knowledge use. This book is the first of a series of publications discussing, from a cognitive point of view, aspects of (1) how teachers think, both individually and cooperatively, (2) the knowledge they possess, (3) how they use this knowledge in teaching, (4) the assessment of expertise in teaching, and (5) the development of expertise in teaching. The present book is the cornerstone of the other manuscripts, since it presents in great details the foundations of the model that is used in the subsequent pieces of work. These foundations hinge on cognitive research that began in the late 1970’s and that is still going on today.

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Chapter 1

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INTRODUCTION TO TEACHER COGNITION Leading researchers in teacher education (Putnam and Borko,2000 ; Shulman, 1998 ; Korthagen, Kessels, Koster, Lagerwerf, and Wubbels, 2001), despite dissentions regarding the means, agree that teachers’ daily practice should be based on current empirical evidence about the efficacy of available interventions. To achieve this, teachers must diagnose problems, design interventions and monitor the efficacy of their interventions, on the basis of pertinent knowledge. In the field of teacher education, the process of using knowledge to guide interventions has been understood as translating theory into practice. The stance adopted in this work is that this translation is a pedagogical problem that can be solved by the design of appropriate instructional tasks in teacher education on the basis of the study of teacher cognition. Another central assertion is that teacher knowledge develops through knowledge use. This book focuses on a process which is generally known as teacher planning. Teacher planning is assumed in this work to serve two important functions. Its first function is to make teacher knowledge influence teacher intervention. Its second function is to promote the development of teacher knowledge. The first function has been much more discussed in the available literature than the second function, as presented next. Because of the links between teacher planning and action (Armour-Thomas, 1989), teacher planning has a high potential as a vehicle for theory to be applied in teaching. These links include, at a certain grain size, the influence of the plan on opportunities to learn, content coverage, grouping for instruction and the general focus of classroom processes (Clark and Peterson, 1986). Micro-level teaching processes such as specific verbal behaviour are not significantly influenced by planning, as they are mostly determined by interactive decisionmaking.

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Indeed, despite the influence of teacher planning on actions, and because of the complexity of teaching, discrepancy between teacher plans and classroom events is likely to arise. Morine-Dershimer (1979) identified teacher-perceived discrepancy between plans and classroom events as a critical variable in teacher interactive decision making. When there is little or no discrepancy, teachers engage in “image-oriented” information-processing and routine decisions. In the presence of minor discrepancy, teachers shift to a reality-oriented informationprocessing and “inflight” decisions. When there is critical discrepancy, teachers engage in problem-oriented information-processing and postponed decisions. Therefore, teacher planning could serve as a mean to integrate theoretical knowledge pertaining to classroom processes above a certain grain size. Although this grain size remains to be precisely identified, the aspects identified before seem to encompass a significant amount of teacher activity. The study of the second function of teacher planning, the development of teacher knowledge, is only beginning. Hashweh (2005), in his theoretical revision of the notion of pedagogical content knowledge, argues that this knowledge, which he calls pedagogical constructions to emphasize the idea that this knowledge is built from experience, results initially and mainly from teacher planning. Indeed, this is supported by cognitive theory. We can add that knowledge use in problem solving in the context of new problems leads to learning. This is the central assertion of the problem-based learning approach. If it can be demonstrated that teacher planning is a problem-solving activity, it follows that planning can foster the development of teacher knowledge. Unfortunately, there is a scarcity of empirical results to support this theoretical assertion. Two empirical studies examined knowledge use in planning and showed than planning was based on knowledge about teaching (McCutcheon and Milner, 2002 ; Milner, 2003). No study has examined the development of teacher knowledge as a result of planning. Research on the development of teacher knowledge as a result of planning should be intensified given the focus of past research of planning on the process (Hashweh, 2005). Hashweh adds that pedagogical content knowledge does not seem to be fostered in pre-service teacher education programs, as discussed in more detail next.

THE PROBLEM AND ITS CONTEXT “Until learning experiences in university settings evolve to match our understanding of situated cognition, the development of teachers’ knowledge will

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Introduction to Teacher Cognition

3

continue to be problematic” (Munby, Russell and Martin, 2001, p.894). Fostering teachers’ use of theoretical knowledge requires models that account for cognitive processes and knowledge involved in the use of theoretical knowledge in practice by novices and experts, and how these processes and knowledge evolve over time (Lajoie, 2003). Despite significant advances made by researchers in a cognitive perspective and reviewed in this text, such models are not yet available. It is known that expert teachers teach better than novices, but mechanisms of how this is done are mostly unknown (Leinhardt, 1990). According to Lajoie, models of how novices learn these skills are also needed. Once this trajectory to expertise is mapped, appropriate scaffolding to support student teachers’ development of expertise can be elaborated and tested. Indeed, it seems productive to emphasize critical skills such as lesson planning in teachers’ pre-service education, so that they become routine as early as possible. The term “pedagogical reasoning”, with its resemblance with “clinical reasoning” is used in this book to convey the idea that teachers’ instructional planning shares important similarities with a well-researched process, that is, physician’s diagnostic decision-making (see Patel, Arocha and Zhang, 2005). The metaphor of teaching as clinical decision-making is not new (Calterhead, 1995). It arose in the 1970’s from three factors: a dissatisfaction with behaviourist views of teaching, a growing interest in teachers’ thought processes and an intensive production in medical education research. It seems still useful today if we consider some advances in cognitive theory that are only partially put to contribution in the study of teacher’s cognition. It seems also useful given the plethora of research on expertise in medicine and medical education that could be reinvested in teaching and teacher education. It should be noted that our use of the term is different from the definitions provided by authors who have used it recently. In the present work, the metaphor emphasizes the information about students that the teachers use in planning instruction, an aspect that is even more salient in special education given the diversity of students. For Schulman (1987), pedagogical reasoning refers to a process of transforming subject matter knowledge into pedagogically efficient forms that are adaptive to students’ characteristics. For Sanchez and Llinares (2003), pedagogical reasoning refers to a transformation of the subject matter for teaching and its underlying rationale in a process of interpretation, representation and adaptation of the content. During the last 40 years, many studies in the field of teacher cognition have studied how teachers plan lessons. In cognitive psychology, teacher planning has been defined “as a set of psychological processes in which a person visualizes the future, inventories means and ends, and constructs a framework to guide his or her future action” (Clark and Peterson, 1986, p.260). Some examined the types and

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Julien Mercier, Caroline Girard, Monique Brodeur and Line Laplante

functions of teacher planning, while others have led to models of the process of teacher planning. These studies are reviewed next. Regarding the types of teacher planning, Yinger (1977) and Clark and Yinger (1979) found eight types of planning that relate mostly to time spans: week, day, long range, short range, year, and term. Two other types refer to unit and lesson planning, and seem to be related to the structure of the curriculum (at the time of the study). Clark and Elmore (1979) found that these types of planning are nested. Clark and Yinger (1979) also studied the functions of teacher planning. They found that teachers plan to satisfy emotional needs, to identify means to the end of instruction and to regulate instruction during the interactive phase of teaching. McCutcheon (1980) adds that teachers plan in response to administrative requirements or substitute teacher’s needs. The products of teacher planning consist of activity routines, instructional and management routines, and executive planning routines (Yinger, 1977) and lesson images (Morine-Dershimer, 1979). The process of teacher planning has been studied since 1950. Tyler (1950) proposed a model of teacher planning that consists of four linear steps: specification of objectives, selection of learning activities, organization of learning activities, and specification of the evaluation procedures. This model was taught in teacher education programs but rarely used, since it was perceived as mostly useful for student teachers (Neale, Pace and Case, 1983). For Taylor (1970), teacher planning begins with the context of teaching, then considers learning activities in relationship with learners’ interests, and finally considers the purpose of teaching. Zahorik (1975) classified the decisions that teachers make in eight categories: objectives, content, activities, material, diagnosis, evaluation, instruction and organization. Decisions most frequently made first were about content (51%) and learning objectives (28%). Morine-Dershimer and Vallance (1976) found that teachers’ plans reflected little attention to learning goals, diagnosis of students’ needs, and evaluation. Peterson, Marx and Clark (1978) classified teachers’ thoughts during planning into four categories: objectives, materials, subject matter, and instructional process. They found that teachers spend the most time thinking about the content, then about the instructional process and finally about objectives. This finding that objectives are the last concern of teachers during planning was explained by McLeod (1981). She found that learning objectives were identified by teachers mostly during the act of teaching (45,8%). Moreover, learning objectives were less often identified before planning activities (26,5%), after planning but before teaching (19,5%) and after a teaching episode (8,2%). Yinger (1977) elaborated a model of planning in three steps: initial problem conception, problem formulation and solution, and finally implementation, evaluation and routinization. Favor-Lydecker (1981) reported

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Introduction to Teacher Cognition

5

five planning styles at the unit level: cooperative planning with students, brainstorming, list and sequence planning, culminating event in sequence planning and culminating event as goal statement planning. These styles are related to teaching experience (Sardo, 1982). Vaughn and Schumm (1994) found that teachers’ planning was driven by (1) content coverage instead of students’ knowledge acquisition, (2) students’ interest and motivation to avoid classroom management problems, and (3) the class as a whole rather than specific individuals. Borko, Livingston, McCaleb and Mauro (1988) found differences in lesson planning related to content area in terms of influences on planning: planning in science was driven by the textbook whereas planning in arts was heavily influenced by personal factors. These authors also found differences related to teaching preparation pertaining to time and effort devoted to planning, the focus of attention during planning (learning the content versus planning instructional strategies), flexibility and self-confidence. Sanchez and Llinares (2003) studied student teachers’ representations of mathematical concepts and the use of these representations in planning lessons. They found that student teachers’ decisions in planning were closely related to the representations of concepts. Schmidt (2005) found that preservice teachers held concerns about how to begin a lesson plan, had difficulty identifying students’ needs, and showed prominence of on the fly decision-making. The previous studies are interesting in that they have shown, substantively, what are the concerns of teachers when they plan instruction. However, they fall short in describing the planning process as a sequence of cognitive steps, the knowledge involved in planning, and how planning is based on that knowledge. From an interventionist perspective aimed at scaffolding teachers’ skills, it seems particularly desirable to focus on processes that account for changes in knowledge over a relatively short period of time, so that links between cognitive processes and learning outcomes can be postulated and empirically tested. Such a micro-analytic preference is embodied in the cognitive modeling approach (Anderson, 2002). In contrast to macro-analytic strategies typical of ethnography that examine long-term changes in teachers’ knowledge, the objective of cognitive modeling is to explain teachers’ behaviour on a moment-to-moment basis. This approach is preferred in order to map processes and knowledge that can be taught and scaffolded. What is needed to elaborate a model of teachers’ pedagogical reasoning in a way that can inform teacher educators is: (1) the identification of a set of cognitive steps, (2) how they are typically sequenced, (3) what knowledge is involved during these cognitive steps and (4) how this knowledge drives the process.

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As will be presented in detail in the following chapters, teacher cognition has been a research topic intensively studied for the past 40 years. Classic studies reported results on individual teacher cognition, mainly regarding the planning of instruction and classroom interaction, as well as aspects of teacher knowledge, beliefs, attitudes, and other socio-affective variables beyond the scope of this text. Initial studies such as Taylor (1970) hinged on early formulations of the concepts of teaching objectives and the then predominant view of classroom interaction as behaviourist classroom management. Progressively, the construct of teacher knowledge has been refined around the notion of schemata (see for example Lenhardt and Greeno, 1986), paving the way for the study of how teaching scripts are created and planned and how they get enacted in interactive teaching (see for example the work of Schoenfeld and colleagues). Teaching expertise is also part of the research agenda and leads directly into issues of teacher training (CochranSmith and Zeichner, 2005). Despite these remarkable outcomes of the study of individual teacher cognition, research on individual teachers’ cognitive functioning could benefit from current conceptual and methodological advances in cognitive modeling. Teacher collaboration is currently an important topic of research on teaching and teacher education (Meirink, Meijer and Verloop, 2007). In recent years, researchers have studied collaboration between teachers through the use of information and communication technology (ICT) (Akpinar and Bal, 2006 ; Suntisukwongchote , 2006 ; Winter and McGhie-Richmond, 2005), in context of inclusion (Wallace, Anderson and Bartholomay, 2002 ; Parmar and DeSimone, 2006), the role of collaboration between student teachers in learning to teach (Arvaja, Salovaara, Häkkinen and Järvelä, 2007 ; Seifert and Manzuk, 2006), the role of collaboration between teachers in learning to teach (Meirink, Meijer and Verloop, 2007), the role of collaboration between teacher educators and classroom teachers (Erickson, Minnes Brandes, Mitchell and Mitchel, 2005) and between teachers (Butler, Lauscher, Jarvis-Selinger, Beckingham, 2004 ; Johnson, 2003) on professional development, the role of collaboration between student teachers and teacher educators on student teachers’ learning (Tillema and Orland-Barak, 2006), collaboration between teachers in planning and implementing lessons (Akpinar and Bal, 2006 ; Chen, Cone and Cone, 2007 ; Davison, 2006), and collaboration between teachers and university researchers in curriculum design (Webb, Romberg, Ford and Burrill, 2005). These studies have shown that collaboration can have beneficial effects on teachers’ learning and production. For example, Erickson, Minnes Brandes, Mitchell and Mitchell (2005) and Chen, Cone and Cone (2007) suggested that collaboration projects involving in-service teachers have enhanced pupils’

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Introduction to Teacher Cognition

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learning. In another study, social support was the main outcome of collaboration between student teachers (Seifert and Manzuk, 2006). However, these studies have also identified challenges inherent to collaboration. Issues of conflict, commitment, control and respect (Erickson, Minnes Brandes, Mitchell and Mitchel, 2005), roles and responsibilities (Winter and McGhie-Richmond, 2005) as well as issues related to individual differences (Seifert and Manzuk, 2006) were raised. Consequently, collaboration in group work may not always represent an added value over individual activity. Arvaja, Salovaara, Häkkinen and Järvelä (2007) call for the study of the reciprocal relationship between individual and collective processes in order to design better collaborative learning tasks. They precisely formulated a fundamental issue: “what kind of social interaction can be called collaborative and how the collaborative opportunities and individual abilities are matched”?. A first step in assessing the added-value of collaboration for performance and learning in the context of pedagogical reasoning is to contrast individual and group performance in terms of processes and outcome. A distinction must be made between the execution of the performance and its outcome or product (Tschan, 2002). Processes include the cognitive activities engaged in, their sequence, and the knowledge on which these cognitive activities depend. One especially interesting way to do this is to have individuals perform a pedagogicalreasoning task individually, and then have the same individuals perform the task in dyads. Groups can also be studied in the same way. In addition, the collaboration between the learners can be examined from the perspective of the functioning of the group and from the perspective of the contribution of each learner to the problem solution. To help further explore this intricate balance of costs and benefits related to group performance and learning, collaboration has to be studied in the context of well-specified teaching tasks that can reveal group processes as well as individual processes of the individuals forming the group. These processes refer to the executive processes of the group during the performance of a (learning) task, as well as the processes by which each individual attunes his own cognitive processes to the group performance (Tschan, 2002). An important assumption in this study is that the executive processes underlying the individual or group performance can be characterized, at a certain level, using the same categories. Such a study requires a complex task that is representative of a significant portion of daily teaching activity. Instructional or teacher planning was selected as an appropriate task, for a number of reasons. Teacher planning is an important part of teaching. It encompasses almost everything excluding the interactive phase of teaching. That is, it includes decision-making before a teaching episode, as well

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as post-teaching reflection and adjustments. Teacher planning is the principal mean for the development of teacher knowledge (Hasweh, 2005), a function that was formulated intuitively almost 30 years ago by McCutcheon (1980). The planning or design of learning activities implies that the teacher provide answers to a series of questions related to educational issues such as content, learning goals, links with anterior/subsequent content and students’ prior knowledge, and assessment. Elements of answer to such questions originate either from knowledge that the teacher already has, or from external sources. Teacher knowledge develops from the integration of these elements of answer. As a process involving the integration of internal and external sources of knowledge, teacher planning can be seen as the entry point of choice for best practices. In the teaching process, planning is the main occasion for making decisions regarding alternative practices. In contrast, decision making in the interactive phase of teaching is restricted to the implementation of scripts and agendas previously determined. These reasons, associated with the development of current conceptualizations of teacher knowledge, have led to renewed interest in teacher planning, teacher knowledge, as well as their relation and how to foster the development of these skills and knowledge (McCutcheon and Milner, 2002 ; Milner, 2003; Hasweh, 2005). In light of the importance of collaboration in teaching and teacher education, the study of teacher cognition should be extended to groups of teachers. Teamwork is widespread in teaching. Most teacher education programs include collaboration as a mean to foster students learning. For example, student teachers work collaboratively in university courses. They are also supervised by mentors during teaching practicum. Moreover, current reforms formulate calls for teachers to work collaboratively on educational issues. As a result, teachers work in teams on shared teaching projects. Specialists of various disciplines work together on a pupil’s AEP. However, how teachers collaborate in their work has not been extensively documented from a cognitive perspective. Indeed, during the last 35 years, the field of teacher cognition has produced many studies of teachers’ thought processes and knowledge (Clark and Peterson, 1986; Munby, Russell and Martin, 2001). The types and functions of teacher planning, and aspects of the process of teacher planning were studied. Aspects of the knowledge on which teacher planning is based were characterized (Hasweh, 2005; Shulman, 1986). The cognitive research reviewed focused exclusively on individual teachers’ cognition. It is worth repeating that, as Munby, Russell and Martin (2001, p.894) point out, “Until learning experiences in university settings evolve to match our understanding of situated cognition, the development of teachers’ knowledge will continue to be problematic”. To this end, it is critical that the study of teacher

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cognition be extended to collaborative contexts in a way that results can be articulated synergistically with a substantial and highly relevant tradition of research regarding individual cognition. Besides the urge for the study of teacher collaboration, many questions about individual cognition still remain to be answered in light of current theory and practice contexts. What are the characteristics of the performance of expert teachers? Which knowledge do they possess? How is this knowledge organized in memory? Which knowledge supports specific cognitive processes (detailed in discrete and fine-grained steps)? Answers to these questions depend on the availability of theory that describes cognitive performance, both optimal and suboptimal. Theory is also required to establish characteristics of the knowledge involved in the performance so that this knowledge can be related to specific cognitive processes. Outcomes of the study of individual cognition pave the way for the study of performance in groups, including issues of coordination and knowledge exchange. As will be argued in the next chapter, these models can be built as extensions of models of individual cognition. The remainder of this book is organized as follows. The next chapter summarizes the epistemological foundations for the theoretical and empirical work that follows, by presenting the cognitive modeling perspective as a fruitful approach for the study of teacher cognition. On these grounds, chapter 3 makes the point that teacher planning encompasses a significant amount of teacher activity and is an important process to consider when addressing educational issues such as preservice and inservice teacher education, especially with respect to innovation in teaching. The main section of this chapter is a very detailed description of a cognitive model of teacher planning, framed as pedagogical reasoning. This model borrows from cognitive theory regarding processes of comprehension, problem solving, reasoning and planning. Chapters 4 and 5 then report on two companion empirical studies. Addressing respectively collaborative and individual performance, the studies aimed at characterizing prevalence and sequential aspects of pedagogical-reasoning cognitive activity across four expertise levels. Given the complementarities of the two studies, chapter 6 presents a global discussion of the results. Then, chapter 7 suggests that the added value of collaboration for learning and performance should not be taken for granted and that further examination of the optimal conditions for individual and collaborative performance is needed. To this end, an extension of the cognitive modeling approach is promoted as a potentially productive framework. Since the consideration of expertise in teaching leads directly into issues of teacher knowledge, chapter 8 presents a characterization of teacher knowledge on the basis of the substantial amount of literature on the topic. In preparation to the

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study of relations between knowledge and fine-grained cognitive processes, this characterization puts a special emphasis on a molecular view of knowledge. A concluding chapter presents the next planned phases of the Pedagogical Reasoning Project research program.

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Chapter 2

2. FOUNDATIONS FOR THE STUDY OF TEACHER COGNITION: A COGNITIVE MODELING PERSPECTIVE

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2.1. INTRODUCTION The study of performance and learning in a cognitive modeling approach implies a conception of cognitive functioning in terms of mental states (Anderson, 2002). This approach is based on the observation and recording of actions and verbalisations of one or more individuals during a task. The objective of this chapter is to lay the theoretical foundations of cognitive functioning in order to highlight the nature of data required for cognitive modeling.

2.2. THEORETICAL FRAMEWORK The goal of this chapter is to prescribe an approach for the study of teacher cognition. Principles discussed are: (1) cognition is sequential, (2) cognition can be decomposed into a hierarchical architecture, (3) cognition is contextualized and (4) competencies can be decomposed into a hierarchical structure. A cognitive architecture is described as the structure and processes critical to performance, regardless of a domain (Sun, Coward and Zenzen, 2005). In their words, “A cognitive architecture is a broadly-scoped, domain-generic computational cognitive model, capturing the essential structure and process of the mind, to be used for a broad, multiple-level, multiple-domain analysis of cognition”. According to Sun (2006), this architecture provides a framework for a more

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detailed modeling of cognitive phenomena through specifying essential cognitive structures, division of modules and their interrelations. In sum, the specification of a cognitive architecture allows for better understanding of cognitive functioning through process-based theories, an approach put forward by Sun, Coward and Zenzen (2005).

2.2.1. Cognition is Sequential Sun, Coward and Zenzen (2005) suggest that the world, including cognition, is composed of basic elements: entities, activities and mechanisms. Activities represent the ways in which entities can interact, while mechanisms, expressed through causal relationships, are composed of entities and activities. It is the causality of these mechanisms that explain the sequential aspect of cognition, since the cause and effect link of causality implies that cause occurs before effect (Pearl, 2000).

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2.2.2. Cognition Can be Decomposed into a Hierarchical Architecture Mainly, a hierarchical architecture asserts the existence of several levels characterized by different amounts of details related to its functioning. These successive levels involve causal explanations between levels (Sun, Coward and Zenzen, 2005). Cognitive science has successively supported many hierarchical architectures. Amongst the better known are Soar, ACT-R, CAPS and GOMS. These architectures affect the essential functioning of an individual cognitive system, but may have levels associated with group functioning, even a series of intelligent agents. Recent studies have also reflected a greater emphasis on the social aspect of cognition, hence the need for multi- agent levels in current architectures (Sun, 2006). The classic individual view (Mahr 1982, Newell and Simon, 1972), Newell’s (1990) view, and Sun’s (2006) emerging one are presented in the following sections.

2.2.2.1. Classic Individual View As shown in Table 2.1, the classic individual view has three levels: computational, representation and algorithm, and material implementation. The views of Marr (1982) and Newell and Simon (1976) have similar emphasis, i.e. the importance of the analysis at the superior level followed by a lower level, in

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other words, from tasks to symbols and symbolic manipulation procedures. This analysis is seen as independent from the subsequent physical system realisation (typically biological or computational). Table 2.1.Classic individual view in cognitive modeling (Marr, 1982 ; Newell et Simon, 1976) Marr (1982)

Newell and Simon (1976) Knowledge level

Description

Representation and algorithm

Symbolic level

Determines the representation of the input and output, and the algorithm for the transformation of the input into the output.

Implementation

Physical level

Physical implementation of the representation and transformation of the previous level.

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Computational

Determines the necessary processing, and the goals and strategies to achieve this processing.

2.2.2.2. Newell’s View Based on Time Current efforts in cognitive modeling aim at depicting cognitive processes occurring at various time scales (Anderson, 2002 ; Newell, 1990). Some cognitive models reside in the ten milliseconds scale while others reside in the hours scale. Other cognitive models apply to scales between these extremes. Newell (1990) argues that cognitive functioning is based on a hierarchical multi-level architecture, representing the solution to a set of functional constraints. In this system, a level corresponds to a set of components that interact to produce behaviour typical to that level. The system is hierarchical since the components of a level build on the components of a lower level. By progressing towards the top

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of the hierarchy and a greater complexity, levels include more components and their speed decreases. Based on these assumptions, Newell (1990) suggests the time scale of human action, in which each level requires about ten times longer than the previous one to operate. This scale is presented in Table 2.2. Newell (1990) identified twelve orders of magnitude ranging from months (107 seconds) to 100 nanoseconds (10-4 seconds) that grasp the totality of human experience, including biological processes (10 msec and below) and social processes (days and above). Because of the state of research at the time, Newell did not provide descriptions of social processes. The shaded part represents the levels targeted in this research program.

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Table 2.2.Time scales in cognitive modeling Time units Months Weeks Days Hours 10 minutes Minutes

Description

Definition (Newell, 1990) Social mechanisms

Task Task Task

10 seconds

Unit task

Seconds

Operations

Tenths of second

Deliberate act

Hundredths of second Thousandths of second Ten thousandths of second

Neural circuit Single neuron Organelle

The description of the three upper time scales as task levels refers to the fact that these levels are composed to fit the task structure and are no longer independent of the context. Compose composed operators. Compose operators from deliberate acts to engage in problem search. Bring available knowledge to bear to choose one operation rather than others. Automatic Biochemistry and biomolecular mechanisms

2.2.2.3. Views of an Emerging Discipline: Social Cognitive Science Cognition is, at least partly, a social and cultural process (Sun, Coward and Zenzen, 2005). In this context, coordination between individuals performing a Collaborative and Individual Learning in Teaching, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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task is a critical factor (Sun, 2006). This coordination has been well studied in several disciplines through the notions of agent and performance (activity, action, work, task), but remains largely unknown. This approach requires the modeling of social phenomena in terms of autonomous agents. This modeling focuses on the interactions between agents. The current problem lies in the relative superficiality of the cognition of these agents, which are, nonetheless, described as "intelligent". This superficiality is all the more problematic as it hampers the ability to resolve the issue of the micro-macro link. This link is represented, on one hand, by individual intentions and actions and, on the other, by social functions and welfare. Thus, better models of individual cognition are required as foundations for inter-agents social models. Inversely, a lack of knowledge of sociological processes may result in a lack of consideration of important structures or cognitive constraints at the individual level. Levels in this view are summarized in Table 2.3. The levels targeted in the studies presented in this book are shaded.

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Table 2.3.Temporal scales in social cognitive modeling (Sun, 2006) Levels Inter-agents processes

Phenomenon Sociological

Description Collective behavior of agents Inter-agents processes Interactions between agents and environments (physical et sociocultural) including sociocultural artefacts

Agents

Psychological

Individual behavior Beliefs Concepts Skills

Intra-agent processes

Components

Sequences of steps in the processing

Substrates

Physiological

Basic primitives on which depend higher-level operations.

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2.2.3. Interactions Between Levels All hierarchical architectures involve interactions between levels. Although modeling entails generally one level, concomitant modeling of many levels (interlevel (correspondence between levels) and multi-level (description from one level to another)) may be interesting, if not essential (Sun, 2006). Sun (2006) regards this interaction as the reciprocal influence between adjacent levels. He adds that modeling is done by first specifying the superior level and, then, adding the lower level. A theory corresponding to a specific level establishes entities and causal relationships that match the empirical data. Entities often correspond to lower level entities enabling causal relationships to be specified without reference to these lower level entities. However, the causal relations between lower level entities must be able to explain higher level causal relations (Sun, Coward and Zenzen, 2005). In fact, substantial inconsistencies between the levels invalidate the theory. Sun, Coward and Zenzen (2005) add that "a phenomenological distinction is caused by / supported by / projected by a corresponding computational distinction" (p.624). The concept of modularity is inherent to the hierarchical nature of a system. Modularity is reflected through fewer external interactions and a greater amount of internal interactions. Modularity results in a performance gain due to the minimization of information exchange between modules. The main challenge related to cognitive modeling is being able, on one hand, to characterize the operation of each level and, on the other hand, to establish the functional relationships between different levels. In this respect, Anderson (2002) supports three theses relating to learning: (1) the decomposition thesis, asserting that learning occurring over one hundred hours can be broken down into shortterm cognitive events; (2) the relevance thesis, stating that very short-term cognitive processes must be considered when thinking about educational problems; and (3) the modeling thesis, which postulates that the necessary methodology for modeling is available. Thus, progress in cognitive modeling is particularly linked to the quality of available data on cognitive functioning. On this matter, Erikson (2006) advocated the use of think-aloud protocols, which entails asking participants to verbalize as they perform a set of specified tasks. If we agree to combine such data only at higher levels of architectures because of the verbal cognitive processing involved, we must recognize the need for other types of data to browse the lower levels. Thatis when data associated with biological substrates of brain function come into effect. These data are derived from techniques such as functional Magnetic

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Resonance Imaging (fMRI) , positron emission tomography (PET), electroencephalography, magnetoencephalography and optical tomography. In an educational perspective, Anderson and Gluck (2001) show how learning can be fostered from the interaction between hierarchical levels. Building on Newell’s vision (1990), they demonstrate the impact of cognitive processes lasting less than one second on learning taking place over several minutes. Their data on eye movement during the use of an algebra tutoring system indicate that: (1) students have shifted their attention to another part of the problem; (2) the solution method can stem from traces of the solution; (3) messages tutorials have not been read; (4) an error can be determined; (5) students failed to include information critical to solving the problem; or that (6) students are more focused on the task. Anderson and Gluck (2001) also stressed the need to refine cognitive models to this high level of granularity in order to overcome the current problems of non-determination within the interpretation of sequences of behavior at higher levels. Moreover, they add that Markovian models (related to those discussed below regarding the analysis method) may provide some solution to this problem.

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2.2.4. From a Deterministic Causality to a Probabilistic Causality To take advantage of the hierarchical nature of a multi-tier architecture, the notion of causality must be examined through the functional correlation between levels. Functional correlations presuppose a mechanism-based account of causation, in which quantities are related by autonomous physical (and cognitive) mechanisms. These functional relations are perturbed by random disturbances (Pearl, 2000). Functional relations within a level can be matched with the functional relations of other levels. These complex functional relations are better described in terms of probabilistic causality rather than deterministic (Sun, Coward and Zenzen, 2005), because of the disturbances to which they are subjected (Pearl, 2000). Again, Markovian and semi-Markovian models may provide an appropriate analytical approach in the context of the exploration of probabilistic causality.

2.2.5. Cognition is Contextualized Cognition is contextualized by its reciprocal relationship with the environment (Sun, 2006). This relationship is reciprocal because it implies, first, that cognition is constrained by the physical and social environment and,

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secondly, that cognition changes the environment through action. Sun (2006) sees this relationship through the cognition-motivation-structure triad. Motivations such as physiological needs are seen as precursors of cognition. These needs can be met only in a physical and socio-cultural environment. Because the environment is not always conducive to satisfying needs, an effort of the agent is often required for this purpose. Hence, cognition can be seen as the way organisms have met their needs and goals through evolution. In contrast, the patterns and structures of the physical and social environment influence cognition. Thus, needs and cognition share a teleological consistency, i.e. in terms of purposes they serve.

2.2.6. Competence in a Domain Can be Decomposed into a Hierarchical Architecture

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Competence in a domain is divided into a set of components and learning occurs within the individual components of that domain (Anderson and Gluck, 2001). Task analysis becomes therefore critical. The unparalleled success of tutoring systems developed with this approach contradicts a radical constructivist vision, stating that decomposing a competence undermines learning.

2.3. CONCLUSION Table 2.4. Time scales in cognitive modeling of pedagogical reasoning Time units

Description

Hours

Task

10 minutes Minutes 10 seconds Seconds Tenths of second

Task Task Unit task Operations Deliberate act

Categories of the proposed pedagogical reasoning model All. Series of pedagogical reasoning cycles leading to a sequence of instructional interventions or using a series of cases. Control structure Components Sub components Segments Automatic. Not observable though talk.

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situate the cognitive events considered in the proposed model of pedagogical reasoning along this time scale, and to begin to articulate the model with surrounding time scales. Such a characterization, presented in Table 2.4, is also useful in describing to which degree the model can be explicit in the data collected.

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Chapter 3

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3. A COGNITIVE MODEL OF PEDAGOGICAL REASONING A cognitive model of pedagogical reasoning has to specify the structure of a pedagogical reasoning episode (i.e. a sequence of pedagogical reasoning actions). That is, such a model has to postulate what actions can occur in the sequence of actions involved in a pedagogical reasoning episode. Such actions are conceptualized after pertinent theory of human cognitive performance in complex domains: comprehension, reasoning, planning and problem solving. In addition, the model has to specify how such actions unfold within an episode. This sequence is based on structural constraints inherent to the nature of pedagogicalreasoning constituent components. Moreover, given its hierarchical nature, the model may imply predictions about how episodes of components of the same hierarchical level in the model are linked. Since comprehension, reasoning and pedagogical problem solving are conceived of as the main components of human cognitive performance in a semantically complex domain, these processes can be examined with respect to how they interact with each other. Finally, the model may imply additional predictions about how episodes of different hierarchical levels in the model are linked. The result is a generic theory of pedagogical reasoning processes that can be used to examine aspects of the performance of individuals and groups in a context of instructional planning. The model is based on the theoretical elements presented next: cognitive processes underlying pedagogical reasoning, the relationship between individual and group performance, and the relationship between pedagogical reasoning and domain knowledge. The presentation of research questions ends this section.

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3.1. COGNITIVE PROCESSES INVOLVED IN PEDAGOGICAL REASONING

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The processes involved in pedagogical reasoning build on the two major manifestations of human higher-order cognition according to Hatano and Inahaki (2000): discourse comprehension and production, and problem solving. These processes are complementary: comprehension is a coherence-seeking process whereas problem solving is a change-seeking process. An emphasis is also put on reasoning, as an extension to comprehension theories (Hatano and Inahaki, 2000) that focuses on how relations between mental representations are used to make inferences (Rips, 2002). Despite their complementary nature, research to date has not shown how comprehension and problem solving are articulated together. This must be done to some degree for the present model. To this end, the concepts of schemas and mental models, as entities that are manipulated both by comprehension (including reasoning) and problem-solving processes, are discussed in conjunction with each of these processes. Finally, aspects of planning in problem-solving are also articulated in the model, since the production of solution to complex problems involves planning.

Figure 3.1. The pedagogical reasoning model.

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The comprehension, reasoning, planning and problem-solving processes underlying the model are presented within a knowledge-centered view of cognition based on research on expertise, in which a large portion of variation in cognitive performance is accounted for by the use of knowledge rather than by generic cognitive operations. After a thorough review of relevant literature, each section ends with a specification of the categories present in the model. Those categories are defined operationally in the methodology of the studies presented in chapters 4 and 5. The model is illustrated in Figure 3.1.

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3.1.1. Understanding a Situation : Building Mental Models of the Case through Discourse Comprehension Processes The postulated model has to specify cognitive processes by which an individual understands a situation (in this case, on the basis of the description of the case). It must also identify the organisation of the information understood. The model also has to distinguish and articulate the information presented in the case that the individual reads and the information (knowledge) that the individual had in memory and uses in understanding the case. The construction-integration model of discourse comprehension has been very influential since its creation and development in the early 1980’s and continues to be so in current research (Foltz, 2003 ; Zaan and Singer, 2003). In presenting his construction-integration model of comprehension, Kintsch (1998) defines comprehension as the bottom-up construction of an interpretation of information through a constraint- satisfaction mechanism based on spreading activation in memory. Information originates both from the environment and from the memory of the comprehender. More specifically, comprehension can be fragmented in a sequence of four steps: perception, understanding of local propositions (microstructure), understanding of large parts or main ideas of a text (macrostructure) leading to a text-based situation model and finally to a situation model, when the gist of the text is integrated to the prior knowledge of the comprehender. Foltz (2003) reframes the process as two main stages: the construction of representations and their integration with prior knowledge. This cyclical process operates on a few local propositions at a time, the equivalent of a phrase or short sentence. There are two mechanisms involved in the construction-integration model: one that activates the related nodes in the memory network and another one that deactivates the irrelevant ones based on the context. Hatano and Inahaki (2000) argue that the constraint-satisfaction mechanism usually involves more than the

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automatic spreading activation posited as sufficient by Kintsch (1998). In this vein, Frederiksen and Breuleux (1990) and Frederiksen, Bracewell, Breuleux and Renaud (1990) argue for a more top-down view of comprehension, in which prior knowledge has a significant impact on the process. Their model is discussed in the upcoming section on mental models and schemas in comprehension.

3.1.1.1. Propositions, Microstructure and Macrostructure In many theories of comprehension such as Kintsch’s (1998) and Frederiksen and colleague’s theory, it is postulated that the information is in the form of propositional representations. Propositions are the smallest unit of meaning that can be conveyed by discourse (Foltz, 2003). A proposition is made of various combinations of predicates (or relational terms), and arguments. It should be noted that propositions are the building blocks of schemas, in which predicates determine the slots and their organisation. A proposition, depending on its level of generality, is organized in relationship to the other propositions as either the microstructure or the macrostructure of the text. The microstructure represents the local information of a text, at the level of sentences. Micropropositions are created by parsing the text. Algorithms for parsing texts are provided by Kintsch (1998) and Frederiksen (1975). The macrostructure represents the global structure of a text by organizing the micropropositions of the text hierarchically. It is a set of propositions that can be either explicit in the text (titles, initial topic sentences, summary statements, etc.) or inferred by the reader. These propositions are organized hierarchically with respect to the level of generality of the information they convey. A perfect summary of a text is a text representing only its macrostructure. Macropropositions are derived from the text using macrorules (Brown and Day, 1983). Propositions in the macrostructure are called macropropositions whereas propositions in the microstructure are termed micropropositions. 3.1.1.2. Textbase and Situation Model The distinction between textbase and situation model refers to the origin of the propositions in the mental representation elaborated through comprehension (Kinstch, 1998). On the one hand, the textbase represents the propositions directly derived from the text read. That is, the textbase represents the meaning of the text, independently of its surface structure (its exact wording) (Oostendorp, Otero and Campanario, 2002). On the other hand, the situation model represents the propositions retrieved from the reader’s knowledge in long-term memory that supplement the information in the text. Since the mental representation of a text is rarely a pure textbase, this mental representation is called the situation model. The

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situation model thus contains the textbase, which can be incomplete and erroneous with respect to the actual meaning of the text, completed by varying amounts of knowledge from long-term memory (Kinstch, 1998). A situation model contains tokens, a specification of their properties, and a specification of the structural relations among the tokens (Copeland, Magliano and Radvansky, 2006). Tokens can be components or goals. These structural relations can be, for example, hierarchical or causal (Whitten and Graesser, 2003). A situation model is created as a function of the task and the comprehender’s prior knowledge. The process of situation models construction can be decomposed into a temporal sequence involving the creation of current models, integrated models and a complete model (Zwaan, Radvansky, and Whitten, 2002 ; Oostendorp, Otero and Campanario, 2002). A current model is the model being constructed at a particular moment during reading a particular clause or sentence. An integrated model at a particular moment represents the integration of all models previously created. The complete model is created when the whole text is read. Updating a situation model may be impossible in some conditions, depending on the match between a reader’s capabilities and the amount of restructuring needed. In such cases, a reader can identify the difficulty as a pending problem or explain the anomaly. Updating mental models during reading is critical for comprehension: a reader constructs a sequence of interlocking accounts necessary for understanding subsequent information in the text. It is interesting to note that a reader can formulate inferences that are later validated or invalidated during a subsequent update of an integrated model. This process seems to be related to the view of reasoning that is presented later in this chapter.

3.1.1.3. Mental Models and Schemas in Comprehension The constructs of mental models and situation models are used interchangeably (Whitten and Graesser, 2003). For schemas to be useful in the proposed model of pedagogical reasoning, the postulated model should specify the nature of schemas, how they affect comprehension and how they are activated. The schema is an indispensable theoretical concept in cognitive psychology (Kinstch, 1998 ; Marshall, 2005). Early views defined schemas as a fixed mental structure that was retrieved when needed and that was used to organize information. The lack of sensitivity to the context, which has a clear adaptive value, led current reconceptualizations of the concept of schemas as algorithms to generate organizational structures in a given context. According to Kintsch (1998), schemas are propositional. They are also part of the comprehenders’ knowledge held in long-term memory.

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Propositions can be incorporated in schemas (Foltz, 2003). Since schemas are propositional, it is reasonable to postulate that they are activated by the same mechanisms as those used for the generation of propositions. Since schemas originate from the knowledge held in memory, this mechanism should be the one associated with propositions from the situation model. Finally, since schemas are organizational structures, they should share activation mechanisms related to macropropositions. Major theorists agree that schemas have a top-down influence on the comprehension process. Schemas can facilitate comprehension: they facilitate the formation of the macrostructure of the text, but do not affect the comprehension of the microstructure (Kinstch, 1998). For Kintsch, schemas act as a perceptual filter that admits relevant material and blocks irrelevant information. Schemas also act as an inference mechanism that fills the information that is inevitably missing from the text. For Frederiksen and colleagues, schemas serve a different function (Frederiksen and Breuleux (1990) ; Frederiksen, Bracewell, Breuleux and Renaud (1990). Their multi-layered model of comprehension is organized around three kinds of symbols: language units, propositions and conceptual structures. The model represents a bottom-up transformation of the stimuli (graphemes and morphemes, for discourse) into meaningful utterances and then into knowledge structures such as schemas, as a definitive form stored in memory. The stimuli can take the form of any array of symbols (text, graphical representations, real-world situations like actions and states, etc.) In this model, whereas there is a bottom-up influence of the stimuli on comprehension, top-down control is achieved by means of frame-level rules. Also, comprehenders may employ control strategies based on their goals, the situation, or their prior knowledge.

3.1.1.4. Specification of the Proposed Model In light of the theory, the model postulates a distinction between information contained in the text (Comprehend textbase) and information retrieved from the individual’s prior knowledge (Supplement textbase with prior knowledge). In addition, the model postulates that question asking (Ask question) reflects breakdowns in the process of situation models construction (Whitten and Graesser, 2003). As discussed earlier, updating a situation model may be impossible in some conditions. In such cases, a reader can become aware of and signal the difficulty by formulating requests for more information. Since the situation model is created during the reader’s interaction with the text, and the pedagogical-reasoning model postulates that reader’s knowledge is activated in response to the text, it is argued that comprehension typically starts with comprehending the textbase. Since comprehension theory indicates that

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knowledge activation occurs both at the microproposition and macroproposition levels, the model postulates that knowledge will be integrated at any moment during reading. Therefore, the conditional probabilities associated with the two links between comprehend textbase and supplement textbase with prior knowledge should be equivalent. As a result of the comprehension step in the model, the individual has created a mental model of the information presented in the description of the case. This mental model ideally contains the gist of this information, supplemented by relevant prior knowledge of the individual(s). A sub-optimal mental model misses a certain amount of crucial information contained in the text, and either contains irrelevant information or misses important information from the individual prior knowledge. Such a model of the case has a critical impact on the other processes of pedagogical reasoning, since a representation of a text (or a situation) constrains problem solving (Whitten and Graesser, 2003) and reasoning (JohnsonLaird, 1983), as discussed in upcoming sections. Without an adequate situation model, the individual(s) will engage in solving the wrong problem.

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3.1.2. Making a Diagnostic: Elaborating and Testing Diagnostic Hypotheses through Reasoning Processes Since a teaching situation typically provides information without an explicit characterization of what the problem is, and therefore from which the problem has to be formulated, the postulated model has to specify cognitive processes that describe how an individual identifies possible characterizations of a problematic situation and chooses the one that best corresponds to a given reality.

3.1.2.1. Reasoning Processes The generation and test of diagnostic hypotheses via reasoning mechanisms has been shown to be spontaneous in both inexperienced and expert diagnosticians (Elstein, Shulman and Sprafka, 2000). The view presented posits that the diagnostic of a pupil’s difficulty is based on abductive reasoning, a combination of deductive and inductive reasoning (Patel, Arocha and Zhang, 2005). Reasoning is a “goal-directed and constrained step-by-step transformation of mental representation of knowledge” (Hatano and Inagaki, 2000, p. 170). Abductive reasoning is a process of elaboration and test of hypotheses. Before examining how reasoning occurs in the elaboration of a diagnostic in a domain such as teaching, a fundamental or generic reasoning mechanism must be posited with respect to how inferences are used to test diagnostic hypotheses.

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Current reasoning theories can be categorized as rule theories, semantic theories, evolutionary theories and heuristic theories (Leighton and Steinberg, 2003). Rule theories postulate that reasoning operates by means of rules or commands. According to semantic theories, reasoning results from the interpretation of assertions. Evolutionary theories specify domain-specific mechanisms that enable individuals to meet environmental needs. Finally, heuristic theories postulate rules of thumb that are fallible but well adapted to everyday reasoning. Because of their close links to comprehension processes presented in the previous section, semantic theories are preferred as a basis for the present model. Of the two candidate theories, verbal comprehension theory (Polk and Newell, 1995) and mental model theory (Johnson-Laird, 2005 ; 1983), mental model theory is preferred because of its applicability to a wide range of reasoning tasks, as shown by Rips (2002). Johnson-Laird (1983) viewed deductive reasoning as a semantic process. He proposed the mental model theory of reasoning. This theory postulates four main stages: the initial interpretation of premises, the combination of these interpretations into a single model representing a situation (these two stages can be referred to as comprehension and as such posit an explicit link to comprehension processes discussed in the previous section), the formulation of a conclusion (description) and the search for alternative models that might refute the conclusion (validation). Moreover, “any step in thought from current premises to a new conclusion falls in one of the following categories : (1) the premises and the conclusions eliminate the same possibilities, (2) the premises eliminate at least one more possibility over those the conclusion eliminates, (3) the conclusion eliminates at least one more possibility over those the premises eliminate, (4) the premises and the conclusions eliminate disjoint possibilities, and (5) the premises and the conclusions eliminate overlapping possibilities” (Johnson-Laird, 2005, p.185). Categories 1 and 2 represent deduction. Category 3 is induction. Category 4 represents situations in which the conclusion is inconsistent with the premises. The last category represents creative thinking. According to the mental model theory (Johnson-Laird, 2005 ; 1983), reasoning is based on the manipulation of meaningful concrete information. The reasoning process involves three steps. It begins with the construction of a mental model representing a possible situation of a premise. Then, the truth value of the mental model is tested, leading to three possible outcomes : the conclusion is possible if it holds in at least one model, is necessary if it holds in all the models, and impossible if it never holds. The third and final step is the construction of an alternative mental model of the situation in order to verify or disprove the conclusion drawn.

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Johnson-Laird (1983) identifies three causes of difficulty in syllogistic reasoning. First, the number of models required to make a deduction increases the difficulty. Reasoning with premises leading to a single model of a situation (a quantifier) is easier than reasoning with many valid models. Second, erroneous conclusions are consistent with the premises, that is, reasoners fail to construct all the models required to make the right conclusion. Finally, the general knowledge (beliefs) of the reasoner can affect the process; conclusions in accordance with his beliefs will inhibit the search for alternative models, and inversely. In other words, the plausibility of the conclusion, determined by the reasoner’s knowledge, affects the validation process. According to the model theory, erroneous conclusions arise from a failure to construct the appropriate model (a typical situation involves premises containing “some” and “only”).

3.1.2.2. Reasoning in a Semantically Complex Domain Since no theory of reasoning in teaching is available, the present model borrows from a well-researched domain that shares its main characteristics, medicine. According to Calderhead (1995), teachers and physicians have to make sense of diversified information, and use eclectic theories and evidence, personal beliefs and expectations to modulate their decision-making with respect to diagnostic and subsequent intervention. These similarities hold for teacher planning activities and not for interactive teaching (when the teacher is actually in the classroom with the pupil(s)), a context during which very few diagnostic decisions are made, as demonstrated empirically by Putnam (1987). Leinhardt and Greeno (1986) have made the similar point by insisting on the assumptions that both domains involve problem solving in an ill-structured and dynamic environment. All theories of reasoning in medicine characterize diagnosis as an iterative process in which possible explanations of the patient’s state (hypotheses) are generated and then tested on the basis of their expected consequences (Patel, Arocha and Zhang, 2005). This 2-stage process – hypothesis generation, hypothesis testing – is based on a mechanism of inference generation. Four types of inferences can be generated: abstraction, abduction, deduction and induction. Hypotheses are generated by abstraction and abduction and tested by deduction and induction. The process of abstraction filters data with respect to their relevance for solving the problem. During abduction, plausible hypotheses are related by means of inferences that identify initial conditions from which the abstract representation of the problem originates. Deduction builds up the mental model described by the consequences of each hypothesis in order to test them. The predictions derived from hypotheses are matched to the description of the

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case through induction, and predictions that do not match the case lead to the rejection of the hypothesis to which they are associated. Patel, Arocha and Zhang (2005) identify one pervasive caveat related to hypothesis testing: the confirmation bias. The confirmation bias is a desire to confirm a preferred hypothesis. The reasoner engages in a search for evidence consistent with a generated hypothesis that often leads to a failure to consider alternative hypotheses. In terms associated with comprehension theory, an inference “is a transformation of a proposition in which the head element remains unchanged” (Groen and Patel, 1988, p.293). For these authors, an inference is a macroproposition in Kinstch’s (1998) terms. Patel and Groen (1991), in summarizing results of many of their studies on reasoning in medicine, indicate that the elaboration of a diagnosis through reasoning can proceed from data to hypothesis (forward or knowledge-based reasoning) or, inversely, from hypothesis to data (backward or goal-based reasoning). Forward reasoning is heavily dependent on the reasoner’s domain knowledge to avoid errors due to a lack of legitimacy of the inferences.

3.1.2.3. Specification of the Proposed Model The model postulates that the diagnostic process begins with the elaboration of one or more hypotheses (Elaborate a hypothesis). When many hypotheses are formulated, they are organized on the basis of their plausibility (Organize hypotheses). Hypotheses are then related to the data (Test hypothesis) in two alternative manners. They can follow from an analysis of the data that leads to a single hypothesis as a series of conditional paths in the reasoner’s mental model or be formulated up front, and then confronted with the data as a set of causal paths. Finally, the cognitive processing associated with each hypothesis ends when each of them are either accepted or rejected (Accept hypothesis or Reject hypothesis). It is expected that one hypothesis will be held as valid in order to proceed with the elaboration of a reputedly appropriate intervention. The elaboration of the diagnosis ends when one hypothesis is accepted as representing the educational problem that has to be addressed. This triggers the elaboration of the solution to the problem identified.

3.1.3. Setting up a Pedagogical Intervention: Elaborating the Best Intervention Possible through Teacher Planning Processes Much has been written about categories pertaining to teacher planning. Characteristics of the process, of the knowledge underlying it, and of the actual

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product of planning were studied. Whereas the debate continues regarding the many and often competing categories describing the knowledge base for teaching (Hasweh, 2005 ; Sherin, Sherin and Madanes, 2000), the consensus regarding those categories that can be applied to the cognitive process of pedagogical planning, however, has remained relatively unchallenged over the last 20 years (Lenhardt and Greeno, 1986; Schoenfeld, 2000). The literature indicates that goals and schemata are central to pedagogical planning.

3.1.3.1. Goals and Schemata Conceived of as a cognitive activity, teaching is goal-driven (Leinhardt and Greeno, 1986 ; Schoenfeld, 2000). According to Schoenfeld (2000), goals are things that an individual wants to accomplish. Specifically in the case of teacher planning, goals may be epistemologically oriented, content-oriented, or socially oriented. They are organized hierarchically, and multiple goals can be pursued at the same time. Goals can be pre-determined as a result of lesson planning or emergent during teacher interactive decision-making, in response to the exigencies of the situation. For the purpose of this theorization, the notions of schema and action plan refer to essentially the same idea. Leinhardt and Greeno (1986) define a schema as a set of organized or ordered actions used to reach a goal. Similarly, an action plan is a set of intended actions to achieve a given goal (Schoenfeld, 2000). Considering the details of both constructs and their implications, the notion of schema is preferred in the present work for three reasons. Firstly, the notion of schema is more general than the notion of action plan (Schoenfeld, 2000). Secondly, Leinhardt and her colleagues (Leinhardt, 1987; 1989) provided profound insights into teacher cognition (especially teacher knowledge) by studying schemas and scripts to establish expert-novice differences. Finally, its constituting elements were carefully documented and empirically demonstrated by Leinhardt and Greeno (1986). Indeed, in addition to actions, a schema contains other elements associated to these actions (Leinhardt and Greeno, 1986). Consequences and effects of actions are included (as expected results of the enactment of an action), as well as conditions for the enactment of these actions. These conditions are either prerequisites (a condition that must be met before enacting an action), corequisites (a condition that must be met during the enactment of an action), or postrequisites (a condition that must be met to end an action). Classic works by Sacerdoti (1977) and Sowa (1984) were consulted in search for additional primitives that would further characterize schemas for teaching. No additional elements were found to be pertinent.

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Having set one or more goals, the planner then considers schemata whose anticipated consequences match its current goal (Leinhardt and Greeno, 1986). More precisely, a global schema is chosen on the basis of its fit to the higher-order goal, and then less global schemata are chosen to satisfy more specific goals that are related to the higher-order goal. The result of planning can be formalized in a planning net linking together goals, actions and their conditions and consequences of actions (as indicators of goals). Schemas, as outcomes of planning, are held in memory as a basis for subsequent action. At the time of their enactment in action sequences, schemas can be contingent on the classroom situation. That is, they are also part of a teacher’s interactive decision-making (Schoenfeld, 2000), and, consequently, manipulated during teaching.

3.1.3.2. The Influence of Diagnosis on the Formulation of Goals The basis of goal formulation in planning has to be specified here because of the postulated importance of the diagnostic process, thought of in the pedagogicalreasoning model as a strong determinant of subsequent planning. Most research evidence suggests that the diagnosis of students’ characteristics is not an important factor in short-term teacher planning. Studies have shown that primary concerns during planning are related to learning content and activities and that student-related factors are relatively unimportant (McCutcheon, 1980 ; MorineDershimer, 1979 ; Peterson, Marx and Clark, 1978 ; Sanchez and Valcarcel, 1999; Zahorik, 1975). Other studies by Clark and colleagues, although in minority, have shown that students’ characteristics are among the most important factors in planning (Clark and Elmore, 1979; Clark and Yinger, 1979). Although characteristics of the students are relatively unimportant, interest and attitudes have relatively more weight than aspects related to learning such as academic ability (Taylor, 1970). The importance of the diagnostic process during teaching was also shown to be negligible for interactive teaching (Putnam, 1987). Despite the conclusions of this body of research describing what teachers do, it is argued here that the diagnosis of students’ difficulties has very important beneficial properties for student learning and that its impact on planning remains or should be significant. This seems particularly important considering recent emphasis on differentiation of instruction (Davies, 2000). The differentiation of instruction is based whether on previous subject-specific learning outcomes or on students’ ability to learn. Questions about the practicability of differentiation were raised in light of the greater demands on teachers’ practice. By showing how the contingency of teaching on students’ needs improves learning outcomes (Wood and Wood, 1999), substantial research in the field of tutoring suggests some reasons why, not only on a moment-to-moment basis during instruction, but for

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the selection and sequencing of learning activities in the context of teacher planning as well. Student’s diagnostic in human tutoring as well as computer tutoring, emulating or not human tutoring is mainly based on diagnostic of students’ antecedents and/or ongoing learning performance. In line with this body of cognitive research, it can be reasonably hypothesized that the goal structure in competent planning of instruction is set as a consequence of the diagnostic hypothesis that was held by the teacher to be true.

3.1.3.3. Specification of the Proposed Model The previous theoretical considerations put emphasis on two major elements in planning an intervention: the identification of goals and the specification of actions that will presumably help reaching the goals. It can be postulated that planning is initiated by the formulation of one or more goal (Identify goal). When more than one goal are set, they are structured hierarchically and causally (sequentially) (Organize goals). Once the goal structure is created, the construction of schemata begins, with the identification of their main elements: actions (Identify pedagogical action). Conditions (Identify prerequisite, identify corequisite, identify postrequisite) and consequences of actions (Identify consequence and effect) are determined in association with each previously specified action. It is unclear whether conditions or consequences need to be specified first for a given action.

3.1.4. Applying Knowledge to Complex Problem-Solving Situations: Articulating the Three Components of Pedagogical Reasoning by Means of Problem-Solving Processes In a very abstract way, problem solving can be seen as a process of performing the required (cognitive) actions to eliminate the discrepancy between an initial state and the desired state (solving an algebraic equation, solving a criptarithmetic problem, etc.). In classical descriptions of the process (Newell and Simon, 1972), problem solving begins with an initial state, a goal (fragmented in subgoals when one runs into an impasse) and implementation of strategies to attain goals toward a desired state. Problem solving is successful when the desired state is attained. In semantically complex domains, problem solving involves cognitive, emotional, personal, and social abilities and knowledge (Wenke, Frensch and Funke, 2005).

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Upon presentation of a problem, individuals will use information in the description and prior knowledge to generate an internal representation of the problem. In this process, the application of prior knowledge is done through the generation of inferences (Williams and Noyes, 2007).

3.1.4.1. Problem Solving as Problem Representation and Solution Problem solving can be defined as “the analysis and transformation of information toward a specific goal” (Lovett, 2002, p.317). Problem solving can be seen as three main aspects: problem representation, search in a problem space, and problem decomposition and planning. In problem solving, it is important to distinguish between the representation of the problem and the solution of the problem (Novick and Bassok, 2005; Voss and Post, 1988). The process of problem solving starts with the representation of the problem (Novick and Bassok, 2005 ; Hatano and Inagaki, 2000). The problem representation is a mental model of the problem summarizing one’s understanding of the problem (Novick and Bassok, 2005).This representation includes the initial state, the goal state, a set of actions that change the current problem state, and constraints that restrict the number of solution paths. In knowledge-rich, semantically complex domains, a problem can be represented differently on the basis of the individual’s knowledge (Hatano and Inagaki, 2000). Research on mental models and schemas in problem solving has provided profound insights in characterizing problem solving, under the assumption that mental models are the objects that are manipulated in problem solving (Johnson-Laird, 2005). Mental models represent a state in the problem space (Newell, 1990). More specifically, they represent entities, individuals, events, processes, and operations of complex systems (Johnson-Laird, 2005). Mental models seem to have a critical role in the representation of the problem, since they can contain and organize the four components of the problem representation discussed by Novick and Bassok (2005): a represented world, a representing world, rules that map the two worlds, and a process that uses the information represented to solve the problem. The representation of the problem affects how the problem is solved: No adequate solution can be elaborated without a representation of the actual problem and all its relevant features (Novick and Bassok, 2005 ; Whitten and Graesser, 2003). In return, the representation of the problem is affected by two main factors: the context of the problem and the solver’s knowledge of the domain (Novick and Bassok, 2005). The context of the problem affects the elaboration of the problem representation (Novick and Bassok, 2005). Specifically, the perceptual presentation format of the problem may provide information about the relevant configuration of the elements of the problem. In addition, the objects present in

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the problem affect the inferences that are created during the elaboration of the problem representation. Finally, the phrasing and narrative of the problem may lead the solver to focus on certain aspects of the problem. Despite the influence of the context on the construction of the problem representation, the solver’s knowledge of the domain exerts the greatest influence on this process. The solver’s ability to exploit previous solutions for analogous problems depends heavily on knowledge, in the form of schemas. These schemas can apply for types of problems, types of solution procedures and types of problem representations. These schemas are abstract because they contain information common to multiple problems but exclude information idiosyncratic to particular problems. Finally, experts’ representations emphasize structural features relevant for the solution such as causal relations, whereas novices’ representations highlight superficial features irrelevant to the solution. Many fundamental mechanisms for problem solution were suggested over the years, articulated as search for a solution. Among search strategies, a first distinction can be made between algorithmic strategies and heuristic strategies (Novick and Bassok, 2005). Algorithms such as mathematical equations and exhaustive search are procedures that will assuredly yield the solution. However, when the number of possible operations is large and algorithms become impractical, heuristic strategies that are likely to lead to the solution come into play. Search heuristics include hill climbing and means-end. Hill climbing refers to the application of the operator that yields a state closest to the goal state. The means-end search in the problem space is more complex than hill climbing: its aim is to find an action that reduces or eliminates the distance between the goal state and the current state. If the action cannot be conducted, a subgoal has to be set to remove the obstacle (this is related to the test of conditions included in the model). Search heuristics are iterative. Complex problems can be decomposed into subproblems that are easier to solve. Planning a solution in terms of a sequence of steps before executing actions accelerates problem solving.

3.1.4.2. Problem Solving in a Semantically-Complex Domain Problems differ depending of the domain in which they are anchored. They can be classified along three dimensions (Lovett, 2002). One dimension is whether a problem involves a routine or non-routine solution. Another dimension is the amount of domain knowledge required to solve the problem. Problems in semantically complex domains such as teaching, medicine or engineering are knowledge-rich problems whereas knowledge-lean problems come from games and puzzles or everyday tasks. A last dimension concerns how well- or ill-defined

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the problem is. This dimension refers to the level of clarity of what is given and of what constitutes a solution (Novick and Bassok, 2005). It became apparent in the 1970’s that the processes of problem solving in knowledge-rich or semantically complex domains do not generalize across domains (Wenke, Frensch and Funke, 2005). During the following decades, theories were created for some domains, such as politics, management, law, electronics, medicine, etc. There is apparently no such theory for the case of teaching. Consequently, the present model borrows from the fields of social science and medicine. Studies of teacher’s planning can supplement a theory from other fields by identifying the components of a plan of actions in teaching. It is particularly enlightening to consider the difference between ill-structured and well-structured problems in terms of constraint resolution (Voss and Post, 1988). Ill-structured problems can be characterized as containing a large number of open constraints that have to be structured by the solver. It should also be noted that the amount of constraints may vary during problem solving, depending on where the solver is in the solution process. There are two strategies for problem representation: problem decomposition (identifying the factors causing the problematic situation, finding a solution for each factor or problem component, integrating these solutions into a general solution for the complete problem) and problem conversion (making a statement about the primary cause of the problem, which can be acted upon). The solution process can include making explicit the history of the problem (previously attempted solutions and current state). Problem representation is achieved through a schema-guided search process. This search involves both an external search of the presented information and an internal search for prior knowledge pertinent to the problem. An expert solution typically includes its justification. Pedagogical reasoning problems share similarities with social science problems. Generally, there is no right answer, but a set of plausible good answers. Since their solution involves planning, the subsequent adoption of a solution is then subject to argumentation. The question of when such a problem is solved is best answered by domain-specific stop rules, which involves a decision by the problem solver. What constitutes a good solution must be judged pragmatically by members of the field, with respect to its quality and usefulness. The quality of a solution is associated with the extent to which it can be rationalized.

3.1.4.3. Specification of the Proposed Model The pedagogical-reasoning model has to specify how an individual chooses a particular course of action to have a desired influence on an unsatisfactory situation, and on which basis these choices are made. Moreover, the overall

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coherence of the postulated pedagogical-reasoning model, beyond its constituent processes, has to be established. In light of the theory presented so far, it can be postulated that this coherence is obtained by a high-level control mechanism based on problem-solving processes that controls the elaboration and use of mental models and schemas to complete the task. Consequently, the operators associated with this process are hypothesized to operate exclusively on mental models and schemas. It is expected that this control will necessarily operate at the beginning and end of the pedagogical reasoning process, and during shifts between its three components, as well as accessorily during transitions among constituents of those components. The problem space for a pedagogical-reasoning problem has a tremendous amount of possible states. For problem representation, it remains unclear from theory whether problem decomposition or problem conversion will be the preferred strategy. Voss and Post (1988) report that problem decomposition was the strategy typically used in solving problems in domains related to social sciences. Since the strategy of problem decomposition must be based on substantial domain knowledge to avoid inadequate solutions, its use puts an emphasis on the interpretation of the case description and its completion by relevant domain knowledge. Consequently, experts are expected to use the decomposition strategy with more success than novices. For problem solution, it can be hypothesized that pedagogical reasoning is based on the heuristic strategy of means-end search. Means-end search involves the selection of actions that match specified goals (Plan goal). The goals can be related with the problem representation through external and internal search, reasoning and problem solution, that is, planning a course of action with reasonable probability of being successful. Planning problem-solving action involves organizing how the problem will be formulated, and how an appropriate solution will be constructed. Planning a course of actions to conduct the pedagogical-reasoning process involves taking into account the sequential dependencies linked to the use of outcomes of antecedent actions as constraints for subsequent actions. When necessary conditions for enacting actions are tested and not met (Test conditions), subgoaling takes place in the form of lower-level goal(s) and associated actions (plan goal and plan action). Sequential dependencies among various aspects of the process have to be identified and prerequisites of the actions have to be identified and verified before executing actions (Execute problemsolving actions). During the intermediate steps involved in this type of means-end search solution procedure, it becomes necessary to monitor the problem-solving process,

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notably by constructing and updating a representation of the problem state (Interpret state). It is hypothesized that the constraints inherent to an ill-structured problem will emerge and get resolved during pedagogical reasoning. In consequence the planning of goals and actions will be recurrent and contingent on those constraints, as they are interpreted. Constraints are numerous, and ultimately refer to educational intentions bearing on policies, resources and many other aspects of a teaching situation. The evaluation of the solution of an ill-structured problem involves checking if a given constraint has been resolved satisfactorily (Evaluate). This evaluation may include the implementation of stop rules which trigger the end of particular actions. These stop rules are associated with the state of constraints that have to be resolved. A good solution that will lead to positive educational outcomes is thought to be adequate if it addresses the student’s condition, and if it is workable given the available resources. As an optional consequence of the evaluation of the solution, the correction procedure (Correct) involves the modification of a solution component or the addition of a new component. Having described the main characteristics of a pedagogical-reasoning model and its theoretical foundations, some comments have to be made about its use in the study of teacher cognition. Indeed, a number of distinctions can be made in the study of group performance in problem solving. One distinction pertains to the relationship between the performance of individuals and the performance of the group. Another distinction is the relationship between the cognitive processes underlying the performance of a task and the domain knowledge in which these processes are anchored. These two distinctions are discussed next to show how a model developed with categories related to individual cognition can be the foundation for integrated modeling of cognition and social cognition (Sun, 2006).

3.2. RELATIONSHIP BETWEEN THE PERFORMANCE OF INDIVIDUALS AND THE PERFORMANCE OF THE GROUP Theories of action regulation are particularly interesting as a unifying framework for the study of individual and group performance. Within this view, the collaboration between the individuals in the performance of a problem-solving task can be examined from the perspective of the functioning of the group and from the perspective of the contribution of each individual to the problem solution. Both perspectives are important and especially interesting to study concomitantly, since, as Wijekumar and Jonassen (2007) assert, “there is no

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distribution of cognition without the individual’s cognition and the individual’s cognitive structures are important to study”. To this end, the notion of system levels (Tschan, 2002) is especially useful since it articulates the idea that processes underlying group performance and individual performance are to some extent similar, independently of the size of the group. More specifically, executive processes at a functional level are similar if the group is considered as an “acting system”. Tschan’s (2002) empirical studies suggest that group performance involves two levels: a first level is the selfregulation of each group member, whereas a second level is the coordination between each individual’s own regulation for group performance. The first level operates within the information-processing constraints of human cognition. The second level can be considered an additional, social layer representing collaborative processes operating within communication constraints. Action regulation at both levels involves the preparation, execution and evaluation of procedures to achieve a given result. Ideally, the performance of each subtask or task component should comprise cycles of preparation, execution and evaluation. Tschan (2002) found that this cycle was associated with the quality of the performance for individuals, dyads and triads. It should be noted that categories associated with these procedures are included in the pedagogical-reasoning model, as the problem-solving level. In complex tasks, these procedures are cycles of action that are “hierarchically nested and sequential” (Tschan, 2002, p. 616) in response to the structure of these tasks. Indeed, complex tasks can be decomposed as a set of subtasks. In the pedagogical reasoning model, a first level of decomposition corresponds to the components. Another level of decomposition is the iterations of the components in response to the multiple elements of the situation. Moreover, the successful completion of given subtasks can represent prerequisites for other subtasks, prescribing that some subtasks be performed in a certain sequential order. Our emphasis on cognitive aspects of performance, including knowledge of the domain, and our consideration of groups as information-processing systems (Arrow, McGrath and Berdahl, 2000) lead us to consider related aspects of information storage, information retrieval and information exchange in groups. The degree of overlap of task-related information held by different members of a group is thought to be a major influence on group functioning (Arrow, McGrath and Berdahl, 2000). There is a strong tendency to discuss information that was available to all members before the group meeting rather than mentioning information available to only one member, resulting in a group’s propensity to confirm and reinforce previously shared information. Groups’ use of information is often based on a very incomplete comprehension of the relative importance of

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various elements of information and their sources. It also depends on the processes by which group members construct a shared understanding of the information. This processing involves the reduction of uncertainty caused by incomplete information and the reduction of equivocality caused by alternative interpretations of the same information. Actions related to group goals can be organized hierarchically in three levels. The higher level is purposeful thought, the intermediate level consists of scripts as discussed before, and relatively automatic behaviour constitutes the lower level (Arrow, McGrath, and Berdahl, 2000). These levels are knowledge based, rule based, and skill based, respectively. The performance of actions can be conceived of as determined by mental goal representations (hierarchical in the sense that some goals are broader in scope than others and sequential since the attainment of given goals serve as conditions for the attainment of other goals) complemented by feedback control (based on information regarding the short-term consequence of action). Feedback control requires some reference values for behaviour against which the short-term consequences of actions must be judged; goals have this function. Since feedback loops are associated with goals and goals are organized hierarchically, feedback loops are organized in levels, resulting in the top-down influence of higher-level feedback loops. Specifically, superordinate loops reset reference values at the next lower level of abstraction. This hierarchical view treats control as simultaneous at all levels of abstraction below the level that’s guiding the activity, that is, the process of carrying out a high-level act consists of carrying out low-level acts. This model shows how intentions are carried out physically. Low-level identifications tend to convey a sense of “how” an activity is done; high-level ones tend to convey a sense of “why”. Movement from a lower level to a higher level depends on an emergent property at the higher level: a given lower-level identification can often be absorbed into several alternative higher-level identifications. Attaining an abstract goal requires it to be broken iteratively into subgoals, until the subgoals are sufficiently concrete that they can be attained by the body’s basic operational mechanisms. How many levels are required is an open question that should be answered empirically.

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3.3. RELATIONSHIP BETWEEN PEDAGOGICAL-REASONING PROCESSES AND DOMAIN KNOWLEDGE (EXPERTISE) In a semantically complex domain, problem-solving processes hinge on pertinent knowledge of the domain. How this knowledge is used to perform the task, both individually and collectively, is thought to be largely determinant of the outcomes of the activity. Comprehension, reasoning, planning and problem solving are all hypothesized to be facilitated by the availability of pertinent domain knowledge. In comprehension, a situation model constructed using expert knowledge is more complete, contains only relevant information for the problem solution, and contains general ideas. Expertise is related to the selective acquisition and use of information. In terms of comprehension, experts recall more of the information presented in the case that novices do (Patel and Groen, 1991). In the same vein, expert teachers recall more classroom events and rely more on procedural knowledge and principles to analyze interactive teaching than novices (Peterson and Comeaux, 1987). Reasoning takes radically different forms whether expert knowledge is available or not. Without knowledge, the individual is forced into backward reasoning, in which hypotheses are formulated and then verified using available data. In contrast, expert knowledge enables the individual to derive the appropriate hypothesis directly from the data. Patel and Groen (1991) argue that experts use forward reasoning (from data to hypothesis) because they have the necessary domain knowledge to guide the elaboration of the hypothese(s). Novices, because of a lack of knowledge, reason backwards in a hypotheticodeductive manner, verifying hypotheses they elaborate on the basis on the data available. Novices use backward reasoning because their do not have the knowledge required to support forward reasoning (Patel, Arocha and Zhang, 2005). Indeed, data-driven or forward reasoning is likely to lead to errors when knowledge is insufficient. In contrast, hypothesis-driven or backward reasoning increases cognitive load since it requires that the reasoner keeps track of the current goals and hypotheses. Studies of teacher expertise have shown differences in how novices and experts plan instruction (Hogan, Rabinowitz and Craven, 2003). The balance between mentally scripting lessons and written plans is shifting, and the propensity for developing long- and short-term educational goals are modulated by teaching expertise. These differences are attributable to the varying level of

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complexity of the schemas experts and novices hold. Experts perceive the classroom as a group of unique individuals whereas novices regard the class as a whole, leading experts to ask for more specific information about a classroom before planning instruction. In light of the importance of constraints resolution in solving ill-structured problems as discussed in the model, we interpret this as a need for experts to look for more constraints that are used in elaborating a solution. In addition, experts focus on both long-term and short-term planning, whereas novices focus only on short-term planning. Experts’ plans include presentation time and pace, and number and types of examples. Novices’ plans include these elements but also integrate scripted portions such as verbatim of introductions and questions to be asked during the lesson. Finally, novices’ planning is more influenced by students’ interest than by students’ achievement. In their review of the research, Borko and Shavelson (1990) found that experts’ reported plans are richer than those of novices. Experts’ plans made greater explicit reference to actions to be performed by students, included test points on students’ understanding, and contained twice as many teacher instructional moves. In terms of the planning process, experts plan more quickly than novices, are more selective in the information they use and incorporate more relevant information in their decision-making. Smith (2005) studied co-planning between an experienced teacher and a student teacher. This situation can be referred to as a heterogeneous dyad, in opposition as homogeneous dyads in the present study. She found that during the first few co-planning sessions, the mentor verbalizes his way of making lesson plans, in order to make explicit the cognitive process involved in planning instruction while the student teacher assimilates and imitate the process. Later on, there is a shift in the co-planning process, manifest in discomfort between the participants, when the student teacher challenges her mentor by suggesting new ways of planning. In light of the challenges of novice-expert interaction she documents, Smith concludes that participants in such novice-expert dyads need to be taught to interact in a way that fosters the novice’s learning and the expert’s innovation. Finally, problem solving is also facilitated by expert knowledge in that this knowledge is essential for the adequate representation and solution of illstructured problems by the identification and resolution of open constraints. It is therefore postulated that differences in expertise have an impact on the performance of a problem-solving task, at the executive level. Experts and novices use different heuristics in solving problems (Hatano and Inagaki, 2000). Experts represent problems by categorizing them. These categories elicit pertinent knowledge and this knowledge indicates potentially useful solution algorithms.

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There is a critical synergy between good knowledge and good reasoning skills in the development of expertise (Lohman, 2005). According to this author, reasoning is heavily dependent on good knowledge, and this well-organized knowledge base is acquired through good reasoning. Indeed, data-driven reasoning, which requires a strong knowledge base, is more likely to lead to the acquisition of a schema for the problem (Patel, Arocha and Zhang, 2005). From a developmental point of view, one salient symptom of the role of knowledge in cognitive performance is the intermediate effect (Patel, Arocha and Zhang, 2005). In contrast with the reasonable idea that performance improves with training or deliberate practice, the intermediate effect refers to a drop in performance during the transition between novice and expert levels of expertise. This effect is accounted for by characteristics of the knowledge underlying these levels of expertise. Novices have sparse knowledge to apply to a problem. During an intermediate stage, newly acquired knowledge is not optimally organized and leads to many inappropriate inferences. Experts’ knowledge is well-organized and improper inferences are eliminated. This discussion of the categories that a cognitive model of collaborative pedagogical reasoning may include from a theoretical point of view is followed by an empirical examination of the extent to which the categories postulated from the theory are useful to account for data and the extent to which the postulated sequences of events are observed in a corpus of data.

3.4. RESEARCH QUESTIONS Empirical questions related to the elaboration of a cognitive model of teacher collaborative pedagogical reasoning include : (1) what is the prevalence of the cognitive steps involved, (2) how this prevalence is affected by expertise, (3) how the process is typically sequenced, and (4) how this sequencing is modulated by expertise. The following chapters present two companion studies. The aim of these studies is to test the model of pedagogical reasoning by providing elements of answer to these questions in the context of individual and collaborative performance. Participants were the same in both studies. Therefore, results regarding their individual performance and their performance in dyads pave the way for examining the costs and benefits of solitary and collaborative settings for learning and performance in teaching by contrasting aspects of the cognitive functioning of each individual in both contexts.

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Chapter 4

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4. A STUDY OF COLLABORATIVE PEDAGOGICAL REASONING This study addresses issues of prevalence and sequencing of the cognitive processes constituting the pedagogical reasoning model presented in chapter 3. Specifically, four questions were formulated: (1) what is the relative prevalence of the pedagogical reasoning processes (2) does this relative prevalence vary across expertise levels (3) what is the typical sequencing of the pedagogical reasoning processes, and (4) does this sequencing vary across expertise levels? Questions 1 and 2 were answered by compiling time-budget information for each step. Question 3 and 4 were answered by computing transitional probabilities between steps. To examine the typical sequence of steps within a system level, the unit of analysis was a transition from one step to another without considering the individuals within the team at the team level. For both set of questions, results for the whole sample are presented, followed by results associated with each level of expertise.

4.1. PARTICIPANTS Participants in this study are special education student teachers and teachers. Years of experience and teaching position were the criteria used in the selection of participants in order to maximize variations in teaching expertise. In this study, teaching expertise is understood as the availability of pertinent domain knowledge accompanied by a capacity to apply this knowledge in solving problems in the domain. The sample comprised 6 second-year student teachers, 6 fourth-year student teachers, 2 teachers and 4 specialists in remedial reading instruction.

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Participants of the same expertise level could volunteer as a dyad, and most did. The other participants were matched in pairs by an experimenter on the basis of compatibility of schedule. Each participant received 25$ as a compensation for the three hours she devoted to this study.

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4.2. TASK AND SETTING Modeling group cognitive performance requires a meaningful and authentic task that that can be performed under relatively controlled conditions. Lesson planning corresponds to these criteria. Participants were asked to plan a series of lessons related to remedial reading instruction. Lessons were planned on the basis of a written description of a case of a student displaying difficulties in reading. The description contained the student’s familial and school history, a phonetic transcription of her reading aloud of a level-appropriate 167-word expository text, the transcription of her free recall of a 259-word narrative text, followed by a transcription of her answers to 10 comprehension questions. A transcription of the student’s metacognitive reflection concludes the description of the case. In total, the description of the case is 12 pages long. A computer and word processor was provided for the elaboration of the written plan. Following their initial planning session, the six similar participants were gathered in pairs for an additional planning session, in which they were asked to elaborate a common lesson plan on the basis of their initial plans. Working in pairs and the resulting negotiation requires that the participants verbalize elements that could otherwise remain implicit (Mercier and Frederiksen, 2007). Pairs used one computer with both individual lesson plans available in electronic format to produce one common lesson plan.

4.3. DATA COLLECTION For each dyad, the collaborative-planning conversation was recorded on audiotape. Participants’ interaction with the word processor was captured by a concomitant video recording of the computer screen. The lesson plans of the sequence of activities were archived as digital files for subsequent analysis.

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4.4. DATA ANALYSIS Protocol analysis procedures were designed to characterize the processes involved in collaborative pedagogical reasoning. Since the data collected in this study reflect particular thoughts about a specific task, protocols from several comparable dyads need to be analysed to induce more general characteristics of the processes (Olson and Biolsi, 1991). Protocols were grouped according the level of expertise of the teams.

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4.4.1. Process Modeling In this study, process modeling serves two main objectives: (1) to examine the prevalence of collaborative pedagogical reasoning activities and how this prevalence is modulated by different levels of expertise (2) to examine the sequential aspect of collaborative pedagogical reasoning and how different levels of expertise are associated with different typical sequences of collaborative pedagogical reasoning activities. Techniques from sequential analysis are used under the assumption that cognitive processes can be decomposed into series of discrete and sequential steps of various grain size (Anderson, 2002). This assumption can be extended to groups, as demonstrated empirically by Tschan (2002). Frequency data was analysed using the SAS CATMOD procedure which provides maximum-likelihood estimations of effects of factors in contingency tables. The detailed significance of tests is reported even for non-significant results, since those results are especially meaningful given the strong statistical power of loglinear analysis in the present context. One important assumption underlying the log-linear approach is the independence of observations. Independence of observations means that chances of an observation being associated with a category are equal, independently of the observations preceding it. This assumption is likely to be violated to some extent in the present study because of the nature of the data. In fact, the objectives of the study consist of assessing the sequential dependence among events, that is, predicting events from past events. Addressing this issue, Bakeman and Gottman (1997) conducted simulation studies and showed that violations of independence have no effect on the use of the log-linear approach in this context. Despite this crucial information, tests with borderline significance will be interpreted conservatively. Sequential data were analysed using the GSEQ 4.1.2 (Generalized Sequential Querier) program developed by Bakeman and Quera (1995). GSEQ is an excellent program

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designed specifically and exclusively for sequential analysis. Sequential aspects of any type of data, including issues of individual differences and group comparisons, can be analysed using GSEQ. The RELF, CONP and PVAL procedures were used in the present study to obtain relative frequencies, conditional probabilities and statistical test of significance of conditional probabilities. Level of expertise is the only factor in the experimental design of this study. With respect to expert-novice differences, Ericsson (2003) argues that it is possible to identify mediating cognitive mechanisms associated with expertnovice differences and analyse them by means of process-tracing methodology. To face the complexity of these mechanisms, a possible strategy is to identify cognitive subsystems and to identify methods for controlling performance. This control of the performance is based on a task analysis, a process that seems especially difficult in the case of knowledge-rich problems like the one used in this study. A first step in explaining differences attributable to domain expertise is to investigate whether or not differences in collaborative pedagogical reasoning are present across levels of expertise. In other words, is there any internal modulation, both in terms of prevalence of given control processes, components or subcomponents and in term of their sequential structure, of the pedagogical-reasoning process that would reflect different patterns in pedagogical reasoning that could be attributed to expertise? Both SAS and GSEQ were used to answer those questions.

4.4.2. Coding Scheme The categories used in modeling the collaborative pedagogical reasoning process are based on the theoretical framework presented earlier. They are identified and organized hierarchically in Figure 4.1 to show the decision process associated with coding. Table 4.1 presents the categories with their operational definitions.

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Figure 4.1. Structure of the coding scheme.

Table 4.1. Categories associated with collaborative pedagogical reasoning Code Plan goal Plan problemsolving action Interpret state Test conditions Evaluate Correct Comprehend textbase Supplement textbase with prior knowledge

Definition Plan the goal to be achieved by this pedagogical reasoning procedure Plan the pedagogical reasoning action to be carried out Interpret the current problem state in pedagogical reasoning Test critical conditions for applying a procedure in pedagogical reasoning Evaluate the result obtained from applying the pedagogical reasoning procedure Correct an error or provide a missing component of the solution Derive meaning of the text’s propositions Provide information not included in the text

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.

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Julien Mercier, Caroline Girard, Monique Brodeur and Line Laplante Table 4.1. (Continued)

Code Ask question Elaborate a hypothesis Organize hypotheses Accept hypothesis Reject hypothesis Identify goal Organize goals Identify pedagogical action Identify prerequisite

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Identify corequisite Identify postrequisite Identify consequence and effect

Definition Diagnose a need for additional information Make inferences to identify the problem in the case In the presence of multiple hypotheses, organize them in terms of plausibility Determine that a hypothesis is supported by the data Determine that a hypothesis is not supported by the data Plan the goal to be achieved by implementing the pedagogical intervention In the presence of multiple goals, organize goals hierarchically Identify an action contributing to the attainment of the pedagogical goal Identify a condition that must be met before enacting an action Identify a condition that must be met during the enactment of an action Identify a condition that must be met to end an action Identify the result of the enactment of an action

Data were coded integrally by a graduate research assistant, after extensive training. During the training, the research assistant coded three transcripts, which were double-coded by the first author. Upon completion of each transcript, the coding was compared and any differences were discussed. When necessary, operational definitions of the categories were refined. The systematic discrepancies in coding were eliminated by the end of the third transcript.

4.5. RESULTS Results are presented in association with the two main goals, which were : (1) to examine the prevalence of collaborative pedagogical reasoning activities and differences in prevalence across levels of expertise (2) to examine how

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collaborative pedagogical reasoning activities are sequenced and how levels of expertise modulate this sequencing.

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4.5.1. Prevalence of Collaborative Pedagogical Reasoning Activities Tables 4.2 and 4.3 present time-budget information regarding how often pairs of participants engaged in particular pedagogical-reasoning activities. It should be noted that this analysis does not consider the duration of the steps, so that these results are complementary to the sequential results that follow (the frequencies of steps match the frequency of shifts between steps i.e. the frequencies should be interpreted as the number of “shifts to” a given category). The duration is typically much longer in the case of actions, especially since their numerous components were not considered, so that the bulk of the time was spent on the performance of those actions. Globally, there is a significant difference with respect to how often the pedagogical-reasoning activities occur (χ26 = 1098.45, p < 0.0001). As indicated in Table 4.2, participants more frequently (62%) engaged in steps related to the executive control of the pedagogical reasoning activities. The remainder of their steps (38%) was devoted to performing those collaborative pedagogical-reasoning actions. Among the activities related to executive control, interpreting the current state was the most frequent (30%), followed by planning actions (13%) and testing conditions for action (10%). The planning of goals, the evaluation of results and correction of errors were relatively infrequent (3%, 4%, and 2% respectively). Table 4.2. Does the prevalence of the control processes of collaborative pedagogical reasoning vary? Category

Frequency

Relative frequency

Plan goal Plan action Interpret state Test conditions Evaluate results Correct Perform action Total

52 251 559 184 69 36 709 1860

0.0280 0.1349 0.3005 0.0989 0.0371 0.0194 0.3812 1.0000

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Table 4.3. Does The Prevalence Of The Collaborative Pedagogical Reasoning Activities Vary? Category

Frequency

Relative frequency

Comprehend case Diagnose Elaborate intervention Total

475 139 539 1153

0.4120 0.1206 0.4675 1.0000

Going down a level in the hierarchy of processes to specific actions, the frequency of the different pedagogical-reasoning activities is significantly different (χ22 = 209.36, p < 0.0001). The elaboration of the pedagogical intervention is the most frequent activity (47%), followed in terms of prevalence by the comprehension of the case (41%). The least frequent activity is the diagnostic of the student’s difficulties (12%), as shown in Table 4.3.

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4.5.2. Differences in Prevalence across Levels of Expertise At the level of the control processes, there is no notable difference in the prevalence of categories attributable to expertise (χ217 = 23.01, p < 0.15). That is, second-year student teachers, fourth-year student teachers, teachers and experts all engaged in pedagogical-reasoning activities in approximately the same proportion of times. The interpretation of results related to question 1 hold across expertise levels. Descriptive statistics are presented in Table 4.4. Table 4.4. Does the prevalence of the control processes of collaborative pedagogical reasoning vary over levels of expertise?

Category Plan Goal Plan Action Interpret state Test Conditions Evaluate results Correct Perform action Total

Second year Freq. Relative frequency 20 0.0382 63 0.1202 152 0.2901 14 0.0267 55 0.1050 14 0.0267 206 0.3931 524 1.0000

Fourth year Freq. Relative frequency 17 0.0236 112 0.1553 213 0.2954 10 0.0139 73 0.1012 37 0.0513 259 0.3592 721 1.0000

Teachers Freq. Relative frequency 3 0.0169 26 0.1461 49 0.2753 0 0.0000 17 0.0955 4 0.0225 79 0.4438 178 1.0000

Specialized teachers Freq. Relative frequency 12 0.0275 50 0.1144 145 0.3318 12 0.0275 39 0.0892 14 0.0320 165 0.3776 437 1.0000

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Table 4.5. Does the prevalence of the constituent components of collaborative pedagogical reasoning vary over levels of expertise?

Category Comp. case Diagnose Elaborate interv. Total

Second year Freq. Relative frequency 135 0.4341 11 0.0354 165 0.5305 311 1.0000

Fourth year Freq. Relative frequency 111 0.3162 32 0.0912 208 0.5926 351 1.0000

Teachers Freq Relative frequency 52 0.4228 9 0.0732 62 0.5041 123 1.0000

Specialized teachers Freq Relative frequency 177 0.4810 87 0.2364 104 0.2826 368 1.0000

Note. Frequency counts do not correspond with those in the “perform action” category in the previous table, because adjacent occurrences of one category are lumped together.

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At the level of actions, many differences can be observed (χ26 = 105.52, p < 0.0001). As shown in Table 4.5, comprehending the case is relatively most frequent in experts (48%) and least frequent in fourth-year students (32%). There is a strong tendency to engage more often in diagnosis and less frequently in the elaboration of the intervention as the level of expertise increases, with experts engaging much more often in diagnosis (24%, compared to between 4% and 9% for students and teachers).

4.5.3. Sequencing of Collaborative Pedagogical-Reasoning Activities Conditional probabilities represent the probability of a particular process of being followed by another given process. It should be noted that probabilities below 0.15 were not included in the figures for clarity. In addition, transitions between two states are often identified in the presentation of the results as a pair of codes separated by a hyphen to simplify the language. The conditional probabilities in the figures should be regarded as descriptive statistics concerning aspects of the sequential structure of the process. To establish the statistical significance of this sequential structure, a procedure similar to the one widespread in multivariate analysis of variance was followed. First, an omnibus test of the entire table of conditional probabilities was conducted, with structural zeros specified because codes cannot repeat. Although the familiar χ2 was considered, the G2 is used for its common use in the log-linear approach (Gottman and Roy, 1990). If the omnibus test is significant (the familiar 0.05 threshold for the alpha was retained), meaning that there is some sequential dependency among the events, statistics related to specific transitional probabilities (between any two codes) are examined. To this end, z scores computed from a ratio of observed and

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expected transition frequencies were used, accompanied by their two-tailed p values (again, 0.05 was set as the threshold). A positive value of a z score significant at the 0.05 level indicates that the conditional probability between the antecedent and consequent states is significantly higher than the expected probability based on the base rate of the consequent state. Conversely, a z score with a negative value accompanied by an alpha below 0.05 indicates that the conditional probability is significantly lower than expected. The analysis considered pedagogical reasoning as a first-order Markov process. The order of a Markov process refers to the number of preceding events that are considered in the prediction of a target event (Gottman and Roy, 1990). A first-order Markov process considers only one preceding event for predicting a given event. A second-order Markov process would take into account the two preceding events for the prediction. Higher-order Markov processes can be more precise as a result of the increase in the amount of information used in the prediction, at the expense of added complexity: an increase of one order multiplies the number of combinations of events by the number of categories used in the analysis. As a consequence, data demands for statistical analysis increase dramatically. A very interesting and clear illustration of the concept of order in Markov processes can be found in Gottman and Roy (1990), chapter four. A complementary notion in sequential analysis is the lag. The lag refers to the distance between the events used in the prediction and the events being predicted (Gottman and Roy, 1990). In the present study, sequential analyses were conducted at lag 1, that is, predicting a given event from the event immediately preceding it. Analysis at lag 2 would predict a given event from the event preceding the event immediately preceding it, not considering the event between the two. Considerations of lag are orthogonal to considerations of order in sequential analysis. In other words, the questions of how many past events are necessary to predict a given state and how far in the past useful events are for the prediction can be examined independently. The following figure may help clarify the ideas of order and lag, by illustrating how a given consequent in a sequence of states is predicted at lag one and two, either as a first-order or second-order Markov process. In the presentation of the results, specific transitions between states are identified as digrams, in the form of antecedent-consequent pairs of states.

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Figure 4.2. An illustration of lag and order in sequential analysis.

Globally for the whole sample, there is first-order sequential dependency between pedagogical-reasoning activities at lag 1 (G255 = 249.96, p < 0.0001). That is, events are at least in part determined by the event immediately preceding them. As shown in Figure 4.3, most frequent paths are reason-comprehend (.48), correct-interpret state (.41), test conditions-interpret state (.41), evaluatecomprehend situation (.38), test conditions-comprehend situation (.36), elaborate pedagogical intervention-interpret state (.36), comprehend situation-interpret state (.33). The performance of the three pedagogical-reasoning actions is likely to be followed by interpret state. Those actions are also likely to be followed by evaluation steps, whereas preparation steps are followed by action steps. To a lesser degree, preparation steps are followed by evaluation steps directly. There are no transitions going to reasoning. Specific conditional probabilities were found to be statistically significantly biased positively or negatively. Precisely, 21 of the 72 conditional probabilities were significantly biased. Of them, 16 are associated with conditional probabilities below .15 and are not displayed in Figure 4.3. Reason-comprehend situation, correct-interpret state, test conditions-comprehend, plan goal-plan problem-solving action are transitions that occur more frequently than statistically expected, and the path from test conditions to interpret state occur less frequently than statistically expected.

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Note. + indicates a conditional probability significantly biased positively. Similarly, indicates a conditional probability significantly biased negatively. Figure 4.3. Typical sequence of collaborative pedagogical reasoning activities.

4.5.4. Differences in Sequencing across Levels of Expertise The following section presents some results regarding the modulations in the sequential structure of collaborative pedagogical reasoning that are attributable to expertise levels. The typical chronology of the process is presented for each of the four expertise levels in the following figures.

4.5.4.1. Second- Year Students For the second-year student teachers, there is sequential dependency among pedagogical-reasoning activities (G255= 80.11, p < .02). The most frequent transitions between activities were interpret state-elaborate intervention, correctinterpret state, correct-elaborate intervention, test conditions-comprehend, reasoncomprehend, comprehend-elaborate intervention. Of the six conditional probabilities that were significant, four were below .15 and do not appear in

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Figure 4.4. The paths from reason to comprehend and from plan goal to plan action occurred significantly more often than expected statistically.

Figure 4.4. Typical sequence of collaborative pedagogical reasoning activities – secondyear students.

Regarding the sequencing of the pedagogical-reasoning activities, there is a loop between comprehending the case and elaborating the intervention. In addition, there is no path leading to reasoning.

4.5.4.2. Fourth- Year Students Sequential dependency in the pedagogical reasoning process of fourth-year student teacher was also observed (G255= 115.79, p < .0001). The most typical transitions include test conditions-elaborate intervention (.50), interpret stateelaborate intervention (.45), elaborate intervention-interpret state (.43), evaluateinterpret state (.34). Interestingly, interpret state seems to be the attractor in the process in the sense that many paths are going to and coming from this state. More specifically, 12 conditional probabilities were found to be significant ; four of them appear in Figure 4.5. Reason-comprehend, evaluate-plan problem-solving

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action, plan problem-solving action-comprehend, and reason-correct occurred more often than expected. Control pedagogicalreasoning task0,29 Plan goal

0,24

Execute problem-solving action (components)

0,18 Plan 0,32 problemsolving action

0,22+

Comprehend the situation 0,32

0,32

0,16

0,20 0,20 Test conditions

0,34+ 0,50

Reason to elaborate a diagnostic

0,34

Execute problemsolving action

0,16+ 0,31

0,16 Interpret state

0,16

0,45 0,30

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Evaluate

Elaborate a 0,15 pedagogical 0,43 intervention 0,16+

0,23+ 0,32

0,27

Correct

Figure 4.5. Typical sequence of collaborative pedagogical reasoning activities – fourthyear student teachers.

Paths involving control processes and pedagogical-reasoning actions predominantly involved the elaboration of the intervention. The elaboration of the diagnostic was followed by comprehension and by correction of perceived errors.

4.5.4.3. Teachers In the case of teachers, the sequence of pedagogical-reasoning activities did not display dependency between temporally adjacent events (G241= 52.44, p < .11). That is, the conditional probabilities among activities only reflect probabilities related to their frequencies. Figure 4.6 presents the sequential statistics. Since the omnibus test is not significant, the individual conditional probabilities were not examined for significance.

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Figure 4.6. Typical sequence of collaborative pedagogical reasoning activities - teachers.

4.5.4.4. Expert Teachers In the case of experts, there is sequential dependency between pedagogicalreasoning activities (G255= 143.35, p < .0001). The most frequent paths were test conditions-comprehend (.58), reason-comprehend (.56), correct-interpret state (.57), interpret state-comprehend (.46), plan problem-solving action (.42), comprehend-interpret state (.33). Of all the 72, 15 conditional probabilities were significantly biased. Six of them appear in Figure 4.7, all positively biased: correct-interpret state, plan problem-solving action-interpret state, comprehendreason, plan goal-plan problem-solving action, test conditions-evaluate, and plan problem-solving action-comprehend.

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Figure 4.7. Typical sequence of collaborative pedagogical reasoning activities - experts.

Frequent and positively biased paths among control activities go from preparation steps to evaluation steps. Preparation steps are also frequently followed by the execution of pedagogical-reasoning actions. In turn, this execution, when followed by control actions, leads to aspects of evaluation of the procedures (interpret state). The typical sequence of pedagogical-reasoning actions includes a loop between comprehend and reason, with elaborate relatively isolated from the two others.

4.5.4.5. Global Difference in Sequential Dependency across Levels of Expertise An important finding regarding expertise differences is that as expertise increases, the general orderliness of transitions between pedagogical-reasoning activities also increases, as reflected by the correspondingly increasing G2 obtained. Pedagogical reasoning in experts appears more strategically driven than in novices. Globally, the sequential results depict collaborative pedagogical reasoning as a relatively unsystematic process for some expertise levels. In contrast,

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collaborative pedagogical reasoning appears more systematic in the case of experts. For example, results from fourth-year students include a great number of transitions with reasonable probability. Because of this difficulty of characterizing the process, comparisons between levels of expertise are difficult to make at the level of specific transitions. Data seem to suggest that experts also plan goals about diagnostic, while others plan about comprehension. Experts, in contrast with the other participants, don’t go from comprehension to elaborating the intervention. For all expertise levels, comprehension and the elaboration of the intervention are more controlled than the diagnostic process.

4.6. DISCUSSION The main goal of this study was to accurately describe what is going on, cognitively speaking, during pedagogical reasoning in hope that this description of the process will make possible studies of knowledge and other factors that bear on teaching effectiveness and has implications for teacher education.

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4.6.1. Prevalence of Collaborative Pedagogical-Reasoning Activities In the sample studied, a significant difference was found regarding how often the different pedagogical-reasoning activities were executed. Frequency data, not considering the length of a specific activity, suggest that episodes of pedagogical reasoning actions (which may be relatively long) are frequently interspersed with planning and evaluation procedures. This finding is consistent with the expectation from theory that this control of the performance was necessary at the beginning and end of the pedagogical reasoning process, and during shifts between any of its constituent actions. Participants were (attempting to be) purposeful or strategic by piloting their performance. The extent to which they succeed is not explicit from frequency data, and would require an examination of the nature of those categories because the potential of success and failure is intrinsic to the enactment of any of the steps in the model. Of the control procedures, interpret state was by far the most prevalent step. Interpreted as a frequent need to make sense of the current state in the performance of the task, this may be due to the considerable complexity of the problem or the complexity of the domain. Those two influences may be difficult to distinguish, but a difference in the prevalence of interpret state attributable to

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expertise would be an indication of the impact of the complexity of the problem and the domain. The scarcity of occurrence of goal planning, evaluation of results and correction of mistakes may be related to the ill-structured nature of pedagogicalreasoning problems. If we agree with the literature that such problems represent difficulties in establishing what the problem is, which steps are required for a solution and what constitutes an appropriate solution, such difficulties may be reflected in the data. Again, expertise differences examined next may corroborate or infirm this supposition by providing evidence of the impact of the required knowledge which experts presumably have to address such issues and perform those steps successfully. Indeed, despite the influence of the context on the elaboration of a representation of the problem, pertinent knowledge of the domain exerts the greatest influence on this process. If experts know from experience that planning a solution in terms of a sequence of steps before executing actions accelerates problem solving, as shown in previous research on problem solving, this is a strong incentive to engage in adequate planning, since this planning is enabled by their knowledge. Finally, experts’ representations emphasize structural features relevant for the solution such as causal relations, whereas novices’ representations highlight superficial features irrelevant to the solution. At the level of the pedagogical-reasoning actions, diagnostic was shown to be less prevalent than comprehension and the elaboration of the intervention. One possible explanation is the possibility that diagnostic naturally and relatively effortlessly follows from an adequate comprehension of the case whether as backward or forward reasoning, which in this study is designed to present information more or less associated with the primary difficulty. This scarcity of diagnostic could alternately be attributable to the difficulty of making a diagnostic, which could be corroborated or not from the examination of expertise differences.

4.6.2. Differences in Prevalence across Levels of Expertise The data revealed an absence of difference in prevalence of pedagogical reasoning activities across expertise levels. At the higher level, this uniformity in prevalence across expertise levels could mean that domain knowledge has no impact on the implementation of the different pedagogical-reasoning actions in terms of frequency, but it could have an impact on the nature of the actions implemented, as well as on the relative length of episodes of given activities.

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These issues have to be further examined using complementary analytical strategies. However, a significant difference across expertise levels was found at the level of actions. In a semantically complex domain, problem-solving processes hinge on pertinent knowledge of the domain. How this knowledge is used to perform the task, both individually and collectively, is thought to be largely determinant of the outcomes of the activity. Comprehension, reasoning, planning and problem solving are all hypothesized to be facilitated by the availability of pertinent domain knowledge. More specifically for planning, differences in prevalence of actions seem to corroborate many aspects of literature on teacher planning: less intervention in experts suggest that they possess in memory more compiled schemas for intervention that either don’t need to be created and/or explicitly detailed. One needs to be careful though about the nature of the data under scrutiny by not equating frequency and length of episodes. Globally, these differences can be explained in part by the level of difficulty of the case study (a real pupil). Experts seem to be challenged by the case in order to adapt the intervention, whereas novices seem to abandon taking into account the case, apparently turning to the elaboration of a relatively generic intervention in reading instruction. In terms of analysis, the absence of differences in prevalence at the higher level makes comparison of conditional probabilities involving exclusively those categories between levels of expertise more directly interpretable. Transitions involving actions should be compared using standardized indices.

4.6.3. Sequencingof Collaborative Pedagogical-Reasoning Activities For the sample under study, pedagogical reasoning was shown statistically to be a first-order Markov process. Although all 72 conditional probabilities can contribute to some extent to the overall dependency between pairs of steps, 21 of them were statistically significant individually. This finding is in line with many other models based on problem-solving theory, which postulate the occurrence of steps on the basis of the steps immediately preceding them. In his synthesis of available data about the human cognitive architecture, Newell (1990) interpreted human cognition as state determined, meaning that future cognitive behavior is determined by its current state. The current state may be constructed from states at the same level (strong level) or at lower levels (weak level). The reason-comprehend transition can be interpreted as either an indication of forward reasoning or a need to go back to the case for retrieving information that

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was not memorized adequately during the initial reading of the materials. According to the view presented, the diagnostic of a pupil’s difficulty is achieved through abductive reasoning, a combination of deductive and inductive reasoning, specifically that hypotheses are generated by abstraction and abduction and tested by deduction and induction. This distinction is orthogonal to the difference between forward and backward reasoning. Forward reasoning is heavily dependent on the reasoner’s domain knowledge to avoid errors due to a lack of legitimacy of the inferences. Because of the impact of knowledge on the reasoning process, the level of expertise must be taken into consideration in interpreting this transition. Correct-interpret state is consistent with theory, since interpret state may involve testing the conditions for the application of stop rules. Test conditionscomprehend may be interpreted by the assumption that comprehending the case is a prerequisite to the diagnostic and subsequent intervention, so that the participants, having determined this, engage in the first step of the process. The transition between plan goal and plan problem-solving actions is consistent with the theory stating that goal setting has to be followed by a plan of actions to attain those goals (Tschan, 2002). The infrequent test conditions-interpret state path is an instance of all those paths not supported by theory that should occur less often than expected statistically. Those paths are many (consider those 16 below .15). It appears that statistics from sequential analysis are misleading in those cases, since low-frequency paths, because of their low frequency, are likely to be detected statistically as departing from expected values. The common pattern of preparation, execution and evaluation found among the more detailed categories of the model is in line with classic problem-solving theories and recent empirical investigations by Tschan (2002). In particular, the performance of actions followed by interpret state and the observation that interpret state is also a very likely consequent of correct and test conditions seem to indicate the complexity of the pedagogical-reasoning process by the need to make explicit the various steps in the process. Finally, the recursive loop between evaluate and comprehension may be interpreted as an indication of comprehension monitoring.

4.6.4. Differences in Sequencing across Levels of Expertise The presence of first-order sequential dependency among pedagogicalreasoning processes was established statistically for three of the four levels of expertise considered in this study. Indeed, pedagogical-reasoning activities in

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teachers were found to be unrelated sequentially. These results are discussed separately for each levels of expertise in the following sections.

4.6.4.1. Second-Year Students The recursive loop between comprehend and elaborate in addition to the absence of paths going to reason can be seen as an indication that the focus on elaboration is accompanied by considerations of the case in terms of presented information or a diagnosis of rather limited quality, and not in terms of the complete and thorough diagnosis for which a transformation of this information is required. This could be an indication that the diagnostic is not satisfactorily achieved, perhaps even skipped, despite the frequent path from reason to comprehend suggesting that hypotheses are being tested in light of the information in the case. Second-year student teachers may lack the domain knowledge necessary to avoid a lack of legitimacy of the inferences, which are responsible for errors in diagnosis. Novices use backward reasoning because their do not have the knowledge required to support forward reasoning (Patel, Arocha and Zhang, 2005). The reasoning activity occurs but is not preceded by any statistically distinguishable step. Is it followed, though, more often than expected by comprehend. However, hypothesis-driven or backward reasoning increases cognitive load since it requires that the reasoner keeps track of the current goals and hypotheses. Cognitive overload may be the cause of this frequent path from reasoning to comprehend. This assertion is based on the assumption that hypotheses are being formulated, which would have to be corroborated by a further analysis of the categories in the model constituting the lower level of the activities. Plan goal-plan action is a transition expected from theory (Tschan, 2002). The two most common targets of the most frequent transitions were elaborate intervention and comprehend. These two actions seem to serve as attractors around which the pedagogical-reasoning process is organized. 4.6.4.2. Fourth-Year Students Interestingly, elaborate intervention and interpret state seem to be the attractors in the process in the sense that many very frequent paths are going to these two states. Among those paths that reached significance, evaluate-plan problem-solving action seems to indicate a need to make explicit upcoming procedures, in the case of a positive or negative evaluation of the performance. Reason-comprehend can be seen as backward reasoning, in which hypotheses are elaborated and then tested against information from the case. Plan problemsolving action-comprehend is probably a by-product of the fact that

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comprehension of the case is a prerequisite to the other actions and that an initial task analysis by the participants leads to the comprehension of the case being performed first. The reason-correct transition is intricate because the object of the correction is not identifiable from the sequential data: it is not clear whether it is the diagnostic or the intervention (as the most frequent consequent of a correction procedure).

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4.6.4.3. Teachers The present results indicate that sequential structure of teachers’ pedagogical reasoning process could not be established statistically. The possibility that this can be due to low frequencies of certain transitions can be ruled out: From a probabilistic point of view, it is more likely for a conditional probability to depart from the expected frequency as the unconditional frequencies of the antecedent and consequent categories are low. Thus, it is likely that this statistical sequential independence among steps is real. 4.6.4.4. Expert Teachers Sequential structure in experts’ pedagogical reasoning is characterized by many very frequent paths pointing to comprehend and interpret state, including a loop between the two. Comprehend-reason can be interpreted tentatively as forward reasoning (Patel and Groen, 1991). Statistically biased paths among the control steps can be thought of as a capacity to be strategic and efficient in elaborating a solution to the problem by optimally organizing the constituent actions. Paths among activities seem to reflect the structure of the pedagogicalreasoning task: activities seem to start with the diagnosis supported by information extracted from the case, which, when done, leads to the elaboration of the intervention. 4.6.4.5. Global Difference in Sequential Dependency across Levels of Expertise In addition to the results associated with each expertise level, it was also found statistically that first-order sequential dependency in pedagogical reasoning augmented as the level of expertise increased. The three G2 that were comparable (excluding the teachers) enlarged with expertise. That is, experts appear to be more systematic in their sequencing of pedagogical-reasoning steps. Pedagogicalreasoning processes in experts appear to be more strategically driven than in novices. These results represent additional empirical support to the importance of pertinent knowledge of the domain for successful problem solving in a semantically complex domain.

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4.6.5. General Discussion The analyses presented in this chapter put a particular emphasis on the executive control of the pedagogical reasoning activities. Future analyses should further examine each of the three main activities postulated, by considering their constituents. To make this task minimally tractable conceptually and statistically, the activities pertaining to the control process should be aggregated into preparation, execution and evaluation steps, more parsimoniously than the six categories used in this chapter. The absence of clearer patterns in the data may also be the result of the added complexity of considering pairs as a unified system instead of two individuals. Future analyses include the modeling of the contribution of each individual in a pair to highlight the coordination of the performance, as well as the comparison of the present results with results from a companion study of individual performance. Future and ongoing research include the study of pedagogical reasoning by heterogeneous dyads (an expert and a novice) in tutoring situations and the study of pedagogical reasoning in authentic settings instead of a laboratory task. Globally, these analyses could contribute to our understanding of more general issues in considering groups as information-processing systems such as information storage, information retrieval and information exchange in groups. Comparisons of the functioning of homogeneous and heterogeneous dyads could further test the theoretical assumption that the degree of overlap of task-related information held by different members of a group is thought to be a major influence on group functioning (Arrow, McGrath and Berdahl, 2000). These theoretical frameworks coupled with modern analytical strategies could lead to interesting insights in the application of an information-processing framework within a social-cognitive science view (Sun, 2006). By showing differences in pedagogical reasoning related to the level of expertise, the results suggest that more emphasis should be put on the diagnosis of student’s difficulties in initial teacher training, especially if this diagnosis is seen as a foundation for differentiated instruction. More analyses considering the modeling of the domain knowledge evoked during pedagogical reasoning and associated to each process are needed to explain these differences.

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Chapter 5

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5. A STUDY OF INDIVIDUAL PEDAGOGICAL REASONING After the presentation of the study of collaborative performance in the previous chapter, this chapter reports on a companion study of individual performance. Similarly to the study of dyads, the main goals of this study are to test the pedagogical-reasoning model in the context of individual performance and to verify the presence of differences attributable to expertise in terms of prevalence and sequencing of cognitive processes. The four questions addressed are the same as those that were formulated in the study of dyads: (1) what is the relative prevalence of the pedagogical reasoning processes (2) does this relative prevalence vary across expertise levels (3) what is the typical sequencing of the pedagogical reasoning processes, and (4) does this sequencing vary across expertise levels? Questions 1 and 2 were answered by compiling time-budget information for each step. Question 3 and 4 were answered by computing transitional probabilities between steps. To examine the typical sequence of steps within a system level, the unit of analysis was a transition from one step to another without considering the individuals within the team at the team level. For both set of questions, results for the whole sample are presented, followed by results associated with each level of expertise. The methodology presents the participants, the experimental task and the procedure for collecting and analyzing data.

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5.1. PARTICIPANTS The sample consisted of 12 special education student teachers and 6 special education in-service teachers. Half the student teachers were in their second year of studies and the other half were in their final year of a four-year special education university program. Of the 6 special education in-service teachers, 2 had between 5 and 10 years of experience and 4 had graduate training in remedial reading instruction.

5.2. TASK AND ENVIRONMENT

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Examining links between cognitive activity and effects on learning through cognitive modeling requires meaningful learning and authentic tasks conducted under relatively controlled conditions. Participants had to plan a series of lessons as part of their remedial reading intervention. The teaching of reading was chosen because of the extent of knowledge on the subject. As soon as they needed to write ideas, participants were instructed to use the provided computers and word processors.

5.3. DATA COLLECTION AND ANALYSIS The data collected are based on think-aloud protocols. Participants were instructed to verbalize everything that came in mind during the performance of the task. Each time a silence of 5 seconds occurred, the research assistant repeated the instructions. The interaction of participants with the computer was collected in the form of a video recording of the computer screen. The data were analyzed taking into account the processes involved in pedagogical reasoning. All protocols were independently coded by the first author and a research assistant. Differences were discussed and coding was adjusted. In this study, the main purpose of processes modeling is used to show how educational activities are planned individually. Process modeling is based on the categories presented in the previous chapter, assuming that individual cognitive processes can be decomposed into a series of discrete and sequential phases and various levels of granularity (Anderson, 2002). Frequency statistics and conditional probabilities are used to present data from the entire sample. The frequencies are calculated based on the occurrence of

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a given category, regardless of the length of the episode. Conditional probabilities represent the probability that a category is followed by another category. The frequency and conditional probabilities are used to group the sample data in relation to levels of expertise. It should be noted that the results presented are limited to control processes and to actions components in order to maintain the number of categories and hierarchical levels within the limits of intelligibility in the context of sequential analysis (Bakeman and Gottman , 1997; Bakeman and Quera, 1995). These results are parallel to the results of the study of dyads presented in the previous chapter and will allow comparisons between both studies.

5.4. RESULTS

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The results on the prevalence of different categories are presented in the first section, followed by the presentation of results relating to the sequential aspect of pedagogical reasoning. The interpretation of these results is integrated; the general discussion serves the purpose of concluding this chapter.

5.4.1. Prevalence of Pedagogical-Reasoning Processes Tables 5.1 and 5.2 present the information on time management with regard to the frequency with which participants engaged in specific activities of pedagogical reasoning. Because of the hierarchical nature of the model, Table 5.1 presents the statistics related to the higher level (the control level), while Table 5.2 focuses on the lower actions level. In total, participants used much of their time (about two-thirds) to organize activities of pedagogical reasoning, while spending the remaining third to the control process. There are no differences in the prevalence of the categories due to expertise levels. Inversely, differences related to expertise levels appear in actions, as shown in Table 5.2. There is a strong tendency to put more time on the diagnosis and less time on the development of the intervention as the level of expertise increases, experts using twice as much time as novices to make a diagnosis. These results suggest that making a diagnosis requires specialized knowledge that most novices do not possess. On the matter of intervention, experts appear to have more "compiled" patterns than novices.

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Table 5.1. Does the prevalence of pedagogical reasoning control processes vary between different levels of expertise? Second year

Fourth year

Teacher

15 46 104 2

Relative frequency 0.0446 0.1369 0.3095 0.0060

Specialized teacher Freq. Relative frequency 19 0.0312 91 0.1494 190 0.3120 21 0.0345

Category

Freq.

Freq.

33 117 261 13

29 138 190 11

Relative frequency 0.0404 0.1922 0.2646 0.0153

Freq.

Plan Goal Plan Action Interpret state Test Conditions Evaluate results Correct Perform action Total

Relative frequency 0.0412 0.1461 0.3258 0.0162

41

0.0512

47

0.0655

20

0.0595

26

0.0427

33 303

0.0412 0.3783

38 265

0.0529 0.3691

14 135

0.0417 0.4018

18 244

0.0296 0.4007

801

1.0000

718

1.0000

336

1.0000

609

1.0000

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Table 5.2. Does the prevalence of pedagogical reasoning activities vary between different levels of expertise? Second year

Fourth year

Teacher

110 60 120

Relative frequency 0.3793 0.2069 0.4138

Specialized teacher Freq Relative frequency 222 0.3700 199 0.3317 179 0.2983

Category

Freq.

Freq.

176 80 262

178 109 258

Relative frequency 0.3266 0.2000 0.4734

Freq

Comp. case Diagnose Elaborate interv. Total

Relative frequency 0.3398 0.1544 0.5058

518

1.0000

545

1.0000

290

1.0000

600

1.0000

Note. Frequency counts do not correspond with those in the “perform action” category in the previous table, because adjacent occurrences of one category are lumped together.

5.4.2. Chronology of Pedagogical-Reasoning Processes The following section highlights some results concerning the variations in the sequential structure of the reasoning attributed to expertise levels. The question being asked is: Does the sequential structure of pedagogical reasoning processes reasoning processes vary between different expertise levels? The typical chronology of the process, depending on expertise level, is presented in the following figures. The conditional probability, presented in a percentage format, must be understood as the probability that the category is followed by the one

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identified by the arrow. Probabilities below 0.15 were not included for the sake of clarity; thus, the conditional probabilities associated with a given category do not total 100% in the figures.

Figure 5.1. Typical sequence of pedagogical reasoning activities – second-year student teachers.

In the case of second-year student teachers, multiple transitions, often with low probability, make interpretation difficult. It is noted, however, that many control and development of intervention processes were followed by the interpretation of the current state of the problem, suggesting that novices experienced difficulties in the understanding of the problem and the developing of appropriate solutions. The recurrent loop between the understanding of cases and diagnosis, including the strong probability of the reasons-understands digram, may be an indication of a hypothetico-deductive reasoning, going from assumptions to facts.

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Figure 5.2. Typical sequence of pedagogical reasoning activities – fourth-year student teachers.

Among fourth-year student teachers, the development of the intervention is the only action that is frequently controlled: this is the main target of controlled actions. It seems that from the viewpoint of performance regulation and because of its particular focus, these student teachers consider the development of intervention as the most important activity, or one that they may be better able to do. The recurrent loop between the understanding of the case and the diagnosis is also present, and involves the same interpretation as with second-year student teachers.

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Figure 5.3. Typical sequence of pedagogical reasoning – in-service teachers.

As noted with the fourth-year student teachers, the development of the intervention is the only action that is frequently controlled by the in-service special education teachers. The frequent digram consisting of test conditions and goals planning suggests that in-service teachers are concerned with task structure and a frequent readjustment relating to the prerequisites of some of the elements to perform the next steps (e.g. a diagnosis justified by available information as a basis for targeted intervention). The recurrent loop between the understanding of the case and the diagnosis is similar to that observed among student teachers. Regarding expert in-service teachers, the often-observed path of going from understanding of the case to the diagnosis can be seen as a propensity to inductive reasoning, operating from assumptions to facts. The test of conditions associated with the three action components suggest that expert teachers are aware of the sequential nature of actions components of pedagogical reasoning.

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Figure 5.4. Typical sequence of pedagogical reasoning activities– expert in-service teachers.

5.5. DISCUSSION This study is the second in a series of works in progress that examine teacher decision-making, teachers’ knowledge and their interrelationships. The main purpose of this study was to accurately describe what occurs, from a cognitive viewpoint, during pedagogical reasoning as performed individually. This process description allows for studies on knowledge and on other factors that support effective teaching and teacher education. In particular, the functions of pedagogical planning relating to the articulation between of theory and practice and to knowledge development (Armour-Thomas, 1989; Hashweh, 2005) should be explored more carefully in order to promote this type of activity in teacher training programs and to determine, for trainers, the optimum conditions that promote learning. So overall, the differences linked to expertise lie in the sequence of pedagogical reasoning processes, and not in its prevalence (with the exception of

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the development of a diagnosis). By showing differences in the pedagogical reasoning related to expertise levels, the results of this study suggest that more emphasis should be placed on the diagnostic of the difficulties of students in preservice teacher training, especially if diagnosis is seen as the basis of differentiation in teaching (Davies, 2000). The literature is unclear about the possibility that forward reasoning, not present in this sample in student teachers (and possibly teachers) is a condition for competent performance in terms of diagnosis of students’ difficulties. Through the relatively coarse distinction of expertise level, the results suggest that domain knowledge has an impact on how pedagogical reasoning takes place. Analyses that consider the fine knowledge modeling of the domain as discussed during pedagogical reasoning and that are associated with each process are needed to explain these differences. These analyses are currently being done. The analysis of the prevalence and the sequence of postulated categories in the model lead to argue that this model characterizes the pedagogical reasoning as individually performed by special education student teachers. Showing some aspects of pedagogical planning, at a cognitive level, the results of this study can specifically support trainers with regard to educational planning, and more generally, in the relationship between theory and practice in teacher education. Thus, student teachers would be better supported by host teachers during internships in terms of the three main components of pedagogical reasoning. Considering the importance that student difficulties diagnosis should have regarding the differentiation inherent to special education (Davies, 2000), particular attention should be paid to the quality of diagnosis and the correspondence of planning of instruction with this diagnosis. To the extent that pedagogical planning is an important gateway for leading "theory" into "practice" it would be advisable to assist student teachers to link the specific elements of their pedagogical planning to their decision-making in the interactive phase of teaching. This specific link would also benefit from additional empirical studies.

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Chapter 6

6. OUTCOMES OF THE TWO STUDIES The contributions and implications of the two studies are presented first. The strengths and limitations of this work and future research conclude this chapter.

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6.1. CONTRIBUTIONS AND IMPLICATIONS These two studies are among the first of a series of studies investigating teacher decision-making in the specific context of lesson planning for a specific student, the relations between teacher knowledge and teacher decision-making, as well as the differences between solitary and collaborative performance. A cognitive model of pedagogical reasoning was developed from theory and then used for the analysis of conversation and think-aloud data. It was developed as a general framework for the research program. It evolved from general ideas of regulation of the performance and general theories chosen on the basis of elements of task analysis of the pedagogical-reasoning process. Since the model includes unavoidable executive aspects of the performance, it can be used to study individual and group differences in pedagogical-reasoning performance. It also makes possible uncommon and less straightforward comparisons between different contexts such as group, dyad, and individual performance in the manner of Tschan (2002). The study of cycles of pedagogical reasoning over an extended period of time is also possible, and is currently undertaken. The strongest claims made to date concern the categories that were included in the model. Aspects of their sequencing were also discussed among sets of categories that were discussed in the literature as groups, such as comprehension, problem solving, reasoning, and planning. Since the model builds on sets of theoretical categories that were not previously considered together, these links

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will have to be established empirically using many different samples. Most of the transitions could not be specified from theory. In these studies, the model was considered as a closed set of theoreticallydriven categories and therefore was not modified to reflect the data. However, definitions of categories were refined during the coding process. More studies are needed to the validation process. Empirical validation is complex given the interest of having a generic model, applicable to various settings and populations. The expected outcome of the development of the model is a unified set of stable categories. Through empirical investigation, these categories will be identified as more or less prevalent for specific populations and in specific contexts. Transitions among steps will also be specified empirically, considering and comparing various performance contexts and different populations. Aside from these considerations of the development of the model, the strategy used for the analysis of coded data has strengths and limitations that are complementary to a more qualitative approach. The focus on sample results underlying the statistical approach used led to a specification of generalizations to the whole samples and indications of similarities and differences across categories related to expertise. This strategy provided accurate descriptions of the process. These descriptions should be confirmatory but are treated descriptively or exploratory in the sense that these interpretations have to be treated mainly as hypotheses that have to be further tested by other means. Most of these results can be explained by the theory underlying the model, but in order to be robust, these explanations would greatly benefit from a qualitative study of the protocols of specific individuals and pairs of participants. The nature of the processes characterized by the results as well as specific transitions (the actual sequence of steps performed by a pair as opposed to aggregated transitions) has to be examined to explain those descriptions. These considerations also apply to the categories pertaining to the third level in the model that were not fully examined in this study and for which both the quantitative and qualitative work has to be undertaken. As Arrow, McGrath and Berdhal (2000) suggest, characteristics of the products of the pedagogical-reasoning process can be tracked during their elaboration and be put in relation with the coordinated actions that resulted in these productions. In so doing, important information could be gained regarding how certain characteristics of the pedagogical-reasoning process are related to the efficacy of the production. The current development of an assessment procedure using scoring rubrics is a prerequisite to such analyses. A pervasive claim in this chapter regarding the impact of knowledge as being largely determinant of the outcomes of the activity has to be verified by such analyses.

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As such, this model can be coupled with other models either representing executive aspects of complementary tasks such as interactive teaching, or representing other levels in the performance of pedagogical reasoning such as a social layer or the use of tools (distributed cognition). Knowledge underlying the performance can also be modeled. Appropriate models of decision-making in interactive teaching include those suggested by Peterson, Marx and Clark (1978) and Shavelson and Stern (1981). Aspects of a social layer applicable to dyad and group data include Searle’s (1979) classic conversation acts framework, which emphasizes the functional aspect of speech. Modeling the use of tools can be either achieved inductively or within a cognitive tools framework (Lajoie, 2000 ; Wijekumar and Jonassen (2007)). Many knowledge modeling procedures exist (see Olson and Biolsi, 1991). A conceptual graph approach (Sowa, 1984) could be particularly useful in investigating the links between elements of knowledge and performance, and is the object of ongoing research. However, these knowledge models are very powerful in categorizing and organizing knowledge elements using sets of primitives but are relatively incompatible with the aggregation of data from multiple units of analysis. Nevertheless, used in conjunction with appropriate data collection and analysis procedures, these models could be powerfully combined to investigate a broad range of issues regarding cognition and social cognition (Arvaja, Salovaara, Häkkinen and Järvelä, 2007; Sun, 2006). The strategy currently being developed for knowledge analysis is presented in chapter 8. Finally, the proposed cognitive model, as a way to characterize proactive decision making, complements models of interactive decision-making. This complementarity represents potential for future studies examining discrepancies between teacher planning and classroom processes in terms of how they arise and how they are resolved. This discrepancy is linked to important findings of earlier studies (Morine-Dershimer, 1978-79) and has implications for the transfer of theory into practice since teachers’ interactive decision-making and informationprocessing is highly influenced by it (Morine-Dershimer, 1979). Initial investigations are leading to descriptive models of teachers’ pedagogical reasoning.

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6.2. STRENGTHS AND LIMITATIONS OF THIS WORK AND FUTURE RESEARCH Choices that were made in these studies concerning the sampling and analysis strategies each translate into strengths and limitations. Sampling four expertise levels made it possible to make comparisons but led to a limited number of units of analysis per category (especially in the case of pairs). Focusing on group prevalence and sequential aspects led to results that generalize very well across the sample, but neglected individual differences within categories. This quantitative approach to data analysis, while providing reliable results about likely events and sequences of events, also neglected critical events in the performance of individuals and pairs of participants. These critical events would be likely unveiled by case studies in the form of a qualitative protocol analysis. Chapleau, Mercier, Laplante and Brodeur (in preparation) began this series of case studies by describing the pedagogical-reasoning performance of a novice and an expert. These two approaches are complementary and should be both undertaken for the present data sets. Statistical results in this study need to be interpreted as generalizability to the samples under study. Therefore, generalizing results to the populations requires either additional studies of comparable samples or a study involving parametric samples of participants (more than 30 units of analysis). Finally, this chapter highlights some benefits and challenges regarding the methodology of sequential analysis for the study of cognition and social cognition. Sequential analysis, with its focus on transitions between steps in a process, seems a sound strategy for extending the tracing methodologies to larger samples of participants, instead of traditional case studies. The possibility of pooling data over multiple participants and performance episodes while taking into account factors in an experimental design, complemented by robust statistical procedures such as log-linear analysis, can provide reliable information possibly with more generalizability, about how cognitive processes unfold. However, the analysis presented also reveals major difficulties related to the level of details included in the model under study. Cognitive theory reviewed in the third chapter of this book led to the elaboration of a model comprising 22 categories organized hierarchically in three levels. Because of the combinatory increase in the number of possible transitions as a function of the number of categories considered, the analysis of this model as a whole appears to be an intractable endeavor. The strategy employed was to collapse the categories of the lower level at the expense of a loss of information,

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deferring the examination of constituents of the pedagogical-reasoning actions to subsequent reports. Even then, these constituents will have to be examined in relative isolation: projected analysis consists of detailing one of the action (comprehension or reasoning or elaborating the intervention) while the other two remain collapsed, so that aspects of the transitions between actions remain visible. Another complementary strategy is to collapse the 7 control actions into three more general categories: preparation, execution and evaluation. The benefits of shifting part of the emphasis from the problem solving to constituent actions could be relatively high, especially since the details related to these categories were presented in the present book. After the necessary study of component actions, the results should then be further interpreted in relation, because of their functional interdependency. No matter the strategy used, minimizing the number of categories seems unavoidable. Most examples in classic books on sequential analysis are based on categorical systems of approximately 2 to 4 categories, and the maximum number of categories found in examples was 7. Occasionally, categories are organized hierarchically, typically in two levels in such cases. Sequential analysis of multilevel processes represents another source of possible challenges. To the best of our knowledge, it is not possible to compute transitions between categories organized in more than two levels in a single analysis, since this would lead to flawed unconditional frequencies. Consequently, it appears that statistical tests of sequential dependency associated with more complex models cannot be obtained. Such parsimony could permit more complete analyses, such as statistical tests of higher-order Markov processes, and group differences related to specific transitions. More complex experimental designs could also be exploited. It should be noted that the gain in generalizability associated with sequential analysis is accompanied by a loss of information regarding how specific pairs of participants performed. Taking into account individuals within pairs would also contribute to the number of transitions as they generate transitions that are not part of the experimental design (although the comparison between individuals in pairs and individuals working alone would be an experimental factor). Beyond the descriptive elements highlighted in this chapter, the establishment of this model allows to consider several research paths. The endeavour currently undertaken is to extend the findings of the studies presented to more authentic and varied performance contexts. Traditional technological means tend to confine the methodology of cognitive modeling to laboratory settings, as was done in these studies. Therefore, the data relate to a predetermined task, carried out in a predetermined location and time. In light of these limitations, it is imperative to supplement and validate cognitive models developed in laboratory settings in light

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of data of greater ecological validity. Some development is required to provide adequate data collection procedures. A computational infrastructure could help extend the methodology of cognitive modeling in authentic contexts by allowing the observation of individuals as part of their daily activities, in their natural setting, at times compelled by their performance context, and during an extended period of time. To complement the laboratory results presented in this book, the developed model and the methodological strategy tested with the two current studies will be reinvested in the investigation of pedagogical reasoning in authentic educational settings, a project for which funding has been granted. The participants (special education student teachers and in-service teachers) will be followed for a few weeks in their teaching of reading through a research infrastructure funded by the Canadian Foundation for Innovation, the LabMECAS. The labMECAS is a fleet of 35 portable computers equipped with applications for automatically recording audio, video and on-screen interactions with, among, and around each computer. It is accompanied by a battery of portable servers for providing wireless local connectivity among the computers and for optional data recording (as an alternative to local recording on the computer’s hard drive). The fleet can be transported off-campus to a single location. Alternatively, computers may be dispersed in various locations and be interconnected and connected to the server via Internet. For this project, each student teacher or teacher will be given a computer, and instructed to use it whenever they plan instruction. When turned on, the computer will automatically start recording. In the eventuality of no speech going through the microphone for 5 seconds, a pop-up window will remind the participant to resume thinking-aloud. In the same context, an important part of the planned studies relates to the pedagogical reasoning occurring in heterogeneous dyads. Students of different level may take part of this study, as discussed by Seifert and Manzuk, (2006) (e.g. second- and fourth-year undergraduate students) or host teachers associated with their student teachers, as suggested by Smith (2005) (e.g. second- and fourth-year students). With the help of knowledge analysis methods (see chapter 8), which are currently being refined by testing with available data, the study of heterogeneous dyads could contribute to the understanding of the benefits, challenges and limitations concerning teacher education in a context which could be described as cooperative or cognitive apprenticeship (see chapter 6 for further details). Future research should investigate at least two important issues: the nature of knowledge and knowledge use in pedagogical reasoning, and how to teach pedagogical-reasoning abilities. Regarding the first issue pertaining to knowledge and knowledge use, Novick and Bassok (2005) insist on the importance of

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conducting educationally relevant research on problem solving, especially in the context of knowledge-intensive problems that are socially critical such as those in science, medicine and technology. We add education to this list of domains. Further discussion of this issue is presented in the next chapter. Regarding the second issue of developing pedagogical reasoning skills in novices, as Hogan, Rabinowitz and Craven (2003) concluded, research is needed to determine whether novices can be taught the skills of experts in teaching, as it has been shown to be possible in other domains such as physics and statistics. The activities hypothesized to be of particular value for the development of teaching expertise are the preparation of instructional materials, the mental and written planning of instructional activities and strategies, the formative and summative evaluation of student progress using graded written work, observation of performance, and teacher-made tests. Since the first two of these activities are directly related to pedagogical reasoning as conceived of in the present model, it seems likely that this study could lead to specific indications regarding a pedagogy of teaching skills. Future studies will examine teacher knowledge as used in pedagogical reasoning and teaching strategies for developing pedagogical-reasoning skills. Ultimately, these models may develop into more prescriptive models that could be integrated in teacher education programs. More specifically, empirically validated models of pedagogical-reasoning skills determine, on the one hand, the nature of teacher pedagogical reasoning skills that should be taught. On the other hand, they serve as a basis for studies investigating the design of methods for teaching and assessing these skills. Since traditional models of teacher planning focused on processes and neglected content (Hashweh, 2005), analysis of the outcomes of planning should be undertaken. Hashweh’s (2005) review of recent handbooks with respect to topics of teacher knowledge and teacher thinking reveals a certain impermeability of the two lines of research. This is even more critical since thinking in complex domains is heavily determined by knowledge. The interest of examining novice-expert differences in terms of curriculum scripts was established a long time ago by Putnam (1987). Cognitive models such as the one developed in this study can be used to study change in teacher cognition across time (Sherin, Sherin and Madanes, 2000). These models can be used either transversally (as was done in these studies) or longitudinally, and this is a matter of research strategy. Finally, the cognitive steps and the knowledge constituting a pedagogical-reasoning performance will be related to characteristics of the instructional activities planned as a result of this process. To this end, scoring rubrics for the assessment of the quality of instructional activities in remedial

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reading instruction have been recently developed by our team (Chapleau, Laplante, Mercier and Brodeur, 2009). More generally, these studies will add to the growing literature in cognitive science about the study of collaboration in authentic and complex situations (Elstein, Shulman and Spafka, 2000). How to design learning activities in order to optimize cooperative learning and how to organize work in order to optimize performance remain empirical questions that need to be addressed domain by domain.

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Chapter 7

7. THE ADDED VALUE OF COLLABORATION IN LEARNING AND PERFORMANCE: COGNITIVE AND SOCIAL COGNITIVE MODELING AS A RATIONALE AND STRATEGY FOR EMPIRICAL INVESTIGATIONS Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

7.1. INTRODUCTION Teacher collaboration is an important topic in current research. Theory, advocacy and empirical results are producing an ambiguous description of the benefits and challenges of collaboration. Indeed, teacher collaboration has been advocated, on the one hand, as a remedy to teacher isolation, perceived as negatively affecting teacher efficacy and professional development, and on the other hand, criticized with respect to its reality, inherent pitfalls, and significance (Seifert and Manzurk, 2006). The picture is even more blurred when the two alternative modes of production are considered and compared. For example, Moreno (2009) formulated convincing arguments promoting both individual and collaborative learning. Her study revealed no differences in retention and a problem-solving transfer task between individual and collaborative learning conditions. In addition, motivation was higher in the collaborative learning condition. Of course, a portion of the literature promotes collaboration. This idea is considered a lever for the improvement of teaching. There is another portion of literature promoting the faculty of individuals to regulate their behaviour to achieve optimal productivity, both in terms of work or learning (Zimmerman, 2000). This approach has also been valued in the field of teaching (Kremer-Hayon

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and Tillema, 1999 ; Butler , Lauscher, Jarvis-Selinger and Beckingham, 2004). These two positions are not incompatible. On the contrary, they can be synergistic, but this beneficial interaction imposes its toll of constraints and challenges. Indeed, it is a mistake to consider every group work situation as collaborative and co-constructive (Volet, Summers, and Thurman, 2009). Among the many factors involved, group interdependence and individual accountability are indispensable elements of an effective collaborative learning situation (Moreno, 2009). These factors and many others have to be studied.

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7.2. THE PROBLEM AND ITS CONTEXT Reports abound regarding learners’ negative experiences in group work (Volet, Summers, and Thurman, 2009). Studies show that coordination and coregulation of group members’ engagement is necessary for successful group learning outcomes, and may be often lacking due in part to the lack of explicit training (Volet, Summers, and Thurman, 2009). Current models of individual and collaborative performance in complex domains do not satisfactorily inform about how to optimize the performance of individuals in an inherently social context, either in terms of work or learning, because they are difficult to integrate. This integration requires a decomposition of the situation into its individual and social components. More specifically, the functioning of individuals and the functioning of groups must be both characterized in a single framework that permits the examination of how these aspects of performance interact. Within such a framework, differences between individual and group performance can be studied with respect to process and outcomes (Tschan, 2002). In the same vein, how group functioning arises from individual contributions can be examined (Volet, Summers, and Thurman, 2009). In this chapter, a rationale and strategy for empirical investigations on the challenges and benefits of collaboration are suggested. Following the argumentation developed by Sun (2005), it is argued that the junction of cognitive modeling and social cognitive modeling could yield valuable insights regarding the optimal configuration of learning and performance in social contexts. The result of this junction is the interaction of “an interactional focus on participatory processes with a cognitive focus on information processes” (Volet, Summers, and Thurman, 2009, p.129).

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7.3. THEORETICAL FRAMEWORK The theoretical framework presents current views regarding action regulation and knowledge use in individual and group performance, the benefits of collaboration in terms of performance and outcomes, and the effect of expertise on performance. This section is largely based on the remarkable work of Arrow, McGrath and Berdahl (2000). A particular emphasis is put on the interface between a group and its members in relation to the performance of a task. The framework of Arrow, McGrath and Berdahl (2000) is particularly adapted to the present purpose since it considers group functioning as a function of “relationships among people, tools and tasks, activated by a combination of individual and collective purposes and goals that change and evolve as the group interacts over time” (p.3). This framework is presented in their book as five propositions respectively concerning the nature of groups, causal dynamics in groups, group functions, group composition and structure, and modes of group life. The five propositions are discussed next in sequence. Proposition 1: groups are open and complex systems that interact with the smaller systems (the members) embedded within them and the larger systems within which they are embedded. Groups are open in the sense that two-way interactions exist between the group, its members, and its context. Groups are complex in that these patterns of interaction are neither rigidly ordered nor highly disordered. Proposition 2: three levels of causal dynamics continually shape the group: local (members using tools to perform tasks), global (system-level variables that emerge from and shape local dynamics) and contextual (features of the context that shape the local and global dynamics of a group). Drawing on dynamical systems theory, the framework focuses on patterns of dynamical variables rather than differences in values of variables. These variables pertain to the three levels identified. Proposition 3: groups have three functions: (1) to complete group projects, (2) to fulfill member needs, and (3) to maintain system integrity, a function that emerges from the two others. Attaining and maintaining system integrity are dependent on and instrumental to the other two functions ; the three functions are linked in a chain of interdependent causation. These competing demands are managed by the group through self-regulation processes: goal setting, planning, and monitoring (accompanied by adjustments if required). Feedback loops inherent to self-regulation imply non-linear effects on group dynamics. Proposition 4: in groups, three types of elements (people, intentions embodied in group projects, and resources) are linked functionally in a coordination

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network. The coordination network is constituted of six sets of relations: the member network (member-member relations), the task network (task-task relations), the tool network (tool-tool relations), the labor network (member-task relations), the role network (member-tool relations) and the job network (task-tool relations). Proposition 5: the life course of a group can be characterized by three logically ordered modes: formation, operation and metamorphosis. Formation is the stage at which a group emerges, and metamorphosis ends the existence of a group. The operation stage encompasses most of the existence of the group, and it may coexist with the two other stages. On the basis of this framework, the notions of system levels, executive control in individuals and groups and knowledge use in individuals and groups are described to support two central assertions for the present research program: (1) individuals and groups can be compared, from a functional perspective, using categories from individual cognition and (2) the functional perspective, from a cognitive point of view, can be decomposed into the cognitive operations that have to be enacted for the successful performance of a task and the knowledge underlying them.

7.3.1. System levels The possibility of comparison between individual and group performance rests on the assumption that similar processes can be observed on different system levels. Tschan (2002), Miller and Miller (1990), and von Cranach, Ochsenbein, and Valach (1986) argue that the execution of a problem-solving or decisionmaking task is determined by the structure and requirements of that task to such an extent that any system capable of performing it will display similar properties in its execution. Many studies of group performance used frameworks developed in research on individual cognition (see Tschan, 2002) that considered groups as complex information-processing systems. This assumption is thought to be applicable to both the processes and knowledge involved in the completion of the pedagogical-reasoning task.

7.3.2. Executive Control in Individuals and Groups This characterization of systems in terms of levels posits, in principle, that a system with less levels, other things being equal, is less complex. It can be

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hypothesized that this reduction in complexity from group to individual performance should lead to improved performance with respect to executive control. Another contrast between individual and groups comes from the fact that performing complex tasks involve the creation of a mental model of the situation (followed by hypothesis testing), a problem space in which solutions to the problem are elaborated and tested. In the case of an individual, these elements are created and acted upon in a single mind. Thus, they are bound to the constraints of working memory. In groups, these elements are held jointly in all members minds and obey to constraints of communication. In addition, the reduction in the pool of knowledge available for the completion of a task should result in lowered performance of individuals in terms of knowledge and results. The next sections show how executive control and knowledge use are processes similar in many respects across system levels.

7.3.2.1. Self-Regulation in Individual Performance Most models of regulation of performance posit a sequence of planning, execution, and evaluation of actions. During planning, a goal (and associated subgoals) is set, and actions aimed at the attainment of the goal(s) are selected and sequenced. During execution, actions are enacted and monitored and adjustments for successful performance are made. Finally, the results of the actions are compared with the initial goals during evaluation. In the eventuality of no discrepancy, the cycle ends. In the case of discrepancy, corrections are executed. These cycles are nested in the structure of the task (Tschan, 2002). Complex tasks such as pedagogical reasoning are constituted of hierarchically and sequentially constrained sub-tasks, as described earlier in the text. 7.3.2.2. Group Regulation in Collaboration Collaboration arises from members’ needs for affiliation, achievement, power and resources (Arrow, McGrath and Berdahl, 2000). As regulation is a requirement for productive individual behaviour, other forms of regulation are required for productive collaboration. At the group level, this regulation involves “elaboration, action, and modification in the service of member needs and group projects to coordinate member interests, understandings and action in a pattern that combines elements of cooperation and competition, convergence and conflict” (Arrow, McGrath and Berdahl, 2000, p.97).

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7.3.2.2.1. Group Regulation Of Members Interests: Conflict And Consensus According to Jehn (1995), there are three types of potential conflicts in groups: relationship conflicts, procedural conflicts, and task conflicts. A relationship conflict is generated by incompatible interests among group members. They are the most troublesome conflicts in groups. To resolve such conflicts, by nature inevitable due to competing members interests, the group must adopt norms specifying how consensus will be reached. The absence of such norms leads to procedural conflicts. In certain situations, the process of discovering and resolving conflicts is one of the main goals of a group. In these situations, the group engage in the resolution of a task conflict. Examples of task conflicts include jury duty and activities involving the debate of ideas. 7.3.2.2.2. Group Regulation of Understandings : Group Problem Solving and Information Processing Information processing and problem solving are uninterrupted processes in group functioning, as sharing information and establishing its meaning is essential for adequate coordination of group performance (Arrow, McGrath and Berdahl, 2000). Group functioning itself continually generates information about the ongoing performance, which must be interpreted adequately by group members. Adequate information processing in groups entails determining needs for information, identifying and evaluating sources of information, interpreting information, assigning members to the monitoring and sharing of given sources of information, and reaching consensus on how and by whom information will be interpreted, integrated and shared. 7.3.2.2.3. Group Regulation of Actions : Synchronization of Member Activity Group action regulation is a two-level process that involves the regulation of individual actions, as discussed earlier, and the regulation of actions on the group level (McGrath and Tschan, 2004; von Cranach, 1996). The synchronization of member activity requires a shared understanding and consensus on the necessary actions and where, when and by whom they will be performed. The enactment of these actions is monitored, and when discrepancies from the intended action plan arise, correction procedures are needed. The regulation of actions at the group level is best understood in light of the coordination network (proposition 4). As can be seen in Figure 7.1, the core of the coordination network is constituted of three types of basic elements: group members, tasks and tools. Group members are the individuals forming the group.

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Tasks are the actions that must be done to complete a group project. Finally, tools are the objects, resources and procedures required to perform tasks.

Figure 7.1. The coordination network.

Three dynamic processes can be applied to these basic elements and the relations between them: elaboration, enactment and maintenance and modification. Elaboration involves the identification of elements and their characteristics and organizing the relations between them. Enactment and maintenance refer to the activation and modulation of these relations through group interactions. Finally, modification is the deliberate alteration of these relations in response to information about group functioning. Basic elements of the coordination network are interrelated. In addition, each type of basic elements is interrelated with the two other types, forming other lower-level networks in the coordination network. Each of the networks is discussed next. The member network. The member network (member-member relations) is the most complex of all networks in the system. The elaboration of the member network is shaped by proximity, perceived similarity, complementarities of needs and preferences and unmet needs of members for social contact. The relationships

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among group members may be considered more important than their functional role in group performance. Indeed, these relationships are related to the fulfilment of members needs. The task network (task-task relations). To elaborate the task network, group members have to break a project down into tasks, then cluster and order them. In a complex domain such as teaching, as a result of a task analysis based on pertinent domain knowledge, a complex project is divided into its components. These components are then organized sequentially and hierarchically on the basis of their inherent functional constraints. The tool network. The tool network (tool-tool relations) may be organized on the basis of the function of tools. Tools complementary for a given function are clustered. Tools may also be clustered according to the links they have with group members. The job network (task-tool relations). The tool and job network may develop concurrently. Groups have to specify the inventory of tools and procedures available to perform a task and specify how these tools are related to the tasks that have to be performed. Tools may be clustered on the basis of their function. These procedures emerge in each members’ cognition in the form of scripts that are then negotiated prior to implementation. These scripts and their relations form the job network. The labour network. The labour network (member-task relations) specifies which group member will do which task(s). Depending on the nature of the group, this assignation of tasks to members can be done collectively or by a leader, and takes into account members’ attributes. These attributes include knowledge, skills, abilities, values, beliefs, attitudes, and personality. The role network (member-tool relations). In groups, members are both “clients” and “resources” and the functioning of the group rests on this sharing of member resources. Roles members play in the group are related to their contribution to the group project in terms of tools. The labour network refers to the sharing of tasks that have to be performed by each member using tools available to them individually or to the group as a whole. In sum, by showing the most basic constituents of group performance and the numerous sets of relations between these constituents, this framework highlights the considerable complexity of the coordination of group processes. By contrasting the member network, the tool network and the task network, it also helps to appreciate in a more subtle way what is social in group performance and which aspects of group performance are outside the social realm. Conversely, new insights could be gained by examining individual performance using this framework and replacing the member network by an individual.

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7.4. SOME CONSIDERATIONS ABOUT COGNITIVE MODELING AND SOCIAL COGNITIVE MODELING AS A STRATEGY FOR EMPIRICAL INVESTIGATIONS The idea repeatedly formulated in this book emphasizing the similarity between functional aspects of individual and group performance represents potential for the study of issues such as the alleged added value of collaboration for learning and performance. However, the complexity of the approach necessitates that some precautions be taken. Attention must be scrupulously paid to the details regarding the tasks and settings. Moreover, a focus on performance benefits from a specification of the task to be performed. Specifying the steps involved in a task as well as their sequence, makes it possible to refine the study of performance in terms of process and outcomes at the level of these subtasks. This specification was the goal of the two empirical studies presented in the previous chapters. The task has to be representative of the domain. Teacher planning represents a substantial portion of teaching. From a cognitive point of view, teacher planning was conceived of as pedagogical reasoning in the most recent literature (Sanchez and Llinares, 2003). Pedagogical reasoning includes most of teacher decision-making with one notable exception: it does not include decision-making that happens during teaching (i.e. in the presence of students) (Clark and Peterson, 1986). This model could be used to study collaborative situations of various kinds in teaching. These results can give indications regarding how to best configure individual and collaborative performance for maximum output. The outcomes refer to the course of actions planned on the basis of the diagnostic of the student’s difficulties. In addition, outcomes can include the teacher’s subsequent behavior in the presence of the student. Particularly, the level of correspondence between the teacher behavior and the initial plan is an important link in the implementation of pedagogical innovations. Because group performance is almost always based on dialogue between group members, understanding group processes is enhanced by the study of group conversations (Kneser and Ploetzner, 2001). Collaboration is different from cooperation in that collaboration implies the concomitant implication of group members to perform a task whereas cooperation can be achieved by the division of labor (Kneser and Ploetzner, 2001). Kneser and Ploetzner (2001) identify three aspects related to the level of success of collaboration and reflected in

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characteristics of the dialogue: the knowledge that group members bring into the situation, the roles of the group members, and the exchange of knowledge between group members. Outcomes of collaboration are superior when group members have complementary knowledge (Kneser and Ploetzner, 2001) and when they externalize it for discussion (Fisher, Bruhn, Gräsel and Mandl, 2002). The impact of roles on the outcomes of collaboration is less clear. However, research has shown that questions related to the performance of the tasks where associated with better performance (Kneser and Ploetzner, 2001). Finally, in-depth explanations in reaction to teammates’ requests for detailed information improve learning (Fisher, Bruhn, Gräsel and Mandl, 2002). The elaboration of a common solution through collaboration can be achieved through the confrontation or through the integration of individual views. Confrontation is conductive of learning whereas integration can lead to superficial solutions (Fisher, Bruhn, Gräsel and Mandl, 2002). These authors (Seifert and Manzurk, 2006) also identify freeloading and overspecialization as potential problems in collaboration.

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7.5. CONCLUSION As discussed previously, collaboration can at times facilitate learning and in other occasions impede learning (Moreno, 2009). Therefore, the interactions between the members of the group must be actively monitored and modified if needed (Faidley, Evensen, Salisbury-Glennon, Glenn and Hmelo, 2000). From the perspective of the functioning of the group, collaboration distributes the cognitive load among the participants (not in every contexts, see Moreno 2009) and creates a pool of knowledge that no single participant possesses (Faidley et al., 2000). These issues are particularly interesting if the level of expertise of the individuals is considered. Examining how groups of individuals of the same level of expertise perform can inform about the impact of knowledge on group performance and learning. Examining how groups of individuals of different levels of expertise function can contribute to our understanding of mentoring situations. Such situations include tutoring situations involving student teachers and their mentor, colleagues working on common teaching projects, teams of student teachers engaging in collaborative learning activities. These considerations will be examined in the next phase of the Pedagogical Reasoning Project.

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Chapter 8

8. AN ESSAY ON THE NATURE AND STRUCTURE OF TEACHER KNOWLEDGE

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8.1. INTRODUCTION The construct of teacher knowledge has been the object of substantial theorization over many decades. Many syntheses are testimony of this interesting body of work (Clark and Peterson, 1986 ; Munby, Russell and Martin, 2001). Although existing work informs on many aspects of teacher knowledge necessary for the cognitive study of how this knowledge affects the performance of tasks, there is a need for a characterization of teacher knowledge in terms of its most basic structure, so that these characteristics can be put in relation to fine-grained cognitive processes underlying the performance of tasks. The stance adopted in this book is to further explore the metaphor of teacher as clinician (Calterhead, 1995). By adhering to the underlying idea that teachers and physicians solve problems in domains that share characteristics in terms of complexity and the nature and amount of knowledge necessary to be competent, this metaphor drives a borrowing of ideas from research on medical reasoning and medical problem solving.

8.2. THE PROBLEM AND ITS CONTEXT The metaphor of teacher as clinician (Calterhead, 1995) has inspired many studies of teacher’s decision making and knowledge in a cognitive perspective over the past 30 years. This metaphor emphasizes the role of teacher knowledge and thought processes in teaching. Studies in this perspective focused on teacher

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planning and interactive decision-making. Despite a persisting interest that lasted three decades, current issues in teaching and teacher education are insufficiently researched from a cognitive science point of view. This scarcity of research is particularly deplorable if related to the possibility that conceptual and methodological advances have not been thoroughly exploited in the field despite repeated recognition that insights from this perspective are valuable (Borko and Shavelson, 1990 ; Clark and Peterson, 1986). The metaphor of teacher as clinician also emphasizes the similarities between the cognition of teachers and physicians (Calterhead, 1995). Despite these alleged similarities between the domains of medicine and education, differences exist between the topics and methodologies used in cognitive studies in these domains. On the one hand, research in medical cognition focused on medical reasoning and on the nature and influence of knowledge involved in that process. This research has shed light on the characteristics of medical knowledge (notably that biomedical knowledge becomes encapsulated in clinical knowledge as a result of experience) and provided evidence of different modes of thinking supported by varying amounts of medical expertise. On the other hand, research on teacher cognition has focused on priorities and constraints in planning instruction and on teacher thinking and behaviour in the classroom. More recent research on teacher cognition (Schoenfeld, 2000) has shifted to the examination of links between pre-active planning and interactive decisionmaking and actions. This research still struggles with issues pertaining to the nature of teacher knowledge (Scherin, Scherin and Madanes, 2000) and knowledge acquisition (Grossman, 2005). In the more specific area of teaching in reading, the situation is similar: teachers’ content knowledge has not been extensively studied, partly because of the difficulty of specifying what constitutes such knowledge (Phelps and Shilling, 2003). Current research in medical reasoning examines issues related to training, in conjunction with a dominant model in medical schools, problem-based learning, augmented by ideas of collaborative and computer-supported learning (Koschmann, Hall and Miyake, 2002). Both fields still struggle with issues of training and assessment. Validated by research, similarities between teacher and physician cognition could lead to important cross-fertilization in both fields regarding training and assessment. Building conceptual and methodological bridges between the study of medical cognition and the study of teacher cognition could propel both fields of research. To this end, successful fundamental and applied research in one field should be replicated in the other to determine the extent to which conclusions hold. As this endeavour progresses, interpretation of similarities and differences

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should become easier. For example, findings in medical problem solving may help orient teacher education as they did in medical education. However, their generalizability to another domain must be carefully assessed empirically. Since human cognition is increasingly seen as knowledge-driven instead of state-driven by generic cognitive operations, one important aspect to investigate is the properties of the knowledge of experts and novices in the domain. Our approach, in the planned studies, will be to examine teacher knowledge as it is used in the context of an authentic task. We contend that knowledge cannot be described without reference to how it is acquired and used. In this context, learning can be associated with knowledge acquisition, new use or as a result of reflection on use (Munby, Russell and Martin, 2001 ; Verhoeven, Schnotz and Paas, 2009). The aim of the planned studies presented is to examine characteristics of teacher knowledge and how teachers use that knowledge in planning lessons. Two general questions are investigated: (1) what is the nature of knowledge used in teacher planning? and (2) what is the relationship between teacher knowledge and teacher thinking in planning instruction? The theoretical framework that follows is based on general concepts from cognitive science, as well as concepts from the fields of teacher cognition and medical cognition.

8.3. THEORETICAL FRAMEWORK To illuminate the study of teacher knowledge and knowledge use, the theoretical framework presents a view of teacher knowledge from a cognitive perspective. The section on teacher knowledge is organized so that the presentation of notions represents a continuum from generic notions borrowed from knowledge-rich domains to notions that are specific to the domain of teaching. Specifically, the notions of propositional representation, schemas, and pedagogical content knowledge are discussed. To help further characterize our approach to the study of knowledge and knowledge use, Sherin, Sherin and Madanes (2000) point out an interesting distinction between cognitive modeling and knowledge system analysis (cognitive modeling being the approach used in this book). A knowledge system analysis is concerned with the categorization of knowledge in a domain, and how this knowledge originates and evolves. In contrast, cognitive modeling is concerned with the explanation of relatively shortterm episodes of activity. A cognitive model is a mechanism that specifies operations hinging on knowledge that explain an individual’s or group’s given performance.

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A theory of teacher knowledge has to describe teacher cognition underlying their teaching actions and their justifications. More specifically, such a theory has to integrate knowledge that teachers use when they elaborate plans about teaching and when they justify what they do in teaching. A model that describes teacher knowledge and how they use it in teaching is needed to study teacher collaboration in order to, among other things, assess its quality and its outcomes in a multiplicity of situations. Many important questions remain to be explored in the development of such a model: (1) what knowledge is involved during these cognitive steps, (2) how knowledge from each teammate gets integrated into a common problem space during collaboration, and (3) how this knowledge drives the collaborative pedagogical-reasoning process. Elements of answer to these questions could contribute to explain the differences found in the present study. Question 1 could be answered by constructing a conceptual graph of the knowledge evoked in the protocol of each pair of participants. To answer question 2, the conceptual graphs could be annotated with indications regarding which participant contributed each of their components. For question 3, the conceptual graphs can be graphically integrated with the corresponding traces of the pedagogical-reasoning process, for each pair and individual. Given the predominant role of knowledge in ill-structured problems, conceptual representation theory may contribute to our understanding of problem solving (Voss and Post, 1988). Schema knowledge for problem solving consists of identification knowledge, elaboration knowledge, planning knowledge, and execution knowledge (Marshall, 2005). Identification knowledge is concerned with the recognition of patterns. Elaboration knowledge intervenes in deciding whether the elements necessary for the solution of the problem are provided, after the pattern has been recognized. Planning knowledge is used to set goals and select associated operations. Execution knowledge consists of algorithms that are executed step-by-step, at the service of the plan. Elements of such a theory are presented next.

8.3.1. A Propositional View of Teacher Knowledge Many views exist about the nature of teachers’ knowledge (Munby, Russell and Martin, 2001 ; Sherin, Sherin and Madanes, 2000). According to Munby, Russell and Martin (2001), three research approaches have led to different accounts of teacher knowledge: information processing, practical knowledge, and pedagogical content knowledge. This review focuses on a propositional view of teacher knowledge because it is compatible with a cognitive, information-

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processing framework. In addition, knowledge, in this view, is amenable to a level of analysis that shows what knowledge is learned and used and how it is acquired, following Carter’s (1990) advice that the focus of research needs to change from a general to an explicit level. Frederiksen, Bracewell, Breuleux and Renaud (1990) identify 11 types of information that propositions can convey. An event is an action that changes a state. A system is a set of objects and a process. A state is a set of objects and their relations. A propositional relation specifies properties of an abstract concept. An identity links concepts or propositions into identity sets. An algebraic relation represents relations between variables. A function is an operation defined on operands. A binary dependency relation makes one proposition depend on another. A conjoint dependency relation represents “and”, “alternating or” and “exclusive or” relations. Leinhardt (1987) used semantic nets to represent teacher knowledge underlying the performance during a specific lesson. Her method lacks a set of “primitives” and is limited to a phenomenological account, that is, a classification of knowledge that is entirely emergent from the data.

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8.3.2. Teacher Knowledge as Schemata In their synthesis on teacher knowledge, Sherin, Sherin and Madanes (2000) distinguish between the form and content of teacher knowledge. These authors note a diversity of views regarding both form and content. Regarding the form, Sherin, Sherin and Madanes (2000) bring together diverse claims by suggesting that many claims can be unified under the notion of schema. A schema is “a template knowledge structure with fixed or default elements and blank slots that are filled in at the moment of use” (p.365). Applied to teachers’ knowledge, the schema is defined as “an ordered representation of objects, episodes, actions, or situations that contain slots or variables into which specific instances of experience in a particular context can be fitted” (Carter and Doyle, 1987, p. 149). The various typologies of the content of teacher knowledge are difficult to unify. Many types of schemas have been proposed to describe teacher knowledge. Borko and Shavelson (1990) make the distinction between scripts, scenes, and propositional structures. Scripts contain information about familiar teaching experiences. Scenes represent people and objects in a familiar setting, such as the classroom. Propositional structures represent declarative knowledge of facts and procedures (Frederiksen, 1975). Action schemas in teaching represent an action that the teacher can perform and includes consequences of the performance of that

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action as well as requisites for this action to be performed (Leinhardt and Greeno, 1986). Schemata of these different types are interrelated to make complete and coherent representations of a situation (a situation model in Kintsch’s (1998) terms) on which to base teaching actions. Action schemas are constituted of scripts and scenes. Empty slots in these schemas are filled in by information contained in propositional structures. The nature of this information is discussed in the next section.

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8.3.3. Pedagogical Content Knowledge The propositional structures discussed previously represent information about students, subject matter, and pedagogical strategies (Borko and Shavelson, 1990). Pedagogical content knowledge or PCK (see Shulman, 1987 for the initial presentation of the construct and Hashweh, 2005 for a current conceptualization), which seems to be a refinement of these early categories, may be the best current account of the nature of information presented in propositional structures in the domain of teaching. Some authors support this position by arguing that there is merit in using Shulman’s framework from a cognitive science perspective (Hogan, Rabinowitz and Craven, 2003). Hashweh (2005) defines PCK as “the set or repertoire of private and personal content-specific general event-based as well as story-based pedagogical constructions that the experienced teacher has developed as a result of repeated planning and teaching of, and reflection on the teaching of, the most regularly taught topics”. Of particular importance to the present study is the assertion that this knowledge develops mainly from planning, seen as an essentially constructive process. Moreover, PCK does not seem to develop in pre-service teacher education programs, this development being postponed to in-service teaching experience. PCK results from the interaction of many types of teacher knowledge and beliefs: (1) content knowledge, (2) knowledge and beliefs about learning and learners, (3) pedagogical knowledge and beliefs, (4) knowledge of context, (5) knowledge of resources, (6) curricular knowledge, and (7) aims, purposes, and philosophy. Hashweh (2005) notes that while this view represents the interactionist aspect of PCK, it does not represent its developmental aspect.

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8.3.4. Knowledge Use in Pedagogical Reasoning In the previous chapters, a cognitive model of teacher pedagogical reasoning was elaborated and tested. The model integrates general theories of human cognition (discourse comprehension, problem solving and reasoning) with findings from medical reasoning under the assumption that teaching and medicine share important similarities (see Calterhead, 1995). In medicine, another applied domain in which practitioners make decisions about what actions to perform on the basis of a complex knowledge base, this process is alternatively called clinical reasoning, medical problem solving, diagnostic reasoning, decision-making or more generally, medical reasoning (Patel, Arocha and Zhang, 2005), and has been extensively studied using theories of human cognition and methodologies from cognitive science. The expression teachers’ “pedagogical reasoning” was used under the working hypothesis (supported by Calderhead, 1995 and Leinhardt and Greeno, 1986) that teachers’ and physicians’ decision-making processes share important similarities, such as the complexity of the knowledge and problem solving and the contextualized nature of the thought processes. The present work is based on the expert approach that focuses on cognitive processes and knowledge structures (Munby, Russell and Martin, 2001). This approach has led to the conclusions that expert teachers have rich stores of knowledge that tie interpretative propositions to features of the teaching environment.

8.4. A METHODOLOGY FOR KNOWLEDGE MODELING In this section, a methodology for modeling teacher knowledge elicited in a problem-solving task is described. In the planned studies of individual performance, the main goal of knowledge modeling is to show how knowledge is used to perform the pedagogical-reasoning task. For the studies of collaborative performance, the aim is twofold: (1) to show how the pool of knowledge resulting from the knowledge of each participant of a pair is built and (2) how this common pool is used in collaborative pedagogical reasoning. The procedure is currently applied to the entire data sets of the two studies reported in this book. Data in these studies of collaborative and individual pedagogical reasoning have to inform about concepts and objects and their associations, and about how these concepts and objects were used by participants in the performance of a complex task. In the context of individual performance, such information can be

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obtained from direct methods such as think-aloud protocols (Olson and Biolsi, 1991). Participants were asked to talk out loud. If a participant stopped talking for more than five second, the research assistant would remind her to resume “saying anything that comes to mind”. In the case of collaborative performance, spontaneous conversation data were used.

8.4.1. Data Analysis

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Protocols were transcribed for analysis. A first step involved the transcription of the utterances. A second step consisted of annotating the transcript with additional information regarding the use of the computer and the production of a written lesson plan. During this second step, the initial transcription of talk was verified and corrected. The segmentation of the protocols was done at this step, on the basis of pauses in the speech. A third step comprises the construction of conceptual graphs. Finally, the last step is statistical analysis.

8.4.1.1. Construction of Conceptual Graphs Available research on teachers’ and physicians’ knowledge does not provide a complete formalism to represent how teachers’ goals, actions, and knowledge are organized in memory (see Clark and Peterson, 1986 and Mumby, Russell and Martin, 2001 for reviews). In addition, the order in which participants discover new knowledge during the performance of a task indicates the problem-solving strategies used (Olson and Biolsi, 1991). According to these authors, the problembehavior graph represents the chronological sequence of appearance of knowledge used in the task. Another common representation is the network of concepts, which ignores the time dimension. Both of these representations are insufficient for the present purpose. The problem-behavior graph is best-suited for knowledge-lean problems, such as those used by Newell and Simon (1972) whereas the network used by Patel and Groen (1991) in knowledge-rich tasks does not represent the temporal dimension. Since mental models are hypothesized to be knowledge structures manipulated throughout the pedagogical-reasoning process, a tactic to represent knowledge used chronologically and in association with specific pedagogical-reasoning activities in conjunction with its organization is essential and had to be elaborated on the basis of existing formalism. Among available alternatives, the problem-behavior graph (Newell and Simon, 1972) is designed to represent the chronological sequence of appearance of knowledge used during the task. However, it has limitations in portraying the organization of that knowledge, and appears to be best used in knowledge-lean

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domains. The conceptual graph representation used by Patel and Groen (1991) in studying medical reasoning is very adequate to represent the organization of knowledge in knowledge-rich domains, but does not display the temporal information. Patel and Groen (1991) describe a formalism for representing links between chunks of declarative knowledge as used in medical reasoning that does not include plans for the intervention subsequent to the elaboration of the diagnosis. Similarly, Leinhardt and Geeno’s (1986) planning net represents the structure of plans without temporal indications. Leinhardt and Greeno (1986) present a structure for representing plans that do not include the declarative knowledge underlying them. Finally, “behaviour by time plots” used in sequential analysis are specifically designed to display sequential data (see Bakeman and Gottman (1997) for examples). They can represent very elaborate sequences of states or events but are limited with respect to the number of dimensions they can put in relation. However, these three formalisms have characteristics vitally useful for representing teacher knowledge. In response to the strengths and limitations identified, a conceptual graph and behaviour by time plot hybrid representation will be used to display the data. The network expands the formalism of Leinhard and Greeno (1986) and the one of Patel and Groen (1991) by linking them together, thereby reflecting the knowledge underlying the complete diagnostic-remediation process hypothesized in the pedagogical-reasoning model. These elements are annotated chronologically on the basis of their evocation in the individual’s think-aloud or dyad’s conversation by links to the behaviour by time plot (Bakeman and Gottman, 1997). The behaviour by time plot represents the complete sequence of pedagogical reasoning states (black dots represent one participants and white dots represent the other in a single line representing the dyad). In this study, multievent sequential data are graphed, since they represent pedagogical reasoning activities coupled with the performer of that action. This analysis yields a network of concepts, goals, actions, and their relations, indexed chronologically and in terms of the pedagogical reasoning activity during which they were used. This formalism, by nature, will inform us about the links between theory and practice by shedding light on how knowledge (traditionally called theory) is associated with goals and actions (practice), thus reframing the theory/practice problem into cognitive terms. Frederiksen’s (1975) formalism is constituted of a finite and universal set of nodes and relations and serves as the foundation for the structure described next. His network representation is used in the present study to expand the formalism of Leinhard and Greeno (1986) and the one of Patel and Groen (1991) by linking them together, thereby reflecting knowledge use throughout the complete

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diagnostic-remediation process hypothesized in the pedagogical-reasoning model. Nodes and relations describing teacher knowledge are selected from this universal set on the basis of the theoretical framework presented. The final product of this analysis is a network containing nodes and their relations, annotated chronologically on the basis of their evocation in the thinkaloud or conversation protocol. Evidence of subject’s strategies can be found by tracing the order in which they worked through the network (Olson and Biolsi, 1991). Categories characterizing nodes and the relations between them are presented in Table 8.1. Table 8.1. Nodes in the conceptual graph Nodes Goal

Action

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Cause Condition Agent Source situation Result Instrument

Definitions A goal is a thing that an individual wants to accomplish. Educational goals may be epistemologically oriented, contentoriented, or socially oriented (Schoenfeld, 2000). The goal has to be the one pursued by the agent of the action (Frederiksen, 1975). An action contributing to the attainment of the pedagogical goal. It is a process that changes state A to state B. The source node causes the target node (Groen and Patel, 1988). The source node is an indicator of the target node (Groen and Patel, 1988). The agent is the performer of an action. The agent can be an object or a process. The source situation is the initial state to which the action is applied. The result is the consequences and effects of the enactment of an action. It represents the new state of the situation. An instrument is a state, process, or event that is used to perform an action. Contextualized to teaching, instruments can be of three types (Learnhardt and Greeno, 1986): Prerequisite: a condition that must be met before enacting an action Corequisite: a condition that must be met during the enactment of an action Postrequisite: a condition that must be met to end an action.

The propositional structure of teacher knowledge can be represented by two main proposition types: events and states. An event is a change in states (VidalAbarca, Reyes, Gilabert, Calpe, Soria and Graesser, 2002). Frederiksen (1975)

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specifies that an event comprises an action performed by an agent that induces a change from an initial state to a new state. An event may also include a cause that drives the agent to perform the action and any condition that must be met, a goal if the action is intentional, a recipient, and an instrument. A state represents ongoing properties of an object in a given “world” (Frederiksen, 1975 ; VidalAbarca, Reyes, Gilabert, Calpe, Soria and Graesser, 2002). States can be physical, social, mental, abstract, etc. These two proposition types constrain the types of nodes and relations used to further characterize teacher knowledge. They also imply composition rules that specify the restrictions in the amalgam of nodes and relations. The nodes, relations, and composition rules are defined next. Elements of a planning net can be augmented by selected elements from conceptual graph formalism. These generic relations are presented and defined in Table 8.2. According to Olson and Biolsi (1991), the main categories of relationships are: causal, conditional, associative, equivalence, and categorical. All of these categories of relations are represented in the network. Table 8.2. Relations in the conceptual graph

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Relations Causal Conditional Associative Equivalence Categorical

Definitions The source node causes the target node (Groen and Patel, 1988). The source node is an indicator of the target node (Groen and Patel, 1988). locative, temporal, durative attribute.state. Identified nodes are asserted to be equivalent, they refer to the same entities (Frederiksen, 1975). A subnode that describes properties of a node, distinguishing the object represented by that node from other objects (Frederiksen, 1975) (Category, Is.A, Part.Relation, IsPart.Relation).

8.4.1.1.2. Composition Rules Graesser and Goodman (1985a) distinguish between three types of graph structures: goal-oriented structures, cause-oriented structure and descriptive structures. In a goal-oriented structure, the agent performs actions in order to achieve given hierarchically-organized goals. Cause-oriented structures represent causal chains. They describe a causal mechanism that specifies how one or more states enable(s) one or more events. Finally, a descriptive structure enumerates

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properties, attributes and features of one or more concepts. The structure of a script or action schema in teaching can be specified within that framework. Indeed, it appears that the planning net of Leinhardt and Greeno (1986) is an amalgam of a goal-oriented and a cause-oriented structure. The present methodology yields a similar amalgam, constituted of a cause-oriented structure that represents the diagnostic process and the goal-oriented structure that schematizes the pedagogical-planning process. The two structures are linked by relations illustrating how the diagnosis constrains the pedagogical planning process. In addition, any two propositional structures can be linked by a state proposition through any two of their constituent nodes. Borrowing from generic views of knowledge representation, this organization can be globally mapped as a hierarchical procedure frame (Frederiksen, 1999) according to the goal hierarchy determined using Schoenfeld’s (2000) method. The hierarchical arrangement of goals is complemented by indications of temporal constraints on the basis of the requisites of their associated actions. Goals are related by categorical relations. Inheritance of attributes is a crucial aspect of hierarchical networks. The postulated hierarchy representing teacher knowledge is based on teaching goals. Therefore, the property of the relation used must be true for all constituent nodes of the target propositional structure. Within these composition rules, how propositional structures are linked to form elaborate teaching schemata is an empirical question. It is expected that they will be subject to significant phenomenological idiosyncrasy. In Frederiksen’s (1975) notation, the label of a relation identifies the nature of the source node whereas the direction of the relation specifies the target node. Thus, in a graph representing an event, a goal, source, result, agent, recipient, cause, and condition labels identify the source node correspondingly. The instrument relation was further contextualized to teacher knowledge by distinguishing three types of instruments: prerequisite, corequisite, and postrequisite. In a graph representing an event, associative, equivalence and categorical relations can be used. Associative relations either specify the location, the time or the duration that characterizes a state. An equivalence relation asserts that two states are equivalent. Finally, categorical relations (is a, is part) specify properties of a node in the presence of sub-nodes. These three types of relations can be used in conjunction with any of the nodes specified in the basic structure, except the central action and the goal nodes. For example, a cause of an action can include more specific constituents, identified with categorical relations. Equivalence between two nodes may occur when the same node is verbalized in different ways

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or in more than one occasion in a protocol. Associative relations apply to states, and are related to source and result nodes in the structure. The treatment of goal and action nodes has been detailed above in the composition rules. In the case of hypotheses, an asserted truth value (POS, NEG, INT) must be specified. At any moment, a formulated hypothesis has to be held as positive, negative or interrogated (Frederiksen, 1975). Hypotheses are integrated in the causal structure of actions. Finally, Frederiksen’s (1975) procedure for propositional analysis provides two alternate representations of the semantic information contained in propositions: a BNF grammar and conceptual network. One of these representations can be translated directly into the other. For simplicity, the conceptual network representation is preferred in this work.

Figure 8.1. A basic structure for representing teacher knowledge.

In sum, we claim that the basic structure for representing teacher knowledge in a cognitive modeling perspective can be represented as a web structure with a teaching action at its center, as depicted in Figure 8.1. A major addition of this

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formalism, compared with the common notion of script used in the study of teacher cognition, is the inclusion of a complex causal and conditional structure as precursors of these actions. This inclusion on the basis of Patel and Groen’s work in medical reasoning is a direct consequence of the emphasis put in the pedagogical-reasoning model on the diagnosis of students’ difficulties and on the rationale behind intended teaching actions. The hierarchical arrangement of many actions and their accompanying structure as reflected in the composition rules is dictated by most theories addressing complex tasks and reflects the widely adopted view that such complex tasks have to be decomposed into sub-tasks (Tschan, 2002).

8.4.1.1.3. Additional Coding: A Typology of Teacher Knowledge A final set of coding categories will be applied at the level of propositions. Conceptual knowledge expressed in conceptual graphs will be examined within Hasweh’s (2005) framework of pedagogical content knowledge (PCK). Propositions (relations between pairs of concepts) representing conceptual knowledge can be further coded with the hypothesized constituents of PCK. Hashweh (2005) argues that planning is a cyclical and interactive process in which the categories of PCK interact. To examine this question, an example of analysis would be to code propositions according the categories of PCK and in relationship with the categories of the pedagogical-reasoning model. Table 8.3 summarizes the definitions of the categories of PCK. 8.4.1.2. Coding Procedure An adaptation of the coding procedure used by Vidal-Abarca, Reyes, Gilabert, Calpe, Soria and Graesser (2002) will be applied in the analysis of the data. This procedure involves three steps: node segmentation, node classification and node connection. In node classification, each node is associated with a category on the basis of the conceptual information it contains. In the last step, node connection, the nodes previously identified and categorized are linked by relationships. A relationship links two nodes and is constrained by composition rules. The planned procedure was adapted with respect to the node segmentation step. These authors define a node as a complete sentence, in which the point is represented by the main clause. In contrast, the segmentation of nodes in this study is independent of grammatical construction of sentences. Segments representing the knowledge involved in pedagogical reasoning protocols were first identified. A segment representing knowledge was defined as a unit identifying a goal, an action, a concept, or a relationship linking two or more of

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these elements. Segments containing only information related to cognitive processes involved in pedagogical reasoning were not coded. As Graesser and Goodman (1985) note, node classification can be ambiguous if the coder does not have access to the context. For this reason, the complete protocol was available during this process. Table 8.3. A typology of teacher knowledge at the propositional level Pedagogical content knowledge categories Content knowledge

Definitions

Knowledge and beliefs about learning and learners

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Pedagogical knowledge and beliefs

Knowledge of context

Knowledge of resources Curricular knowledge

Content knowledge refers to knowledge of concepts, principles, relations, topics, higher-order principles, and ways of relating topics to other disciplines. This PCK category contains conceptions of learning (see Deaudelin for more specific definitions) and knowledge of student characteristics such as experiences, abilities, interests. This category includes beliefs about the importance of representations, knowledge of planning and knowledge of classroom management. It also contains knowledge of general lesson types, such as developmental lesson, lecture, demonstration, laboratory, group work, etc. Knowledge of context comprises knowledge of local educational system, knowledge of community, and knowledge of particular students. This PCK category consists of knowledge of available textbooks, software, films, equipment, etc. Curricular knowledge refers to knowledge of a subject matter curriculum for a given grade level (horizontal curricular knowledge) and to knowledge of a subject matter curriculum across grade levels (vertical curricular knowledge).

8.5. CONCLUSION The aim of this chapter was to present a formalism for modeling the knowledge used in pedagogical reasoning, seen as problem-solving task, in a manner that would make it possible to make detailed links between knowledge and fine-grained cognitive processes, as specified in the model in chapter 3. The proposed formalism takes the form of a finite set of primitives organized into a

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basic structure. Basic structures are assembled together by hierarchical, sequential and causal composition rules. The resulting knowledge network complements the early formalism of Leinhardt and her colleagues (Leinhardt, 1987; Leinhardt, 1989; Leinhardt and Greeno (1986) by highlighting the complex goal structure underlying a complex task such as pedagogical reasoning and still retaining the sequential dependencies present in their formalism that are necessarily part of complex action plans. A perhaps more notable addition is the causal structure representing the particular characteristics of students, which are supposedly driving the teacher’s intervention as a result of the diagnostic process. This addition was motivated by and borrowed from classic studies of clinical reasoning in medicine. Finally, it was argued that the most primitive constituent of the knowledge network, the proposition, can be coded using typologies of teacher knowledge such as pedagogical content knowledge (Hasweh, 2005). As a framework for articulating teaching skills as goal-directed actions motivated by complex rational and situational constraints, the formalism can become a way to improve teacher education. Making explicit the logical components of goal-directed actions can help student teachers and their mentors articulate their thinking about teaching. Moreover, cognitive studies of teacher knowledge and knowledge use can provide tools to assess the effect of many instructional settings in place in teacher education. They can also inform the choice of existing methods (case studies, teaching portfolios, discussion forums, etc.) and the design of new strategies such as scaffolding for planning instruction. Conceptual graphs are domain-specific and specific to a teacher. Although these graphs are useful in isolation, procedures to aggregate graphs that share characteristics (domain, level of expertise of the teacher) are necessary. They have to be elaborated and tested. The comparison of network representations is difficult (Olson and Biolsi, 1991). To this end, a strategy is to compute ratios between categories of nodes, relationships and types of PCK. These ratios can be compared among individuals of a given level of expertise and between levels of expertise. Types of propositions identify necessary and accessory constituents of conceptual graphs. Such elements can be found explicitly in the protocol or inferred. These structural constraints in the semantic information conveyed in conceptual graphs can be used to investigate aspects of teacher thinking.

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9. EPILOGUE: FROM A RESEARCH AGENDA TO CONTRIBUTIONS TO TEACHER EDUCATION ON A TRAJECTORY TO EXPERTISE IN PEDAGOGICAL REASONING The main motivation behind this book was to present, in a sufficient amount of details, and in a coherent manner, key epistemological, theoretical and empirical aspects underlying the Pedagogical Reasoning Project, a research program aiming at the study of teacher cognition and teacher knowledge. This research program on pedagogical reasoning can be divided in three sequentiallyrelated phases: (1) the modeling of cognitive processes and knowledge involved in pedagogical reasoning, (2) the design and test of scaffolding strategies for the development of pedagogical-reasoning skills (both in university classes and teaching practicum settings) and (3) the design, development and test of computer tools as scaffolds for learning pedagogical-reasoning skills. The first phase, which is now in its fifth year, is well under way. Cognitive modeling of the pedagogical-reasoning processes is for the most part completed, whereas knowledge modeling is also almost finished. A theory-driven cognitive model of pedagogical reasoning was postulated and aspects of the model were tested empirically. Whereas the higher-level categories were discussed in the studies presented, the lowest-level categories associated with comprehension, reasoning, and planning remain to be analyzed. To this end, tactics for dealing with a relatively high number of categories in the context of sequential analysis must be devised. The categories and procedures for knowledge modeling were also developed, as described in this book. Finally, the relation between knowledge and cognitive processes is the culminating aspect of the first phase of the project. Analytical strategies regarding the fine-grained relation between knowledge and

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cognitive functioning have been reviewed and candidates are chosen, but the details regarding the aggregation of data over multiple units of analysis remain to be addressed. The second planned phase of the project has partially begun regarding aspects of teacher education that are not specifically related to pedagogical reasoning. Various tools commonly used in teacher education such as concept-mapping software, digital teaching portfolio, and discussion forums are integrated in various courses, sometimes being revisited in multiple occasions during sequences of courses including teaching practicum. These tools and their current use are presented here as precursors of scaffolding strategies that could be elaborated when the modeling of pedagogical-reasoning processes and knowledge will be completed. The digital teaching portfolio is currently being updated regarding both technical and pedagogical aspects. The portfolio software currently being implemented, ePEARL was developed by Phil Abrami and his colleagues at Concordia University. ePEARL is based on database technology, allowing for more flexibility in the quantity and variety of materials that students can choose to integrate. Aiming at fostering self-regulated learning, ePEARL supports selfreflection and feedback functionalities from peers and instructors. In this new form and because of these feedback functionalities, it is expected that the teaching portfolio, if appropriately used, will contribute to sustain the teacher education program’s functioning as a community of learning. Specifically addressing the need for a community of learning, discussion forums are being used in a variety of ways. In their first year in the program, students communicate among themselves about issues of culture in teaching. Second-year and fourth-year students are engaged in a tutoring relationship. During their teaching practicum, second-year students post two messages describing significant teaching problems they are struggling with (excluding problems with their mentors). Four-year students are required to chose a problem and respond to it by giving advice to the student. Aside from the social aspect, we hypothesize that this setting contributes to the self-reflection of all students. Second-year students can anticipate the competency they will likely acquire upon graduation, whereas fourth-year students can realize the improvement they have made in the last two years. The use of concept maps in learning to teach is being refined on an ongoing basis. Concept maps are currently being used as an alternative to written essays as a way to help student teachers reflect on their teaching. For example, a map is provided in some occasions to structure their reflection around self-regulated learning processes. It contains the main components of a self-regulated learning

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model (Zimmerman, 2000). The students are requested to complete the map with additional concepts and links that are related to all aspects of the self-regulated learning process. In addition, upon their first semester in the program, students are provided with another map of the complete content of all the courses they have to take during their four-year training. This gigantic map also contains a specification of teaching competencies that they must develop to be qualified as teachers. One use of this map is to help students make links between course contents and teaching competencies. It is expected that learning activities using these tools will be enhanced by the anticipated results from the studies of pedagogical reasoning. It is our contention that learning activities can be more beneficial for the development of teaching skills when they are appropriately anchored in a well-defined and authentic teaching task. The anticipated third phase of the project concerning the design, development and test of computer tools as scaffolds for pedagogical-reasoning skills can be seen as either accessory or essential to the whole research project. Indeed, the goals underlying the development of dedicated software applications are twofold. On the one hand, they could lead to more efficient teacher learning. The field of medicine has seen many of such tools, many of them being widely used in the training of physicians. Other remarkable examples from general education come from the cognitive tutors developed by Anderson and his colleagues (see Anderson and Gluck, 2001). Some of the functionalities of these tutors are to provide hints, adapt the sequence of exercises or content, diagnose learners’ mistakes, and assess learners’ progress. Independently of the computational approach underlying these functions, they hinge on an extremely detailed specification of the learning domain. Aspects of such a specification should emerge from our current analyses of teacher knowledge. In planning the construction of a tutoring system on the basis of this model or any model of teacher knowledge, many concerns arise. One of them is that before inducing students into thinking a certain way, we have to ascertain that experts are thinking that way and that this way fosters learning across a significant portion of the learning curve in the domain. Current analyses of our dataset will address this concern. On the other hand, as a research environment, a tutoring system could make possible a variety of cognitive studies of learning to teach. The control of parameters related to instruction permits the examination of learning in the domain. In addition, it enables the study of the efficacy of the scaffolds for learning by the systematic manipulation of the functionalities of the system. These

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strategies are common practice in many domains but have yet to be exploited to their full potential in the field of teacher education. The research presented in this book is funded by the Social Sciences and Humanities Research Council of Canada, the Canadian Foundation for Innovation, and the Fonds de Recherche sur la Société et la Culture.

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INDEX

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A academic, 37 accountability, 104 achievement, 48, 108 activation, 26, 29, 30, 111 adaptation, 4, 131, 139 administrative, 5 advocacy, 103 AEP, 10 aggregation, 95, 136 algorithm, 15 alternative, 10, 32, 33, 34, 46, 47, 99, 103, 136 alternatives, 124 amalgam, 127, 128 American Educational Research Association, 145 analysis of variance, 63 antecedents, 37 application, 39, 40, 76, 80, 139 applied research, 117 argument, 42, 105 articulation, 90 assessment, xiii, 9, 95, 101, 117, 140 assumptions, 16, 33, 86, 88 attitudes, 7, 37, 112 attractors, 77, 78 availability, 11, 47, 53, 74

B base rate, 64 behavior, 18, 20, 75, 113, 124, 146 beliefs, 7, 33, 112, 121, 132, 147 beneficial effect, 8 benefits, 9, 50, 97, 98, 100, 103, 105, 112, 142 bias, 34 biological processes, 16 biomedical knowledge, 116 biomolecular, 17 borderline, 56 borrowing, 115 brain, 19, 142 brain damage, 142 brainstorming, 5 building blocks, 27

C candidates, 136 case study, 75, 140, 144 categorization, 118 category a, 56, 63, 85 category d, 85 causal relationship, 14, 18 causality, 14, 20 causation, 20, 106 childhood, 144

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Index

classes, 135 classical, 38 classification, 120, 131 classroom, 1, 2, 6, 7, 8, 33, 36, 47, 48, 96, 116, 120, 132, 139, 144, 145 classroom events, 2, 47, 145 classroom management, 6, 7, 132 classroom teacher, 8 classroom teachers, 8 clients, 112 clinician, 115, 116 Co, 147 codes, 63 coding, 57, 58, 60, 83, 94, 131 cognition, xiii, 1, 3, 4, 7, 10, 11, 13, 14, 17, 21, 24, 25, 36, 44, 45, 95, 97, 101, 107, 111, 116, 117, 118, 130, 135, 139, 140, 142, 143, 145, 149 cognitive activity, 11, 35, 82 cognitive function, 7, 13, 14, 16, 19, 51, 136 cognitive level, 90 cognitive load, 48, 77, 114, 147 cognitive models, 16, 20, 99, 141 cognitive performance, 11, 23, 25, 50, 54 cognitive perspective, 3, 10, 116, 118, 149 cognitive process, 3, 6, 9, 11, 12, 16, 19, 20, 23, 25, 31, 35, 44, 49, 53, 55, 81, 83, 97, 115, 123, 131, 132, 135, 142, 143, 149 cognitive processing, 19, 35, 142 cognitive psychology, 4, 29 cognitive research, xiii, 10, 38 cognitive science, 80, 101, 116, 118, 121, 122, 143, 149 cognitive system, 14 cognitive tool, 95, 143 coherence, 24, 42 collaboration, 7, 8, 9, 10, 11, 44, 101, 103, 104, 105, 108, 112, 113, 114, 118, 140, 141, 142, 143, 145, 147,148 communication, 7, 45, 108, 145, 147, 149 communities, 147 community, 132, 136 compatibility, 54 compensation, 54 competence, 21, 143

competency, 136, 139 competition, 108 complement, 99 complementarity, 96 complex systems, 39, 105, 139 complexity, 2, 16, 48, 56, 64, 73, 76, 79, 107, 112, 115, 122 components, 16, 21, 22, 23, 28, 39, 41, 42, 45, 57, 60, 62, 83, 89, 90, 104, 111, 119, 133, 136 composition, 105, 127, 129, 130, 131, 132 comprehension, 11, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 46, 47, 54, 62, 69, 72, 74, 76, 78, 94, 97, 135, 140, 142, 149 computer conferencing, 148 computing, 53, 81 concept map, 136 conceptualization, 121 conceptualizations, 10 concrete, 32, 47 conductive, 114 configuration, 40, 105 confirmation bias, 34 conflict, 8, 108, 109 confrontation, 114 connectivity, 99 consciousness, 143 consensus, 35, 109 constraints, 16, 17, 23, 39, 41, 43, 44, 45, 48, 49, 104, 108, 111, 116, 128, 133 construction, 26, 28, 30, 32, 38, 40, 124, 131, 137, 139, 147 constructivist, 21 contingency, 37, 56 control, 8, 30, 42, 46, 56, 57, 61, 62, 69, 71, 73, 78, 79, 83, 84, 86, 98, 106, 107, 137 convergence, 108 conversion, 41, 43 cooperative learning, 101 correlation, 20 correlations, 20 course content, 137 creative thinking, 32 cross-fertilization, 117 curriculum, 4, 8, 101, 132, 147

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Index

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D data analysis, 96 data collection, 95, 99 data set, 97, 123 decision making, 2, 10, 96, 116, 140 decision-making process, 122 decisions, 2, 5, 10, 33, 122, 146 declarative knowledge, 121, 125 decomposition, 19, 39, 41, 43, 45, 104 deduction, 32, 33, 76 deductive reasoning, 32 differentiation, 37, 90 discomfort, 49 discourse, 24, 26, 27, 29, 122, 141, 142, 149 discourse comprehension, 24, 26, 122 dissatisfaction, 3 distribution, 45 diversity, 4, 120 division, 14, 113 division of labor, 113 duration, 60, 129 dynamic environment, 33 dynamical systems, 106

E ecological, 99 education, 135, 140, 141, 142, 143, 145, 146, 147, 148 educational psychology, 143 educational settings, 99 educational system, 132 educators, 7, 8, 149 elaboration, 31, 34, 40, 42, 48, 50, 54, 61, 63, 69, 72, 73, 74, 75, 77, 79, 95, 97, 108, 110, 111, 113, 119, 125 electroencephalography, 19 elementary school, 144 emission, 19 emotional, 4, 38 encapsulated, 116 engagement, 104 environment, 21, 26, 33, 123, 137, 145

131

epistemological, 11, 135 equating, 75 ESL, 141 evolution, 21 execution, 9, 45, 71, 76, 79, 98, 107, 108, 119 executive processes, 9, 45 expected probability, 64 experimental design, 56, 97, 98 expert teacher, 3, 11, 47, 89, 123

F failure, 33, 34, 73 feedback, 46, 136 flexibility, 6, 136 fMRI, 19 free recall, 54 functional aspects, 112

G games, 41 gene, 94 general education, 137 general knowledge, 33 generalizations, 94 generation, 29, 31, 33, 39 goal setting, 76, 106 goal-directed, 31, 133 goals, 5, 9, 15, 21, 28, 30, 35, 36, 38, 43, 46, 48, 59, 60, 61, 72, 76, 77, 81, 88, 105, 108, 109, 119, 124, 125, 126, 128, 137 grain, 1, 2, 55 graph, 95, 119, 124, 125, 126, 127, 128, 129, 142 group interactions, 111 group processes, 9, 112, 113, 148 group work, 8, 104, 132 grouping, 1 groups, 10, 11, 23, 45, 55, 80, 94, 104, 105, 106, 107, 109, 112, 114, 139, 144, 147 growth, 147

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Index

H heterogeneous, 49, 79, 100 heuristic, 31, 40, 43 high school, 144, 148 human, 16, 23, 24, 37, 45, 75, 117, 122, 149 human cognition, 45, 75, 117, 122 human experience, 16 hybrid, 125 hypothesis, 33, 34, 38, 48, 59, 77, 107, 122, 129 hypothesis test, 33, 107 hypothetico-deductive, 48, 86

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I ICT, 7 identification, 7, 38, 47, 49, 110, 119, 144 idiosyncratic, 40 implementation, 5, 10, 15, 38, 44, 74, 111, 113 incentive, 73 inclusion, 7, 130 independence, 56, 78 indication, 73, 75, 76, 77, 86 indicators, 36 indices, 75 individual action, 109 individual differences, 8, 56, 96 induction, 32, 33, 76 inferences, 24, 28, 31, 33, 34, 39, 40, 50, 59, 76, 77, 142 information and communication technology (ICT), 7 information exchange, 19, 46, 80 information processing, 109, 119, 147, 149 information retrieval, 46, 80 infrastructure, 99 initial state, 38, 39, 126, 127 innovation, 11, 49, 99, 138, 144 instruction, 1, 4, 5, 7, 37, 48, 49, 54, 75, 80, 82, 91, 99, 101, 116, 118, 133, 137, 139, 140, 145, 147, 149 instructional activities, 100, 101, 140

instructional materials, 100 instructional planning, 3, 23 instructors, 136 instruments, 126, 129 integration, 9, 26, 28, 104, 114 integrity, 106 intelligence, 143, 148 intentions, 17, 44, 46, 106 interaction, 7, 8, 18, 20, 30, 49, 55, 82, 104, 105, 106, 121, 139, 146, 147 interactions, 17, 18, 19, 99, 106, 111, 114 interdependence, 104 interdisciplinary, 140 interface, 105 interpersonal relations, 148 interrelations, 14 interrelationships, 89 intervention, 1, 33, 35, 38, 59, 61, 63, 65, 67, 68, 69, 72, 74, 75, 76, 77, 78, 79, 82, 84, 86, 87, 88, 97, 125, 132 intrinsic, 73 inventories, 4 investigations, 103, 112 isolation, 97, 103, 133

J jury, 109 justification, 42

K knowledge acquisition, 6, 116, 117, 142 knowledge construction, 139, 147

L labor, 106, 111, 112 language, 29, 63, 143, 145, 149 law, 41 learners, 5, 9, 104, 122, 132, 137, 145 learning, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 19, 20, 21, 37, 49, 50, 82, 90, 101, 103, 104, 105,

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Index 112, 113, 114, 117, 122, 132, 135, 136, 137, 140, 141, 143, 144, 145, 146, 148, 149 learning difficulties, 145 learning outcomes, 6, 37, 104, 144 learning process, 136 learning task, 8 lesson plan, 3, 4, 6, 35, 49, 54, 55, 93, 124 lesson-planning, 146 life course, 106 likelihood, 56 limitations, 93, 94, 96, 99, 100, 124, 125 linear, 5, 56, 63, 97, 106 links, 1, 6, 9, 30, 31, 82, 94, 95, 111, 116, 120, 125, 131, 132, 137 location, 99, 129 long-term memory, 27, 29 low-level, 46

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M magnetic resonance imaging, 19 magnetoencephalography, 20 maintenance, 110 management, 5, 6, 7, 41, 83, 132 manipulation, 15, 32, 137 manners, 34 mapping, 136 marketing, 149 Markov process, 64, 75, 98 Markovian, 20 Marx, 5, 37, 95, 146 mathematical thinking, 148 mathematics, 145, 148 measures, 146 medical expertise, 116, 142, 145 medical school, 117 medicine, 4, 33, 34, 41, 100, 116, 122, 132, 137, 145 memory, 11, 26, 28, 29, 36, 74, 108, 124, 140 mental model, 24, 26, 28, 30, 32, 34, 39, 42, 107, 124 mental representation, 24, 27, 31 mental states, 13 mentor, 49, 114 mentoring, 114

133

messages, 20, 136 metamorphosis, 106 metaphor, 3, 115, 116 microstructure, 26, 27, 29 minority, 37 misleading, 76 modeling, 6, 7, 11, 13, 14, 15, 16, 17, 18, 19, 22, 44, 55, 57, 79, 80, 82, 83, 90, 95, 98, 99, 105, 118, 123, 130, 132, 135, 136, 139, 147, 149 models, 3, 4, 11, 16, 17, 20, 22, 24, 26, 28, 30, 32, 39, 42, 75, 95, 96, 98, 99, 101, 104, 108, 124, 140, 141, 143, 145, 149 modulation, 57, 111 modules, 14, 19 morphemes, 29 motivation, 6, 21, 103, 135 multiplicity, 118 multivariate, 63

N natural, 99 negative experiences, 104 negotiation, 54 network, 26, 106, 110, 111, 112, 124, 125, 126, 127, 129, 132, 133 nodes, 26, 126, 127, 128, 129, 131, 133 norms, 109

O observations, 56 omnibus, 63, 70 operator, 40 opposition, 49 optical, 20 overload, 77

P peers, 136 perception, 26 personality, 112

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134

Index

PET, 19 philosophy, 122 physicians, 33, 115, 116, 122, 124, 137 physics, 100 physiological, 21 plausibility, 33, 34, 59 play, 40, 112, 139 politics, 41 portfolio, 136 portfolios, 133 positron emission tomography, 19 power, 56, 108 practical knowledge, 119 prediction, 64 preference, 6 preservice teachers, 6 primitives, 18, 36, 95, 120, 132 prior knowledge, 9, 26, 28, 30, 39, 42, 59 private, 121 proactive, 96 probability, 43, 63, 66, 72, 78, 83, 85, 86 problem solving, 2, 11, 23, 24, 25, 30, 33, 38, 39, 41, 42, 43, 44, 45, 47, 49, 58, 66, 68, 70, 73, 74, 75, 76, 78, 79, 94, 98, 100, 103, 107, 109, 115, 117, 119, 122, 123, 124, 132, 141, 143, 144, 145, 148 problem space, 39, 40, 42, 107, 118 problem-based learning, 2, 117 problem-solving strategies, 124 problem-solving task, 44, 49, 123, 132 procedural knowledge, 47 production, 4, 8, 24, 95, 103, 124 productivity, 104 professional development, xiii, 8, 103, 140, 141 program, xiii, 12, 16, 56, 82, 93, 107, 135, 136, 137, 144 property, ix, 47, 128 proposition, 27, 34, 110, 120, 127, 128, 133 protocol, 96, 119, 126, 129, 131, 133 protocols, 19, 55, 82, 94, 123, 124, 131 psychological processes, 4 psychology, 141, 142, 143, 146, 148 pupil, 10, 31, 33, 75 pupils, 8

PVA, 56

R range, 4, 32, 95 reading, 28, 30, 54, 75, 82, 99, 101, 116, 140, 145, 146, 149 reality, 2, 31, 103, 144 reasoning skills, 49, 100, 101, 135, 137 recall, 47, 54 recognition, 116, 119 reflection, 9, 54, 117, 121, 136 reforms, 10 regulation, 44, 45, 87, 93, 104, 105, 106, 108, 109, 110, 140, 148, 149 relationship, 5, 8, 21, 23, 27, 44, 90, 109, 117, 131, 136, 142 relationships, 14, 19, 105, 111, 127, 131, 133 relevance, 19, 34 remediation, 125, 126 research and development, 139 resolution, 41, 48, 49, 109 resources, 44, 106, 108, 110, 112, 122, 132 responsibilities, 8 restructuring, 28 retention, 103 rubrics, 95, 101, 140

S sample, 53, 54, 65, 73, 75, 81, 82, 83, 90, 94, 96 satisfaction, 26 scaffolding, 3, 6, 133, 135, 136, 145 scaffolds, 135, 137 scarcity, 2, 73, 74, 116 schema, 29, 35, 36, 42, 50, 120, 128 schemas, 24, 26, 27, 28, 29, 36, 39, 40, 42, 48, 74, 118, 120, 121 school, 54, 117, 140, 144, 145, 146, 147, 148 scores, 64 scripts, 7, 10, 36, 46, 101, 111, 120, 121 search, 17, 32, 33, 34, 36, 39, 40, 42, 43 segmentation, 124, 131

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Index self-confidence, 6 self-reflection, 136 self-regulation, 45, 106, 140, 149 semantic, 31, 32, 120, 129, 133, 141 semantic information, 129, 133 sensitivity, 29 sentences, 27, 131 sequencing, 37, 50, 53, 60, 68, 79, 81, 94 series, xiii, 9, 14, 22, 34, 54, 55, 82, 83, 89, 93, 97, 140, 144 shape, 106 shares, 3, 33 sharing, 109, 112 short period, 6 short-term, 19, 37, 46, 48, 118 similarity, 111, 112 simulation, 56, 147 skills, 3, 6, 10, 49, 100, 101, 112, 133, 135, 137 social cognition, 44, 95, 97 social cognitive model, 18, 105, 149 social context, 104, 105 social environment, 21 social phenomena, 17 social sciences, 43 social support, 8 sociocultural, 18 sociological, 17 software, 132, 136, 137 special education, 4, 53, 82, 88, 90, 99 speech, 95, 99, 124 speed, 16 stages, 26, 32, 106 statistical analysis, 64, 124 statistics, 62, 63, 69, 76, 83, 84, 100 storage, 46, 80 strategies, 6, 15, 30, 38, 40, 41, 74, 80, 96, 100, 101, 121, 124, 126, 133, 135, 136, 138 strategy use, 94, 98 student characteristics, 132 student teacher, 3, 5, 7, 8, 10, 49, 53, 62, 67, 68, 69, 77, 82, 86, 87, 88, 90, 99, 100, 114, 133, 136, 146

135

students, 4, 5, 9, 10, 20, 37, 48, 49, 63, 67, 72, 90, 100, 113, 121, 130, 132, 136, 137, 145, 146, 147 substrates, 19 subtasks, 45, 112 subtraction, 143 surface structure, 27 symbolic, 15 symbols, 15, 29 symptom, 50 synchronization, 109 synergistic, 104 synthesis, 75, 120 system analysis, 118 systems, 21, 39, 45, 80, 98, 105, 107, 139, 140, 144

T tactics, 135 targets, 77 teach better, 3 teacher instruction, 49 teacher thinking, 101, 116, 117, 133, 140 teacher training, 7, 80, 90 teaching effectiveness, 72 teaching experience, 5, 120, 121 teaching process, 2, 10, 146 teaching strategies, 101 technology, 7, 100, 136 temporal, 28, 124, 125, 127, 128 testimony, 115 text analysis, 147 textbooks, 132 thinking, 5, 19, 99, 101, 116, 133, 137, 140, 141, 143, 145, 146, 148 threshold, 63 top-down, 26, 29, 46 tradition, 11 traditional model, 101 training, 7, 50, 60, 80, 82, 90, 104, 117, 137, 145 trajectory, 3, 149 transcript, 60, 123 transcription, 54, 123

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Index

transcripts, 60 transfer, 96, 103 transformation, 4, 15, 29, 31, 34, 39, 77 transition, 50, 53, 64, 75, 76, 77, 78, 81 transitions, 42, 63, 65, 66, 67, 68, 72, 77, 78, 86, 94, 97, 98 translation, 1 tutoring, 20, 21, 37, 80, 114, 136, 137, 139, 146, 148 two-way, 106 typology, 131

V validation, 32, 33, 94 validity, 99 values, 46, 64, 76, 106, 112 variables, 7, 106, 120 variance, 63 variation, 25 vein, 26, 47, 104 verbalizations, 141 visible, 98 vision, 20, 21

U W working memory, 108 written plans, 48

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uncertainty, 46 undergraduate, 100 units of analysis, 95, 96, 97, 136 updating, 30, 43, 145

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