Problem Solving Procedure in terms of Cognitive Theories
 9786057691064

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Current Studies in Educational Measurement and Evaluation

Editors Prof. Dr. Salih ÇEPNİ Assoc. Prof. Dr. Yılmaz KARA

Paradigma Akademi – August 2019

Current Studies in Educational Measurement and Evaluation Editors: Salih ÇEPNİ, Yılmaz KARA ISBN: 978-605-7691-06-4 Certificate Number: 32427 Printing House Certificate Number: 43370 The responsibility of each chapter belongs to its author(s). Paradigma Akademi Basın Yayın Dağıtım Fetvane Sokak No: 29/A ÇANAKKALE Tel: 0531 988 97 66 Layout: Fahri GÖKER [email protected] Typesetting: Gürkan ULU [email protected] Cover design: Gürkan ULU Printing House Address Ofis2005 Fotokopi ve Büro Makineleri San. Tic. Ltd. Şti. Davutpaşa Merkez Mah. YTÜ Kampüsiçi Güngören / Esenler İSTANBUL

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Paradigma Akademi – August 2019

Content

PREFACE ........................................................................................ V

Part I Problem Solving in Education Chapter 1 Problem Solving Procedure in terms of Cognitive Theories Salih ÇEPNİ & Yılmaz KARA Introduction ............................................................................................ 1 Cognitive Theories for Learning and Problem Solving ............................ 1 Human Cognitive Architecture ................................................................ 3 Cognitive Load Theory ......................................................................... 11 Cognitive Processes in Problem Solving................................................ 16 Conclusion ............................................................................................ 19 Chapter 2 Improving Item Validity through Modification in Terms of Test Accessibility Yılmaz KARA Introduction .......................................................................................... 25 Conceptual Understanding of Test Accessibility .................................... 26 Test Accessibility Model ....................................................................... 27 Item Modifications for Accessible Test Items: Theory to Practice.......... 31 Conclusion ............................................................................................ 36 Chapter 3 Traditional Measurement and Evaluation Tools in Mathematics Education Cemalettin YILDIZ Introduction .......................................................................................... 41 Verbal Exams ....................................................................................... 43 Long-answer Written Exams ................................................................. 46 Short-Answer Written Examinations ..................................................... 50 True-False Tests.................................................................................... 53 vii

Salih ÇEPNİ, Yılmaz KARA

Chapter 1 Problem Solving Procedure in terms of Cognitive Theories Salih ÇEPNİ & Yılmaz KARA

Introduction People live in nature as a social being. In order to live in a better environment with better conditions, it has been the goal of human beings to discover and learn the rules of nature. This situation required learning and research. Both in learning and research procedures, people try to overcome with the faced problems. In earlier times, people tried to solve problems in order to survive. They facilitated their life with the simple tools that they developed and made researches to unhide the mystery of nature. In today's complex and human interacted world, people try to make sense of the many faceted problems, seek for the necessary information leads to the solution and discover a solution to the problem. While doing all this, people make efforts with his human knowledge and cognition. In this section, the most accepted theories about human cognition will be introduced at first. Then, human cognitive structure and functioning will be revealed in the direction of theories. Finally, mechanism of human cognition will be explained in the process of problem solving. Cognitive Theories for Learning and Problem Solving The realization of effective learning and overcome the encountered problems in an easy manner depend on the clarification of the processes taking place in human cognition. Many theories have been put forward to explain the human cognition structure, functioning and problem-solving processes (Kala, 2012). The most frequently discussed cognitive theories by the researchers are presented in Table 1.1.

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Problem Solving Procedure in terms of Cognitive Theories

Table 1.1 Basic theories for human learning and problem solving Theory Dual Coding Limited Capacity Active Processing

Basic Approach Audio and visual information are processed in two distinct channels. Information that can be processed in cognitive processes is limited. Learners create meaningful mental presentations and models by operating the received information cognitive processes.

Dual Coding Theory The dual coding theory has been considered as a fundamental theoretical explanation for the representation of information in memory. The theory states that two coding systems exist or there are two ways of representing information in memory. These are “non-verbal mental imagery” and “verbal symbolic processing”. Visual and verbal coding can be done in the processing of the information. However, one of them is more dominant. The information in the learning environment perceived by the learner is symbolized and encoded and stored in memory through a conversion in visual or verbal symbols. The symbolisation operations which occurs in two ways as visual and verbal symbolization indicate that information is processed in two independent channels. One of these channels processes the non-verbal information such as visual presentation and the other processes verbal information such as spoken words and text. In this respect, it is stated that remembering the information received through both the eye and the ear is easier when compared with the information received through a single sensation (Moreno, 2017). Limited Capacity Theory The limited capacity theory is founded on the assumption that human shortterm memory has limits in executing information at a time. Short-term memory is limited in terms of time and data storing. The longer stay in short-term memory can be enabled through thinking on information, grouping information, and continuous repetition. The stay of data in the short-term memory is determined according to its necessity. It is essential to transmit the data to long-term memory for later use. In this case, the information is processed through repeating, coding and associating with the data in the long-term memory. In this respect, it is important to process information through dividing information into meaningful pieces, associating with each other or existing knowledge and by increasing interaction (Brydges, Gignac & Ecker, 2018). 2

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Active Processing Theory The active processing theory focuses on the processes in which learner constructs meaningful mental presentations and models through processing the received information in cognitive processes. The active processor explained with the cognitive processes such as attention, editing the received information, and integrating the new information to existing ones. The learners are active in the learning process, if they are aware of their own cognition and learning characteristics. It is emphasized that learners who are active processors should be accepted as individuals who can use executive cognitive strategies by carrying the awareness of knowledge rather than being passive receivers that receive and store as much information as possible. Five different processes were defined which can be used to create consistent mental structures: process, comparison, generalization, listing and classification. Learners can actively participate in the process by constructing their own information (Acuna et al., 2011). Human Cognitive Architecture Both cognitivists and behaviourists tried to explain the information processing through the regulation of human behaviour by environment. But unlike behaviourists, cognitivists claim that there is a variable between environment and behaviour. This variable is the memory of the learner. At first, memory was thought to be a mental function where information could be stored for a long time. But later studies have shown that memory is a more complex mental apparatus than simply storing information. In general terms, memory can be defined as the place to process and store the external stimuli. The information processing procedure focuses on two basic elements. The first is a collection of information structures consisting of three structures; sensory memory, short-term memory or working memory and long-term memory (Table 1.2). The second involves cognitive processes. These are intrinsic, mental actions and enable the transfer of knowledge from one structure to another (Sun, 2011). Table 1.2 Memory types of human cognition system Memory Sensory ShortTerm

Function Receive stimulus and processes instantly. It imposes meaning to the stimulus and combines the information units. It enables the learner to make sense through visual and spatial logic operations.

Capacity 3-7 digit 7-9 digit

Recall Time 0.5-3 second 5-15 second

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LongTerm

Provides permanent storage for different types of information.

Unlimited

Constant

Sensory Memory The individuals are exposed to dozens of stimulants at any time in their daily life. For example, in a laboratory environment, the sensory organs are constantly stimulated by elements such as the voice of students talking among themselves, the sound of the equipment working in the lab, the smell of chemicals, the smell of fragrance from students, coloured dress of students and so on. These instant messages received by our sensory organs are transmitted to the brain through our nervous system.

Figure 1.1 Multi-Memory Store Model (Takir, 2011). The capacity of sensory memory is unlimited, but the information that is received is lost very quickly if it is not processed immediately. Thus, a limited number of information is transferred to short-term memory from the unlimited stimulus to the sensory memory. Others disappear from sensory memory (Widrow & Aragon, 2013). Short-Term memory This part of the human cognition system is the place to hold several pieces of information in a related manner at the same time. It is the memory for the mind to execute information, making organizations to store and discard, relating one to another. It can also be described as part of the memory to transitory hold and manipulate the information during the execution of various cognitive processes. The short-term memory executes the information through its components (Figure 1.2). Central executive enables to direct attention on related information and 4

Salih ÇEPNİ, Yılmaz KARA

coordinates the cognitive operations. Phonological information is held and stored in phonological loop more than a few seconds. Visual and spatial information is executed through the visual-spatial pad. Episodic buffer is the component to retain combined episodes together and provides the interface among the entries which have various features. It is the base for conscious awareness that connect the compounds of short-term memory with long-term memory (Addis, Barense, & Duarte, 2015).

Figure 1.2 Cognitive Memory Model (Chen et al., 2016). Long term memory This type of memory is the storage for more persistent information. The knowledge and skills can be stored in here with an unlimited capacity. Some theorists claim that long-term memory is composed of two basic parts as episodic memory and semantic memory, while some theorists add procedural memory. The episodic memory is the part of personal life. It relates to a specific time, place and events. For example; the meal that eaten at dinner, the clothes that worn on a special day, the trip that enjoyed is in episodic memory. It is also referred as autobiographical memory. During our lives, all the events, jokes, rumours are stored in the episodic memory. Memories are learned without any effort. But memories tend to intermingle. Therefore, it is difficult to recall the information. However, important and traumatic events are remembered in detail. In addition, it is difficult to recall ordinary and repetitive events, because new events may disrupt the former. Semantic memory is the part where general information is stored such as generalizations, concepts, problem solving skills. Information is stored in semantic memory in both visual and verbally coded and interconnected 5

Problem Solving Procedure in terms of Cognitive Theories

networks. Semantic memory stores the information in propositional networks and schemas. Procedural memory is the basis for motor, cognitive or visuospatial skills. It stores the necessary information to execute a procedure such as walking, riding and driving a car (Wixted, 2018). Schema Formation Schema are considered as the cognitive structures that provide harmony between the cognitive commands triggered regarding the encountered situation and physical actions. Information elements are categorized according to the way they are used and stored in schemas in memory. Schema formation and use form the basis of cognitive expertise. One of the most important tasks of schemes is providing a process for the regulation and storage of information. Another task is to reduce the load of short-term memory. This is because, although the schemes are composed of numerous sub-elements, they cause less load than the processing of a large number of information units, which are independent of each other, because they are operated as a single unit in the short-term memory (van Kesteren et al., 2012). Automation The information and abilities are saved in long-term memory and executed reflecting to the encountered situation through the operations in short-term memory. If the cognitive operations are conducted repeatedly for the similar situation in each time, cognitive procedures gain automaton. In other words, continuously repeated operations for the familiar situations provide automation through requiring relatively less memory sources. Automation enable completely executing familiar cognitive tasks. Unfamiliar tasks still can be operated but require more cognitive sources. Formerly faced cognitive tasks can be executed without automation, but the operation is probably will be slow and require more time (Addis, Barense, & Duarte, 2015). Capacity of the Short-Term Memory The boundaries of the memory cannot be determined based on the amount of information returned after being sent to memory. Because if the individual keeps the information in his memory by making large groupings, then the amount of returning information will be too much. The memory is overloaded when more than seven new grouped information (chunk) are processed simultaneously in the short-term memory. As a result of his work Miller; the number of elements (chunk) in a young adult, in other words the width of the memory, is 6

Salih ÇEPNİ, Yılmaz KARA

approximately 7 ± 2. These elements can be numbers, letters, words and other units. Again, these elements can be a single element or a group of related information. Miller has done this measurement using a kind of memory (digitspan) test. Several numbers listed in this test is read and individual immediately asked to say what they remember (Kamiński, Brzezicka & Wróbel, 2011). Although the number of operational items is limited in short term memory, the complexity, level and size of the unit are not limited. The human brain can group a set of related information and operates it as a single unit. However, individuals can increase capacity by increasing the size of each unit. In short, this process (chunking) increases the limitation of short-term memory. For example; a 7 units number set such can become 4 units if grouped as “5 7 2 8 9 1 0” (Ejones, 2012). The short-term memory is also considered to have limits since the duration of the information is very short in here. According to the researchers, the duration is around 5 to 20 seconds, although it varies. The information remains longer in the short-term memory through thinking on information and repeating it. More remained data in the short-term memory is more possible to be transmitted to the long-term memory by repetition. Owing to the limited capacity of short-term memory, the unoperated or transmitted data will be lost very soon due to the force of new information. In summary, grouping related small pieces into large parts and mental repetition is required to keep more information in the short-term memory longer (Brydges, Gignac & Ecker, 2018). There are factors draw the boundaries of cognitive capacity. The capacity of short-term memory is different from one individual to another with respect to the operated cognitive tasks. Individual differences become apparent when the operated cognitive task require to use the cognitive sources at the limit of cognitive capacity. In addition, initial knowledge of the individuals plays important role in cognitive processes since the individual differences are effective on the availability of sorted schemas in the memory. Furthermore, cognitive organization abilities are different among individuals. Cognitive strategies can be learned to improve cognitive organization abilities. Thus, the boundaries of the cognition capacity can be broadened through leaning how to learn (Brydges, Gignac & Ecker, 2018).

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Cognitive Architecture Principles The natural selection and the human learning process are similar in natural environments. Living things fulfil their vital functions and survive through the genetic information that they have. Information that fulfils vital functions is stored in genes and transmitted over generations. Living in new or changing conditions requires differentiation of genetic information. Genetic information is used and transferred over generations if the differences in genetic material are appropriate for the organism to survive in a new or changing environment. Genetic differentiation cannot survive if it is not suitable for new or changing environment. This information cannot be passed on to new generations and disappear. The information changes are stored and disseminated in this way (Pickering & Clark, 2014). According to evolutionary perspective, knowledge can be derived from primary and secondary biological information. Primary biological information is gained through the generations that obtained as a result of activities such as the face recognition establishing social relations, speaking our native language and listening. This type of information can be gained unconsciously and without any effort. The opposite, secondary biological information, is acquired consciously and often requires a mental load. Almost everything taught in teaching-related institutes is secondary biological information. Reading and writing are also the examples of secondary biological information (Churchill & Fernando, 2014). Human cognition is characterized by five main principles managing the operations and functions (Sun, 2011). These principles are also valid for processes managing biological evolution and constitute the natural information processing system. Cognitive architecture principles are summarized in Table 1.3. Table 1.3 Cognitive Architecture Principles Principle Information store principle Borrowing and reorganizing principle Randomness as genesis Narrow limits of change Environmental organizing and linking principle

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Function Store data for a long time Enable constructing data storage Compose new data Entry of environmental data to the data storage Use data in data storage

Salih ÇEPNİ, Yılmaz KARA

The Information Store Principle According to the theory of evolution, the genetic material (DNA) that determines the activity of the organism in the surrounding environment contains large amounts of information. This genetic information must be large enough because the organism must survive in complex and information-rich environments. There is no consensus about the complexity or dimensions of the genetic material. The ability of living things to maintain their genetic function in such environments depends on their ability to keep large quantity of data. In the same way, humans need a structure that has the capacity to keep large quantity of data for the learning process. Otherwise, the learned information is quickly forgotten. In cognition system, the long-term memory meets these needs through saving the learned information (Schweickert, Fisher & Sung, 2012). The Borrowing and Reorganizing Principle Long-term memory is the cognitive component enable to save large amounts of data. A large quantity of data can be obtained both through the natural selection process of evolution and the borrowing and reorganization principle for the human learning process. The data that saved in long-term memory is mostly taken from other people in different ways. These are acquired by listening, reading or looking at visual materials. In this way, the information is obtained by listening to what others are saying, by reading what they write, or by studying the animations or visuals they put forward. Thus, the data is transferred from the long-term memory of others to our own long-term memory. This information is usually combined with the data existing in long-term memory and is reorganized. This transformation may have negative, neutral or positive effects. If the transformation has a negative effect, the data is then later transformed or discarded for meaningful learning to take place. If the conversion has a neutral or positive effect, it is going to be saved in long-term memory. In this way, the borrowed information is reorganized by combining the existing data in long-term memory and a new schema is created. Once the reorganization is finished, the validity of the extended schema must be tested. The validity of the information can only be determined after testing. However, this principle is incapable of explaining the emergence of new knowledge (Phillips, 2014). The Randomness as Genesis Principle In terms of the principle of borrowing and reorganization, data is transmitted from long-term memories of other people to our own long-term memory in different ways. According to this, new information cannot be created. For a new 9

Problem Solving Procedure in terms of Cognitive Theories

encountered problem, most of the solution steps needed to solve the problem will be based on data saved in long-term memory obtained by the principle of borrowing and reorganization. However, the student has no information about which of the possible solution steps will be applied to solve the problem. Under these conditions, one of the possible solution steps is applied randomly and the accuracy is tested for the solution of the problem. This is inevitable in the lack of information. Many students cannot reach the correct results many times when solving complex and new problems. It is understood that each possible solution step which does not reach the correct result is not suitable for the complete solution. The validity of the possible solution step is proved when the correct result is reached. According to this principle, the randomly generated solution steps and their validation can be shown as an example of the principle of randomness as genesis. So, new information is produced. The principle of borrowing and reorganization and the randomness as genesis principle work together. With the principle of randomness as generation, new information is formed, the generated information by the borrowing and reorganization principle is transferred to other people and stored in their long-term memory (Kaya, 2015). The Narrow Limits of Change Principle According to the principle of randomness as genesis, new data is obtained from the outer environment. Randomly produced data is not organized and therefore the information processing system has limitations to process unorganized information. For this reason, the number of information to be processed in processing systems should be keep in limits. Short-term memory is a component of human cognition system which used to make change in long-term memory and does not have the capacity to process large quantity of new data. Short-term memory cannot hold more than seven new unit and cannot process more than four unit. Knowledge and skills are derived from the large quantity of data held in long-term memory and are often borrowed from others. This principle requires that data should be well structured and schemas to be effectively created and transmitted to long-term memory to prevent over-load of short-term memory (Takır, 2011). The Environmental Organizing and Linking Principle This principle explain how information should be used in the learning environment. Since there are boundaries for the short-term memory, the processing of more than four units becomes difficult. If the information comes from long-term memory, in other words, if the information has already been 10

Salih ÇEPNİ, Yılmaz KARA

organized in long-term memory and its effectiveness has been tested, there is no known limitation in the processing of such information in the short-term memory. The principle of environmental organizing and linking emphasizes that large quantity of organized data can be transmitted from long-term memory to shortterm memory without exceeding the limitations of short-term memory in order to realize the complex actions required in the learning process. This principle is the last step of the cognitive data processing procedure which allows working in an environment. The first four principles allow the environmental organizing and linking principle to function in a learning environment. Without this principle, there would be no aim in the creation of new information through the principles of randomness as genesis and the narrow limits of change, the storage of new data through the principle of information store, or transfer of new data from other data stores through the principle of borrowing and reorganizing (Sussman & Hollander, 2015). Cognitive Load Theory This is a teaching theory based on how people construct knowledge in their cognitive structure. The theory argues that learning is optimized as long as it is compatible with the cognitive structure of human beings. The theory primarily focuses on cognitive processes and related in learning of intricate cognitive tasks due to the amount and interaction of knowledge that must be simultaneously processed before the beginning of learning (Sweller, Ayres, & Kalyuga, 2011). Cognitive load is described as a multifaceted construction that indicates the load that the student loads on his cognitive system while performing a task. It was defined that the cognitive load as the pressure on the student's own cognitive system when dealing with various tasks such as problem solving, graphic interpretation, and concept learning. Cognitive load refers to the resources used by short-term memory working in a certain time period. It can also be defined as the sum of the mental activities that must be performed at the same time in the short-term memory. According to the definitions, it is possible to conclude that the cognitive load is all the mental processes that happen in the short-term memory trying to process the information (Plass, Moreno & Brünken, 2010). The theory is based on assumptions that are closely related to cognitive construction and their functions. The main focus of the theory is short-term memory has limited capacity and learning, remembering and transferring will be reduced if there is an overloaded in short-term memory (Paas, Renkl, & Sweller, 2003). 11

Problem Solving Procedure in terms of Cognitive Theories

Types of Cognitive Load According to Cognitive Load Theory, there are three types of cognitive load as intrinsic load, extrinsic load (ineffective load) and germane load (effective load) (Unlu, 2015). Intrinsic Cognitive Load This load is formed on the short-term memory from the complexity of the content of the subject and is basically determined by the objectives of the teaching. The main source of intrinsic cognitive load is element interaction. Element interaction simply means the information arrangement in the short-term memory that must be used to enable the learner to achieve a given task. Some learning tasks have low element interaction. For example, knowing what words mean when learning a foreign language is an example of low element interaction. Because each word can be memorized independently of the others. But when a sentence tried to be created, the interaction of the item will increase. It is not only enough to know the meaning of words when establishing a sentence, but also the grammar and spelling rules. All these rules must be considered simultaneously in order to establish a correct sentence. This load is mainly identified by the knowledge and skills related to the teaching objectives. Designer of the learning procedure can control the intrinsic cognitive load (Kalyuga, 2009). It can be controlled by the designer of the instruction. Even though the intrinsic cognitive load from the teaching content cannot be directly modified (reduced), it is possible to manage complex tasks more easily in the form of a series of ordered tasks. Extraneous (Ineffective) Cognitive Load This is the load that any content on cognitive structure is not associated with learning objectives. The extraneous cognitive load plays an impeding role in learning as it unnecessarily utilizes the capacity of working memory. Including unrelated data or materials adversely affect the information processing procedure and lead to the increase in extraneous cognitive load. For example, if a visual and the necessary information to make this visual easier to understand is given separately, the extraneous cognitive load will increase. Instead, the information should be integrated into the relevant places of the image or the information should be presented as a voice narration because the short-term memory has verbal and visual sub-channels. In this way, the information will be shared among the sub-channels of the short-term memory and the cognitive load will be decreased. As understood from the example, designer of the educational environment can control the extraneous cognitive load. Therefore, visual, written 12

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text, voice narration, animations and simulations should be prepared appropriate to the learning objectives in terms of cognitive load theory in instructional design procedure (Kalyuga, 2015). Germane (Effective, Relevant) Cognitive Load This is the load that all kinds of teaching activities contribute to the learning objectives on cognitive structure. Teaching has two main objectives. First, students create new schemas. The second, teaching helps students to automate the newly acquired schemes. The operations such as interpretation, illustration, classification, deduction, differentiation and regulation are carried out during schema formation and automation. The performed operations will cause a load on the short-term memory. This load is a germane cognitive load since derived from activities that increase learning. For example, providing students with examples of the same structure but with different contents increases the germane cognitive load (Plass, Moreno & Brünken, 2010). Cognitive Overload Total cognitive load is composed of the combination of intrinsic, extraneous and germane cognitive load. In order to ensure effective teaching, the sum of these three types of load should not exceed the limited capacity of short-term memory. If the teaching program consists of a complex content, it means the intrinsic cognitive load is high. If the teaching program also includes design components that add extraneous cognitive load, it may lead to a small capacity remaining for the germane cognitive load. In this case, the teaching program will not be effective (Figure 1.3). As a result, acquiring the desired skills will take longer or more time for learners or learning will not be realized as expected level (Kaya, 2015).

Figure 1.3 The relationship between task demands, performance, and workload (Chen et al., 2016) 13

Problem Solving Procedure in terms of Cognitive Theories

The cognitive overload describes the situation of having more total cognitive load than the limited capacity of the short-term memory. In this case, effective learning does not take place. In here, effective learning means high performance without overloading the short-term memory capacity. In order to create effective learning, it is necessary to minimize the sources of extraneous cognitive load and maximize the sources of germane cognitive load. Although intrinsic cognitive load related to learning objectives cannot be controlled in general, content can be fragmented and sorted to optimize the required amount of interaction of the material component at any given time (Clark, Nguyen, & Sweller, 2006). Effects of the Cognitive Load Theory The explanations of cognitive load theorists on human cognitive structure and learning process highlight the cognitive effects. Studies on learning procedure and materials through considering the definition of cognitive effects, determining effects on learning, and cognitive principles have become possible through cognitive load theory. The cognitive effects that occur during the learning process are considered in accordance with the type of related cognitive load (Kalyuga, 2015; Uyulur, 2011). Extraneous Effects Worked-Example Effect: It may be useful to use the worked examples instead of the traditional problem-solving strategy. The practiced examples include a problem statement, solution steps, and the solution. The worked examples focus attention on problem situations and related processes (solution steps), helping students to create general solutions or schemes. Completion Effect: When attempting to solve a problem, referring to the worked examples requires to process the problem and the worked example in the short-term memory at the same moment. This causes overloading of the working memory. Alternatively, it is recommended to use problem completion samples. Split-Attention Effect: The presentation of multiple data that addresses the same perception channel of short-term memory causes distraction. This effect should be avoided since increasing the cognitive load. Modality Effect: If the information required to be handled through a channel exceeds the capacity of the channel, excessive cognitive load occurs. To prevent this, some of the data needs to be handled must be shifted to another empty channel. This is described as the modality effect. 14

Salih ÇEPNİ, Yılmaz KARA

Redundancy Effect: The presentation of data that does not conduce to schema formation or automation has a negative impact on learning. This is called as redundancy effect. Expertise Reversal Effect: Using effective teaching techniques may result the increase in expertise of novice learner but have impeding effects on expert learners. This situation is called the reversal effect in expertise. Guidance Fading Effect: Learners should be provided guidance in gaining expertise and schema construction. This guidance should be convenient to learners and specific to the objectives. Unnecessary guidance has negative effects. Goal-Free Effect: This type of problems is designed to decrease the irrelevant cognitive load caused by means-ends analysis and to support schema formation. Goal-free problems do not allow learners to discern differences between the present problem state and the target situation. Because, there is not any stated goal situation. Therefore, cognitive load will also decrease as there will be means-ends analysis. Learners must develop an alternative strategy to means-ends analysis while solving goal-free problems. Transient Information Effect: This effect can be defined as the occurrence of learning losses depending on the disappearance of the information before integrating it with the new information that will come before or after the information can be processed in an enough time period. It underlines that under certain circumstances transient information may interrupt learning. Intrinsic Effects Element interactivity Effect: If learning is related to a high element interactive material, it seems to exceed the limited capacity of short-term, memory. The effects of cognitive load are more difficult to see because the low element interactive material requires lower germane cognitive load. Isolated/interacting Effect: When the material is presented with all its interactive elements, it will not be processed in the memory as the capacity of the short-term memory will be exceeded. In such a case, interactive elements need to be taught as isolated and non-interacting elements for the realization of learning. In this way, primarily schemes related to items are formed. As soon as the sufficiently developed schemas are created, the 15

Problem Solving Procedure in terms of Cognitive Theories

interactive elements will be understandable because they will be able to be processed in the short-term memory. Germane Effects Variable Examples Effect: Modifying the variables in the example makes it easier to learn as it will influence the processing of similar samples in cognitive processes. Imagination Effect: Imagination requires cognitively review of the procedure in the short-term memory. For the materials including high cognitive load, processing data in short-term memory is impossible before the creation of schemas. Imagination techniques can be applied as soon as schemas are created. The application of imagination helps the schema automation. Cognitive Processes in Problem Solving Human nature interacts with its environment. The faced people, objects and events activate our cognitive system. Objects or changes are recognized, interpreted and reflected through cognition. The meaningful cognitive processes that we do can be considered as problem solving. The problem is solved by converting the given state to a target state. For this reason, a problem consists of given state, target state and cognitive processes that must be carried out to convert given state to the target state. The problem-solving process can be considered as the investigation of knowledge elements for the required for the solution in the problem space. As a result, the problem solution is finding the cognitive operations required to convert the given state to target state in the problem space (Robertson, 2017). While solving a problem, our cognitive system initiates set of algorithms. In other words, problem solver makes a search on problem space for operators for the solution of the problem. For this, problem solver chooses a state among active states. Then, an operator is chosen which is operable to the state. Later, the chosen operator is applied to the selected active state to produce new state. Finally, the new state is tested whether it is a target state for the solution. If there is a match between the new state and the target state, there is as success. If there is a mismatch, problem solver places the new state in active states. In any failure of this process, a subset of states is chosen among active states and the procedure is repeated until find a match between the new state and target state (Kiesewetter et al., 2013). 16

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In problem solving procedure, problem solver also can follow set of strategies. The problem-solving strategies can be learned and transferred into other problem situations. The transfer of problem-solving strategy requires of deducing solution rules. Problem solver can gain expertise through knowledge elements, cognitive operators, and cognitive problem-solving strategies which are deductible. Knowledge elements are effective on cognitive task domains. Problems can be examined in two groups according to their task domain (Allard, Verhaeghen, & Hertzog, 2014). Knowledge-lean task domains The problems desiring any specific training or initial knowledge are categorized in knowledge-lean task domain. In this domain, problem solver generally operates three types of strategy. In back up strategy, problem solver keeps the set of old states and choses one when necessary. Problem solver can follow proceed strategy through choosing the operator to operate current state, apply it and test the resulting state. Both backup and proceed strategy is considered as nondeterministic strategy since the followed procedure contain number of choice points but doesn’t specify any criteria to make selection. The strategy is called heuristic since setting criteria and narrowing the set of choices (Liu et al., 2012). Novice problem solvers generally use weak cognitive problem-solving methods. One of the most used weak methods is forward chaining method as proceed strategy. Procedure take start with the initial state. Then, an operator is selected among the possible ones through heuristic strategy. Last, the operator is applied and cognitive procedure repeats. In backwards chaining method, procedure is initiated with the final state. Next, the procedure continues with operation selection and application to the final state. Inversely applied operator produces a solution path from the final state to the initial state. In operator subgoaling method, problem solver selects the most possible operator but does not consider whether the operator is suitable for the current state. If the operator turns out since some operator preconditions are not met, a subgoal is formed to find a way to change the current state and used as the solution state. Analogy method enable problem solver to use the solution procedure for a problem to another problem (Montague et al., 2014). More experienced problem solvers tend to use weak methods in combined forms. In means-ends analysis, problem solver uses forward chaining and 17

Problem Solving Procedure in terms of Cognitive Theories

subgoaling method together. First, an operator is searched to decrease the disparity between target state and given state. Then, the subgoals are set up to provide a pathway to reach target state. So, the given state is compared to the target state and operators are chosen to reduce the difference (Díaz et al., 2015).

Figure 1.4 Performance and Task Demand (Chen et al., 2016). Through using cognitive problem-solving methods, problem solvers are not only expected to come with the solution but also, they are supposed to induce solution rules (Figure 1.4). Solution rules enable the problem solver to transfer successful algorithms to another problem-solving procedure. Even if the problem solver come with the solution and complete couples of problems by using cognitive problem-solving methods, they may not induce a solution rule. The rule induction requires to provide extra information and successfully solving corresponding problems to construct schemas. On the other hand, the weak cognitive problem-solving methods can be unsuccessful to solve the problem and problem solution can demand combined methods. But combined methods require more cognitive resources since demanding to complete cognitive steps such as focusing attention on features of the problem, choosing the right operator and accomplishing subgoals. In other words, the more cognitive operations and considering the proceed of the method increases the cognitive load. The high cognitive load also occupies the space that can be used to learn important features of the problem. Thus, the problem solver can fail to solve problem since lack of

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Salih ÇEPNİ, Yılmaz KARA

schema acquisition and high cognitive load even executing the cognitive problem-solving methods (Kiesewetter et al., 2016; Díaz et al., 2015). Knowledge-rich task domains This domain demand specific knowledge for the problem solution as a prerequisite. The most of the knowledge peculiar to the domain can be categorised in conceptual and procedural. The conceptual knowledge is the information about the concepts and principles of the related domain such as genotype in biology, reaction in chemistry, or gravity in physics. The knowledge about the steps to successfully complete a task can be described as procedural knowledge. A problem solver should have developed a schema including both conceptual and procedural knowledge to solve the problem from knowledge-rich domain. In other words, problem solver should develop enough expertise on specific domain. Once the schema is formed including the pre-required knowledge of the domain, problem solver can use it for the similar problems (Kurniati & Annizar, 2017). In this domain, problem solving take start with the activation of prerequired domain specific knowledge. This require short term memory to searching a schema related to pre-required conceptual and procedural knowledge in the longterm memory which is suitable for the features of the problem. Then short-term memory also choice an operator among the domain specific ones and apply it to the given state to produce a problem solution. This means extra cognitive load for the memory and potential failure of the problem solver to come with the solution (Schilling, 2017). The domain specific knowledge brings extra complexity in problem solving since require to know as much as experience with the domain specific principles, concepts, and interactions among them in addition to how to use information to produce solution. Problem solver is expected to seek for a proper schema in long term memory and fill the domain specific parameters in the problem. The features of the domain specific problem are the determiner for domain specific knowledge, operator and the schema to activate. Thus, problem construction process becomes prominent because the demand on domain specific knowledge, operator and schema construction as pre-requirement (Decker, & Roberts, 2015). Conclusion In today's education system, learners are asked to solve problems starting from early ages. Learners are evaluated as successful or unsuccessful according to their 19

Problem Solving Procedure in terms of Cognitive Theories

problem-solving situations. In fact, interests, attitudes, skills and abilities of individuals are decided according to the results of the evaluation and serious decisions are making such as assigning to the next level education, defining the school type, deciding the occupation. It is necessary to develop cognition and put in to work in order to success all these cases. Many theories have been put forward to explain the complex nature of human cognition. When cognitive theories are examined, it is understood that problem solving is a complex process and cognitive structures must be effective in this process. Individuals who are aware of their cognitive structures, develop experiences and make practice, have the potential to be successful in problem solving processes. The individual who is not aware of the cognitive structures fails because of problem misunderstanding, lack of the necessary pre-structures for the solution, inability to choose cognitive algorithms and lack of enough problem-solving experience. The cognitive approach of the problem-solving process requires the introduction of learning experiences that will enable the learner to become aware of the cognitive structures and procedure. This does not mean that learners should meet with routine problem-solving situations as much as possible. In the conducted studies, it was reported that the learners did not develop the desired level of cognitive skills even after continuous problem-solving practices and had difficulty in applying the acquired knowledge to similar problem situations. Therefore, learning should be designed by taking into account the cognitive structures, operations and principles. In addition to teaching activities, cognitive principles should also be taken into consideration when designing problems especially used in evaluation processes.

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References Acuna, S. R., Garcia Rodicio, H. & Sanchez, E. (2011). Fostering Active Processing of Instructional Explanations of Learners with High and Low Prior Knowledge. European Journal of Psychology of Education, 26(4), 435-452. Addis, D. R., Barense, M., & Duarte, A. (2015). The Wiley handbook on the cognitive neuroscience of memory. Oxford, UK: Wiley Blackwell. Allard, E., Verhaeghen, P., & Hertzog, C. (2014). The Oxford handbook of emotion, social cognition, and problem solving in adulthood. New York: Oxford University Press. Brydges, C. R., Gignac, G. E., Ecker, U.K.H. (2018). Working memory capacity, short-term memory capacity, and the continued influence effect: A latentvariable analysis. Intelligence, 69, 117-122. Chen, F., Zhou, J., Wang, Y., Yu, K., Arshad, S. Z., Khawaji, A., Conway, D. (2016). Robust Multimodal Cognitive Load Measurement (Human– Computer Interaction Series). Cham: Springer International Publishing. Churchill, A., & Fernando, W. (2014). An evolutionary cognitive architecture made of a bag of networks. Evolutionary Intelligence, 7(3), 169-182. Clark, R., Nguyen, F., & Sweller, J. (2006). Efficiency in learning: Evidencebased guidelines to manage cognitive load. San Francisco: Pfeiffer. Decker, S., & Roberts, A. (2015). Specific cognitive predictors of early math problem solving. Psychology in the Schools, 52(5), 477-488. Díaz, Córdova, Cañete, Palominos, Cifuentes, & Rivas. (2015). Inter-channel Correlation in the EEG Activity During a Cognitive Problem-Solving Task with an Increasing Difficulty Questions Progression. Procedia Computer Science, 55, 1420-1425. Ejones, G. (2012). Why chunking should be considered as an explanation for developmental change before short-term memory capacity and processing speed. Frontiers in Psychology, 3, Article 167. Kala, N. (2012). The effect of instructional design prepared on thermodynamics unit by using Cognitive Load Theory on chemistry students’ learning at

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retention and transfer level. Unpublished Doctoral Dissertation. Trabzon: Karadeniz Technical University. Kalyuga, S. (2009). Cognitive Load Factors in Instructional Design for Advanced Learners. New York: Nova Science. Kalyuga, S. (2015). Instructional Guidance: A Cognitive Load Perspective. Charlotte: Information Age Publishing. Kamiński, J., Brzezicka, A, & Wróbel, A. (2011). Short-term memory capacity (7 ± 2) predicted by theta to gamma cycle length ratio. Neurobiology of Learning and Memory, 95(1), 19-23. Kaya, E. (2015). Determining the effectiveness of technology supported guided materials based on cognitive load theory principles related to "solar system and beyond: Space Puzzle" unit. Unpublished Doctoral Dissertation. Trabzon: Karadeniz Technical University. Kiesewetter, J., Ebersbach, R., Görlitz, A., Holzer, M., Fischer, M., & Schmidmaier, R. (2013). Cognitive Problem-Solving Patterns of Medical Students Correlate with Success in Diagnostic Case Solutions. PLoS One, 8(8), 1-8 E71486. Kiesewetter, J., Ebersbach, R., Tsalas, N., Holzer, M., Schmidmaier, R., & Fischer, M. (2016). Knowledge is not enough to solve the problems - The role of diagnostic knowledge in clinical reasoning activities. BMC Medical Education, 16(1), 1-8. Kurniati, D., & Annizar, A. (2017). The Analysis of Students' Cognitive ProblemSolving Skill in Solving PISA Standard-Based Test Item. Advanced Science Letters, 23(2), 776-780. Liu, C., Liu, J., Cole, M., Belkin, N. J., & Zhang, X. (2012). Task difficulty and domain knowledge effects on information search behaviors. Proceedings of the American Society for Information Science and Technology, 49(1), 1-10. Montague, M., Krawec, J., Enders, C., & Dietz, S. (2014). The Effects of Cognitive Strategy Instruction on Math Problem Solving of Middle-School Students of Varying Ability. Journal of Educational Psychology, 106(2), 469-481.

22

Salih ÇEPNİ, Yılmaz KARA

Moreno, O. A. (2017). Attention and Dual Coding Theory: An Interaction Model Using Subtitles as a Paradigm. Doctoral Dissertation. Barcelona: Universitat Autònoma De Barcelona. Paas, F., Renkl, A. & Sweller, J. (2003). Cognitive load theory and instructional design: Recent developments. Educational Psychologist 38(1), 1–4. Phillips, S. (2014). Analogy, cognitive architecture and universal construction: A tale of two systematicities. PloS One, 9(2), E89152. Pickering, M. J. & Clark, A. (2014). Getting ahead: Forward models and their place in cognitive architecture. Trends in Cognitive Sciences, 18(9), 451456. Plass, J. L., Moreno, R., & Brünken, R. (2010). Cognitive Load Theory. New York: Cambridge University Press. Robertson, S. I. (2017). Problem solving: Perspectives from cognition and neuroscience (Second ed.). New York: Routledge. Schilling, J. (2017). In Respect to the Cognitive Load Theory: Adjusting Instructional Guidance with Student Expertise. Journal of Allied Health, 46(1), E25-E30. Schweickert, R., Fisher, D. L., & Sung, K. (2012). Discovering cognitive architecture by selectively influencing mental processes. New Jersey: World Scientific. Sun, R. (2011). Memory systems within a cognitive architecture. New Ideas in Psychology, 30(2), 227-240. Sussman, A., & Hollander, J. (2015). Cognitive architecture: Designing for how we respond to the built environment (Online access with DDA: Askews (Architecture). New York: Routledge. Sweller, J., Ayres, P., & Kalyuga, S. (2011). Cognitive Load Theory (Vol. 1, Explorations in the Learning Sciences, Instructional Systems and Performance Technologies). New York, NY: Springer New York. Takir, A. (2011). The effect of an instruction designed by cognitive load theory principles on 7th grade students‟ achievement in algebra topics and cognitive load. Unpublished Doctoral Dissertation. Ankara: Middle East Technical University. 23

Problem Solving Procedure in terms of Cognitive Theories

Unlu, M. (2015). The investigation of studying and learning strategy based online activities in terms of achievement, retention and cognitive load. Unpublished Doctoral Dissertation. Ankara: Gazi University. Uyulur, A. (2011). Evaluation of the efficiency of learning environments: A cognitive load approach. Unpublished Master Dissertation. Istanbul: Bahcesehir University. van Kesteren M.T., Ruiter, D. J., Fernández, G., Henson, R. N. (2012). How schema and novelty augment memory formation. Trends in Neurosciences, 35(4), 211-219. Widrow, B., & Aragon, J. (2013). Cognitive memory. Neural Networks: The Official Journal of the International Neural Network Society, 41, 3-14. Wixted, J. T. (2018). Stevens' Handbook of Experimental Psychology and Cognitive Neuroscience, Learning and Memory. Newark: John Wiley & Sons, Incorporated.

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