Vitalizing arithmetic in the second grade through integration with the social studies program

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VITALIZING ARITHMETIC IN THE SECOND GRADE THROUGH INTEGRATION WITH THE SOCIAL STUDIES PROGRAM

A Project Presented to the Faculty of the School of Education The University of Southern California

In Partial Fulfillment of the Requirements for the Degree Master of Science In Education

fey Marie Parmelee August

1950

UMI Number: EP46510

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T h is project report, w ritte n under the direction of the candidate’s adviser an d app ro ved by him , has been presented to and accepted by the F a c u lty of the School o f E d u catio n in p a r t ia l fu lf illm e n t of the requirements f o r the degree

of M a s t e r of

Science in E ducation.

A d v is e r

P* 7-

13 Temperature.

Children in grade two will find

It necessary to be able to read the thermometer in school and at home., since situations will arise when this inform' ation is required in their activities. Different types of thermometers used by children will make the reading of degrees on a thermometer ingful.

mean­

They will be curious in learning how the mer~-

cury rises and falls and why this occurs.

A discussion

of healthful temperatures for their homes should prove interesting and vital. Linear measure.

Second grade children will

have a need to use Inches, feet, and yards in order to measure height, length, and width of the things they decide to construct.

To do this, they will have to use

a ruler, yardstick, or tapeline.

Many children will

understand the length of half inches and quarter inches. From experience in using a yardstick, some students will know that there are thirty-six inches in one yard, three twelve-inch rulers in one yardstick, and twelve inches \

in one foot. Time.

When many children finish the second

grade, they are able to tell the time when school starts and when it is dismissed.

They may also know lunch time

and recess time.

Some children will be able to tell

time to quarter hours.

They will know that the long

hand is the minute hand and that the short one is the hour hand.

They will have had opportunities to plan and

schedule excursions.

The time of leaving, length of

traveling time, length of time remaining at the place visited, necessary leaving time, and the length of time required to return back to school are some of the time concepts developed. Children in the second grade are interested in the calendar, especially in the dates of their own birthdays and some of the holidays.

Most of the child­

ren will know that there are twelve months in a year and that there are seven days in a week.

A classroom

calendar kept daily and marked by the children makes the study of the calendar more meaningful. Prom participation in the events of the day second graders will develop an understanding of the sequence of activity peculiar to the morning, lunch time, afternoon, and evening.

Also, from group living,

they will learn the concept of being on time. Speed.

If children are to have an intelligent

understanding of their environment, the need to develop an understanding of speed is evident.

When riding in

the school bus, they will note that they travel at a certain speed.

When riding in the family car, they will

ride at still another speed.

From observing the move­

ment of street cars, fire engines, and trucks, they will note that each travels at different rates of speed. There are many opportunities available to help child­ ren develop concepts of speed. Capacity.

Second grade children will find op­

portunity to use cup, pint, and quart measures in their daily living activities, as well as in their playhouses. Ice cream cartons in pint and quart sizes have meaning to-them.

Milk cartons in pint, quart, half-gallon,

and half-pint sizes brought into the classroom will develop concepts of these capacities.

Through the

use of these cartons many.will find that there are two pints in a quart and that there' are four quarts in a gallon.

Halves, quarters, and thirds concepts

can be developed through the use of measuring cups in their play activities. Weight.

The need for second graders to de­

velop weight concepts is necessary because it is re­ quired in many experiences in their living.

Children

should understand the terms pound, ounces, and ton.

16

They should be able to choose a quarter pound of butter, a half pound of butter, and a pound of butter.

Some will

realize that there are sixteen ounces in a pound and that there are eight ounces in a half a pound. An opportunity should be given children to have various types of scales available in the classroom that they can actually use.

This would give meaning to the

situation. Number measures.

Prom experiences at home and

at school, second graders will know that there are twelve eggs in a dozen and six eggs in a half dozen.

They will

also know that a pair of shoes or a pair of gloves means two of the same kind. III.

TO DEVELOP UNDERSTANDING OF NUMBER

The purpose of this section of the project is to state the types of number processes that children will have need for in their activities.

The experiences

necessary to help meet that need are also presented. Counting.

As children use numbers to one

hundred, the idea of place value in numbers should be developed.

They will have need to read and write

numbers in their daily activities.

Counting can be made meaningful by the use of objects.

Just counting by rote memory does not indicate

that meaning is present.

The placing of objects in

groups of fives and tens makes counting by those numbers meaningful. Interpreting numbers by means of an abacus is helpful to make number facts more easily understood. The o n e ’s, ten's and hundred's places can be discussed. Second grade youngsters will have a need to understand the ordinals through tenth. Reading and writing numbers.

Second grade

children are usually interested in large numbers and the need for using these numbers may exist for some of them.-

To be able to write their house numbers may be

a felt need by some.

Others may be interested in read­

ing the license plate numbers on their cars. Ideas of fractions.

Children in the second

grade use fractions in many ways.

They may divide things

into halves, thirds, and fourths.

They may find through

experiences with objects that there are two halves in a whole, three thirds in a whole.

Experience will also

show them that a pint is half of a quart, a foot is a third of a yard, and six inches is half a foot.

Addition and subtraction combinations♦

The

combinations through six are within the ability of most second graders and are the numbers that affect their daily living experiences. "Twenty-five families are listed.

A family con­

sists of four (in case of the doubles, two) related 4 combinations." The major part of a second grade class will not progress beyond the fourteenth family.

4. 8 -4

6.

54 +4

8

7

6 -I

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1 i7

California State Department of Education, op. cit. p. 34.

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9

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24.

25-

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47

7

7

3

Children will be helped to understand and use the terms plus, sum, remainder, differences, and minus.

They

will be shown the relation between subtraction and addition.

21

Column addition Is presented to second graders after they have discovered three or more groups within a larger group. top downward.

They will be taught to add from the Second graders will also have need to

add and subtract ten and hundreds in functional situ­ ations .

i

CHAPTER I I I

ACHIEVING NUMBER OBJECTIVES IN A SECOND GRADE SOCIAL STUDIES PROGRAM The needs of children in the area of arithmetic and the opportunities for purposeful activltes in the social studies program have been discussed.

It is the

purpose of this chapter to show how arithmetic and the social studies can be integrated to vitalize the study of arithmetic. Care must be taken in the organization of an arithmetic activity program that all needed number ex­ periences for second graders will be covered.

Teachers

need to realize that guidance and planning are neces­ sary if this program is to meet the needs of their students.

A richly planned environment by the teacher

will do much to stimulate interest in meaningful act­ ivity.

The program cannot be left to chance.

Children

may not feel the need for the desired activity on just their own direction. Students need careful guidance.

For teachers '

to know the needs, interests, and capacities of each student is of prime importance.

A chart or notebook

kept on daily progress and further needs is also

23 essential if the teacher is to do a successful job in planning her work. Activities in a social studies program will pre­ sent opportunities to

develop the objectives in a vital

arithmetic program for children in the second grade. I.

TO DEVELOP A MEANINGFUL QUANTITATIVE VOCABULARY

To develop a meaningful vocabulary.

There are

many activities for teachers of second graders to use in stimulating the desire in youngsters to acquire a meaningful vocabulary.

The social studies program has

many opportunities for purposeful activities that will present second graders with experience that will make their arithmetic vocabulary meaningful to them. The childhood urge to satisfy curiosity is met in the farm unit.

This urge presents many possibili­

ties for developing a meaningful number vocabulary of comparison.

Children's interest in farm animals and

the activities of the farm produce many questions. The following are typical of those asked by second grade children.

The words underlined in the answers

are words found in the vocabulary list on pages 9-11 of this study that might come out of discussing the questions.

24 1.

How often does the farmer feed the chickens? The farmer always feeds all the chickens after he eats a very big breakfast and again before he eats supper at six.

2.

How often do chickens lay eggs? Most of the time chickens lay only a single egg each day.

3*

How often does the farmer milk his cows? 'The farmer always milks his cows twice every day in the same stalls.

Children’s questions are endless because of their interest in the study of the farm unit.

It is not dif­

ficult to develop an understanding of the vocabulary ofcomparison when the environment possibilities.

is so rich with

However, an accurate record of the com­

parative words used by each child must be kept by the teacher. The excursion to the farm is one of the best means of stimulating interest and will give many op­ portunities for vocabulary development.

The discus­

sion of the group concerning its desire to visit, the planning of the visit, and the actual observations to be made at the farm are rich with possibilities.

25 Dramatic play has endless possibilities for the development of a meaningful vocabulary of comparisons. The following experience is an example of the numerous possibilities of imitation of the farm and its activ­ ities : A farmer rises at 5=30 in the morning to milk his cows.

He hoses off the six cows.

He then

takes his stool and four sterilized pails and milks the cows, weighs the foaming milk, and then takes it to the milk house. Before children can play this situation, many concepts will have been acquired.

By observation of

the play activities, the teacher can discover incor­ rect concepts and the need for further understanding. II.

TO DEVELOP AN UNDERSTANDING OP MEASURES

Linear measure is needed by second graders in their construction activities.

Children of this grade

level always want a red barn for their farm.

In con­

sidering the needs for using linear measurement in constructing the barn alone, one realizes that there are many possibilities.

The children on the "barn

committee" will have to decide on the height, length,

and width that they wish their barn to be.

Having de­

cided to build one four feet long, they will understand that they can use four twelve-inch rulers or one yard­ stick plus one twelve-inch ruler.

To make it three

feet high they will learn that they can use one yard­ stick, three rulers of twelve inches each or thirty-six inches.

To make the barn two feet wide, they will ac­

quire the concepts that twenty-four inches

or two

twelve-inch rulers, are the same as two feet. To construct the sections that are found inside of most barns requires the use of smaller sized lumber. Children will find for the mangers that they will need wood ten inches long and six inches wide.

They may

decide to make the stalls fourteen inches high and three inches wide.

To make the ladder to be used in

getting up to the hay mow, in dramatic play, they will need lumber one-quarter inch wide, one-half inch thick, and twenty-four inches long.

After the children have

measured and sawed their needed lumber to the correct size, they will then need to choose the right nails. For the main part of the barn, they will need six penny box nails.

To make the mangers and stalls will require

four penny box nails, and for the real small pieces two penny lath blue nails are needed.

When the child­

ren are ready to paint their barn, they will find that

a brush about two Inches wide will be the best one to use.

Paint will be available in half-pint cans, pint

cans, quart cans, and gallon cans.

They may find that

a pint is not enough paint, but that a quart can of paint is more than they need. The construction of the barn is only one of the many activities they may experience.

Second graders

will want to build a farm-house, make furniture for the house, pig pens, chicken houses, farm implements, trucks, and wagons.

To construct each object requires

the understanding of measurement. The planting of the garden gives many oppor­ tunities to develop the understanding of measurement. The length of the garden, the amount of space to be allotted>to each vegetable, the depth required of the furrows in which the seeds are planted, and the width between the rows are questions which will need to be answered.

The children may use the yardstick or a

tapeline with which to answer their questions. Time. .Time concepts can be developed in con­ junction with the excursion. can

The date of the event

be checked or circled on the calendar and the

number of days to expire before the trip should be noted.

28 The concepts of today, yesterday, and tomorrow can be easily developed by watching the calendar days pass before the trip is to be made. Clocks made from paper plates with movable tag board hands fastened in the center with brads and placed on a bulletin board are of interest to second graders. Captions written on tag board and placed under the charts give more meaning to the study.

If the chart

is constructed with pockets, other captions can be used on the same chart to illustrate other concepts. 'Opportunities are available to study the seasons in the farm unit.

Learning the duties of the farmer

and his wife during the four seasons is always inter­ esting to children.

They are also interested in the

crops that grow at various times of the year on a farm. Capacity.

Capacity concepts are developed in

situations in which food is needed.

The preparation

and planning of a party offer endless opportunities to use measures of capacity.

In making ice cream and

cookies, the children will need to use one-half cup, cup, pint, and quart measurements. tablespoons will also be used.

Teaspoons and

For making ice cream

one pint of cream may be needed for each two quarts of milk.

The pupils will observe that a two quart

29 ice cream freezer makes one-half gallon of ice cream. Weight.

Weight concepts will be learned from

observing that on the excursion to the farm they saw that the milk was poured into pails to be weighed and a record was kept of the weight.

From this experience

will come the knowledge that there are different kinds of scales. Dramatic play offers the children opportunities to use classroom scales to meet needed opportunities for concept building.

From experience in using the

scales3 children will know that one pound equals six­ teen ounces and that eight ounces is the same weight as one-half of a pound. Money.

Money *concepts are developed through

the use of real coins

in the classroom.

Children will

enjoy making a fruit and vegetable stand to have in front of their farm house from which they may sell their clay produce.

Captions using dollars and cents signs

may be made to advertise the selling price of their wares.

Eggs can also be sold by the dozen and half

dozen.

Some second graders may understand that one

half-dozen will cost one-half as much as a dozen. Temperature.

Temperature concepts are developed

30

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FIGURE I DEVELOPMENT OF TEMPERATURE CONCEPTS

20

Alilk Cooled a .g a .in

by giving the students opportunities to read real thermometers and by using thermometers made on tag board with colored tapes that can be moved to the de­ sired temperatures. III.

TO DEVELOP NUMBER UNDERSTANDING

Counting.

Counting concepts can be developed in

many situations in the farm study.

On the visit to the

farm children will be interested in counting the baby chicks, the different kinds of animals, the piglets, and the different kinds of fruit and vegetables they saw growing on the farm. When they return to school, they will be inter­ ested in making some of the things they saw out of clay. Their interest can be stimulated in counting by having objects in an interesting environment.

The following

may be an example. Mary has twenty-two pigs in her pens.

By

selling ten to Bob, ten to Bill, and two to John she will have none left. In counting the pigs that she sold, it should be pointed out that ten for one child, ten for another child, and two more make twenty-two.

The number written on the

board should be discussed.

It is necessary to call the

group's attention to the fact that the tens number is placed to the right of the ones column.

On another

occasion, the children may find a box of clay apples and ask, "How many apples are in the bcx;?"

Six. child­

ren can then volunteer to each pick out ten apples. They establish that seven are left.

After several turns

at counting by the children, the teacher may write six­ ty-seven on the board.

They will, through counting

experiences, understand that six children have ten, so sixty is six tens and the seven additional ones make sixty-seven.

The next morning the teacher may

prepare sixty-seven paper apples which could be placed in a chart made from tag board.

When the children would

enter the room, they would be interested in the chart. Various groupings of these apples by the children and counting and combining the groups will give children the opportunity to participate in meaningful counting activities. These games should be continued until the pupils' needs for counting— to two hundred for some— have been met.

When it is necessary

for them to understand the

hundred concept, tag board charts are helpful to make the concepts more readily understood.

A chart containing

33

C an y o u p u t. th e apples in t h e

______________ riqVix pocKet P_______

rn

Ones

Tens

FIGURE 2 DEVELOPMENT OF NUMBER CONCEPT

34

How m a n y eggs did +he fa r m e r ^

chicKens lay ?

--------

y H u n d re d s

Tens,

FIGURE 3 DEVELOPMENT OF NUMBER CONCEPT

°

O nes

" 'I

three pockets, a place for one, tens, and hundreds, is of interest to children.

By changing the captions and

objects in these charts, children's interests will con­ tinue until the correct concepts have been developed. Addition and subtraction combinations.

Addition

and subtraction combinations are needed by most second graders through six.

These combinations will be pre­

sented by families.'*'

From children's experiences in

the grouping of objects, they will discover group rela­ tionships.

Each family of combinations can be devel­

oped meaningfully through dramatic play, needed clay construction, and the planting of a class garden.

There

are endless possibilities to present the materials in a meaningful way.

It must be remembered that it is

necessary for the teacher to stimulate and call stu­ dents' attention to these facts in an interesting ap­ proach.

She also has need to keep an accurate record

of the material covered, and know the needs that still exist.

The following experiences during dramatic play

in the fruit stand will illustrate how needed concepts in arithmetic and subtraction can be developed:

1 California State Department of Education, o p . cit., p. 3^*

36

How many apples can yoa pick?

fi w

FIGURE 4 ADDITION AND SUBTRACTION COMBINATION PRACTICE

5 °%BrSA 4#£>

38

Canyoa hitch the hordes to the wagon? — wmm wmm —

m m m m w m w ^m s m m w w m m m ...■ h .i m

FIGURE 6 ADDITION AND SUBTRACTION COMBINATION PRACTICE

■_ .—

m i . i—

—

39

Can you h e lp th e f a r m e r deliver his mi IK ?

FIGURE 7 ADDITION AND SUBTRACTION COMBINATION PRACTICE

Bill had seven dozen eggs to sell. one dozen, so six were left.

Mary bought

She returned home

and decided that she didn't want the one dozen eggs, so she returned them.

Now Bill has seven

dozen eggs again.

A visitor from the city

bought six dozen.

Bill now sees that he had

only one dozen left.

The eggs are gathered

and the hired man brings Bill six dozen eggs, so he understands that he has seven dozen boxes again. During the evaluation period of the social studies the teacher should ask Bill to tell his number story to the group.

While he is talking and illustrating with

his egg cartons, the teacher should write the numbers he talks about on the board. be 7-1 - 6,

64-1 = 7 ,

In this case it would

7-6 = 1 , and 14-6 = 7 .

The remaining groups of combinations can be developed in the same way.

The teacher may plan for

the same combinations to be repeated several times with different stories resulting from different situations. Number games, stressing the addition and subtrac­ tion combinations, usually prove to be of interest to children and will aid them in developing needed con­ cepts.

Various schemes that appeal to children's

interests can be used.

Games in which ladders, trees,

and wagons are drawn on tag or chip board are good. These games will provide more opportunities for act­ ivity, if slits or pockets are made on them.

Cards

with various combinations written on them should be available for children to place in these pockets or slits.

They enjoy manipulating the cards and placing

them in various positions on the charts. A group of number story papers should prove interesting and helpful to further aid children in ac­ quiring these arithmetic combination concepts.

If

these papers are readily available, children will en­ joy doing them at various times during the social studies period.

The following are examples of period

when children will welcome these story papers.

John

may feel that he has worked enough in his garden today. Mary may wish to get the group's opinion on the freeze on which she is working.

Tom may have finished making

his truck and doesn't believe that he should start to make something new today.

While a few children are

waiting for the remainder of the group to complete their work, these papers will prove helpful to the children.

42

M o th e r 1 tb b b it h a s 2 b a b y ra b ­ b its . She q a v e each b a b y 2 c a r r o ts and saved 3 c a r r o t s f o r h e r s e lf H ow m a n y c a r r o t s d id

the Ifabbit family have ? P rd W th e c a r r o t s M o th e tfa b b it gav/e -to h e r b a b ie s .

FIGURE 8 DEVELOPMENT OF NUMBER PROCESSES

43

The -Farmer w e n t to the meadow to b rin q in h is 1G h o rd e s. He f o u n d 2 o f th e m by the stream. O v e r th e h ill he fo u n d 2 m ore.

3acK of the barn he found the r e s t o f h is 1 0

horses.

many did he fin d b a rn ?

How back of the

D raw the horses by the stream. t

FIGURE 9 DEVELOPMENT OF NUMBER PROCESSES

M o b h e r P iq h b a b y pigs. O ne d a y 3 of bhe b a b ie s a

ran aw ay.

d

5

H ow m a n y baby

p*>go o ia y e d w it h Ih e ir mother? D r a w the baby pigs th at stayed hom e.

FIGURE 10 DEVELOPMENT OF NUMBER PROCESSES

CHAPTER I V

PROVIDING FOR NUMBER EXPERIENCE IN A SECOND GRADE SOCIAL STUDIES PROGRAM The farm unit was chosen as the unit of work in the social studies program because this area provides for the stimulation of interest from the children be­ cause of its varied and yet comparatively simple act­ ivities . The children of second grade level are usually interested in: 1.

Growing things, because they can plant seeds and see results.

2.

Moving things; the animals on the farm will capture their fancy.

3*

Working activities on the farm, such as the feeding of the chickens, the milking of the cow, the driving of the tractor, the churn­ ing of butter, and the loading of produce on the trucks.

4.

Visiting a farm.

5.

Finding out about food and where it comes from.

6.

Constructing.

46 Through this study children may have opportun­ ities to appreciate the contributions of the farm, the interdependence on a farm, and the ways in which farmers serve their communities. I.

TO CONSTRUCT A PLAY FARM IN THE ROOM •#

Children will want to make a farm after being Initiated into a stimulating farm environment which contains books, pictures and realia on the unit.

The

following techniques may lead to the desired construc­ tion.'

After allowing the children to explore the room

for as long a period as interest prevails, the teacher may invite the children to evaluate the things they saw.

This discussion may determine future planning

by the teacher and students.

They may enjoy returning *

to the things set up in the r o o m ,and playing with them. From these initial play period, children will find their needs for construction and for gaining more information about the farm.

After more group discussions, the

class may decide on the extent of their needs and the methods of meeting these needs.

Various committees

may be organized to work on different problems of con­ struction. To build a barn.

One of the first things that

47 second graders usually want to construct In a farm unit Is a red barn.

The building of a barn is rich with

possibilities for developing arithmetic concepts. Counting objects will be done many times during the periods that the barn committee meets.

Some of the

questions involving the need for the concepts of count­ ing may be the following. How many sections shall this barn have? How many stalls and stanchions will you need for your cattle? How many stalls and mangers will you need for the horses? How many windows and doors are you planning to make in the barn? *

How many corrals will be needed? How many nails are you going to use? Many mensuration concepts are needed in building a barn.

The words, height, width, and length will take

on meaning when children need to determine how high to make the barn.

The following questions asked by the

teacher will also take on meaning.

"If your barn is

this high, how long do you think it should be? wide are you going to make the barn?"

How

The need to use

the yardstick and ruler is apparent. to measure inches and feet.

Children will need

They will know from act­

ivity that there are twelve inches in one foot or in one ruler and that there are thirty-six inches in a hard or three feet. In planning and making the inside of the barn many opportunities to develop concepts of smaller mea­ surements are available.

After looking at pictures,

reading books, sharing ideas, and looking at films, film strips and slides, children will find that the most common type barn consists of several parts.

Stalls

and mangers for horses, stalls and stanchions for cattle, a hay mow, and a section for storing grain are common to most barns.

The measurement of these inside sections

depends on the size of the barn the children have built. This will lead to beginning concepts of building to scale.

Children will see the relationship of objects

to size by actually planning and constructing these in­ side parts.

If they find that the cows are to be made

twelve inches tall, they may decide the stanchions need to be twenty inches tall and wide enough so that the cows may be comfortable while they are being milked. The hdight of the mangers must be of correct proportion so that the cattle can conveniently reach their food.

^9

When they decide to build the corrals for their cattle, they will consider height of the fences, length of the corral, and the width of the corral.

These second grad­

ers will also need to decide on the size that they should

make the doors through which the cows enter •*

and those through which milk is taken from the milking barn to the thermos tank. Time concepts may be developed in the building of the barn.

The following questions arising from plan­

ning needs for the construction period will provide children opportunities to acquire understandings nec­ essary to successfully complete their construction. The teacher may ask, "If we start to build at 9:15 A.M. and must finish at 9:30 A.M., how long will we have to work?

If we start cleaning up at 9:50 A.M. and finish

at ten, how long will it take us? we been building this barn? the barn yesterday?

How many days have

What did you finish on

What shall we plan to do today?

When do you think that you may be finished? " Capacity concepts may be developed when children find that a pint of red paint is not sufficient to cover the barn.

They will not need a whole quart, so

they will find that they needed a pint and one-half of paint.

Prom painting the interior of the barn, they

will have opportunities to develop concepts of capacity

50 through comparing the amount of paint used to paint a stall with that of painting the hay loft. The selection of the correct size nails will aid in developing weight concepts in the building of the barn.

Children may be sent to the supply cupboard

to get one-half pound of six penny box nails or onehalf pound of four penny box nails.

They will see that

they will have more smaller nails in a half pound than they have of the larger ones. As the pupils use a yardstick and ruler for measuring their lumber they will be given opportunities to read the numbers beside the inch marks.

They will

have a need to write the number of inches and feet in their plans for the barn. The building of the barn presents many oppor­ tunities for developing the vocabulary of comparison. These words may be used during a planning or evaluating period of the social studies period.

A conversation

concerning their plans for constructing the barn may result in the following underlined words being used: "The back side of the barn will have Just one big window.

We will have two small windows and

one large window in our barn when we are all finished.

The doors will have to be high enough

so that the trucks can be driven in.

If the

51 doors are too low the farmer will get hurt." From a discussion concerning the painting of the barn the following sentences may result in using the follow­ ing underlined words: "We will paint the top part of the barn after we finish painting the bottom part.

When we -

finish both the upper and lower parts, we must be very careful where we put the barn while the outside is drying.

We will then paint the

inside of the barn.” ■»

To construct the farmhouse and its furnishings: In drawing plans for the house and the furniture, many uses for linear measures are needed by the students on this committee. may be needed.

Quarter inches, half-inches, and inches Children will soon understand that two

one-half inches make one inch and that four quarter inches are found in one inch.

First, the pupils will

need to determine the height, length and width of the house.

After making the correct measurements on their

lumber they will need to saw the wood the correct sizes. They will plan the size of each room and decide on the furniture needed.

Here again building to correct size

scale should be stressed. In constructing the house and furnishings, the

52 children will learn the use of the yardstick as well as the ruler.

They will understand that six inches is

one-half a foot through needed measurement for construc­ tion.

These children will also understand that twelve

inches equals one foot and three feet are found in one yardstick. Some of the measurements used for the chest may be two inches by three inches and one and one-half by two and one-quarter inches.

The drawers may be

drawn on after the places for them have been determined by measurement. Their bed measurements may be one-half inch by three inches.

They will also want to make bedding that

will fit the bed. These second graders may decide to make the stove top two inches by two inches, the legs, one-half inch by one-half inch. The chair seats may require lumber one and onehalf inches by one and one-half inches.

The chair backs

might need one-quarter inch by one and one-half inches. Table tops might measure one-quarter inch by three and one-half inches and the base might require one and one-half inches by one and one-half inches. Time concepts may be developed in the construction

53 of the farmhouse.

The following questions may be dis­

cussed . How long has it the house?

When shall

for building the house?

taken us to make the plans for we start to

measure the lumber

We worked twenty-five minutes

today; how long will we have left to clean up our room? We started, making the chairs on by Thursday.

How many

Monday and finished two

days did it

take tomake all of

the chairs? Number measures are made meaningful by developing an understanding of the need for a pair of kitchen cur­ tains or three pairs of living room drapes.

Prom making

these, children will know that a pair consists of two of a matched kind.

They may wish to make a pair of

lamps to be used on end tables near the davenport. The need for nails in making the house and furn­ ishings, will give opportunities for counting.

Children

may be encouraged to do their work neatly by planning a pattern for the number of nails used.

nHow many

nails do you need to liSe-bo make the legs fit securely to the stove?” may be asked if children are inclined to use too many nails.

The number of children needed

to work on the house committee is a counting experience. The number of rooms desired and the amount of furniture

54 needed for each room will also require correct counting concepts. The need for reading and writing numbers may be met through the making of plans for the house and the furnishings.

Children will need to acquire concepts

in reading the numbers on the ruler and yardstick for measurement in their constructions. Opportunities are also available in the construc­ tion of the farmhouse and its furnishings to develop concepts in the addition and subtraction combinations. The second graders on this committee may decide to make three chairs.

Billy and Mary have made two.

more chairs are needed? do we have?

How many

Bob finished his, so how many

If you place two chairs in the kitchen,

how many will you have left to put in’ to the living room? When you take those two chairs that are in the kitchen into the living room, how many chairs are in the living room?

The following family of combinations has been

made meaningful: 3-1 = 2,

2+1 = 3,

3-2=1,

1+2 = 3.

Another experience during construction in which combination concepts are developed may be the following: Mary had four nails and lost one. had she left.

How many nails

She got one nail from the box.

How many

55 has she now?

When she used three nails, how

many nails does she have left?

Mary found

three more nails on the floor.

How many has

she now? The following family has meaning for children whoa it is presented in this manner: 4-1 = 3 ,

3+1 = 4,

4-3 - l,

1+3 = 4

There are also opportunities available in which children may acquire skills in adding and subtracting tens.

When the committee would decide to get the nails

needed for their construction, they may find that the nail box contains bundles of nails.

After some discus­

sion, the pupils would find that each bundle has ten nails and that there are seven bundles.

One bundle

i s n ’t as large as the other six, so after counting the nails in the small bundle, they find that there are five nails in the smaller one.

After having counted

the nails in the other bundles, they will find that each one contains ten nails.

The children will find

from counting objects that seven tens make seventy and the five in the other bundle make a total of seventyfive.' . The blackboard is used as the teacher writes the number seventy-five and calls attention to the fact that the placement of the tens place is to the left of

56 the ones place.

Counting and grouping by fives and tens

will also have meaning when objects are used by the stu­ dents . The teacher stimulates interest in subtraction of tens by asking the children to determine the number of nails that are left when ten nails are taken from seventy nails.

She will write the story, 70 - 40, on ;

the board, and point out that the zero is a place holder in the tens place. Another concept that may be developed is that of children understanding adding and subtracting ones to, and from, ten.

In using the bundles of nails, the

children will find that four nails from thirty-four nails leaves him thirty.

The teachef should then ex­

plain the purpose for writing the number four under the four in thirty-four.

The same procedure should be.

followed when John finds that sixty and three will give him sixty-three.

He will also understand the reason

for placing the three under the ones place in sixty. Vocabulary development of words of comparison is possible.

The children working on the construction

of the farmhouse may acquire the use of the words through discussion of their needs.

The words underlined in the

following sentences are part of those needed by second

graders. The front porch of this house should have a large porch where both the farmer and his wife can sit outside after their work is finished. We will need to smooth this wood down with sandpaper because it is too rough to use for the porch.

The wood for the back porch also

has to be surfaced before we begin to build. Another discussion may result in teaching the following concepts by making the following statements: We will need a pair of drapes for the living room and a rug for the center of the floor. Would you like to make a round table and twin beds for the bedroom? between the beds? over the beds. table.

Shall we put the table

Blue covers would be pretty

The cat can sleep under the

If everyone is quiet while he works,

the house will be finished sooner than if the group is very noisy. To construct the remaining objects needed for the farm.

A great deal of comprehension in the meaning of

inches and feet Is gained in the construction of the truck.

To make the base of the truck children will need

58

to measure wood three-quarters inches by four inches, three-quarters inches by three and one-half inches, and one-half inch by four inches.

Lumber two inches by four

inches is needed to make the motor.

For the truck seat,

the children will need to measure wood one inch by one inch, and thre-quarters of. an inch by one inch.

The

cab rook will require one-quarter inch wood by four inches and the cab back will require one-half inch by four inches.

For wheels for the truck they may need

two and one-half inch button molds. The children's plan for their fields and orchard will give opportunity for using the yardstick.

Measur­

ing the length of rows and the distance between rows is needed.

Thirty-six inches are in one yard, three

feet in a yard, and twelve inches in one foot are the concepts learned through, experience. Children in the second grade understand that if they begin work to make the pig pens at 9 ’15* they will have thirty minutes to work, if they work until 9:^5* They also understand that the social studies period begins at nine in the morning and continues until ten. This gives them one hour in which to plan and work on the chicken houses and pig pensTo determine the number of animals needed for

59 the play farm Involves many counting experiences.

The

number of pig pens needed, the number of chicken houses desired, the number of different fruit trees wanted, the number of farm implements needed and the number of chickens and other poultry wanted, are all activities which involve counting activities. In making plans for the play garden, they will need to be able to write the numbers as they use the measuring devices of rulers and yardsticks. Youngsters may want to plan an area for an alfalfa field.

Prom their reading they may find that

the farmer has 150 acres of alfalfa. write this number on the board.

The teacher may

She will then develop

with the children the idea that ten tens equal one hundred.

She will demonstrate that the one to show

one hundred is placed to the left of the tens place and that the two zeros are place holders for the tens and ones place.

The children will then find that fifty-

five is five tens and five ones and that to write the number 155# no zeros are used because place holders . are not needed.

In making the plans for the arrangement

of the play orchard, children will have an opportunity to group the trees.

The teacher and children may pic­

ture possible groupings and regroupings.

Suzan may

find that she has three rows of apple trees and that

60 there are twelve trees in each row. twelve"trees but only two rows.

Ann may also have

Through discussion and

arrangements of groups of trees, children will acquire concepts of multiplication and division. The following family will take on meaning from planning the play vegetable gardens: 7-1,

7-6,

6 4 1,

14

6

James may decide that he would like to have seven rows of carrots, but the rest of the committee may decide that six rows are enough. row is needed by the group.

James may think that one less James might prepare to

plant his six rows, but after more discussion the group may decide the other row of carrots is advisable.

If /

he should find that he has seven rows, James may be given the task of planting one row.

Since there are

seven rows, the group would understand that six more rows need to be planted if they are to have seven.

The

six rows and James’ one row would then total the seven rows. The orchard plans are helpful in presenting mean­ ingfully 8-4 and 444.

Rita may decide to have eight

rows of peach trees, but has only four rows drawn.

Finding

that she needs four more rows when she has finished the first four rows, she will then find that she has eight

61 rows of peach trees. Rita found that she had one-half of her trees planned for when she had four out of the eight trees. Tom understood that when he has three chicken coops built and he wants nine, that he has completed only one-third of hi's;;Construction. Opportunities are available to develop the vo­ cabulary of comparison in the building of the pig pens, chicken houses, trucks, farm implements, animals, and the planning of the fields.

The underlined words in

the following sentences may be acquired through these construction activities; Many things are still needed for the farm. Another truck should be made.

Both trucks

will be used when the products are taken to market in the middle of the summer. Children enjoy discussing the pig situation on the farm. The following thoughts may be expressed; The pig pens should be put behind the barn. We will need to make many things for them to eat, because their troughs are always empty. They never seem to be full, even if nothing is left when they finish eating. John may say:

62 "I would like to measure your chicken house to see how it compares in height with the other houses.

The young chickens should be put to­

gether.

The old chickens can be put in a pen,

off by themselves."

II.

TO TAKE AN'.EXCURSION TO SEE A FARM

Children will discover that they have many ques­ tions about the farm that pictures and books do not answer.

They may decide that a trip to a farm will

help them to solve some of their problems. To plan the excursion.

The reasons for visiting

the farm and the things that the children wish to see may be listed by the teacher. There are opportunities to develpp an understand­ ing of time in the planning period for the excursion. Children may discuss the time of the various farm choresj decide on the time of leaving school, plan a schedule of how they might spend the day, discuss the length of time it will take to get to the farm, and return the parent permission notes on time. Some opportunities to develop the ideas of speed are present.

Children may be stimulated to observe the

readings of the speedometer on the school bus if they

63 are seated in the front seats. While the children are planning to visit the farm, they may decide to list the products the farmer sells and those he may find necessary to buy. The number of children and the number of adults planning to take the trip may then be discussed.

The

discussion that only two children sit in one seat may be necesaary.

The room plan may call for the need to

assign ten children to stay with Miss Brown, ten with Mrs. Smith, and ten with Miss Jones.

The students will

see that the room of thirty children can

be arranged

into three groups of ten. The family of 6 - 1 ,

6-5*

5 +

1* arid 1 + 5

can be presented during the excursion planning period. If six children still need to bring back their permission to travel notes, and one child brings his back at noon, then five children still hav@ not brought back their slips.

If the next morning five children return their

notes, then one more child still has to bring his note back to school.

Five children brought their notes the1

first morning and one boy brought his at noon. children have brought their notes.

Six

One child lost his

note in the morning and five children lost their notes on the way home from school. notes that day.

Six children lost their

64 Many opportunities are available for vocabulary development during the excursion planning session. following sentences may be heard.

The

The underlined words

are comparative vocabulary concepts needed to be ac­ quired: A' short letter needs to be written to the farmer. His permission will be asked to allow the class to visit a short time on his large farm.

The

time of leaving school may be about nine o'clock so that the visit can last several hours. pupil must be quiet on the bus.

Every

If the group is

noisy, the driver will be very unhappy.

All

children must stay together, so no one will, get lost.

Each child wishes to kno_w more about the

many chores which the farmer does each day. To visit the farm.

Time concepts developed on

the farm visit may be the following: forty-five minutes to get to the farm.

It took the bus Since the group

left at nine o'clock, the time of arrival was 9:45. Lunch may be scheduled for twelve o'clock. must meet at the bus at three o'clock.

Every child

The driver plans

to leave for school at 3 :15* so the.class should be back at school by four o'clock. The children may develop concepts of morning,

65 afternoon, and evening by noting the chores peculiar to each time. While observing the tractor at work, the child­ ren may have observed that the tractor went slower than the school bus. Concepts developed while visiting the farm con­ cerning capacity may be that the chickens laid six dozen eggs yesterday.

The, farmer may have told the

children that his cows gave ten gallons of milk that morning.

The farmer's boy may have sold two lug boxes

of potatoes and six baskets of strawberries from his roadside stand. Weight concepts developed from a farm visit may be that the farmer's wife made four pounds of butter this morning.

The children may have been told that the

sacks of feed for the chickens weighed one hundred pounds.

They may have observed the milk being poured

into a weighing pail and that the scale was a different kind from the ones used in the classroom. Many opportunities present themselves in count­ ing on a visit to a farm.

Trying to count the number

of white chickens and the number of black chickens may be an aid in concept building. seieing the piglets.

Children always enjoy

Counting them may also be helpful.

66

Calling the children's attention to the number of cows in the barn, and the number outside, may be of interest. Listing the different kinds of fruit and vegetables seen on the farm will give many opportunities for count­ ing. On the way back to school from the farm visit the children may have fun with the following combination family:

8-1,

8-7*

7+1*

1 { 7-

may have eight paper pigs in an envelope.

The teacher She may say,

"Eight pigs were in the pen b.ut^one got out. were left in the pen? the pen.

How many

Seven pigs finally got out of

How many were left?

The farmer came out and

found the seven and put them back with the one pig. many pigs were in the pen now? a nap.

How

One pig decided to take

Soon the other seven also decided to take a nap.

How many pigs were sleeping?" They may also like the family of 10 minus 5* and 5 plus 5*

The teacher has ten paper peach trees pre­

pared, and asks, "John, if you give Mary five of your ten trees, how many are left?

Susan, if you gave five

trees back to John, how many would be have?” Many words of comparison may be developed while the children are observing on the farm.

The following

sentences may develop and the underlined words acquired:

67 The last cow In the row behind the door was black.

The farmer sat beside the cows when he

milked them.

I tried to milk two cows, but no

milk came out.

III.

TO DRAMATIZE LIFE SITUATIONS ON THE FARM

Many situations occur in dramatic play concern­ ing time in the farm unit. may occur:

The following opportunities

The farmer rises early to milk cows.

The

farmer goes to bed at eight o'clock after all his work is finished. Opportunities are present to use measures of capacity during the dramatic play period.

Concepts of

capacity are necessary to dramatize the following sit­ uations : The farmer got four gallons of milk this morning.

This made sixteen quarts.

When the

farmer's wife finished canning twelve quarts of peaches, she made a cake.

She used three-

fourths cup of flour, two eggs, one-half cup of milk, one-half cup of butter, one-half cup of sugar, one teaspoon vanilla, and one tablespoon of brown sugar.

The farmer's wife decided to

make ice-cream, so she used one-half gallon of

68

milk, one quart of cream, one pint of straw­ berries, and two cups of sugar. From the above experiences, children may under­ stand that two one-half cups make one full cup, that two quarts equal one-half gallon or four quarts make one gallon.

They may also understand the relative sizes

of the cup, the

pint, the quart, and the gallon.

Various things are weighed in connection with the farm unit during dramatic play. the milk after he milks the cows.

The farmer weighs A customer may wish

to buy five pounds of alfalfa seed, three pounds of wheat seeds, and one-half pound of carrot seeds. Different types of scales are desirable in the classroom. Temperature concepts function in the following situation.

The farmer’s wife bakes the cake in an oven

at 325 degrees.

The milk is poured into thermos trucks.

During the dramatic play the farmer buys supplies. His boy sells produce from the fruit stand. should be used in the classroom.

Real coins

A child may decide to

sell three dozen eggs.

Another customer only want to

buy a half dozen eggs.

When the farmer’s wife went to

town, she bought a pair of shoes.

From these experi­

ences children will soon understand that six is onehalf of twelve.

They will also know that there are

69 twelve things in one dozen and that a pair consists of two like items. There are many opportunities present for devel­ oping. an-understanding of counting in dramatic play. Children may count their clay chickens in the chicken pens, the clay fruit in the basket, the eggs in the boxes, and the cows in the barn. The family of combinations: 4-2,

and

2+4,

6-2,

4+2,

may be presented by means of the

following story. Mary finds that she has four piglets left after her father sells two of the six piglets.

The

next morning two more piglets are born, so she has six again.

Pour piglets get sick, so she

finally has only two left.

Mary felt so sad

that a neighbor gave her four more, so she has six piglets again. Another number story during the dramatic play period may prove interesting to the students.

Tom went

out before breakfast to the hen house to gather eggs. He found nine, but he dropped one. eggs.

So he had only eight

Tom went back to the hen house and after looking

again, he found another egg.

Now he has nine again.

His

mother decides to make a cake, so she uses eight of the

TO eggs.

Only one is left.

However, that evening, he

goes back to the hen house and finds eight eggs. he has nine e.g^‘again. 9-8,

and

1 + 8

The family:

9-1,

So

8 + 1,

was presented.

Many opportunities for developing a vocabulary of comparisons are present in dramatic play concerning life activities on the farm.

A group of second graders

may wish to feed their chickens in their play.

The

following concept and underlined comparative words' may be presented in these sentences: The farmer always feeds all the chickens after he eats a very big breakfast. again before he eats supper.

He feeds them (From observing

the milking of the cows when they visited the farm, the children may wish to milk their cows in the play farm.)

The farmer milks his cows

twice every day in the tall stalls..

IV.

TO PLANT A GARDEN

Planting a real garden is rich in opportunities to develop an understanding of linear measure.

The fol­

lowing questions may give rise to acquiring necessary concepts: How deep should the seeds be planted?

71 How long should the rows be? the space be between the rows?

How wide should

How far apart should

the seeds be planted? Several opportunities are available to develop time concepts in garden activities.. Children may be interested in recording the growth progress of the plants. Experiences in determining the cost of seed and fertilizer should be a valuable experience.

A committee

of children may be chosen to purchase the necessary things needed for planting a garden. Many opportunities for meaningful counting ex­ periences are available in the garden activity.

The

children will need to determine the kinds of seeds they wish to plant.

In getting the soil ready, they will

need to make the correct number of furrows.

Deciding

who will do the three jobs necessary to the soil ready for planting the seeds is needed.

When the vegetables

and flowers are ready to pick, a record of the number picked each day may be of interest to the group. Opportunities are also available to use addition and subtraction facts meaningfully. of garden.

John had six feet

Mary, a new comer to the class, had none,

so, John gave her three feet of his plot. he had three feet left.

He found that

Mary left after a few days, so

John received Mary's three feet of garden.

He had six

72 feet of garden space again. 3 + 3

The family of

6 - 3

and

was presented to the group. When the garden vegetables were picked, Susan

counted 121 carrots.

The teacher may ask for volunteers

to write the numbers on the blackboard.

She may say^

"Let's see, how many tens can you get from 121,?" children may be given ten carrots each. over.

Twelve

One is left

They may discuss the fact that no zeros are nee-

'■essary as place holders because there is a tens number and a ones number.

Zeros were not needed as place

holders. Beth may suggest that they eat some of the car­ rots for lunch.

If they decide to 'eat sixty, two each,

they would have sixty-one carrots left.

The teacher

may direct the class's discussion to understand that sixty is six tens..

They had twelve tens, so, after

eating six tens of carrots, they will understand that they have six tens, or sixty carrots, left, plus .the one left over, or sixty-one. on the blackboard:

This story may be written

121 - 60 = 6l.

Planting a real garden is rich in opportunities to develop a vocabulary of comparison.

The class may

decide they want some tall stemmed flowers and some short stemmed flowers.

They may want the vegetables

in back of the flower garden.

They may decide to put

up a fence in front of the flower garden. must get the ground ready.

First, they

Next, they will plant the

seeds, and last, they will water the garden every day. They may fill their buckets full of water and then empty them carefully along the long straight rows..

At

first, the seeds will seem to grow slowly but with care ful watching, they will grow quickly.

V.

TO PRESENT AN ASSEMBLY PROGRAM

Many questions of time enter into the activity of presenting a program.

The following are some of

the questions needed to be considered: What time does the program begin? the program be?

How long can

What time shall the program end?

Counting experiences in preparing an assembly are .present.

An estimate of the number of children who

may see the program may be made. that attend may be calculated.

The number of adults The number of costumes

needed may present counting experiences.

Also, the

number of children needed to appear in each number of the program may be a good problem. The learning of the addition and subtraction combinations is also possible in the preparation of the

Jb assembly program.- The following may make it more meaninfgul:

If five children are chosen for the first num­

ber, and one child got sick, how many will be in the number?

Since there are only four now, one child may

have to be borrowed from the other group. again present in the group. have their costumes ready. get his finished.

So five are

Four children out of five One child must hurry to

The next day his costume is finished,

so now all five childrens1 costumes are ready for the assembly. 1 4 ^

The family:

5-1*

4-41,

5 - ^*

and

was presented. Another number story that may prove helpful is

the following: program.

Three children wrote stories for.the

Because Tom decided that his story was too

long, two other stories were selected.

Tom rewrote

his story, so now three children have stories to read for the assembly.

However, two other children were

sick on the day of the program. to read his story.

Only Tom was present

At another assembly the two child­

ren who were absent, read their stories.

All three

children had an opportunity to read their stories. The family of combinations: and 1 4

2

3-1*

241,

3-2,

was presented.

Children will be given opportunities to use the

75 vocabulary of comparison in preparing the assembly pro­ gram.

The underlined words may be developed in the

following sentences: Before the program is planned, one must find out how much time is allowed.

After that is

known, the program can be planned. the program begin?

How should

What is the last number to

be that is used at the end of the assembly? Be sure and stand in the center and to the front of the stage.

People can't hear you if

you stand too far back.

The children in the

rhythms may form a circle in the center and dance clockwise. slowly.

The announcer should speak

If he talks too quickly, he can't

be understood.

CHAPTER V

EVALUATING THE SECOND GRADE ARITHMETIC PROGRAM In evaluating this second grade arithmetic program Brueckner's basic concepts of evaluation have been ac­ cepted for the study.

The steps to be considered in

a total evaluation are:1

"(l)

Formulating the educa­

tional outcomes to be appraised, expressed if possible in

terms of pupil behavior,

(2)

Selecting or design­

ing suitable means of evaluation. record of performance and behavior.

(3)

Securing a

(4)

Interpreting

and evaluating the information gathered." I.

FORMULATING ARITHMETIC. OUTCOMES

Modern education centers its forces on the needs of all children. at the same time.

All children do not have the same needs Therefore, it seems contrary to the

concepts of child development to set arithmetic outcomes as separate teaching units.

In the past the Isolated

arithmetic program presented much material, which had

1 Leo Brueckner, and T. Grossnickle, How to Make Arithmetic Meaningful. (Philadelphia: The John C. Winston Company," 1947), p. 374.

77 little functional relationship to the total program, and which had little purpose or meaning.

The arith­

metic program, which is centered In the daily activi­ ties of the children, meets vital, and worthwhile, classroom needs. Therefore, the final results in this type of program are difficult to isolate.

.In determining re­

sults it is common to find that these results are overlapping.

Standardized arithmetic tests can mea­

sure only a small part of the total individual learning through a socialized activity program of this type. Many meaningful concepts have been built and developed. Worthwhile, and qualified, group goals have been planned, developed, and realized.

Total child development is

therefore difficult to determine by any single method of measurement. II.

SELECTING METHODS OF APPRAISAL

As already stated, standardized tests evaluate only a small part of the learning outcomes in this social type of arithmetic program.

It would be doubt­

ful that use of a standard arithmetic test in a second grade would be of much value as a test must measure the program taught in each situation.

It, therefore, seems

logical that pencil and paper tests would test only a

developed skill in computation.

Other types of tests

-might include problem situation tests, teacher observa­ tion of individual pupil responses to the environment, teacher observation of individual pupil's interaction with the group in planning, teacher observation of teacher-pupil interaction.

Pupil growth could best

be determined by these methods in a second grade act­ ivity program. III.

KEEPING A RECORD OP RESPONSES

It is important that the teacher keep an accur­ ate record of each child's needs and accomplishments. It is only through the teacher's knowledge of these „ things that she can stimulate and build pupil interest in purposeful participation in further activity.

This

activity is, of course, on-going and continuous through­ out the study, with one concept being built upon another, one idea enlarging, expanding, and clarifying past ideas and concepts. A simple method of- recording individual pupil development could be devised by any teacher by check­ ing pupil growth and listing the points where the child needs further participation for developing understand­ ing in certain areas.

79 IV.

EVALUATING UNDERSTANDING OF NUMBERS

Evaluating a pupil's growth in an arithmetic activity program does not take place on every Friday at ten o'clock.

Evaluation is constant observation

by the teacher of her students' needs, interests, and understanding. Evaluating understanding of quantitative vocab­ ulary.

A check by the teacher to determine the use

each child makes of terms of comparison in conversation is a means of evaluating the child's understanding of his vocabulary.

In dramatic play, construction activ­

ities, and in- other school activities, opportunities arise wherein children's understanding and use of the comparative vocabulary can be checked. Evaluating understanding of standard measures. The teacher may give the children papers on which fruit trees of different height are pictured.

She may say,

"Put an apple on the tree that is nine inches tall. Put an apple on the tree that is three inches tall. Draw a tree twelve inches tall. tall.

Draw a tree four inches

How tall is the tree on the bottom of the paper?" A similar procedure can be used with other mea­

sures and pictures.

---------

80

Questions and statements about the comparison of weights is a method that may be used in testing weight concepts: a chicken?

Does a turkey weigh more or less than

Which weighs heavier, eight ounces of seeds

or a pound of butter? Children's number concepts of temperature may be evaluated by means of thermometers made on tag board charts.

The teacher may ask the students to choose

the thermometer that indicates the temperature when the farmer gets up in the winter. Time concepts of second grade children may be evaluated by means of pie plate clocks.

The teacher

may say, "Show me the clock that -tells the time the farmer gets up in the morning.

Show me the clock that

tells the time that the farmer goes to bed.”

Children

can also be asked to indicate certain stated times by moving the hands on play clocks. The teacher may evaluate money concepts through asking the child being tested to choose the correct coins in answer to questions that she may ask.

She may

say,, "John, bring me the correct change from a dime, if. you paid five cents for an apple.” a quarter.

”Mary, here is

Bring three coins that are the same amount

as the quarter.

Susan, bring me two coins that can

buy the same amount as a dime can.”

81

Children's concepts of measures of capacity can be evaluated through their manipulation of various size cartons.

The following examples illustrate this point:

The teacher may say, "Susan, bring the carton that Mrs. Jones would use if she wanted a pint of milk.

Ted,

bring two cartons that hold the same amount as one quart carton.

Jerry, find one jar that will hold four

quarts." Evaluating understanding of number.

The teacher

of second grade children may find the following sugges­ tions helpful in evaluating the ehild's understanding of number.

Charts made from tag board are helpful be­

cause they can be used many times, and can be available when needed.

A chart containing rows of numbers, with

three numbers to each row, may be used. may write:

55#

7#

90

on one line.

"John, point to the largest number.

The teacher She may say,

Mary, point to the

smallest number." Asking children to write numbers on the black­ board, or on paper, is another method of evaluation: "Susan, write 101 on the board, please," may be asked by the teacher.

Each number will be more significant

if it is connected by vocabulary to the farm.

The last,

request would have been more inviting if the teacher

82

had said, "The farmer gathered 101 eggs today.

Susan,

please write that on the egg chart for today’s eggs." "John, Susan made two more trees today. committee had twenty trees yesterday.

The

Write the total

number of trees that are ready to use on the farm on this chart." Testing children's knowledge of the combinations. The tests listed in the California State Arithmetic 2 Guide will be accepted for the testing of children's knowledge of the combinations. Evaluating understanding of vocabulary.

A check

by the teacher to determine the use each child makes of terms of comparison in conversation is a means of eval­ uating the child's understanding of his comparison vocabulary.

In dramatic play, in construction activities,

and in other school activities can be found situations which afford opportunities where the teacher may check the children's understanding of the vocabulary by the uses they make of it.

Some of the questions teachers

may find helpful for evaluating vocabulary are the following:

How well does each child use the words of

comparison in his conversation?

How many of the words

are used effectively by each child during a discussion

4-

83 period?

Do the students use the comparative vocabulary

correctly?

2

California State Department of Education, o p . cit., pp. 5^-57•

CHAPTER V I

SUMMARY AND CONCLUSION The purpose of this study has been to suggest activities for the development of a vitalized arithmetic program for second grade children by Integrating the arithmetic program with the .social studies program.

The*

area of work chosen for developing the desired concepts centered on the farm unit.

Excursions, observations,

construction activities, and social activities were experiences suggested to be used by teachers to give pupils first-hand information that would aid In devel­ oping the desired concepts. It has been shown In several studies that arith­ metic is a needed tool in the life of every child, so numbers in the primary grade program cannot be omitted. Recognized arithmetic concepts for the second grade were presented.

It was shown that the social

studies program contains adequate situations in which these concepts can be developed.

Both the social and

mathematical phases'of arithmetic can be provided for in an integrated program of arithmetic and social stu­ dies.

Rich and varied experiences with numbers in vital

situations are necessary if children are to function

85 successfully In their daily living. Arithmetic in the second grade of today can be a series of pleasant and meaningful experiences.

Child­

ren are not required to spend the greater portion of their time memorizing meaningless number facts if the program is of a vital nature.

Many children in past

years not only did not understand arithmetic, but also developed attitudes of dislike and fear toward numbers. Since number experiences, to be meaningful, should bear a close.relation to life and to actual need, and since the social studies program consists of schobl subjects which deal directly with actual rela­ tions between people, the method of vitalizing the second grade arithmetic program through integration with the social studies should prove to be successful. The answer to the question, how should arith­ metic be taught and how much arithmetic should be taught, lies in the program of vitalizing arithmetic through integration with the social studies program.

In such

a program, the needs of the children in the group are met through purposeful activity.

A good learning situ­

ation is present because the children are interested, needs are present, and children fill these needs through activity.

The goal is not less arithmetic, but arith­

metic that is meaningful.

The program, to be adequate,

v.

I

86

must be well planned and stimulated by the teacher, and not presented in a haphazard, or by chance fashion. This study has also shown that the needs in the various phases of the arithmetic program can be ade­ quately met in the activities of the social studies program.

The development of quantitative thinking con­

cepts can best be learned by use in meaningful activ­ ities.

The three major objectives for second grade

arithmetic discussed in this study, meaningful vocab­ ulary, understanding of measurement, and the under­ standing of number processes to solve simple problems, will help pupils to be able to perform quantitative thinking when the situation requires its use. Children's needs should determine the rate at which these studies are taught in arithmetic.

All

second graders will not be able to complete the ob­ jectives suggested for this grade because of varying levels of development.

These interests and needs are

influenced by intellectual, social, and background differences.

However, each child should experience

success in the number program as his needs arise.

From

opportunities to participate in first hand meaningful situations, he will be more inclined to develop concep­ tual values.

8?

In evaluating the arithmetic program one must consider more than written and oral results.

Pupils

should actually manipulate materials to see whether or not their understanding is clear.

The objectives in

arithmetic of transfer and retention are better at­ tained when children really understand the materials to which they have been exposed.

In other words, the

child must see sense in arithmetic if retention and transfer are to be made. Teachers need to understand, in evaluating children's progress, that pencil and paper tests are not the only means of determining pupil growth In num­ bers.

Constant observation of students by teachers is

necessary if the total learning experiences are analyzed as to individual differences and needs of children.

The

actual use and attitudes- which pupils show in their daily social situations indicate the rate of success of the school program.

B I B L I O G R A P H Y

B IB LIO G R A P H Y

A.

BOOKS

Adams, Wesley, Teaching Social Studies In the Elementary Schools. Boston: D. G. Heath and Company^ 1946. 362 pp. Brueckner, Leom and Grossnickle, F. E . , How to Make Arithmetic Meaningful. Philadelphia: The John C. Winston Company, 1947* 501 PP* California State Department of Education, Guide to the Teaching of Arithmetic in Kindergarten and Grades One and Two. Sacramento, California: Bulletin of the California State Department of Education, Vol. 18, Wo. 8, November, 1949* 75 PP* '-""Good, C. V., Dictionary of Education. Hill Book Company, Inc., 19^5*

New York:

McGraw-

Storm, Grace E . , The Social Studies in the Primary Grades. Chicago: Lyons and Carnahan, 1931. 598 pp. Stern, Catherine, Children Discover Arithmetic. York: Harper Brothers, 1949* 295 PP* B.

New

PERIODICAL ARTICLES

Brownwell, W. A., "When is Arithmetic Meaningful?" Journal of Educational Research, 38:481-98,

T93H: Clark, John R . , "Child Development Through an- Arithmetic Program," The National Elementary Principal, 29, No. 3:24, 19^9* ”

'90 Harap, H. L . , and E. Mapes, "Learning the Fundamentals in an Activity Curriculum," Elementary School Journal, 3^:515-21.

C.

PUBLICATIONS OF LEARNED ORGANIZATIONS

Spencer, P. L., "Newer Instructional Practices of Promise," Twelfth Yearbook of the Department of Supervisors and Directors of Instruction of the National Education Association, 1939« 2 6 9 PP•

UNIVERSITY OF SOUTHERN CALIFORNIA LIBRARI