Bar Graphs for Five-Year-OldsAuthor(s): Robert F. SmithSource: The Arithmetic Teacher, Vol. 27, No. 2 (October 1979), pp. 38-41Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41189461 .

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Bar Graphs for Five- Year-Olds By Robert F. Smith

A group of kindergarten teachers was asked recently if they did any graphing with the children. The major- ity of the teachers indicated that they did not, but one proudly responded, "Oh, yes! I did some bar graphs with them." When this teacher was asked if the children had used concrete objects or pictures for graphing activities prior to their introduction to bar graphs, she responded that they had not.

This brief conversation raised two important questions for further dis- cussion: Do kindergarten teachers rec- ognize the values of early graphing ex- periences for young children? Do they recognize the need for providing chil- dren with graphing experiences appro- priate for their level of development?

Values of Early Graphing Experiences

Graphing lends itself effectively to pro- moting readiness for more formal in- struction in arithmetic. It provides ex- periences in matching, counting, and comparing quantities, and helps chil- dren develop an understanding of terms like more than, less than, big, little, and so on. All such experiences help to lay the foundation on which the young child can begin to develop the concept of number.

Graphing also provides the teacher with a practical means of integrating an early childhood curriculum. Science activities such as finding out what things sink and what things float; mea- suring the growth of a plant; testing water's reaction on different types of paper and cloth; and classifying

An assistant professor and coordinator of the Divi- sion of Early Childhood Education in the School of Education, Brooklyn College, Brooklyn, New York, Robert Smith serves as a mathematics con- sultant for a local school district in which he works with classroom teachers of transitional classes. He also conducts mathematics enrichment classes for children in kindergarten through second grade.

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sounds, seeds, fruits, trees, and animals can culminate in graphs of the chil- dren's findings.

In social studies, graphs could result from activities designed to demonstrate likenesses and differences among people (shoe sizes, heights, weights, colors of eyes); discussions about the family (family size, family leisure-time activities, family origins); and surveys related to the children's immediate community (types of houses, types of food stores). In general, "graphical representation can be an integral part of many kinds of classroom activities. The discussions about alternate strate- gies for making graphs and the inter- pretation of the graphs can be as im- portant as the actual making of the graph" (Bruni and Silverman 1975, p. 366).

Practical Illustrations of Stages of Development

Collecting information, organizing it, and representing it pictorially are im- portant skills that children should be- gin to acquire in their early years in school. By providing children with a sequence of activities appropriate to their level of development, teachers will help them develop these skills more readily. The Nuffield Foundation (1967), in its book Pictorial Representa- tion, outlines the stages through which children should progress in the devel- opment of graphing skills. These stages closely parallel Piaget's stages of cogni- tive development during which the young child progresses from thinking that is dependent on "activity" - the manipulation of, and interaction with, real objects and events in the immedi- ate environment - to thinking that in- volves abstract thought processes.

One of the most important pedagog- ical skills a teacher must possess is the ability to put theory into practice. To illustrate how this could be done in

teaching graphing skills at each stage of development as described by Nuf- field, activities were developed and used with a group of kindergarten chil- dren. These activities are presented here as prototypes of similar activities that early childhood teachers could de- velop for each level of representation.

Stage 1

Concrete objects are used in a simple one-to-one correspondence - for ex- ample, one bead for one child. There should always be one object for each child, and comparisons should only be made between two rows or columns. In the comparison of two unequal rows of objects, the concept of inequalities is il- lustrated, and the appropriate vocabu- lary can develop from a meaningful context - for example, "greater than," "less than," "more than," "fewer than."

Activity 1

To compare the number of children with pets to the number of children without pets, the children matched themselves in front of the classroom, one child with a pet to one child with- out a pet. After making this one-to-one correspondence, the children saw that there were more children with pets than children without pets.

Activity 2

Next, two clotheslines were strung across the blackboard. The top clothes- line was for children with pets; the bot- tom clothesline, for children without pets. A picture of common household pets ideatified the row for children with pets; the same picture with a black line drawn diagonally across it identified the row for children without pets. Each child attached his or her name tag to the appropriate clothesline with a clothespin (fig. 1). (The teacher must make sure that the tags match one to one as they are put on the line.)

Arithmetic Teacher

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Activity 3 To make a more substantial record of this comparison, a sheet of oaktag was attached to a pegboard. Two rows of hooks were hung across the pegboard. The children were given plastic curtain rings (yellow for children with pets, blue for children with no pets), which they hung in the appropriate row.

Throughout these activities, the teacher asked questions to highlight such concepts as "more than," "fewer than" or "not as many as," and "same as."

October 1979

Activity 4

The children were given the opportu- nity to play with magnets. Each child was given a small magnet and a group of objects and asked to fine out which objects the magnet picked up and which objects the? magnet did not pick up. Each child was given two paper plates. One plate had a picture of something adhering to a magnet; the other showed space between the mag- net and the item and a line drawn through the picture (fig. 2). The chil- dren were asked in which plate they

should place the objects the magnet picked up. They correctly chose plate a. They also clearly understood that the second plate (b) was for the objects the magnet did not pick up.

After the children sorted thè objects and discussed their findings, the teacher suggested that the children make a record of What they had dis- covered. A chart was made oil a large sheet of oaktag (fig. 3). The children took turns coming up to the chart to tape an object either in the row for ob- jects the magnet picked up or in the row for objects the magnet did not pick up.

Questions were asked to focus chil- dren's attention on what the chart rep- resented. Are there the same number of objects in each row? Which row has more objects? Which row has fewer objects? How many objects did the magnet pick up? The children under- stood that the chart was providing them with the answers to these ques- tions. They were, in effect, "inter- preting" the graph, although the term graph had not yet been introduced.

Stage 2 At this stage children can begin mak- ing comparisons among several rows ör columns. A more permanent form of recording data- pictures of objects, for example- is used.

Activity 1 The activity began with a discussion of the different kinds of footwear the chil- dren were wearing. The children iden- tified three types: shoes, sneakers, and boots. The teacher suggested that the children make a picture of their find- ings. On a sheet of oaktag, a chart was prepared and titled "Our Footwear." There were three rows on the chart, and each row was identified by an ap- propriate picture (fig. 4).

The children were given cutouts of a shoe, a sneaker, or a boot, depending on what kind of footwear they were wearing. Each child then taped his or her cutout in the appropriate row. Per- tinent questions were again asked to help the children interpret the graph. How many children are wearing shoes? Are there more children with shoes than children with sneakers? Are there fewer children with boots than children with shoes?

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Stage 3

Children move from using pictures to using square pieces of paper to record their data. Thus, at this stage, the tran- sition is made from a pictorial chart to a block chart.

Activity 1

At the beginning of this activity, the teacher reviewed with the children the pictures they had made and what the pictures represented, and the term graph was introduced. The children understood the term to represent a cer- tain kind of picture that enabled them to compare different numbers of ob- jects. At this stage, the children's com- prehension of the word graph is not as important as their ability to make the graph and interpret, in their own words, what it means.

Each child was given a packet of pattern blocks. Each packet contained the same number of blocks: four red shapes (trapezoids), three blue shapes (parallelograms), three orange shapes (squares), and two green shapes (tri- angles).

The children were given the oppor- tunity to play with the blocks and make designs with them. During this period of free play, the teacher dis- cussed with individual children how the blocks were alike and different. Af- ter a sufficient period of exploration with their blocks, the children were asked to group them according to color.

Activity 2

The children were given a worksheet on which to record the number of blocks of each color (fig. 5). Colored gummed labels matching the four col- ors of the blocks were distributed to each child, who in turn pasted the cor- rect number of labels in each row. The children had no difficulty in making the transition from the use of pictures to gummed labels to represent the number of blocks of each color. What Nuffield refers to as thç "block graph" was clearly understood by these five- year-olds.

Stage 4

Children who have had sufficient expe- rience in making block graphs and are

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Our Footwear

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Fun With Blocks

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Our Favorite Food

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Arithmetic Teacher

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Balloon Colors

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able to interpret them accurately are ready to move into the next stage of pictorial representation, which involves the use of squared, or graph, paper. Children record the number of objects in a row or column by coloring in the appropriate number of squares. Young children should work with paper that has large squares, at least five centime- ters square. Even older children might begin with larger squares before using the normal graph paper sold com- mercially.

Activity 1

In this activity, which provided the children with a smooth transition from Stage 3 to Stage 4, numbers were used to label each column. Thus, the chil- dren were now seeing a horizontal as well as a vertical axis. They had no dif- ficulty in understanding the meaning of both axes. The term axis, however, was not used.

The children made a block graph of "Our Favorite Food." The original chart (fig. 6), which the children filled in with squares, was drawn on oaktag. The children had a choice of three foods: hamburger, frankfurter, or fried chicken. Squares of colored paper had been prepared (orange for hamburger, red for frankfurter, brown for fried chicken). Each child selected his or her favorite food and was given the appro- priately colored square, which was then taped in the correct row. The re- sult of the children's vote was dis- cussed.

October 1979

Fig. 8

Balloons Big & Small

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Activity 2

The children were each given a copy of the original graph, "Our Favorite Food," and were asked if they could think of another way to record the class's vote without using squared pieces of colored paper. Several of the children suggested coloring in the cor- rect number of boxes in each row. The teacher proceeded to give each child three crayons - orange, red, and brown - and instructed the children to record the group's vote on their own graphs. Several children needed some assistance during this phase of the ac- tivity, but the majority seemed to un- derstand what was expected of them. With the teacher asking appropriate questions, interpretation of the graph followed.

Activity 3 Each child was given a packet of bal- loons that varied in shape, size, and color. The children were asked to sort or group the balloons so that the bal- loons in each group were alike in some way. The children responded enthusi- astically: some grouped the balloons by color, others by shape, and a few by size. Throughout this sorting activity, the teacher asked questions that helped the children focus on the balloons' var- ious attributes.

Then all the children were asked to sort the balloons by color. There were four different colors of balloons, so the children were given four matching crayons and a chart labeled "Balloon

Colors" (fig. 7). The children were in- structed to label their four rows by col- oring the balloon at the beginning of each row one of their four colors. They then had to color in a box for each bal- loon of that color. As the children worked on recording their data, the teacher made certain, through individ- ual questioning, that each child clearly understood what he or she was doing.

Activity 4

The children next sorted the balloons by size (big and small) and completed the graph of balloon sizes (fig. 8) with little difficulty. Less individual atten- tion was needed at this point, and the children readily answered the ques- tions that were asked about the graph. Their first attempts at making and reading bar graphs had been success- ful.

Conclusion

Once young children have reached the stage of abstract representation, Stage 5 according to Nuffield, they under- stand the function of both vertical and horizontal axes of bar and line graphs, are able to read simple graphs quickly, and interpret them accurately. These skills do not suddenly appear but de- velop gradually through the various stages of pictorial representation that have been described.

Since a bar graph is essentially an abstract representation of numerical relationships, a teacher should not ex- pect that young children will under- stand it without prior experience in concrete representation. These prior experiences, sequenced according to developmental stages, will enable the young child to progress smoothly in ac- quiring graphing skills. Graphing skills, acquired early, will provide young children with increased oppor- tunities for systematic recording of nu- merical relationships between and among observed phenomena in their immediate environment.

Bruni, James V., and Helene Silverman. "Let's Do It! Graphing as a Communication Skill." Arithmetic Teacher 22 (May 1975V.354-66.

Nuffield Foundation. Pictorial Representation. London: Newgate Press; New York: John Wiley & Sons, 1967. D

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