Elementary Math Education and the Draw a Picture Strategy

Introduction: I will discuss the problem-solving strategy "Draw a Picture" and why it is such an important strategy for elementary school-age students. Drawing a simple picture helps summarize and organize information given in word problems and helps students think about the situation and visualize possible solutions. Also, the calculations are easier and less confusing for students when information is organized and clear.

Students/Instructional Approach: This approach can be used with any age group of students, from kindergarten to college. For example, younger students can use the "Draw a Picture" strategy to solve simple fraction word problems while older students can use the strategy to solve more complicated geometry problems.

For young students, drawing a picture is especially helpful when a physical situation is involved. The "Draw a Picture" strategy is also helpful when teaching fractions to young students who are encountering them for the very first time, usually around third or fourth grade. Having a visual representation helps students fully understand what they're doing.

For example, using the "Draw a Picture" strategy in conjunction with Polya's four-step problem solving process would help young students solve this simple fraction problem.

Example: Sam has a bag with three green buttons, four blue buttons, and one red button. What fractional part of the bag of buttons is green?

According to Polya's four-step problem solving process, students must understand the problem, devise a plan, carry out the plan, and look back to check their work (Musser, 2006, p. 4).

1. Understand: What information does the student need to find?

The student needs to find out how many buttons there are in all, and then find out what fraction of those buttons are green.

2. Devise a Plan: How should the student solve the problem?

The student will use the "Draw a Picture" strategy to solve the problem, creating a simple diagram to represent the buttons.

3. Carry out the Plan: Draw a simple picture to represent the information presented in the word problem.

Draw eight circles to represent the eight buttons in the bag. The circles labeled "G" represent the green buttons, the circles labeled "B" represent the blue buttons, and the circles labeled "R" represent the red buttons.

The student will see that there are three green buttons out of eight buttons altogether, therefore 3/8 of the buttons are green.

4. Look Back: When looking back on the picture, it is clear to the student that there are three green buttons out of the eight buttons in the bag, or 3/8.

Discussion: According to Polya's four-step problem solving process, step one is to understand the problem. Students must be able to understand all the words and know what information is given. They must also understand why they're doing the problem in the first place and know what the goal of the problem is (Musser, 2006, p. 4). Drawing a picture helps students fully understand the information presented and figure out how to accurately solve the problem.

If a student has trouble comprehending all the information presented in a word problem, drawing a picture will help them organize the information and understand better. When the student understands how the information is organized, the calculations will be much quicker and less confusing. The picture will also help the student visualize possible solutions or even look at the problem a different way (Baker, 1992, p. 70).

Students commonly encounter standard word problems in their school's math curriculum, but it is generally agree that mathematical word problems are difficult for young students to solve (Baker, 1992, p. 72). Training students to use pictures to solve problems results in more improved problem solving performance than training students in any other strategy (Musser, 2006, p. 9).

However, students who are more advanced may resist this method (Beckmann, 2003, p. 4). If the student is able to correctly perform the necessary calculations mentally, he or she might think that drawing a picture is a waste of time. Teachers can encourage these students to participate in enrichment math activities that are more challenging.

Some students might also view the "Draw a Picture" strategy as not being "mathematical" enough (Beckmann, 2003, p. 5). These students often view mathematical thinking as tricky calculations using formal language. The students must be taught that this strategy is an option. Teachers should stress that mathematical reasoning can involve pictures as well as equations and formulas.

Summary/Conclusion: The "Draw a Picture" strategy can be used by students of any age. According to Polya's four-step problem solving process, students must first understand the information given by the problem before they can solve it successfully. The "Draw a Picture" strategy makes this easy for students because the information presented by word problems is organized and made less confusing. Students are able to perform the calculations to solve the problems more quickly and easily because the information is made more comprehensible.

References

Baker, D. E. (1992). The effect of self-generated drawings on the ability of students with learning disabilities to solve mathematical word problems. Retrieved June 15, 2006, from http://proquest.umi.com.ezaccess.libraries.psu.edu/pqdweb?index=8& did=744683711&SrchMode=1&sid=1&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1150396927&clientId=9874.
Beckmann, S. (2003). Mathematics for Elementary Teachers: Making sense by explaining "why". Retrieved June 15, 2006 from http://www.math.uoc.gr/~ictm
2/Proceedings/pap174.pdf.
Musser, G.L., Burger, W.F., & Petersen, B.E., (2006). Mathematics for Elementary Teachers: A Contemporary Approach (7^th ed.). Hoboken, N.J.: John Wiley and Sons.