Problem Solving: Tips For TeachersAuthor(s): John A. Van de Walle and Marilyn BurnsSource: The Arithmetic Teacher, Vol. 35, No. 9 (May 1988), pp. 30-31Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193408 .

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Problem totoing Tip) for Teacher^ он .1A$4

Щ 1988

ф //strategy Spotlight IL

>| Organizing the Classroom I I for Problem Solving Щ

A growing body of research points to the benefits of having students learn in small cooperative groups. When students work in cooperative groups, the ac- tive participation of each student is maximized. More students have the chance to speak than in whole- class discussions, resulting in more opportunities for students to clarify their thinking. Also, many students feel more comfortable in small-group settings and are therefore more willing to explain their ideas, specu- late, question, and respond to the ideas of others. In small cooperative groups, students' opportunities to learn with understanding are supported and enhanced.

Choosing Problems Suitable for Cooperative Groups 1 . Choose problems for which a collaborative effort will benefit students, both in sharing ideas and in ac- complishing the task.

2. Select problems that allow for different approaches.

3. Be sure students understand both the problem and how they are to present their results.

4. When appropriate, have students post their findings for the class.

5. Allow for discussion time to summarize, during

Edited by John A. Van de Walle Virginia Commonwealth University Richmond, VA 23284-000I Prepared by Marilyn Burns Marilyn Burns Education Associates Sausali to, С А 94965

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which groups present their findings and respond to other groups' results.

An Early Grade Example- "Making Change" Young children need opportunities for continued practice both with basic facts and with money. "Ma- king change" is a problem-solving activity that offers both kinds of practice and also lends itself to cooper- ative group work.

Each group of students works to find all the ways they could be given $0.50. For example, they could receive two quarters, or one quarter and five nickels, and so on. They make a group record of their find- ings to present to the class. During a follow-up dis- cussion, they also need to tell why they think they've found all the ways.

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An Example for Older Children- "Number Bracelets1' "Number bracelets" appeared in the May 1980 issue of the Arithmetic Teacher. In this activity, students look for patterns while practicing basic addition facts. Several benefits emerge as students tackle this prob- lem in groups. They share the task, thus making the

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work manageable, and they are able to check their conjectures and evidence with each other.

Students start by writing any two numbers from 0 to 9 and applying the following procedure: Add the two numbers and record just the digit that appears in the ones place in the sum. For example, if you start with "8 9," then the number that comes next is "7." Then add the last two numbers, the "9" and the "7," and record "6." Continue in this way, "897639 2 . . . ," until the pattern begins to repeat.

Each group of students is asked to answer the fol-

lowing questions:

1 . How many different possible pairs of numbers can you use to start?

2. What is the shortest bracelet you can find? 3. What is the longest bracelet? 4. Investigate the odd-even patterns in all your

bracelets. 5. Make up one more question and try to answer

it.

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Part of the Tip Board is reserved for techniques that you ve found useful in teaching problem solving in your class. Send your ideas to the editor of the section. W ^B

May Ì 988 31

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