One Point of View: Let's Talk about Talking MathematicsAuthor(s): Werner LiedtkeSource: The Arithmetic Teacher, Vol. 35, No. 8 (April 1988), p. 2Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193378 .

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Let's Talk about Vara Talking Mathematics 1988 W By By Werner Werner Liedtke Liedtke I W WW_ By By Werner Werner Liedtke Liedtke

As elementary school teachers we continually strive to make our mathe- matics teaching as effective as we possibly can. One way of reaching this goal involves changing the pro- portion of time allotted for develop- mental activities and individual seatwork for a lesson. Some evidence suggests that increasing the time spent on developmental tasks and student participation and thus decreasing the time students spend on practice can have a positive effect on mathematics achievement. This evidence implies that we, as teachers, should search for and collect strategies that are condu- cive to the implementation of devel- opmental activities.

Giving students the opportunity to talk is just one possible way of in- creasing the time spent on develop- mental tasks. Since being able to talk about a skill or idea implies that it is understood, and since talking can lead to understanding or better under- standing, we need to promote talk with our students. Many valuable learning outcomes can be accommo- dated in a setting where the focus is on student discussion and participa- tion.

As an example, let us consider the simple setting of encountering a page in a pupil text that shows twenty-five or more practice tasks.

1. 26 x 17 = 2. 12 x 88 = 3. 73 x 54 =

Werner Liedtke teaches mathematics education courses to elementary school preservice and in-service teachers at the University of Victoria, Victoria, British Columbia V8W 2Y2.

Now I think it could be advantageous for our students if the last thing that came to our minds and the last thing we would do is to request the comple- tion of each item by every student. Indeed, few valuable learning out- comes for such a setting result. Many, many more learning outcomes can be accommodated by letting students talk about these items and by having students respond to questions of the following type.

• When you think about finding the answers, which of the items do you think is easiest (most difficult)? Why?

• Just by looking at the examples, which item do you think might have the greatest answer? The least an- swer? Why do you think so?

• In this collection of items, do you think that two or more are in some way the same? If so, how are they the same?

• Do you think two or more will have similar answers?

• Do you think that one item is in some way different from the others? If so, how is it different?

• Look at the first three examples. Without calculating the answers, which item do you think would have the greatest answer and which would have the least answer?

• Let's look at the first five (or more) items. As you think of the pos- sible answers attempt to order the items from least to greatest.

One of the items is identified and the challenge of identifying an item

that would have an answer that is about twice (or one-half) the answer for the given item is presented.

The task of identifying items that would have a 4 in the ones place of the answer is given. Items could be iden- tified according to even and odd prod- ucts. Another type of task could in- volve searching for an item with 24 as the last two digits in the answer, or for a product that would have the great- est, or least, number in the ones place?

After students have talked and after we have listened, we could ask them to demonstrate their understanding by finding the answers for a few of the items.

A few suggestions for "more stu- dent-talk" have been made. These ideas can easily be modified to make them suitable for other topics or for different groups of students. Letting students talk and listening to their responses will give valuable insight about their level of conceptual under- standing of a given topic - insight that offers important information for fu- ture lessons. Having students listen to each other's responses and comparing the reasons given (a very important part of such settings) to one's own is a valuable learning experience, m

[¿ZZ-l PROBLEM-SOLVING TECHNIQUES tarn HELPFUL IN MATHEMATICS AND SCI- ^t^ ENCE, by Charles A. Reeves. Specifi- cally for elementary school teachers - a well-illus- trated book that, will lead you, step by step, through the different problem-solving strategies: working backward, using a chart or list, drawing a diagram, searching for patterns, and guessing- checking-revising. Excellent help for laying the foundation for your students' mastery of prob- lem-solving techniques. 35 pp.; #366; $4. See the NCTM Materials Order Form in the back of this issue.

2 Arithmetic Teacher

By By Werner Werner Liedtke Liedtke

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