Incorporating reasoning and communications into Mathematics

Thompson, D. R. (2012). Modifying textbook exercises to incorporate reasoning and communication into the primary mathematics classroom. In B. Kaur & T. L. Toh (Eds.), Reasoning, communication and connections in mathematics: Yearbook 2012, Association of Mathematics Educators (pp. 57-74). Singapore: World Scientific Publishing.

Background

Textbooks are used everywhere and are a tool for turning national curriculum goals into pedagogical strategies. However, it is necessary to consider whether the textbook fully covers the intent of the curriculum or whether there is a need to make modifications to its content. One issue is whether the exercises in the mathematics textbooks provide teachers with the opportunities to see into their students’ thinking and, as a result, adjust their teaching to suit their students’ needs. A related issue is whether students have sufficient opportunity to reason and communicate with others regarding mathematical concepts.

Aims

The author uses textbook example exercises to show how they can be redesigned to give students the opportunity to discuss mathematical concepts and procedures.

Sample

The author takes 11 examples from primary textbooks and rewrites the problems.

Method

The approach is to modify an exercise that asks for a single answer in such a way that there appear to be multiple possibilities. The students must come up with an answer, say why they think their answer is correct and then describe how they got to the answer they did. The first example is:

Original:	12 + 8 = ___ 12 x 8 = ___
Modification:	Find two whole numbers whose sum is 20 and whose product is 96. Explain why your numbers are correct. How did you start to think about the problem?

Findings

The author shows that, in answering the revised question, the students are likely to practice addition and multiplication a number of times and will be forced to explain their thinking. In the process, their thinking will be clarified to themselves and to their teacher. The teacher can then modify the teaching to suit the needs of the students.

Implications

Teachers should look at ways of ensuring that students vocalize their thinking and computation to help the students consolidate their mathematical knowledge and concepts and allow the teacher to check that they are thinking along the right lines.

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