Incorporating reasoning and communication into Mathematics
Discover how tweaking textbook exercises can prompt students to reason and explain their thinking in maths, helping teachers better understand and meet their students' needs.
Last updated 9 September 2026
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:
Example modification of a mathematics exercise to require reasoning
Original: | 12 + 8 = ___ 12 x 8 = ___ |
|---|---|
Modification: | Find two whole numbers whose sum is 20 and whose product is 96. |
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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