Teaching Mathematical Thinking: Tasks & Questions to Strengthen Practices and Processes

by Marian Small

foreward by Linda Dacey

published by Teachers College Press, 2017

In this recently published book, well known math educator and author Marian Small highlights an important aspect of the discipline of mathematics – the thinking practices and processes that are “the doing of mathematics” when engaging in mathematical problems and learning content.

For those wanting clear examples of practices such as mathematical modeling, structure and argument are – the author clearly defines these with examples from across grade bands (K-2, 3-5 and 6-8).

For each practice/process, the author includes:

1) a definition with examples

2) where that practice/process is seen in K-8 mathematics

3) examples of problems, across grade bands, that might bring out that practice/process, often with examples of student responses

4) assessment questions for the educator to use to help notice and reflect on the students’ use of the practice/process

5) a short summary

I can’t think of another book that makes such careful nods to the Canadian mathematics education landscape. Although the focus is on the eight American Common Core standards for mathematical practice, the author connects these to our mathematical processes/competencies in Canada (with slight differences in different provinces/regions). Because our Canadian emphasis on visualization and mental math and estimation is not explicit in the American practices, the author has added a final chapter dedicated to these processes.

The problems are chosen to connect to each practice/process but should not be considered practice-specific. There are different types of problems – if you are familiar with Marian Small’s other books, you will understand the type of open-ness, differentiation and complexity built into the problems provided. For each practice/process she provides at least one problem for each grade band and then discusses how students take up the problems, with student examples.

I highly recommend this book. So so many wonderful problems for K-8 students and great information for teachers to help us think about the discipline of mathematics.

~Janice