Making Sense: Teaching and Learning Mathematics with Understanding

Making Sense: Teaching and Learning Mathematics with Understanding

Hiebert, J., Carpenter, T.P., Fennema, E., Fuson, K.C., Wearne, D., Murray, H., Olivier, A., Human, P.
Review by: Gudrun Mackness

In an increasingly technological society, conventional skills are being rendered obsolete, while flexible mathematical thinking, attained through true understanding of the subject, is becoming essential. Making Sense: Teaching and Learning Mathematics with Understanding offers elementary teachers a simple, practical guide to developing a classroom that promotes understanding in mathematics. Hiebert et al. present a research-based framework of five essential classroom features for teaching math for understanding and bring these features to life through several classroom examples. The framework grew out of the authors’ discussions of their collective involvement in four research and development projects in math instruction which shared the goal of “understanding what it means to teach for understanding” (p. xix). The text is intended to help teachers achieve this same goal, while also reflecting on their own practice. Detailed stories drawn from the authors’ research projects help bring together theory and practice. The stories illustrate how the elements of the framework are necessarily interconnected, how teaching for understanding makes learning explicit, and how this type of classroom design develops in a classroom over time. The clear structure of the text makes it cohesive and easy to navigate, but the authors’ delineation of the framework at multiple junctures results in somewhat excessive repetition of the concepts. The authors emphasize equity and accessibility in their framework, but do not offer a lot of depth to this discussion. They discuss the importance ensuring that all students can participate and contribute, and provide illustrations of differentiated instruction and teaching within students’ zone of proximal development. Yet, given the range and depth of possibilities for teaching math and social justice together, this book falls short in this area.  Overall, the simple set of features is a manageable number of elements to tackle, while the authors’ emphasis on their interconnected nature reminds the teachers that it is a systemic matter that cannot be accomplished with a few minor adjustments to their program. Thus, the authors provide the necessary elements for teachers to understand and apply their framework.