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Fractions, Percentages, Decimals and Proportions: A Learning-Teaching Trajectory for Grade 4, 5 and 6

Frans van Galen, Els Feijs, Nisa Figueiredo et al
Sense Publishers
Publication Date: 
Number of Pages: 
[Reviewed by
Elizabeth Burroughs
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This book is part of the series “Learning-Teaching Trajectories for Primary School Mathematics,” a project of the Dutch Ministry of Education, Culture and Science. The book provides a curricular overview, along with teaching suggestions and sample problems, of fractions, percentages, decimals and proportions in grades 4, 5 and 6. It is thorough in its explanations of issues related to teaching these concepts and in its treatment of the relationships between them.

The perspective of the authors is that the complex topics of fractions, percentages, decimals and proportions require teaching and learning that is focused on insight, and that all students must be given opportunities to engage with the subject’s complexities in ways that go beyond practice with procedures and algorithms. Each topic is given a separate treatment explaining the authors’ teaching approach, and each of these discussions is accompanied by attention to the relationship between the four topics. The book’s explanation of using the fraction bar and ratio tables to teach these concepts provides useful models that are likely novel to most American pre-service elementary school teachers.

One chapter is devoted to approaches for differentiating classroom instruction in fractions, percentages, decimals and proportions. The authors assert that the best way to accomplish differentiated mathematics instruction is through common classroom discourse and distinct individual work. The chapter offers several classroom-tested examples to illustrate the varied ways to differentiate instruction of this topic at this level.

This book will be of benefit to pre-service and in-service teachers at the K–12 level and university instructors of pre-service teachers. The examples of classroom problems, the discussion that focuses on “core insights” in each topic, and the chapter on differentiation are particularly useful to these audiences. One drawback for American readers is that the examples use European units of measure, so  some adjustment is necessary to ensure that the context-embedded problems are relevant.

About the reviewer: Elizabeth Burroughs is an Assistant Professor of Mathematics Education in the Department of Mathematical Sciences at Montana State University. She is a 2003 Project NExT fellow.

Foreword 7

Introduction and overview 11

Relationships 27

Core insights for proportion 43

Core insights into fractions 63

Core insights into percentages 89

Core insights into decimals 107

Differentiation 123

Final and intermediate attainment targets 147