________________ CM . . . . Volume XVI Number 31. . . .April 16, 2010

excerpt:

Kim and his mom bake together. They will bake treats for a party....
Kim looks at the next batch of cookies.
He tries multiplying by 3. He multiples 3 × 4.
He can skip count by 4s. 4, 8, 12
He can add. 4 + 4 + 4 = 12
He can make an array. So 3 × 4 = 12. Kim says, "Three times four equals 12."
Kim's mom turns the tray sideways. Then she asks, "What is 4 × 3?
Kim says, "Four times three equals 12." Then he writes 4 × 3 = 12. (From
Multiplication.)

The eight books reviewed here represent half of the 16 books in the series "My Path to Math" by Crabtree Publishing. The series is designed for primary grade students and teachers. Each of the volumes has 24 pages. Each double-page in a volume addresses one particular aspect of the mathematical concept and idea with which the whole volume deals. The text is printed in larger font (appropriate for primary school children), and there are many coloured pictures and images used that often provide a pictorial representation of the respective mathematical concepts and ideas. Each volume has an index page at the end as well as a double-page glossary in which the central terms used in the respective volume are explained in one sentence.

All the volumes reviewed here are written to help students with developing conceptual understanding of mathematical concepts and ideas. The volumes do a very good job in extracting the central ideas of each concept with which a volume deals and provide some meaningful activities for students to engage in (mentally or physically). The Multiplication volume, for instance, links the concept of multiplication to the routine of skip counting, to the idea of repeated addition, to the concrete and pictorial representation of multiplication in arrays, and the symbolic representation of multiplication (see the excerpt quoted above).

However, while the basis upon which each volume deals with a particular mathematical concept and idea is sound in terms of what a teacher should consider in her/his teaching of mathematics, the volumes are, in my view, of only limited value as books for students to learn from by reading them on their own. This has to do with what the publisher seems not to acknowledge. The book series has a motto that is printed at the bottom of each cover: "Math Concepts Made Simple." Mathematical concepts and ideas are complex and abstract, and they cannot be made simple. Understanding mathematical concepts and ideas requires engagement with those concepts and ideas in meaningful and various ways. Mathematics education research would strongly suggest that the different aspects of mathematical concepts, like multiplication, division, symmetry, and so on, cannot be learned by students reading a double page. It requires engagement with a number of different tasks, generally facilitated by a teacher; and it is as a teacher's resource to engage students in thinking about mathematical ideas that I see being the primary value of the "My Path to Math" series. Supplemented with other materials and activities, the volumes provide teachers with a number of mental and physical activities and visual representations that teachers can use to engage students with the respective mathematical ideas and concepts in a meaningful way.

The volumes Addition, Subtraction, Multiplication, and Division each deal with one of the basic number operations. The fundamental aspects that students should understand of each of the four operations are addressed in the respective volume. Each of the other four volumes, Symmetry, The Metric System, Math Words and Symbols, and Sorting deals with the mathematical concepts and ideas suggested by the title. Recommended for use by teachers with their students, but Recommended with reservations for use by students alone.

Recommended with reservations.

Thomas Falkenberg is a mathematics teacher educator in the Faculty of Education at the University of Manitoba.

To comment on this title or this review, send mail to cm@umanitoba.ca.

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 Published by The Manitoba Library Association ISSN 1201-9364 Hosted by the University of Manitoba.

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