The following is a review of Pictorial Mathematics that appeared on Teaching Mathematics, a math education journal published by NCTM, the largest mathematics education association in the world.
The book is available through amazon for $32.95, but it is available here as a E-book for $20.
“Modifying one’s instructional practice to reflect the NCTM’s Standards is challenging. It is particularly true when creating ways for students to “see” mathematics in more than the rote symbolic manner that dominated the classrooms in which most teachers (myself included) learned mathematics as children. Mendieta’s Pictorial Mathematics represents the experience of more than fifteen years as a mathematics teacher in the diverse classrooms of Los Angeles and the insights gained from studying and enacting a concept-focused approach to mathematics learning. It also contains a wealth of high-quality, classroom-tested ideas that teachers can explore on their own and easily implement in their classrooms. In the author’s words,
“This book is grounded on the research of
the role that multiple representations plays
in the development of conceptual understanding”
This book provides tremendous help in supporting students in working toward this goal. Pictorial Mathematics is not simply a compendium of visual representations that one decides how and when to insert into the curriculum. Rather, it is written by a teacher, for use by other teachers, with an appreciation that important in students’ developing conceptual understanding is their ability to “transform” and “translate” within and between representations. Thus, Mendieta provides exercises that require
students to generate equivalent representations within the same model (transformations) as well as those requiring translations from one form of representation to another. This feature makes the book exceptional in terms of its pedagogical value and potential to positively impact student learning.
The book’s accompanying “teacher notes” make transparent what are often subtle yet pedagogically powerful modifications to the way in which students are asked to engage in thinking about, and reasoning with, the representations. What is more, the resources inside the book go beyond visual representations to include games and investigations that support the development of conceptual understanding. The material appears as blackline masters, making it easy for teachers to adapt it for use on an overhead projector or in printed form.
I strongly recommend this book for teachers who want to expand their ability to support students’ development of conceptual understanding through the use of visual representations. Although the resources offered are drawn from several content strands—Number and Operations (including whole numbers, integers, and rational numbers), Algebra, Geometry, and Probability and Statistics—the book has just over one-half its pages devoted to decimals, fractions, ratios, and algebra. This makes sense, given that students often find these topics challenging to understand.
Although useful to teachers from K–12, Pictorial Mathematics is invaluable to those who teach mathematics from grade 4 through algebra.”
Mark Ellis, California
State University—Fullerton, Fullerton, CA
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