Eyes on Math

I just finished Marian Small's Eyes on Math: A Visual Approach to Teaching Math Concepts. What a delightful and useful book. The illustrations by Amy Lin demonstrate the math concepts in a simple way that would be easy to use a springboard to other real life examples. The explanation of the underlying math is clear. Too many of the elementary and special ed teachers that I have worked with over the years are weak in math. The author details the math, why it is important, and common errors that students make. I love the latter because it is in that area that teachers can provide invaluable assistance to students. The phrase, "Many students make a mistake here..." is a common one in my math instruction because it allows us to focus attention on correct responses and gives students a place to look to for corrections.

Another truly brilliant piece of the book is the question portion. Ms. Small has listed critical higher level questions that can be applied to the math topic under discussion. For example under the topic of multiplication: 2 digit by 2-digit, she lists:

• Why does determining the area of the grassy field in the picture represent multiplication?
• What are the areas of each of the four sections?
• Why is it easier to multiply 20x40 in your head than 23x45?
• Why was it a good idea to break up 23 as 20+3 instead of 17+6?
• How would you use the same idea to multiply 39x42? (p. 87)

Each question is followed by an explanation of why this question represents critical understanding.

The last piece of each section is extension. Ideas for students who got it and need something more challenging. (Differentiation spelled out.) As a parent of a gifted child, this piece offers me hope that my child might not be left with no on-going learning when the rest of the class is still exploring a concept.

The book is well indexed and references back to the common core on each subject. Each topic is addressed for only two pages. The authors assume that once they jump start your thinking, you will be able to move from there. While the book covers the K-8 CCSS, for students who are struggling learners at the secondary level, this book could be a teacher's friend in helping to model the missing concepts. For teachers who need to bolster their understanding of the math curriculum across the elementary and middle school years, this book is a good primer.

Weaknesses? This book is purely operating from a graphic/pictorial basis. Real manipulatives would be essential especially with early topics. The choice of when to move from manipulatives to illustrations is highly dependent upon the students in the class. A group of very abstract thinkers might need nearly no time with manipulatives or even illustrations, whereas a group of struggling concrete thinkers might need to stay with manipulatives for an extended amount of time and then be taught to draw models to help them with their thinking. Teachers need to know their students. With testing that requires explaining how answers were arrived at, using graphic models helps to prepare students.

This easy to read source is a wonderful addition to any elementary of middle school professional library. For people who work with struggling learners at all levels, it is a great resource. Just remember that illustrations must be tempered with real physical practice as well.