The Glass Wall: Why Mathematics Can Seem Difficult [Paperback]

Frank Smith (Author)

Book Description

Publication Date: July 1, 2002

What makes mathematics understandable? What makes mathematics confusing? Could something be wrong with the way mathematics is taught?

Following his years of studying human intellectual accomplishments such as language, reading, writing, thinking, and learning, Frank Smith now turns his critical lens on the teaching and learning of mathematics. In The Glass Wall, Smith helps us to understand why some people find the world of mathematics so compelling while others find it so difficult. This original volume examines two different worlds: the physical world (our familiar world of objects and events) and the world of mathematics (a completely different domain of experience), and the glass wall that can exist between them. Smith argues that, because the language used to talk about these two worlds is not the same, many people find themselves behind the glass wall, on the outside looking in.

Chapters discuss:

* What Is Mathematics?
* Making Sense of Mathematics
* The Mathematics in Language
* The Meaning of Numbers
* Getting Beyond the Glass Wall

Editorial Reviews

From the Publisher

"Mathematics isn't necessarily complicated or difficult, nor is it something that is accessible only to an intellectual elite. Mathematics should be open to everyone, provided no unnecessary obstacles are encountered." -- From The Glass Wall: Why Mathematics Can Seem Difficult

About the Author

Frank Smith has been a professor at the Ontario Institute for Studies in Education, the University of Toronto, the University of Victoria, British Columbia, and the University of the Witwatersrand, South Africa. He holds a Ph.D. from Harvard University. A number of his books and professional articles have become classics among educators.

Product Details

• Paperback: 176 pages
• Publisher: Teachers College Press; illustrated edition edition (July 1, 2002)
• Language: English
• ISBN-10: 0807742414
• ISBN-13: 978-0807742419
• Product Dimensions: 9 x 6.2 x 0.5 inches
• Shipping Weight: 9.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #437,436 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

11 of 11 people found the following review helpful:

5.0 out of 5 stars Reviewers need to do their homework, August 7, 2006

By 

Julie Brennan "Living math" (San Diego, CA) - See all my reviews
(REAL NAME)   

This review is from: The Glass Wall: Why Mathematics Can Seem Difficult (Paperback)

Negative reviewers seem to enjoy taking pot shots at this author without researching who he is or where he is coming from. Frank Smith is a highly regarded educator, researcher, author and speaker. He has written many articles and books on learning in general, as well as reading, math and learning disability issues. A minute or two on Google would yield sufficient answers to the questions posed.

This book has been enormously helpful to me as a home educator and part time teacher of mathematics, to understand the history of how mathematics developed, the complexity involved in mathematical concepts we tend to take for granted as being "simple", and why not every child seems to grasp ideas we consider to be simple on the timetable set for them by typical scope and sequence math.

I did not read this book to see if an author could prove a "thesis" to my satisfaction. I read it to try to understand why my oldest child seemed to have difficulty learning math in his elementary school years, and years of networking with other parents showed me his problems were common to certain types of learners. My son has now gone on to high school and excels at math. This book helped me as a parent and educator mentor his math learning in a way that facilitated his success.

Whether you agree or not with every idea he presents, it is thought provoking and will provide insight in how humans developed and process mathematical thought.

7 of 8 people found the following review helpful:

5.0 out of 5 stars Looking at math from the inside out, July 6, 2003

By 

Norene Rolle (Auburndale, MA United States) - See all my reviews

This review is from: The Glass Wall: Why Mathematics Can Seem Difficult (Paperback)

I read this short little book from beginning to end, savoring and thinking my way through the chapters one after another. I wanted to experience the enlightenment of getting behind thinking (in mathematics) the way Frank Smith intended. The Glass Wall provided a delightful journey of looking at math from the inside out.

Now I'm thinking differently about things I already knew about numbers, and have an understanding about math education based not on pedagogy but on how math works.

As a literacy consultant I am always looking for materials and readings to bridge the subject domains, for teachers and students. I think this book would help any teacher look at the thinking of math, which would inform the doing of math. That has been the trick to improving teaching reading (understanding what good readers do and making visible reading moves) and I think this could contribute in the same way to math instruction. This book does not explain, so much as it leads the reader to experience mathematical thinking, making special note of where the natural world and language part company with the world of math, which many people don't acknowledge.

What made me realize the impact this book had on my everyday thinking was fishing coins out of my purse to pay the toll for the Mass Pike and, in the crush of traffic, thinking of the units of money the coins were.

Norene Rolle

7 of 8 people found the following review helpful:

5.0 out of 5 stars Common Sense Math, September 24, 2002

By 

rosemary mathey (Millers Falls, ma United States) - See all my reviews

This review is from: The Glass Wall: Why Mathematics Can Seem Difficult (Hardcover)

Wow! This is a terrific book on mathematical thinking. It is very readable, full of insights, aha's, and quotable thoughts like, "The heights of mathematics are scaled by standing on tables". This is a must read for classroom teachers and essential to student teachers. Frank Smith is an outstanding educational theorist, and his newest offering is a worthy addition to educational libraries.