The Glass Wall: Why Mathematics Can Seem Difficult

Rating:
Summary: Looking at math from the inside out
Review: 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

Rating:
Summary: Looking at math from the inside out
Review: 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

Rating:
Summary: A weak thesis that goes undefended
Review: The thesis of this book is that math can't be truly understood through language. The language of mathematics is numbers, and it can only be truly understood through numbers.

While that is true, language is an effective means of teaching people how to think about the numbers. Also, despite Frank Smith's thesis, he spends almost the entire book using language rather than numbers to explain mathematics. I would say he proves his own thesis wrong, except he doesn't explain mathematics that well, either.

It did get me thinking about math in terms of how the numbers interact, vaguely, because he stated that. That helped a little, even if he didn't elaborate on how exactly one should think about math in terms of numbers rather than language. That's why I give it an extra star.

Skip onto something more truly informative.

Rating:
Summary: Common Sense Math
Review: 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.

Rating:
Summary: Common Sense Math
Review: 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.