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The Glass Wall: Why Mathematics Can Seem Difficult Paperback – July 1, 2002
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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.
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.
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.