Jeff's Reviews > How to Solve It: A New Aspect of Mathematical Method
How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)
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George Polya's classic How to Solve It is a seminal work in mathematics education. Written in 1945 and referenced in almost every math education text related to problem solving I've ever read, this book is a short exploration of the general heuristic for solving mathematical problems. While the writing is a bit clunky (Polya was a mathematician and English was not his first language), the ideas are so deeply useful that they continue to have relevance not just for solving mathematical problems, but for solving any problem in any field.
Polya's general steps for solving problems include the following four steps: 1. understand the problem, 2. devise a plan, 3. carry out the plan, and 4. look back and examine the solution. These are simple and easy to remember steps, but powerful in their applicability to the most basic to the most complex problems that we face and are at the heart of learning. Over the years, different writers have revised these steps (added, taken away, shifted the wording and emphasis) the essential points still hold.
In addition, to the overall framework of Polya's heuristic and its generalizable nature, what I really like about this work is the fact that I can revisit it for nuggets of wisdom. The third section and roughly half of the book is taken up with "A Short Dictionary of Heuristic" which is a great resource. Each entry is a short essay on a given topic that weighs on either the nature of problem solving or the history of problem solving. One useful framework, that I took away immediately is the difference between "Problems to Solve" and "Problems to Prove." Making a distinction between these two types of problems it is easy to see that we often focus in education on problems to solve, but I and many students love finding out why (problems to prove).
So that said, I think this is a book that I will come back to and reference: a true classic in the educational literature.
Polya's general steps for solving problems include the following four steps: 1. understand the problem, 2. devise a plan, 3. carry out the plan, and 4. look back and examine the solution. These are simple and easy to remember steps, but powerful in their applicability to the most basic to the most complex problems that we face and are at the heart of learning. Over the years, different writers have revised these steps (added, taken away, shifted the wording and emphasis) the essential points still hold.
In addition, to the overall framework of Polya's heuristic and its generalizable nature, what I really like about this work is the fact that I can revisit it for nuggets of wisdom. The third section and roughly half of the book is taken up with "A Short Dictionary of Heuristic" which is a great resource. Each entry is a short essay on a given topic that weighs on either the nature of problem solving or the history of problem solving. One useful framework, that I took away immediately is the difference between "Problems to Solve" and "Problems to Prove." Making a distinction between these two types of problems it is easy to see that we often focus in education on problems to solve, but I and many students love finding out why (problems to prove).
So that said, I think this is a book that I will come back to and reference: a true classic in the educational literature.
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November 24, 2010
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November 24, 2010
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November 24, 2010
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November 24, 2010
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education
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Solomon
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rated it 5 stars
Mar 21, 2021 12:54PM

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I also read a fair amount of general mathematics books. Happy to give recommendations on history of math or a few other topics. Check out my math bookshelf if you are interested.