The Art of Problem Solving: Exploring George Polya's Heuristics

We will explore the art of problem solving via George Pólya's exquisite 1957 book "How To Solve It: A New Aspect of Mathematical Method, Second Edition". What do you think of Pólya's book and its methods? Do they make sense to you? Does the Pólya method work? Is this the approach you use in solving problems? What do you like (and dislike) about this approach? What is missing in Pólya's approach? With what other systems of heuristical problem-solving could we compare Pólya's methods? What do you think of "the list"? Would you change the list in any way to make a poster to put in your work area?

Did reading Pólya's book improve your problem-solving skills? Are there problem-solving heuristics that you use which are not discussed in the book? Were you able to solve the 20 problems in Part IV of the book without looking at the solutions? Please bring some problems to the meetup that we can use to test out Pólya's heuristics.

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More information is available on the Wikipedia page "How To Solve It" (https://en.wikipedia.org/wiki/How_to_Solve_It).

You can find a PDF copy of "How To Solve It" on Helga Ingimundardottir's site (https://notendur.hi.is/hei2/teaching/Polya_HowToSolveIt.pdf). The book is still widely available in print, you can find it at your favorite bookseller. Amazon has two printings available: 2004 Printing (http://www.amazon.com/How-Solve-It-Mathematical-Princeton/dp/069111966X) (with a forward by John Conway) and a 2009 Printing (http://www.amazon.com/How-To-Solve-It-Mathematical/dp/4871878309/); there is also a Kindle edition (http://www.amazon.com/How-Solve-It-Mathematical-Princeton-ebook/dp/B0073X0IOA).

Here are two video resources that are interesting:

• A very good 60m 1965 lecture by George Pólya about Guessing (https://vimeo.com/48768091)

https://vimeo.com/48768091

• A nice 8m video summarizing Polya's problem solving method with some very nice examples (http://www.youtube.com/watch?v=uCS7GO0fkc4)

http://www.youtube.com/watch?v=uCS7GO0fkc4

John Conway's forward to Pólya's book mentions Alan Schoenfeld's December 1987 article in Mathematics Magazine on "Pólya, Problem Solving, and Education" which is interesting and can be browsed on-line for free (after registration). Schoenfeld wrote another relevant 37 page article "Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics" (1992) (http://gse.berkeley.edu/sites/default/files/users/alan-h.-schoenfeld/Schoenfeld_1992%20Learning%20to%20Think%20Mathematically.pdf).