Perhaps inspired by my regular reading of Mathematics Teacher's “Delving Deeper” department, I recently took another look at two sets of equations that I usually give to high school students for practice in discovering and then verifying patterns.
Anyone who is looking for insights into the problem-solving process in mathematics is well advised to start with two books that have been in print for more than seven and three decades, respectively: How to Solve It (Pólya), first published in 1945; and The Art of Problem Posing (Brown and Walter) in 1983.
Recently, I had occasion to re-read George Pólya's (1957) classic work on problem solving in mathematics, How to Solve It. Early in the book, Pólya describes the different phases of problem solving, including the fourth and final phase— “looking back.” Describing that phase, he writes:
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