There is a video of Prof. Georg Polya, giving a lecture to a group of students. Polya was a mathematics professor at Stanford, known best perhaps for his seminal work on problem solving called “How To Solve It”. In the 60’s, the Mathematical Association of America filmed a lecture of his on the role that guessing plays in mathematics.
It is worthwhile watching the video (linked to above). Polya is very charming and gives a good lecture. Unfortunately, the lecture tends to get misinterpreted.
In the past, I have offered criticism of the trend in math ed to give students a type of problem called the “growing tile” problem. Students as young as fifth graders are given these type of problems in which they attempt to find the pattern that describes the sequence of a growing number of tiles or dots. These types of problems are given supposedly to…
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