Abstract
Problem solving and problem posing are very important at all stages of mathematics education. We will give examples from (1) A graduate course on matrix theory conducted using the pedagogy of problem solving before instruction, (2) A course, problem solving, problem posing, and problem choosing, given to primary school teachers in a M.Ed program. The examples will include challenging problems given to the teachers to upgrade their mathematical thinking and their mathematical knowledge and problems that the teachers posed, by adapting the challenging problems for use in their teaching, (3) Problem solving by excellent high school students, and (4) An enrichment course, based on problem solving, for middle school students.
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