Unraveling the Mystery of the Origin of Mathematical Problems: Using a Problem-Posing Framework With Prospective Mathematics Teachers

In this article, I model how a problem-posing framework can be used to enhance our abilities to systematically generate mathematical problems by modifying the attributes of a given problem. The problem-posing model calls for the application of the following fundamental mathematical processes: proving, reversing, specializing, generalizing, and extending. The given problem turned out to be a rich source of interesting, worthwhile mathematical problems appropriate for secondary mathematics teachers and high school students.