Teaching through Problem Solving (TtPS) is an effective way to teach mathematics "for" understanding. It also provides students with a way to learn mathematics "with" understanding. In this article, the authors present a definition of what it means to teach through problem solving. They also describe a professional development vignette that…

Describes the entire process involved when an untried problem was presented to a group of teachers. The lessons learned from their struggles are helpful reminders that open-ended problems should be presented to high school students. (Author/NB)

Illustrates how engagement in worthwhile mathematical tasks can provide rich opportunities for professional development. Presents different solution strategies for the effective tax rate problem. Emphasizes that, to help students recognize differences among the preceding arguments, teachers need to recognize reasoning based on part-whole…