Mathematical Sciences (21) This project is creating a flexible set of instructional modules for use as supplementary resources in mathematics content or pedagogy courses taken by future mathematics teachers. The content of the modules is based on the Math Forum's Problems of the Week (PoW) service that consists of open-ended, engaging, and relevant problems to which students submit solutions and explanations over the Internet. This existing collection of problems, the associated student solutions, and the supplementary resources represent a rich collection of genuine student work and teacher commentary that can support faculty in their interactions with pre-service mathematics teachers. The intellectual merit of this work builds on companion research from the Math Forums "Online Mentoring Project," which bears out the need for greater development of teachers' mathematical and pedagogical knowledge for teaching. The project's broader impacts lie in the flexibility of the materials that are designed for use in multiple ways within an existing curriculum and courses, including as in-class activities, as homework assignments, or as stand-alone online modules that operate in parallel to the other course activities and assignments. In addition, the extensive use of the Math Forum is well documented and provides a natural dissemination vehicle for the materials that assists in the field-testing of the modules. Finally, the project is researching how a focus on i) the analysis of student thinking and ii) instruction that places student understanding and problem solving at the core of instructional decision making, can affect the beliefs and practices of university faculty, and their school math instructor colleagues.
