What role does authentic problem solving play in teachers understanding of math as part of a liberal education? To look at how teachers come to value mathematics as part of learning. Do they see problem solving rather than exercise doing as a centerpiece of their teaching? What effect do problem solving experiences in a capstone course, a geometry course, and a first year workshop course play in this?

What is the central question or issue? (50 words) Future teacher's conceptualization of math My central question is what aspects of coursework are most effective in affecting students' conceptualization of mathematics as part of a liberal education. My main focus will be on future teachers, and ideally on two or three courses, and the relationships between moments of difficulty and learning to value problem solving experiences in mathematics for themselves and their students.

Why is your question/issue important? (50 words) Importance All too often mathematics education in this country turns into having students learn a set of mindless algorithms for solving exercises as was documented in the TIMMS study. Finding methods of changing teachers conceptions of what and how to teach is the first step in fixing this problem. How will you make your work public? (50 words) Going Public We plan to present our work at the Joint Mathematics Meetings and we hope to present at conferences on mathematics teacher education (NCTM, AMTE). I also hope to develop a reflective portfolio on teaching problem solving in various contexts.

How will you conduct your investigation? (50 words) Methods I will look at 2-3 current teachers and current students. We will analyze coursework, conduct interviews, and look at questionnaires throughout the year. I will also journal my teaching reflections. What questions still remain? (50 words) Questions I will only have a few students to study (particularly teachers). How do I address this project with so few? What aspects of teachers work should I look at for evidence in? What would be good interview and survery questions? What are good prompts for students to reflect on difficulty in problem solving and learning?

Go to my IdeaBank