Math 502A: Teacher Thinking and Student Thinking in Mathematics

Steve Monk

Winter 2001, Time TBA

Teaching is a highly personal and individual activity that each of us does in his or her own way, in the light of one's own history and inclinations.  There is no such thing as a teaching technique or method that works for everyone.  There never will be a "science" of teaching.  Yet, there are points of view, ways of asking questions, and significant examples that most of us would find illuminating and helpful in our teaching.  To paraphrase an old expression, "Unexamined teaching is not worth doing," not for our students and not for ourselves.

This course will have two goals.  The first is that students acquire new approaches to thinking about teaching, drawing upon the points of view of researchers, teachers, and one another.  The second goal is that students sharpen their ability to reflect on their experiences and address the question of how activities such as those of the course can be helpful in making one's teaching more productive and/or satisfying.

Goal #1.  The main goal for this course is that the students become more systematic and analytic in their thinking about teaching, both their own individual teaching and teaching in general.  They will read and discuss a variety of published papers and cases that focus on students' mathematical thinking in classrooms and in other settings.  Some of the papers present a point of view or a way of thinking about mathematics learning that many have found valuable, while others are of interest primarily because they provide particularly rich learning situations for us to discuss and understand together.

All the readings will be based on specific learning situations, in order to ground our conversations in reality.  Among the learning situations that may be used are: (1)  A student predicting the motion of a car based on its graph of velocity vs. time.  (2)  A beginning instructor managing a discussion about functions in a precalculus class.  (3)  A group of young students discussing whether an object "stops" as it changes its direction of motion from forward to backward.

The issues we will work on together will include:  What intellectual and experiential resources do individual students bring to particular mathematics learning situations?  What obstacles do students encounter as they attempt to learn mathematics?  What is the actual experience of learning mathematics like for various kinds of students?  How can a teacher be helpful in students' struggle to learn mathematics; what are the limitations in the help teachers can provide?

Goal #2.   The second goal is that the students in the course become more aware of the ways in which we, as mathematicians and mathematics teachers, think and talk about teaching.   Toward this goal, we will examine our own conversations and our reflections on them in order to understand the possible relationship between one's daily teaching and one's reflections and analysis about teaching.  We will take up such particular questions as:  What kinds of conversations do we have that work better for us as a group?  Are some modes of discussion more illuminating and helpful than others?  Are there moments in our interactions that are more useful than others in making sense of the process of teaching and in finding ways to do it more productively?

More generally, we will consider questions such as: Can one "learn" to be a more effective teacher?  What can one gain from "experts," as well as from other teachers about the teaching of mathematics? What is the relationship between one's analysis and reflections about teaching and the particulars of what one actually does in working with students?

This is a 3-credit course that meets once a week for 2 1/2 hours, with the time to be decided on by the participants.  The students will be expected to do the weekly readings in preparation for the weekly meetings as well as a number of writing assignments (mostly informal, but shared with others) in relation to the readings, the cases we consider, and the activities of the course.

If you have any questions about the course, please contact Steve Monk at monk@math.washington.edu.