Teaching, With Respect to Mathematics and Students
For over 20 years, I have been trying to teach elementary school mathematics in ways that honor and are rooted in concerns for the integrity of mathematics as a discipline and that attend to and make serious use of students' thinking. Although these may be laudable aims, exploring what this might mean has presented interesting intellectual and practical problems. On one hand, possible mappings between the construction of knowledge in the discipline and school learning are far from simple or obvious. And, on the other hand, for any defensible instantiation of such practice, too little is known about what it takes for teachers and students to work in these ways in school. Hence, my work has entailed both invention and inves tigation. I use my teaching to explore what these ideas might mean in practice. I study the resulting teaching and learning-both mine and my students'—in order to explore the problems and demands of such practice (see, for example, Ball, 1993a, 1993b, 1997; Ball & Wilson, 1996).