Theory for Teaching and Teaching for Theory: Artifacts as Tangible Entities for Storing and Improving Professional Knowledge for Teaching

Abstract

In discussing theories of teaching, we take the position that there is a two-way street between what we call theory for teaching and teaching for theory. We articulate the linkages between these two dynamic processes through a particular conceptualization of professional knowledge for teaching carried by tangible artifacts. Within this context we have tried to answer a set of questions about theory and teaching: (1) What is a theory (of teaching)? (2) What should it contain and why? (3) Can such a theory accommodate differences across subject matters and student populations taught? If so, how? If not, why? (4) Do we already have a theory or theories on teaching? If so, which are they? (5) In the future, in what ways might it be possible, if at all, to create a (more comprehensive) theory of teaching? To answer these questions, we draw on the lens of Confucian learning as well as examples from Chinese and U.S. mathematics education to elaborate on understanding, assessing, and accumulating professional knowledge for teaching.