In deciding what to code we had to keep two goals in mind: We wanted to code aspects of instruction that relate to current definitions of instructional quality, and we wanted the codes we used to provide a valid picture of instruction in three different cultures.

For the first goal, we sought ideas of what to code from the research literature on the teaching and learning of mathematics, and from reform documents - such as the the National Council of Teachers of Mathematics Professional Standards for Teaching Mathematics - that make recommendations about how mathematics ought to be taught. We wanted to code both the structural aspects of instruction, i.e., those things that the teacher most likely planned ahead of time, and the on-line aspects of instruction, i.e., the processes that unfold as the lesson progresses.

Our second goal was to accurately portray instruction in Germany, Japan, and the United States. Toward this end, we were concerned that our description of classrooms in other countries make sense from within those cultures, and not just from the American point of view. We wanted to be sure that if different cultural scripts underlie instruction in each country, we would have a way to discover these scripts. For this reason, we also sought coding ideas from the tapes themselves (see the next page).