Evaluating a classroom mathematics lesson is difficult unless you first know what the teacher was trying to accomplish in the lesson. We asked teachers, on a questionnaire, to tell us what they wanted students to learn from the lessons we videotaped. Most of the answers fell into one of two categories:

1. Skills - answers that focused on students being able to DO something: perform a procedure, solve a specific type of problem;
   
2. Thinking - answers that focused on students being able to UNDERSTAND something about mathematical concepts or ideas.

The graph shows the percentage of teachers who gave responses in each of these two categories. Japanese teachers focused on thinking and understanding; German and US teachers on skills.

These different goals lead Japanese teachers to construct different lessons than US and German teachers, as we will see on the next page.