Referring to a study done compar­ing American, German, and Japanese approaches to teaching elementary mathematics, Green summarizes the key differences:

"Japanese math teachers led class with a different pace, structure, and tone than did other countries' teach­ers [Germany and the US]. Instead of a series of problems, the teacher used just one, and instead of leading students through procedures, they let students do much more talking and thinking.... The American and Japa­nese scripts were the most different from each other....some American teachers called their pattern 'I, We, You': after checking homework, teachers announced the day's topic, demonstrating a new procedure: 'Today we're going to talk about dividing a two-digit number by a one-digit number' (I). Then they led the class in trying out a sample problem together: 'Let's try out the steps for 24 divided by 6.' (We). Finally, they let students work through similar problems on their own, usually by silently making their way through a worksheet: 'Keep your eyes on your own paper. If you have a question, raise your hand.' (You)

The Japanese teachers mean­while, turned 'I, We, You' inside out. You might call their version 'You, Y'all, We.' They began with an in­troduction, but a single problem [like Magdalene Lampert] that students spent ten or twenty minutes working through alone: 'Come up with as many solutions as you can.' (You). While the students worked, the teacher wove through the students' desks, studying what they came up with and taking notes to remember who had which idea. Sometimes the teacher then deployed the students to discuss the problem in small groups (Y'all). Next, the teacher brought them back to the whole group, asking students to present their different ideas for how to solve the problem on the chalkboard. Give the answer and the reason for your answer. Finally, the teacher led a discussion, guiding stu­dents to a shared conclusion: 'What did you learn from today's problem, or what new questions do you have, if any?' (We).

Americans asked a lot of simple questions and sought quick answers. '1 - 4: What does it equal?' Japanese teachers, working at the slower pace provided by a single focused problem, used questions not simply to under­stand whether the child had the right answer, but to peek into her mind, discerning what she understood and what she didn't: Who had the same thinking? Anything to add to this way of thinking? Did anybody else use another way?"