I am continuing the series today with Chapter Five ["Teaching"] on pages 57-70. Please feel free to comment as we lead up to all the Boston meetings.
1. The author says, "In addition to beckoning with the light of future understanding at the end of the tunnel, we need even more to increase illumination in the interior of the tunnel." An interesting quote! What does it have to do with "retrospective understanding of mathematics"?
2. React to this myth: "The best way to learn how to solve complex problems is to decompose them into a sequence of basic skills which can then be mastered one at a time."
3. The author points out that the United States is "one of the few countries in the world that continues to pretend--despite substantial evidence to the contrary--that elementary school teachers are able to teach all subjects equally well." What recommendations for change would you make to ameliorate this situation?
4. The author argues for less directive strategies of teaching and claims that "less teaching will yield more learning." What is the price to pay for less directive teaching, and on what basis could such claims of more learning be made?
Ron Ward/Western Washington U/Bellingham, WA 98225 firstname.lastname@example.org