The Authors Referenced in Chapter 8

Anyone looking for an interesting should check out the work by Brown, Collins and Duguid, 1989, referred to on page 123 of the text. Their analogies and common sense comparisons really bring the light the notion of having our students use their mathematical tools in a hands on manner. It would be very unlikely that an instructor of carpentry for example would spen their time showing their students tools such as a hammer or a square and never letting them use these tools for themselves in a variety of situations before expecting them to preform with their tools in a testing situation.
We need to take the same approach with our students and their mathematical tools we are teaching them to use. The authors have a section of their work called cognitive apprenticeship that is really worth reading. It definitely shows the need to approach teaching and learning of mathematics in a different way. In particular they discuss Schoenfield's work on problem solving.  By having the students wrok with him on problems he had given them he was able to let the students see how these situations are viewed and solved through the eyes of a mathematician. The refer to this as bringing the students into the culture of mathematics.
There is also discussion of how Lampert uses coins to teach multiplication to fourth graders, the idea here is of course how in their real lives the coins and money are something these students are both familiar and comfortable with.
All very interesting and very real mathematics that may be missing from our classrooms from time to time.