The last approach is teaching via problem solving. In this approach problems are valued not only as a purpose for learning mathematics but also as a primary source of doing so. "The teaching of a mathematical topic begins with a problem situation that embodies key aspects of the topic, and mathematical techniques are developed as reasonable responces to reasonable problems."(pg. 33) The article states that a goal of learning math is to take the non-routine problem and make it routine. Learning in this way goes from concrete to abstract(Where have we herd this argument before). These problems are usually in the form of a real world situation in which the student needs no abstract algorithm but can be solved with a little common sense and thought as to what is going on. The problems build on each other and latter on more abstract ideas are pushed but not forced on the learner. These problems are much more open ended in there wording.
This is the third approach. How does this approach fit the NCTM standards? Has anyone used this approach? What do you think about the three approaches? How have you used them(if you used them at all)?
Scott Powell University of Hawaii University Lab school Honolulu, HI. 96822 firstname.lastname@example.org