Two comments

I wanted to address two related comments made to an earlier post I made.

Rudbeckia Hirta said...

The problems don't lie entirely with the NCTM Standards. Example, from the document itself (pages 5-6): "some of the pedagogical ideas from the NCTM Standards -- such as the emphases on discourse, worthwhile mathematical tasks, or learning through problem solving -- have been enacted without sufficient attention to students' understanding of mathematics content."

I agree to an extent. However, the problems with the standards is (a) they are generally so vague that they can (and do) mean anything that you want them to mean and (b) they generally end up meaning what math education professors want them to mean because nobody else has either the time or the authority to flesh out the details.

Chris C. said...

Constructivism is a theory of learning, and so it states that it's the way students learn (building on what they already know; contructing understanding) regardless of pedagogical specifics; even during a lecture or when the teacher is an authority figure.

I agree, but that brings two questions to mind.

First, if constructivism as a theory of learning (and it is), then we can conclude that as far as introducing it into the teaching of mathematics, it applies equally to lectures and other traditional techniques as to these new student-directed activities which are all the rage. In that case, we need to investigate what value it brings to the teaching and learning of mathematics. What are the insights that constructivism sheds on the question which will allow us to develop better teaching techniques? I have never seen this addressed in any research (well, U.S. research anyway, more on that in a minute). All I have seen is the quasi-religious belief that student-directed activities are intimately tied to constructivism in some way which the uninitiated can not hope to comprehend.

This ties directly in to my second point. Constructivism, as you point out, is not an instructional technique. However, in 6 years of teaching and 2 years of graduate education, I NEVER saw constructivism applied in any manner other than "Students construct their own understanding in geometry, so stick them in front of Geometer's Sketchpad." and "Students construct their own understanding in statistics, so stick them in front of a simulator." and "Students construct their own understanding in algebra, so give them blocks to play with to solve equations."

If anyone out there can point me to any applications of constructivism which are not of this nature PLEASE pass them along.