# Practices and Knowledge

I was introduced to a new person today. By introduced, I mean through her work. I have never met Dr. Jo Boaler (a professor of mathematics education at Stanford University). I began reading her work today. I suppose I have Dr. Joe Kretovics (professor of educational leadership at Western Michigan University) to thank for the introduction since I am working on a final annotated bibliography from his class. So, thanks for that.

Before today I’d never heard of Dr. Boaler and but today I read an article that I think sums up where my mind has been headed for the last year and a half. (Actually ever since I watched this video by Dan Meyer and this one by Sir Ken Robinson) I love articles like this because they give words to a feelings that I’ve been having. Below I am going to quote an excerpt from an article written by Dr. Boaler in which she is describing the type of knowledge that results from different type of models of mathematics classrooms.

“There is a pervasive public view that different teaching pedagogies influence the amount of mathematics knowledge students develop. But students do not only learn knowledge in mathematics classrooms, they learn a set of practices and these come to define their knowledge. If students ever reproduce standard methods they have been shown, then most of them will only learn that particular practice of procedural repetition, which has limited use outside the mathematics classroom” (pg. 126).

What strikes me the most about this quote is the simple logic in it. Now, she didn’t use deductive reasoning to come up with the quote. These conclusions are the result of an extended longitudinal study involving, as she puts it, “open, project-based instruction” and “textbook-based instruction.” But, she moves past the mathematical knowledge, which is typically the focus of the conversation and begins taking note of the practices and habits that the students are learning along with the mathematics.

Open, flexible, contextual problems yield knowledge that can be used in open, flexible, contextual situations.

Procedural, specialized, algorithmic problems yield knowledge that can be used in procedural, specialized, algorithmic situations.

Which skill set are our students going to encounter most? Which of the sets will reach the most places?

If we are to convince our students that they will indeed “use math everyday,” then, by golly, it seems like we should be preparing them as best we can for the type of math they are going to have to do. And most of the problems our young people find aren’t going to have answers in the back of the book…

Reference

Boaler, Jo (2001). “Mathematical Modelling and New Theories of Learning.” Teaching Mathematics and Its Applications. Vol. 20. No. 3, p 121-128.