This comes from the Math Future email list discussion: http://groups.google.com/group/mathfuture/browse_thread/thread/71711320007c2f47/67e4e32417b09153

Algot Runeman linked this article: http://www.freakonomics.com/2011/11/02/the-way-we-teach-math-and-language-is-wrong/

I said that the phrase that learning must be idiomatic caught my eye. And Sue Hellman responded:

I decided to take a look at the article referenced in tkosan’s response to Linda’s question (link– http://206.21.94.61/misc/permalink/procedural_vs_functional.html).

I think ‘math idioms’ might be related to ‘functional units’ in this article. They would be stand-alone skills that allow one to perform real tasks but which can also be nested in/scaffolded into larger tasks in a way that makes them also meaningful and uesful.

Using meaning or function, instead of procedure, as the starting point is akin to the way I was taught to teach a second language. The initial phrases learned enable a person to do something real (eg. to say good morning, or introduce yourself, ask for a glass of water). The vocabulary and structures one learns in these ‘functional’ units in turn become the framework upon which more complex functional units are built. Everthing links to everything else and always to something that was simple, comprehensible, meaningful, and useful in its own right.

I’m in the process of creating a unit on fractions for a school in the Caribbean. If I follow this process, I have to start by asking myself what a kid there would want to be able to do that having some ‘fraction language’ would make possible or easier. That becomes the starting point rather than what I think of as the easiest skill or normal first step. What would they want to be able to do?

What an excellent question to ask for curriculum development!

I am adding this as a task to our upcoming School of Math Future fraction seminar: http://p2pu.org/en/groups/fraction-interactives-seminar/