The Point of Grade 9 Math...

...might not be the math. Just listened to a CBC Ideas broadcast featuring Jean Briggs, an anthropologist, talking about Inuit strategies of child rearing and teaching and, somehow out of that it occurs to me that my focus in Grade 09 math doesn't necessarily have to be the math. It's about learning to learn and about seeing the world differently. It's about the mental equivalent of what a good masseuse might do to your spine in loosening it up and allowing you to move not just more freely, but differently altogether as a result.

Just remembered a connection to the Inuit. According to Briggs, children were often asked things like "Do you (incorrectly) imagine that such and such is the case?" The method is extremely open-ended and non-prescriptive and forces/expects that the child will generate their own response. Prescriptive right and wrong responses are eschewed.

Also, according to Briggs, some variation of counter-factuals are used. An answer might be given that is intentionally wrong with the expectation that the child will know it is wrong and deduce the "correct" and opposite answer.

Imagine if, in my math class, I said to one side of the room "For this class, I want you to only give me wrong answers." And, at the same time I tried to lead/push/divert them into productively wrong answers. Maybe I could (a) make them less afraid to be wrong and (b) get some good insights out of it.

I wonder how some of my super-keen kids would take to this?

Cognitive Load

Gary Davis at Republic of Mathematics (which is starting to look like a v. interesting read from the POV of mathematics education) refers to an interesting concept (apparently originating with John Sweller). The notion is "cognitive load" and it deals with the idea that some concepts or operations just require so much cognitive processing that most or many students get stumped by them. The key point here is that teachers should keep the cognitve load in mind when teaching and actively try to manage it.

The example he gives is of students trying to expand -3y^2(4y^3 - 6y + 7). It's one thing to get them to expand something like y^2(4y^3 - 6y + 7) but throw in a coefficient of 3 - not to mention a minus sign and it's just too much to process. But if we're thinking about the "cognitive load" then we can break it down into smaller chunks. First you could multiply through by the y^2 to get -3(4y^5 - 6y^3 +7y^2). Then you could "bring in" the 3 to get -(12y^5 - 18y^3 + 21y^2) and finally bring in the minus sign, switching the signs of every element within the brackets to give -12y^5 + 18y^3 -21y^2.

Many or most teachers would do this anyways but I think I too frequently overlook this and, for everyone, I think the notion of managing the cognitive load is a useful one.

Mathematics Technology Reource

In the course of researching for an assignment in my Mathematics ABQ, I came across the following resource from the University of Illinois' Math Teacher Link site. It's an elearning resource targeting teachers interested in using technology to teach Mathematics.

There's some particularly good stuff on using and teaching Geometer's Sketchpad. They also have modules on Mathematica and Fathom.

Math Jeopardy

The following is a link to the location an electronic version of Jeopardy about Grade 9 Applied Math.

http://ped3101jeopardy.pbwiki.com/FrontPage