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.