Factoring

Factoring, or Why I Understand That Some Kids Hate Math

This is the first year that I’m teaching math full time and the first topic that I’ve jumped into is Factoring and Polynomials.  It seems to be a fairly substantive topic in terms of Prescribed Learning Objectives and the amount of space it gets in the textbook.  However, it also seems to me that it is a fairly twisted topic.  Twisted, as in sick or deranged.

Sure, most of us would agree that knowing how to factor a term is pretty important.  But this unit goes well beyond that simple desire.  Factoring and Polynomials is learning a succession of skills for seemingly no purpose at all.  Imagine that you’re a middle of the road student that has no ill toward math.  You start this unit and before you know it, you’re trying to factor:

$x^2 + 5x + 6$

Bear in mind that in BC, grade 10 math students don’t know anything about graphs and curves other than straight lines.  No parabolas yet.

Question #1: What the hell is  $x^2 + 5x + 6$ ?

Question #2: Why the hell do I want to “factor” it?

Question #3: Ok, I got the factors through that algorithm you showed me.  So what?

So we’re stuck with factoring polynomials, without any kind of context. Worse still, there is no possible way to frame some inquiry or problem based learning around this topic because it’s a discrete skill unconnected to, well, everything.

But my question is this: what do other regions do?  What do grade 9 or grade 10 students do for polynomial factoring in NY, for example? Do they just deal with it as needed?  In other words, do they learn factoring in situ?

I’ve tried to find the answer to that question, without any luck. However I have found out one interesting thing. It looks like in the USA they cover topics in our grade 8, 9 and 10 by grades 7, 8, 9. In my observations so far this year, I’d say that for most kids that demonstrate reasonable understanding in math, they are being held back by a curriculum that is slow to develop ideas and concepts.