Teaching Factoring – Should we?
There is a point of view that says that factoring is over-emphasized in algebra. I disagree strongly. Proponents of marginalizing or eliminating factoring make two major arguments.
1. Students don’t need factoring in order to do anything else. You know? Real-world wise, I buy it. But real-world wise, I can’t make a good argument for studying past per cents or making change. And I can’t make much of a real-world argument for most of what we teach, in most subject areas. But we expect knowledgeable adults, we expect young adults who can pursue studies in multiple areas, including those that are math-dependent, and we expect young adults who are conversant with a body of knowledge most of us share.
By deemphasizing and marginalizing factoring, we cheat our students.
2. The other argument is slick. Factoring, they put forward, is not necessary. The people who use this line agree that math is necessary, but usually focus on problems requiring numerical solutions: Set up the quadratic, use the formula or read approximate values from a graph. Let’s agree with them, but then ask, is factoring a useless skill? Of course not. Can it be avoided? Up to a point, perhaps, but you need to make a conscious effort to avoid it. Why not teach the skill?
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Here’s what’s happening. 1. Factoring is hard. 2. We have a societal attitude that says innumeracy is okay. 3. We have an undercurrent that says cut out as much math as possible. 4. We have another trend that says challenge everyone (a reaction to racist tracking) and so 5. instead of saying, forget about math, we have anti-math people saying: forget about hard math. And 6. We have teachers who either find some topics difficult themselves, or who have limited flexibility in relation to teaching or reteaching more difficult topics. And the result: factoring and geometry proof are marginalized.
It ends up looking like this: more students do more math at the level of algebra and up than ever before, but watered down. The critics of difficult, procedure-heavy math have given us easier, procedure-heavy math. But more of the procedures are calculator keystrokes. And they are winning. Factoring in particular has been reduced to a secondary place in the curriculum. Most text books are written with factoring coming after parabolas and the quadratic formula, ie, intentionally shunting factoring aside. And the problems are too few and too basic.
This is, of course, the wrong answer. We should be teaching real factoring. Our curricula should develop the mathematics in a natural way, (the ordering in most books supports, instead, early introduction of topics without appropriate background, in order to do graphing earlier. Bravo TI! See what money buys?) with factoring preceding quadratics, and with both of them preceding parabolas. We should do our best to teach real math to all of our students, and we should recognize that some of our students will not have great success with some of the more difficult topics.
We should approach each student as if s/he has potential to study much more mathematics, and offer that student appropriately challenging work. When a student stumbles, we should provide support. And if a student eventually reaches harder math than they can handle, well, we have brought them as far as they will go (at that time). Far better to push a student to their limit, then to assume lack of ability in advance.
So I do teach factoring, fairly substantial factoring. In subsequent posts I will describe how I organize the topic (for bright high school students who don’t necessarily like math, and for weaker college students who are looking for the minimum amount of mathematics to graduate).