How Not to Teach Factoring (part 0 of 2)

As a young teacher, I was awesome at teaching factoring. My mentor teacher had a system that was brilliant — she’d analyzed every factoring problem and broke them down into types — greatest common factor, difference of squares, easy trinomial, hard trinomial, grouping, sum/difference of cubes, two-step, etc. So she explicitly taught the kids how to identify what type of problem they were looking at, and then she taught them sweet tricks to factor each type efficiently.

Exactly like this, but with polynomials

Exactly like this, but with polynomials

So that’s how I taught. And boy, did I think I was good at teaching factoring. Because when I was going through school, I was taught using the tried and true “figure it out” method. This was where the teacher put up a factoring problem — like 3×2 – 5x + 2 — put a couple parentheses below it (      )(      ) — then said “Figure it out!” This process was then scaffolded by smacking the blackboard and saying “Figure it out!”, except louder, and then eventually jumping up on the desk, waving the hands wildly and yelling “FIGURE! IT! OUT!”…. because learning.

I’d share this story with my own students and it had the desired effect — it made them super-glad that they had me, extra-helpful teacher, with my rules for identifying types of problems and my efficient tricks for solving them. And all was good until I moved to a small school district, had kids for more than one consecutive year, and realized that none of my former Algebra 1 students could factor.


What idiot did these kids have last year?
…….. oh right

Sure, they all could factor during the factoring UNIT, and many could factor on the Algebra 1 exam, but in Geometry? In Algebra 2?


Yeah, after review some of it would come back, there was always trouble with those sneaky two-step GCF problems (“stands for Gotta Check First,” I’d say, for the billionth time, debating the utility of jumping on my desk for emphasis), but what got them, every time, no matter how much we reviewed and no matter how many reminders and hints and prompts and blahs I gave were those damn trinomials with a leading coefficient greater than 1.


Because no matter how slick I could make the trick, the cognitive demand was too high for many of my students. They could remember the easy tricks, but when you started talking about rainbows, or cows jumping around, or any of the crazy “best ways” I heard from other teachers how to teach these problems, it was just a procedure and it was a procedure that did not make sense.

So I burned it all down. I threw out my beloved sequence: 1. GCF (Gotta Check First), 2. DOS (get it? “dos” means “two”, there are two terms, it’s the second type), 3. ET (easy trinomials), 4. HT (hard trinomials, or rainbows, or whatev) 5. Grouping (let’s put this last because it has more than three terms so it looks really hard), and 6. SODOC (eh, leave this for the Algebra 2 teacher, poor sucker, oh wait that’s gonna be me in two years).

And I threw out the “Field Guide to Factoring” we’d make every year, I threw out all the tricks that I used as a student and that I diligently had taught my kids, and I taught every factoring problem the same way. EVERY. SINGLE. ONE.

With that one switch, I all of a sudden noticed something. Some of the “easier” problems under my old system became harder. But all of the “harder” problems became easier. Much easier. And I found that even when kids didn’t know how to complete a problem, they knew how to start one — without hints, without prompting, without any help but my standard stonewall: “Well, what do you think you should do here?”


“Mr. J, you ask questions like my psychiatrist.”
“And when I ask questions like your psyciatrist, how does it make you feel?

And I felt dumb. Because what I was teaching was dumb. It was basic, basic, basic. No special teacher skills required, no flashy tricks, no special techniques. No secret knowledge. But, by gosh, it worked.




OK, this testing thing

A Facebook friend posted an interesting overheard conversation between a NYC student and a friend of hers.

Kid: I hate standardized testing. My mom says I don’t have to do it next year and she might even home-school me.
Friend: I have a dozen little cousins in Nigeria swinging machetes in the field for 14 hours a day. Any one of them would love to trade places with you even if it means sitting through tests for a week out of the year.
Kid: (pause) Point taken.


So, what’s your reaction to this? I mean, #firstworldproblems, amiright? Kid got a taste of real life, got the smackdown! YEAH!

But seriously, this needs some unpacking, and the more I unpacked, the deeper I got in until I realized that I couldn’t solve this with a Facebook comment…. I needed to BLOG.

Yes, that is what I look like when I open wordpress

Yes, that is what I look like when I open wordpress.

Because is this how far we’ve fallen in US education — To draw a favorable comparison for what we do to students, we’ve got to reach for kids in Nigeria swinging machetes for 14 hours a day? That’s not even a real comparison! No one in Nigeria is making those kids swing machetes to EDUCATE THEM. They are swinging machetes to PRODUCE FOOD. The two situations are not analogizable (trust me, that’s totally a word) — they are completely different contexts, with completely different social purposes. If your farmhand is whining about sitting on a tractor to harvest wheat, by all means, bring up the agricultural production system in Nigeria. But we’re supposed to be EDUCATING these kids, not using them as cheap labor!

That’s like saying: “You think your boss sucks because he yells at you all the time? If you were in solitary confinement, you’d pray for that kind of human contact.” And you know the boss in Nigeria is saying “Man, if you kids were in the Congo, you’d be using these machetes to save your families from the LRA. Feel lucky that the only thing you need to hack is cassava.”

People use false analogies all the time as weapons against teachers, and it’s important to call them out when it happens. My friend is a speech therapist who is awesome with kids, and totally on the side of the angels — she even disclaimered her post before I jumped in there, but I just couldn’t get it out of my head. We’ve all worked under administrators whose only response to teacher pushback was “Well, if you really cared about kids, you’d be willing to …..” followed by the most cockamamie educational scheme this side of a Dukes of Hazzard episode.

"See, if you crash through the barn at the juuust the correct angle, they'll learn Algebra!"

“See, if you crash through the barn at the juuust the correct angle, they’ll learn Algebra!”

Let’s be clear: No one is opposing the testing regime in this country because they think America is an awful place to grow up, compared to the rest of the world. We are opposing it because we think it’s harming kids, and that this country can do better.

But here’s what really kills me: Go back to that conversation again, the last line, which goes “Kid: (pause) Point taken.
Now, I’m guessing the way this “(pause)” was meant to be read was “spoiled American kid learns life lesson.” But there’s another way to read it, which is this: Someone told the kid that instead of being educated in the greatest city in the entire United States of America, he could instead be in Africa, doing hard physical labor in a field for 14 hours a day, and….






…wait for it….