Task First
I shared these two slides in my earliest talks on the need to embed problem solving into the mathematics curriculum.
Of course I wanted to show off. Not because I got first place (totally because I got first place), but because that piece of paper is the only personal possession that says I won something. You’d think my family would put it in frame, but nobody cared so I put a border of Scotch tape around it. Seeing the obvious care in my taping job is both impressive and pathetic.
When it surfaced while I was cleaning out files (the ones that lived in a massive tall ugly metal file cabinet), I immediately questioned its authenticity. The internet came through with this article from Boise State two years prior to the event. Apparently I got to participate because I was in TAG (talented and gifted). You know what’s dumb though? My English teacher transferred me to TAG—a class full of students who were actually talented and gifted—because of my writing. I remember dreading the transfer and telling my teacher, “But… I’m just trying to learn English.”
The now decades old shift from “back to basics” to “problem solving” in school mathematics makes me wonder why we even begin with the basics and fluency as if they were absolute prerequisites to problem solving and reasoning. We don’t do that with other learnings, like riding a bike or making a batch of cookies. We teach writing by having students do three things: 1) write, 2) write some more, 3) don’t stop writing. So when NCTM (1980) stated that problem solving needs to be “the focus of school mathematics,” we each went our separate ways and implemented what we thought that meant.
Our separate ways might be what I read in Chapter 3 of New Directions for Elementary School Mathematics: 1989 Yearbook (Schroeder & Lester, 1989) where teachers’ approaches to problem-solving instruction fall into three categories:
Teaching about problem solving
Teaching for problem solving
Teaching through problem solving
While it is the third approach, teaching through problem solving, that I subscribe to and advocate for, it’d be foolish (perhaps even impossible) to ignore the other two approaches as I believe teaching about and for are byproducts when teaching through. The converse is not true, however, meaning the first two approaches do not yield problem solvers and deep thinkers the same way that teaching about bicycle wheels and chains does not yield bike riding. At least it does not elicit the wind-in-your-hair kinda joy from actual bicycling.
Below is the best evidence I see that we’re not on the same page.
The person tweeted out this reply when Open Up Resources quoted what I’d said in a talk. And what I’d said was to challenge all students, not just a select few, and we shouldn’t equate struggle with arithmetic/computation as an inability to problem solve.
But we can be on the same page, at least be in the same book, with a shared vision that mathematics learning must be inclusive. I wonder if the exactness of math calculation—that 2 + 5 = 7, and 20% of 80 is 16—somehow translated into the perceived need for exactness of math teaching, at least in its sequence. It reminds me of when a teacher observed me facilitate a lesson on stacking cups and was genuinely surprised that I didn’t teach “the y-intercept” prior to this task.
All that to say we should start presentations with a task, best icebreaker I know, even one like this from Thinking Mathematically (Mason, Burton, & Stacey, 1982):
I have just run out of envelopes. How should I make myself one?
Maybe that was a bad example. Hurry before it becomes obsolete like a file folder.
