It’s Pre-service Teacher Time in my building. I’m hosting 3 students from the nearby regional campus of Purdue University. They’ll be making 8 hours of observations, occasionally helping groups of students work through problem sets, and trying out some textbook tactics for redirecting wayward students.
As we all were, they are well-scrubbed and eager. When they arrived (midway through a class period) earlier this week, I gave them about a 20-second rundown on what we were doing and let ‘er rip. After a class and a half, during my plan period, we spent a little time debriefing.
Pre-service teacher takeaway: “This school… is nothing like ours.”
(Covered “not pretty, but real” here, last fall, with my first round of observers this school year.)
For years I’ve been on a mission to make sure my students aren’t just robotically following a set of steps, but instead working towards real understanding of the math we do. As an example, when multiplying binomials, we talk about using the Distributive Property twice, rather than the shortcut FOIL (first-outside-inside-last) which names the four partial products of the multiplication. The idea is that by using terminology “distributive property” , students will be prepared to multiply any polynomials, not just a pair of binomials. I literally have said “FOIL” zero times this school year.
And no one has asked about it. Until now.
One of my 19-year-old observers, fresh out of calculus class at a suburban high school, asked me: “Have you heard of FOIL?”
As Shoeless Joe Jackson said, famously, with a shake of the head: “Rookies”.
They meant well. I just let it ride and we continued our quick debrief before they had to head out. I sent them on their way with two assignments: go look up the free e-book “Nix The Tricks” by Tina Cardone, and do a search for the MTBoS. I figured that would be way more effective than me trying to squeeze in an explanation before they had to take off. (Note To Self: ask them if they did a little googling when they come back around next week). But, Long Story Short: as Cardone says on pg 117:
As students repeat the procedure they will realize that each term in the first polynomial must be multiplied by each term in the second polynomial. This pattern, which you might term “each by each” carries through the more advanced versions of this exercise.
Here’s what that looked like in our class notes:
I used that pattern as a set-up for factoring trinomials of the form ax^2 + bx +c, hoping that it would lead seamlessly into factoring by grouping. I took great pains to remind them they already know how to do the distributive property, and how to factor out a GCF.
I planned this out intentionally, to make learning happen. I think all I really did was confuse them. But on the second day, when we finished the notes and carved out time in class to begin the practice set… a glimmer of understanding.
We’ve been working hard to create a culture of perseverance in solving problems (SMP 1 baby!), counting on that mindset carrying over to a willingness to struggle with new concepts. It’s an uphill battle, when we’ve trained our kids for 10 years to sit there, be quiet, copy what the teacher writes down, and maybe regurgitate it on a test. It’s a big leap for a student to say “hey, it doesn’t matter if I’m wrong, I’m gonna try to figure this out”. And I’ve actually heard that this year. No lie.
Students gotta have the tools to be able to struggle with a problem tho. The first tool: understanding the math that holds up the new skill we’re learning. I’m happy to play the role of the helpful hardware man.