The Best Math Teacher I Ever Had Was a Cardboard Box
If I could have been granted one wish as a 5th grade math teacher years ago, I would have pushed for two: I needed to get inside the heads of my students to see why they were getting stuck with what seemed to me to be very simple problems, and I needed them to check the reasonableness of their answers before committing to them. Not a day passed without students submitting answers indicating that I had failed to get across the material, failed to get them to see if their answers made sense, or both.
One day, after metaphorically banging my head on the chalkboard for the umpteenth time, a solution popped out. “Who Wants to Be a Millionaire?” was the most popular show in the US at the time, and its climactic catch phrase “Final answer?” was everywhere. I suddenly envisioned a cardboard dropbox marked “Final Answer?” where students could anonymously submit answers to specific math problems - along with their work - on folded slips of paper. Such a box would add drama to the practice portion of each lesson, especially when I revealed the correct answers after a simulated drumroll. More importantly, the collected slips of paper would give me a glimpse into what students actually had in their heads, and the question on the front of the box would remind them to see if their answers made sense before submitting them.
I suspected the “Final Answer?” box would give me detailed insight into students’ thinking and help them develop habits of self-reflection, and I was right. (Things like formal assessments and “exit tickets” weren’t enough to give me the kind of anonymous moment-by-moment feedback I needed.)
I had no idea, however, that the “Final Answer?” box would change my life.
It may sound crazy - and I would have thought it crazy earlier in my career too - but I now know it to be fact: almost everyone can master math given the right materials/instruction.
Prior to the “Final Answer?” box, if you had pried open my head, you would have found that I didn’t r-e-a-l-l-y believe that all of my students could learn math. I had seen too many bizarre and seemingly random “solutions” to what should have been easy problems over the years to be convinced that math could ever be understood by all.
The “Final Answer?” box showed me in an instant that I was wrong. It happened on a typical day after a typical question. As I started going through the answers the students had dropped in the slot, I sighed - yet again - at how many of them were wrong. But as I unfolded the last one, I got a shock I’ll never forget: half of the class may have gotten the wrong answer - but it was the same wrong answer. The ones who had gotten stuck had all run into the exact same roadblock! “Remove the roadblock,” I thought, “and they should all get the next question right!” I did …and they did! I had chills as the students cheered their own perfect performance.
I now knew it wasn’t the math that didn’t make sense to the kids; it was me. This would have depressed me to no end in the past, but at the same moment this problem revealed itself, a means of finding the solution did too: the “Final Answer?” box! The kids never tired of it, it was teaching them to think deeply about their answers, and it could teach me where they were getting stuck and how to “unstick” them!
Over the next few years, the “Final Answer?” box taught me far more about teaching basic math than my math training ever had. It taught me that if I didn’t have students total up more than two addends at a time when practicing multi-digit addition, many of them would mistakenly conclude that the regrouping digits were always 1’s, and would develop no understanding of the place value involved. It taught me that a series of multiplication problems like 526 x 3, 526 x 33, and 526 x 333 was far more effective for introducing the concept of place-holding zeros than if I had them solve, say, 753 x 3, 892 x 34, and 615 x 348. It taught me that if I didn’t include zeros in the answers (quotients) of the long division problems I asked students to solve, many of them would get stuck when zeros did appear and settle on answers like 57 remainder 8 when the real answer was 507 remainder 8 or 5,007 remainder 8 - even though they knew these answers were unreasonable! The “Final Answer?” box taught me all of these things and hundreds more besides. I’m now systematically incorporating everything I’ve learned over the years into the example-based You Teach You book series.
But far more importantly than any of these things, the “Final Answer?” box taught me that almost anyone can master basic math - for real. Math is logical. Kids understand logic (because it’s logical!). When math is presented logically - in sequence, in stages, in detail, and with an eye toward sticking points and special cases - there’s literally nothing to prevent kids from learning it.
It may sound crazy - and I would have thought it crazy earlier in my career too - but I now know it to be fact: almost everyone can master math given the right materials/instruction.
And yes, that’s my final answer.
