I like to keep an eye on the Google search terms that bring people to this blog. Some warm the cockles of my heart. Some chill the cockles of my soul. Some bewilder the cockles of my mind, forcing me to Google things like “why do people search for such strange terms” and “what exactly are cockles.”
And the occasional search term will tap into a matter of real depth, like this one: “my students are failing my math class.”
It’s bleak. It’s discouraging. And if you’ve taught math, it’s an experience you know.
We’ve all endured days when it felt the whole class was falling short. You demonstrate how to bake brownies; the kids burn theirs into coal. You model a skateboard move; they gasp for air, having somehow placed the elbow pads over their nose and mouth. You say, “Don’t divide by zero.” They light their hair on fire and then, while you sprint for the extinguisher, they divide by zero.
On such days, my psychic antibodies kick in. “This isn’t my fault,” I say. “Their prior teachers didn’t teach them anything. Or maybe they’re lazy. Or wait—why didn’t I think of it before?—it’s all the administration’s fault.” School administration, federal administration, National Aeronautics and Space Administration; it doesn’t really matter, as long as the blame weighs upon shoulders other than mine.
Of course, “blame” has no good place in the classroom. The question “How did we get here?” matters only insofar as it informs the real question: “What do we do next?”
When a whole class fails, nobody wins. The kids suffer twice—first on their transcripts, and second in their blessed little hearts, where they’ll lose faith in themselves, or in the fairness of schooling, or (most likely) in both. The teacher suffers, too—facing worried administrators, outraged parents, and inner doubts about being “cut out” for the profession.
So let’s take it as a given that you can’t fail ‘em all, and explore some possible causes.
My first year teaching geometry, I sampled the whole platter of teacher mistakes. But I really gorged myself on one in particular: bad pacing. I marched through one topic per day, with no breaks for water or rest. Who needs synthesis? Who needs review? Isn’t this stuff obvious?
Well, math you know is always obvious. Math you’re learning never is. It’s healthier to learn one thing well than to “see” five.
When I write a test, I’m often tempted to overload it with interesting, challenging, novel questions. To make it a true test of wits and wills. But a test should assess basic skills, too. It needs a good mix of easy, medium, and hard, if it’s going to hold an honest mirror to students’ abilities (rather than a horror-movie mirror in which they can’t see their own reflection).
A bad grading scheme can create problems, too. It’s easy to turn a test into an all-or-nothing affair—by asking lots of similar questions, or many short questions with no partial credit, or questions where 1c is impossible unless you nailed 1a and 1b. That’s a recipe for whole-class failures.
Grades aim to reflect the quality of a student’s work, and “quality” is one of life’s most flexible concepts. Mathematics—despite its reputation as objective—leaves teachers a lot of latitude.
There is no “first rule of math teaching,” except perhaps “talk about math teaching.” (This is math education’s primary difference from Fight Club, which it resembles in all other respects.) However, there is a truth that I find to be almost universal: Whatever you expect students to know upon arrival, they probably know less.
That’s okay. Learning is hard. Teaching is hard. Summer wipes a giant eraser across all of our mental whiteboards.
Every student has gaps: concepts they’ve never learned, techniques they’ve never nailed, anxieties they’ve never addressed. I can’t pretend those gaps reside in the past, that they’re debits on the ledger of some prior teacher, irrelevant to my work. Those struggles are here, in the present, weighing down my students, derailing their learning. I’ve got to survey the landscape of their thinking—to see what’s there, not what I want to see.
When you ask Google something you should already know—“how much do library books cost” or “who is Tom Hanks” or “what is pasta made of”—the search engine doesn’t snark or seethe or pass quiet judgment. It just shows you the answers: “they’re free”; “the mayor of Hollywood”; “pasta molecules.”
A good teacher is like a sentient Google. No finger-pointing. No recriminations. Just a benevolent omniscience, helping everyone to take the next step.