It’s happened again: a math question made students cry.
This time it was in Scotland—very discouraging, as I’ve always assumed the Scottish raise a tougher, more stoic, northerly breed of mathematician. Alas; it seems they’re as skittish and frightened as the rest of us.
Here’s the offending question:
(My two cents? This question is more than just fair; it’s really good!)
But students panicked. Then they tweeted their panic. The BBC quoted a former examiner denouncing this question as “unfit for purpose.” And commentators leered at the spectacle—by this point routine—of students freaking out about a hard math question.
This sort of ordeal threatens to confirm our darkest and most cynical suspicions about students. They’re incurious. They’re mercenaries. They’re on a witch hunt for anything that pushes them out of their comfort zone. They worship at the Church of the Right Answer.
So who do we blame? The students? Their parents? Their teachers? Educational bureaucrats, who are always a fun punching bag?
I believe that this flawed state of affairs emerges not through someone’s sinister design, but by well-intentioned increments. The problem isn’t that we want too little from our tests.
It’s that we want too much from them.
We want our tests to be objective. So we stop testing fuzzy, hard-to-measure things like creativity, insight, and broader perspective.
We want our tests to be consistent. So we stop asking questions with any degree of novelty or surprise.
We want our tests to be fair. But deep and authentic understanding is hard to measure fairly—much harder than procedural fluency—and so in the end we abandon that, too.
Every step of the way, we’re trying to sanitize our tests, to cleanse them of idiosyncrasy and irregularity. But those rough edges—surprising questions, strange twists, subversion of expectations—are what make tests work. They’re how we measure actual thinking and understanding, rather than just the narrow ability to carry out prescribed steps in a mechanical way.
Eliminating the surprises from a math test is like eliminating the bacteria from your stomach. It might sound like a good idea, but only if you don’t know how a stomach works. Without those bacteria, you die. They’re the active ingredient, the metabolic engine, the weird but powerful secret to the organ’s entire functioning.
And, if you’ll forgive the somewhat gross analogy, the same is true in math education. The attempt to sanitize a math test is precisely what kills it.
My colleague Richard recently remarked that every math test is, at its heart, a Turing test. Is there a thinking intelligence behind those answers? Or are they just the mechanical replies of a robot, blindly executing an algorithm? Can the test-taker really reason about mathematics, or can they merely fill a few pages with the right symbols?
Such assessment is inherently messy, incapable of perfection. You need to ask students questions they’ve never seen before. You need to surprise them, to provoke them, to challenge them, to push them, to…
Well… to test them.
I’m saying nothing new, of course. Ever since we’ve had schools, we’ve had folks like me, wringing our hands and shouting through clenched teeth that This emphasis on rote learning has got to stop!
But perhaps there’s something different about this moment in history.
The UK now has many exam boards, each competing for customers. This seems to have created a “race to the bottom.” Nobody has any vested interest in making the tests authentic and challenging. Instead, everybody—parents, teachers, students, and administrators—wants tests that are predictable and coachable. The exam boards, forever in search of new clients, are only too happy to oblige.
In the US, meanwhile, the landscape is shifting. For more than a century, we’ve had a deeply idiosyncratic and localized system, suspicious of standardized tests. But now, before our eyes, it’s coalescing into something more unified and national. The accountability movement has placed a sharp new focus on big, standardized exams.
And so we, too, hunger for assessments that are objective, consistent, and fair. We’re designing our whole system around the belief that such things exist.
And hey, maybe they do exist. I’ve always respected the AP exams. I teach now at an IB school, which I love. Even the English A-Levels of a generation ago seem to have done a better job of assessing real mathematical thinking. I certainly don’t mean to oppose all testing or centralization. Goodness knows that, at times, the US could do a lot more to live up to its “U.”
But we need to temper our expectations for these tests. We seem to want from our exams the diagnostic precision you’d get from an X-ray scan or a blood test, but education isn’t like that. Our kinds of tests seek to measure something subtle and slippery, a nebulous but absolutely vital thing called “understanding.”
These tests won’t be perfectly objective.
They won’t be totally consistent.
They might not even be 100% “fair” (however you define that word).
Instead, think of a math test like an interview with a politician. You ask a question, and from the way they respond, you learn something about them—how they reason, how they frame issues. Ask easy, familiar questions, and you’ll get prepped, robotic answers. But ask something fresh, thought-provoking, and just a little bit weird, and you might get a glimpse of what’s really going on inside.
Are these methods perfect? Of course not. But, short of telepathy, they’re the best we’ve got. They’re far better than nothing, and far, far better than the lifeless, sanitized spectacle that British exams are in danger of becoming.