There was a student I worked with years ago who kept getting the same type of question wrong. Not every time — but often enough that it stood out.
My first instinct was to reteach the topic in front of me. Go over it again, slower this time, more examples, more repetition. It seemed like the obvious thing to do. It’s usually the first thing any of us try.
It didn’t help. Not really.
A Wrong Answer Is One Piece of Information
It took me a little while to realise the actual problem wasn’t the topic I was looking at. It was something earlier — a step underneath it that hadn’t quite been secured. The student wasn’t struggling with what I was teaching. She was struggling with something the lesson quietly assumed she already knew.
That’s the case more often than we probably credit. An incorrect answer can mean a lot of different things. Sometimes it’s a genuine misconception — the student has learned something incorrectly and is applying it consistently. Sometimes it’s a missing prerequisite from an earlier year level, one that never quite solidified and has been quietly working against everything built on top of it since. Sometimes the student understands the concept perfectly well and simply made a careless error, or the question was worded ambiguously, or they were tired, distracted, or rushing to finish. One piece of evidence, on its own, rarely tells the whole story.
A Closer Look
The student I mentioned was working on equivalent fractions. On the surface, she seemed to have the concept — if I gave her a target denominator, she could find the matching equivalent fraction without much trouble. It looked, from that alone, like the concept was solid.
But when it came to genuinely working with equivalent fractions — explaining why two differently-written fractions represented the exact same value, or working out an equivalent fraction without being handed the target denominator to aim for — she struggled. She could carry out the steps when the destination was given to her, but she couldn’t reason her own way there.
It turned out the two things weren’t actually the same skill. She’d learned a procedure — multiply top and bottom by the same number to reach this denominator — without the understanding underneath it: that a denominator describes the size of the parts something is divided into, and that changing it while keeping the value the same is the whole point of an equivalent fraction. Without that understanding, she had no way to work out what to do when the target wasn’t already given.
Once we went back and rebuilt what the denominator actually represents, equivalent fractions stopped being a memorised procedure and became something she could reason through for herself.
Why Gaps Like This Tend to Compound
An unresolved gap rarely stays contained to one topic. Curriculum content is sequential by design — each new skill is built with the assumption that the ones before it are solid. When one isn’t, it doesn’t just affect that single lesson. It quietly undermines every lesson that assumes it’s already there.
That’s often why a student can seem to be “struggling with maths” broadly, when the real issue is narrower and more specific than it first appears — a single concept, sitting a year or two back, that’s been working against them ever since without anyone quite tracing it to its source.
What This Means for How We Approach Assessment
This is part of why curriculum-aligned diagnostic evidence matters as much as it does. A single incorrect answer, viewed against the relevant achievement standards, can help indicate what’s actually worth checking next — not just which topic to reteach, but which earlier concept might be the real place to look.
In practice, that usually means looking at a work sample less as “right or wrong” and more as a set of clues: which specific step broke down, whether the same kind of error appears more than once, and which earlier-year skills that error tends to trace back to. None of that replaces professional judgement — it can’t tell you everything a student knows, and a single sample shouldn’t be treated as the final word on where a student is. But it can narrow down where to look first, instead of starting from a guess and hoping it’s the right one.
Teaching the Level Underneath
Good tutoring often means being willing to step backward before stepping forward. Not because the current topic doesn’t matter, but because building on a gap rarely holds for long, no matter how much time is spent on what sits on top of it.
Sometimes the difficulty really is exactly where you first think it is. But sometimes it isn’t — and the only way to know for certain is to check.
Tracey Hand | TutorPro Hub