Why Bright Students Still Struggle With Maths (And It's Not About Effort)
Many capable students struggle with maths not because they lack ability, but because mathematics asks more of working memory, executive functioning and conceptual understanding than traditional teaching often accounts for. Here’s what’s actually going on, and why it changes everything about how we teach it.
- By Esther White.
Why Capable Students Can Still Struggle
A boy I'll call Sam sat in front of me a few years ago, working through two-digit addition. The week before, he had solved the same type of problem without any trouble. This week, he stared at 47 + 28 as though he had never seen a plus sign before. His teacher had gently suggested he “just wasn't a maths person.” His mother thought he wasn't trying hard enough. Sam had started saying the same thing about himself.
None of that was true. Sam understood addition perfectly well. What he didn't have, that afternoon, was enough spare mental capacity to hold the numbers, remember his plan, manage the regrouping and keep track of where he was up to, all at once. Once we slowed things down and took some of that load off him, he solved the problem easily.
I've seen a version of this play out many times, over more than 25 years working alongside classroom teachers, tutors, intervention specialists and parents. A capable student understands something on Monday and seems to have lost it by Thursday. That raises an obvious question. How can a student solve a problem successfully one week, then appear unable to do it the next?
The answer usually has little to do with ability or effort, and a great deal to do with working memory, executive functioning, how securely a concept was understood, and how consistent the mathematical language around a student has been.
When Working Memory Gets Full
Working memory is the mental workspace we use to hold and manipulate information while we are actively thinking. It is where a student holds a partially solved problem, a sequence of steps, and the next thing they need to do, all at once. That workspace is limited, and for some students, mathematics fills it very quickly.
Take a simple multiplication fact. A student who has 6 × 7 firmly memorised retrieves it almost instantly, at very little mental cost. A student who hasn't yet secured that fact has to reconstruct it, perhaps by counting in groups, while also holding onto the larger problem it sits inside. Put that same fact inside a multi-step word problem and the cost adds up further, because the student also has to hold the structure of the problem and remember what step comes next.
This is why a student can understand something perfectly well on its own and still struggle once it becomes one part of something bigger. A student might explain regrouping ten ones into a ten with real confidence when it's demonstrated in isolation, then lose track the moment that same regrouping becomes one step inside a longer subtraction problem. The understanding hasn't disappeared. There simply wasn't enough spare capacity to hold the whole task at once.
Executive functioning sits closely alongside working memory, and the two are often talked about together because they work together in a maths lesson. It's what helps a student plan an approach, organise information, maintain attention, monitor their own progress, shift strategy when something isn't working, and manage a task with several steps. A single word problem can call on most of these before the actual mathematical thinking even begins. When a student starts confidently and then stalls, or applies a strategy correctly once and abandons it the next time, that is often executive functioning under strain rather than a lack of mathematical understanding.
There is a simple, useful idea underneath both of these. Working memory is limited, and good instruction reduces unnecessary demands on it so a student has more capacity left for the mathematics itself. Confusing instructions, inconsistent language and cluttered worksheets all add demands that have nothing to do with the maths a student is meant to be learning. This isn't only true for students who are struggling. Every student's working memory has limits, and for some, those demands press up against the ceiling more often than others, which is worth being curious about rather than something to diagnose from behaviour alone.
Why Mathematics Magnifies the Problem
Mathematics makes this harder than most other subjects because it is relentlessly cumulative. A student can study a historical event without needing last term's unit to make complete sense of it. Mathematics rarely offers that. Almost everything a student learns builds directly on something learned earlier, and a gap in that earlier learning tends to resurface later, usually at an inconvenient moment, disguised as a brand new difficulty.
Fractions are a clear example. A student's whole number instinct, that more digits means a bigger number, works against them the moment fractions arrive, because a bigger denominator actually means smaller pieces. Without a secure, concrete sense of what a fraction represents, many students carry that whole number thinking straight into fraction problems and land on answers that feel logical but are mathematically wrong. When the earlier foundation is insecure, a student has to reconstruct old knowledge and process new knowledge at the same time, which is exactly the kind of double demand that overloads working memory.
This is also why what looks like forgetting is often something else. It's tempting to call it forgetting when a student who seemed to understand something last week can no longer do it this week. Genuine forgetting usually needs only a small reminder to come back. More often, the student's understanding was never quite connected in the first place. It was a fragile, temporary hold on a procedure rather than a genuine grasp of why it works.
Memorised procedures and real conceptual understanding behave differently over time. A memorised procedure, held together mostly by repetition, can be recalled well immediately after learning, then fall apart the moment the numbers, context or format of the question changes. A student who understands why regrouping works, rather than only how to do it, has something to reconstruct from if they lose their place partway through. A student relying entirely on memorised steps has far less to fall back on. None of this is an argument against practice or fluency. Once genuine understanding is in place, regularly recalling a concept, rather than simply reviewing it passively, helps strengthen those connections over time.
Understanding Before Abstraction
If fragile understanding is part of the problem, the answer isn't to abandon memorisation. It's to make sure understanding comes first, and that mathematical language and instruction stay consistent enough for a student to build on.
Many of the misconceptions I see in students aren't carelessness. They are logical conclusions drawn from incomplete information. A student who has only ever multiplied whole numbers greater than one may reasonably conclude that multiplication always makes numbers bigger, a sensible pattern that simply needs updating once fractions and decimals arrive. Our job isn't to treat this as an error to correct quickly, but to identify precisely where the student's reasoning diverged and rebuild from there.
Mathematical language matters here too. Maths has its own precise vocabulary, and when it's used inconsistently, that creates unnecessary work. If one teacher describes division as sharing and another as how many groups fit into, without ever connecting the two explicitly, a student has to decode which meaning is intended before they can begin thinking about the mathematics. That decoding uses working memory the problem itself needs.
This is where concrete materials and visual representations earn their place. Used well, they externalise information that would otherwise have to be held entirely in a student's head, so a student can see a mathematical relationship rather than hold it in their mind alone. A student building an array to represent 4 groups of 6 can see, directly, that it's the same total as 6 groups of 4 arranged differently. Abstract notation becomes far more meaningful once it represents something the student has already built and understood, rather than a symbol met for the first time.
None of this means concrete materials are automatically better than symbols. Manipulatives and visual representations only help when they are purposeful, mathematically accurate, and explicitly connected both to the concept they represent and to the abstract notation that follows. At Maths Australia, we believe new mathematical understanding is generally best introduced through purposeful, multi-sensory teaching: concrete materials, visual representations, precise language, physical interaction and explicit teacher modelling, used together with a clear purpose. The aim is never sensory stimulation for its own sake. It's mathematical understanding, built in a way that reduces unnecessary strain on working memory while a student learns something new.
How I-CRAVE Maths® Puts This Into Practice
Everything above points towards a practical way of teaching, and an evidence-based one, which is exactly what the I-CRAVE Maths® Methodology was built to provide.
Identify comes first. Before teaching anything new, we find out precisely what a student already understands and where their understanding starts to break down, rather than assuming it from their age or year level.
Concrete follows. We build the mathematical idea physically, using materials chosen with a clear purpose, so the concept becomes something a student has experienced rather than only heard described.
Representational comes next. Students represent the same idea visually, bridging what they built with the symbols that come later, and giving them something to return to rather than relying purely on memory.
Abstract introduces the mathematical symbols and notation, once understanding is secure enough for those symbols to mean something rather than needing to be memorised as isolated facts.
Verbal asks students to explain their thinking using precise mathematical language, often where a gap or misconception first becomes visible, well before it hides inside a harder problem.
Explicit sits underneath all of this. Teaching is clear, sequential and consistent, with modelling, guided practice and genuine checking for understanding at every stage, rather than left to chance.
The point of this sequence isn't the sequence itself. It matters because it reduces unnecessary cognitive demands so students can put their effort into the mathematics rather than into working out what's being asked of them, surfaces gaps before they compound into something larger, and builds genuine conceptual understanding before students are asked to rely heavily on abstraction. It gives students a connected framework they can draw on later, rather than a set of steps that only work under ideal conditions.
Confidence Comes From Understanding
Students who struggle with maths are very rarely students who lack the capability for it. More often, they're meeting mathematics in a form asking more of their working memory, executive functioning, or still developing conceptual understanding than that particular moment can support.
This is genuinely encouraging, because unlike innate ability, this is something teaching can influence directly. How much unnecessary load a task carries, how consistent the language around it is, and the order in which concrete, visual and abstract experiences are offered, are all decisions an educator makes.
Automatic recall of key facts still matters. Knowing something instantly frees up working memory for the harder thinking a problem actually requires. The distinction worth holding onto is that fluency supports mathematical thinking, while memorised procedures without real understanding underneath them tend to be fragile.
Confidence grows when students repeatedly experience genuine understanding and successful mathematical thinking, not simply from getting through more worksheets. A student who understands why something works has somewhere to return to when memory fails under pressure, which is very different from relying entirely on a sequence of steps shown once.
Sam, the boy from the beginning of this article, went on to become one of the more confident maths students in his year. His underlying ability never changed between that difficult afternoon and the following year. What changed was the load the task was placing on him, and the order in which he was given the chance to build his understanding.
If these ideas are useful to you, I'd love for you to explore them further. The I-CRAVE Maths® Methodology brings all of this together in practice, and Maths Australia offers professional learning, including Numeracy Intervention Training, for teachers, tutors and intervention specialists who want to put it into action in their own classrooms.
References
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