There is a moment that many maths teachers in secondary school know well. A Year 8 student sits in front of a problem involving fractions or ratio, and something fundamental is simply absent. Not forgotten, never fully formed. The student can add. They can subtract. They may even recall multiplication tables under pressure. But the moment the problem requires them to think multiplicatively (to understand that quantities can scale, that relationships are proportional, that division is not merely sharing equally but a way of reasoning about groups), they reach for procedures that don’t quite fit, and the answer unravels.
What that teacher is looking at is not a secondary school problem. It is a primary school problem that arrived late.
The Gap That Travels Quietly
Research has been pointing at this dynamic for decades, though it has yet to fully reshape how schools think about early assessment. A large-scale study conducted by Professor Dianne Siemon and colleagues at RMIT University, involving nearly 7,000 Victorian students across Years 5 to 9, found something that should give every curriculum leader pause: there was a seven-year range in mathematics achievement within any single year level in the middle years of schooling. Students sitting in the same Year 7 classroom were, in terms of their actual mathematical development, anywhere from three years ahead to four years behind each other.
The research identified one factor as the overwhelming cause of this spread: access to multiplicative thinking. Students who had not developed genuine multiplicative reasoning by the upper primary years were not simply behind. They were structurally disadvantaged in ways that compounded with every subsequent year of secondary mathematics.
This finding, initially established through the Middle Years Numeracy Research Project and later confirmed and extended through the Scaffolding Numeracy in the Middle Years (SNMY) project, is not a fringe observation. More recent studies involving up to 32 secondary schools across Australia have since confirmed that access to multiplicative thinking remains the primary explanation for the significant gap in student maths achievement in Years 7 to 9.
What Multiplicative Thinking Actually Is, and Why It Matters
It is worth being precise here, because “multiplicative thinking” is sometimes treated as a synonym for knowing times tables. It is not.
Multiplicative thinking is the capacity to work flexibly with multiplication and division across a wide range of contexts, including fractions, decimals, percentages, ratio, and proportion. It is the conceptual bridge between the arithmetic of primary school and the abstract reasoning of secondary mathematics. Without it, topics like algebra, geometry involving scale, statistical reasoning, and proportional problems in science all become procedural guesswork rather than meaningful understanding.
The SNMY project data put a precise number on how many students were crossing that bridge incompletely. Approximately 70 per cent of Year 5 students, and still around 35 per cent of Year 8 students, did not have reliable access to multiplicative thinking at the time of assessment. A subsequent 2014 study using the same tools (this time with over 1,700 Year 7 to 9 students from lower socioeconomic schools) found that the figure for Year 8 students was closer to 55 per cent.
That is not a marginal group. That is more than half of a cohort entering the second year of high school without the foundational reasoning that secondary maths silently assumes they have.
The Assessment Blind Spot
The reason this gap travels so far undetected is structural. In most school systems, the formal assessment calendar is not designed to catch a problem that develops gradually across the upper primary years. A student can perform adequately on end-of-year tasks, demonstrate fluency with procedures, and still lack the conceptual depth that will matter enormously two or three years later.
In England, the 2024 Key Stage 2 national results illustrate the scale of the underlying problem at the point of primary exit: only 61 per cent of pupils met the expected standard in reading, writing, and maths combined, a figure still below the 65 per cent recorded in 2019, before pandemic disruptions. Maths attainment at primary exit, in other words, was already fragile before those students transferred to secondary.
But the more pointed concern is not about the students who visibly fail to meet the standard; it is about those who ‘just’ meet it. A student who reaches the expected standard at the end of primary school may still carry significant conceptual gaps into Year 7, gaps that are invisible precisely because they cleared the formal threshold. The threshold, as currently designed, does not distinguish between a student with deep multiplicative understanding and one who has learned to replicate procedures well enough to pass.
This is where the role of more targeted, curriculum-aligned assessment becomes not a bureaucratic exercise but a genuine diagnostic one. A standardised maths test designed to probe specific domains (numbers, patterns and algebra, proportional reasoning) can surface the difference between procedural mimicry and conceptual understanding before a student walks through the door of a secondary school that has every reason to assume they are.
What Secondary Teachers Are Left With
The downstream consequence for secondary teachers is well-documented if rarely named plainly. When students arrive in Year 7 or Year 8 without consolidating multiplicative thinking in primary school, their secondary maths teachers are not building on a foundation. They are searching for one while simultaneously trying to deliver new curriculum content.
This creates a particular kind of invisible overload. The teacher can see that a student struggles with algebra or ratio, but tracing that struggle back to an unresolved conceptual gap from Year 5 or 6 is not something a secondary maths classroom is resourced to do routinely. The student, meanwhile, experiences a growing sense that they are simply not “a maths person”, a belief that, once formed, tends to persist.
The equity dimension here is also significant. Research has consistently shown that students from lower socioeconomic backgrounds, and those in under-resourced schools, are disproportionately represented among those who arrive at secondary school without consolidated foundational numeracy. The SNMY research explicitly flagged this, and more recent Australian and UK data has reinforced it. The maths gap is not randomly distributed; it clusters where early targeted intervention is least available.
The Case for Earlier, More Targeted Review
None of this is an argument against secondary mathematics teaching. It is an argument for identifying the gap before it arrives at the secondary school’s door.
The SNMY research demonstrated something important and practically useful: when students with multiplicative thinking gaps were identified early and given targeted, structured support (rather than repetition of the same procedural content), significant progress was possible. Students shifted multiple levels on the Learning and Assessment Framework within a single intervention period. The gap was not fixed at primary; it was addressable, provided it was seen in time.
Seeing it in time requires assessment that goes beyond what annual curriculum tasks or biennial national tests can provide. It requires instruments that are specific enough to distinguish conceptual readiness from procedural competence, and frequent enough to catch the gap while it is still in primary school, where intervention is far less structurally and pedagogically expensive than in Year 9.
The question for school leaders is not whether their students have maths gaps. The research suggests most cohorts do, at varying degrees of severity. The question is whether those gaps are being identified early enough to do something meaningful about them or whether they are being left to announce themselves in a secondary classroom, years after the point when they were first forming.
The student struggling with fractions in Year 8 did not develop that struggle in Year 8. The data has been telling us where it began for a long time. The more useful question is whether the assessment structures in place are designed to see it while there is still time to act.
