Beyond the NAPLAN Score: Why Mathematical Understanding Matters More Than Memorisation
By Esther White, founder of Maths Australia and creator of the I-CRAVE Maths® Methodology
Every year, Australian students complete NAPLAN and schools receive another set of numeracy results. The question that almost always follows is: “How do we improve next year?”
I understand why. Schools are accountable to boards and to parents, and a result on a page feels like something concrete to act on. Having spent years working alongside teachers, tutors and school leaders, I have come to think this is the wrong first question, or at least a premature one.
A NAPLAN result can indicate that a student may be struggling. It is a different matter to explain why, or to identify exactly where that student’s understanding first became insecure. Two students can arrive at the same low proficiency level for entirely different reasons. One may have a genuine gap in place value dating back to Year 2. Another may understand the mathematics reasonably well but lose time in the non-calculator section, or lose focus partway through an item type they rarely encounter in class. Responding to both in the same way, typically with more practice questions in the area the test flagged, rarely helps either of them.
This article draws on the most recent official Australian data on NAPLAN, on the Australian Education Research Organisation’s synthesis of the cognitive science of learning, and on the international research that this synthesis itself draws on. A note on the data: at the time of writing, the 2025 NAPLAN National Results Commentary is the most recent complete national dataset published by the Australian Curriculum, Assessment and Reporting Authority, known as ACARA. Individual school and student reports for the 2026 testing cycle may be released before ACARA publishes its national results commentary for that year, so the national, aggregate figures discussed below are drawn from the 2025 commentary, the latest verified official source available at the time of writing.
What NAPLAN Actually Measures
According to the National Assessment Program, NAPLAN numeracy tests are designed to measure students’ application of mathematical knowledge, skills, procedures and processes as set out in the Australian Curriculum, across number and algebra, measurement and geometry, and statistics and probability. This is genuinely useful information. Since 2023, ACARA has reported achievement against four proficiency levels (Exceeding, Strong, Developing and Needs additional support), replacing the earlier numerical band system and giving schools and systems a clearer, more consistent reference point. NAPLAN is not without value, and nothing in this article should be read as suggesting otherwise.
But a single test, completed once a year under standardised conditions, provides a narrow window into something as layered as mathematical understanding. As the National Assessment Program explains, Year 7 and 9 numeracy tests include a short non-calculator section, in which students demonstrate arithmetical calculation skills, before an online calculator becomes available for the remainder of the test. A test built this way can tell us a great deal about a cohort. It tells us comparatively little about why one particular student answered one particular question incorrectly.
The 2025 national results illustrate why aggregate figures need careful reading. According to ACARA, achievement at a national level has been broadly stable since the proficiency levels were reset in 2023, with year-on-year differences generally classified as not statistically significant or negligible in size. Numeracy was also the domain with the smallest proportion of students achieving Exceeding in the upper year levels: 15.8% of Year 7 students and 11.9% of Year 9 students achieved Exceeding in 2025, lower than the average across all learning domains at those year levels, where 19.0% of Year 7 students and 17.1% of Year 9 students reached Exceeding. Those figures are what the official data show. My own reading of them, informed by years in classrooms rather than by the dataset itself, is that this stability suggests the underlying challenges are not new. The national figures cannot tell us why individual students are struggling or where their understanding first became insecure, and that requires a closer look than any national dataset is designed to provide.
What a NAPLAN Result Cannot Diagnose
A single result, however carefully constructed, cannot tell a teacher where a student’s mathematical understanding first became insecure. It cannot distinguish between a difficulty that is conceptual, one that is procedural, and one that is really about fluency, a student who understands a concept well enough but has not yet automated the calculation skills that support it. Nor can it tell us whether a correct answer reflects genuine understanding or a memorised procedure that happened to work under test conditions on that day.
Performance on a timed assessment is also shaped by factors that sit alongside mathematical knowledge itself. Working memory, the mental workspace used to hold and manipulate information while reasoning through a problem, has a limited capacity, and research shows that some students experience additional limitations in using it. Executive functioning, the reading demands embedded in word problems, and processing speed can all affect performance on a given day, somewhat independently of what a student actually knows. Mathematics anxiety is well documented in psychological research and appears to have a reciprocal relationship with achievement: anxiety can affect performance, and repeated difficulty or failure can, over time, contribute to anxiety. This does not mean every student with a low result is experiencing mathematics anxiety, and it would be a mistake to assume so. It does mean a result cannot be read as a pure measure of mathematical knowledge, uncomplicated by everything else happening for that student on the day.
Finally, a result cannot tell a teacher what to teach next. It can flag that a student needs closer attention in a broad area, number and algebra, or measurement, for instance, but identifying the specific prerequisite gap requires investigation that sits outside what any standardised test was designed to provide. None of this is a criticism of NAPLAN. It simply reflects what the test was built to do, and what it was never built to do. NAPLAN is one source of evidence among several, a snapshot and a starting point for further investigation, not a diagnosis in itself.
Why More Practice Isn't Always the Answer
When a NAPLAN result identifies an area of weakness, the instinctive response in many schools is to give the affected students more of what didn’t work the first time: extra worksheets, additional homework, more test-style questions in the same content area. I understand the logic. If a student got fraction questions wrong, surely more fraction questions will help.
Often, it doesn’t, and the reason lies in how learning happens. John Sweller’s Cognitive Load Theory, developed in the late 1980s and refined over several decades since, describes the limits of working memory when students process new information. A synthesis of this research prepared for the New South Wales Department of Education puts it plainly: working memory can hold only a limited amount of new information at once, and when a task exceeds what a student can currently manage, learning is compromised even when the student is motivated and capable. AERO’s explainer on managing cognitive load makes a related point: overload can occur when students process too much new information at once, when material is more complex than their current knowledge can support, or when the environment is distracting, affecting what a student retains regardless of underlying ability. Cognitive load is one important part of this picture, not an explanation for every mathematical error; gaps in prior knowledge and the quality of instruction matter as well.
When a student has not yet built a secure schema, a connected mental structure that lets related pieces of knowledge function as a single unit, every element of a problem has to be processed individually. This uses up working memory quickly, and the student’s attention is consumed by managing the mechanics of the task rather than by the mathematics itself. More practice at this stage will not build that schema if it simply repeats the same task without addressing the missing understanding. A student working through fraction problems without understanding why a common denominator is needed may not be consolidating anything new each time they attempt a question. They may instead be re-experiencing the same confusion, sometimes managing to guess or half-remember a procedure that gets them an answer, but without the underlying structure that would let that knowledge transfer to a slightly different question next term.
This matters because of how long-term memory works alongside working memory. As AERO’s research on how students learn best explains, once a schema is well formed, it can be handled by working memory as a single, familiar unit rather than a set of separate steps, which frees up capacity for genuinely new problem solving. A student who understands place value deeply does not need to consciously reconstruct what “carrying” means every time they add two three-digit numbers. That knowledge has become automatic, which leaves room in working memory for the actual problem at hand, whatever it happens to be.
Practice still has a genuine role. AERO’s guidance on managing cognitive load recommends spaced and varied opportunities to retrieve, review and practise material, an approach that echoes Barak Rosenshine’s widely cited principles of instruction, because actively recalling information tends to strengthen long-term retention more reliably than passive re-reading of the same worked format. But practice is only as good as the understanding it reinforces. Practice without understanding entrenches fragile procedures. Practice built on a genuine schema, aimed at fluency once meaning is established, consolidates something durable.
Memorisation, Fluency and Understanding
This distinction is often misread as an argument against memory itself, and it is not. Fluent recall of number facts, formulas and procedures is genuinely valuable, and automaticity frees up working memory for the harder reasoning a problem actually requires. The relevant distinction is not between knowledge and understanding. It is between a procedure a student has memorised in isolation, with no sense of why it works, and automatic recall that developed after the underlying meaning was already established. Strong mathematics learning depends on conceptual understanding, procedural fluency, reasoning, problem solving, and enough retrieval and practice that important knowledge becomes automatic, not on avoiding memory altogether. AERO describes proficiency as built through several interrelated strands rather than fluent recall of isolated facts alone, a structure that mirrors how the Australian Curriculum: Mathematics has long organised its content around understanding, fluency, problem solving and reasoning.
Take multiplication facts. A student who has memorised that seven times eight is fifty-six, without any accompanying sense of what multiplication represents, has a fact that exists in isolation. Ask them what seven times eight would be if they only knew six times eight, and they may not be able to reason their way there, because there is no underlying structure to draw on. A student who understands multiplication as repeated groups, and who has built that understanding through concrete and visual experience before moving to the abstract symbol, can derive seven times eight from six times eight plus one more group of eight. They are not just faster in the long run. They are resilient to questions they have not seen phrased in exactly this way before.
Place value offers a similarly clear example. A student who has memorised the steps of a written addition algorithm, carrying digits according to a rule they were told rather than one they understand, will often perform reasonably well on straightforward vertical addition. Change the format, or ask them to explain why the carried digit represents ten of the previous column, and the cracks tend to show. A student who understands that our number system is built on groups of ten, and who has physically grouped and regrouped materials before seeing the written algorithm, can apply that understanding flexibly, because the procedure is anchored to something meaningful.
Fractions are perhaps where this distinction matters most, because so much later mathematics depends on them. A student who has memorised “find a common denominator, then add the numerators” without understanding what a fraction actually represents, a part of a whole, a relationship between two quantities, a point on a number line, will struggle the moment fractions appear in an unfamiliar context: as ratios, as probabilities, as coefficients in early algebra. David Geary’s research on mathematical cognition points to fraction understanding as one of the clearer predictors of later mathematics achievement, precisely because it requires integrating several conceptual strands rather than following one linear rule.
Algebra makes the same point in a different register. Students taught to “move the number to the other side and change the sign” as a memorised instruction, without understanding that an equation represents a balance that must be preserved, often cope with simple linear equations and then falter when equations become more complex or the unknown appears on both sides. Students who understand the underlying structure, that whatever is done to one side must be done to the other to maintain equality, can adapt that understanding to situations well beyond what they were originally taught.
In every one of these cases, a memorised procedure and a genuinely understood one can produce identical answers on a simple, familiar question. AERO’s explainer on mastery and application draws exactly this distinction: mastery is the accumulation and retention of knowledge and understanding, but application, the transfer of that knowledge to new and unfamiliar contexts, is what reveals whether the underlying understanding was ever really there. The difference only becomes visible when the question changes shape, which is precisely what happens across a student’s schooling. The problem, in other words, is not memory. It is reliance on fragile, disconnected procedures that a student cannot explain, adapt, or retrieve outside the exact context in which they were taught.
Why Learning May Not Last
Teachers often describe a frustrating pattern: a student appeared to know something in Term 2, and by Term 4, or the following year, it seems to have gone. Some of this is simply normal. Forgetting is a routine feature of human memory, and no teaching approach eliminates it entirely. But in mathematics classrooms, what looks like forgetting can often reflect something more specific, and it is worth examining a few of the more common explanations, without treating any single one of them as the whole story.
One possible explanation is that the learning was never sufficiently consolidated. AERO’s explainer on knowledge and memory describes how learning depends on information being stored in long-term memory in a form that can genuinely be retrieved later, not simply produced once under familiar, prompted conditions. Its companion explainer on retention and recall notes that both processes depend on how securely information was consolidated at the time of learning, not merely on how many times it was rehearsed. Cognitive scientist Daniel Willingham reaches a similar conclusion: material understood conceptually and connected to other knowledge tends to last, while material processed only at a surface level, enough to answer one question in one format, may never have been consolidated into a genuinely retrievable form.
Apparent forgetting can also occur when new content is introduced before earlier content has been properly consolidated, particularly when knowledge was taught in an isolated format rather than connected into a broader schema. Learning of this kind tends to be more vulnerable to interference over time, as AERO’s research on cognitive load and how students learn best both indicate. A student who moves through school with an insecure understanding of place value does not simply have a place value problem in isolation; that instability often resurfaces in multi-digit operations, decimals, and measurement conversions, anywhere flexible thinking about our base-ten system is required.
Lynn Fuchs and colleagues, whose research programme has focused on students with persistent mathematics difficulties, have shown that these students often have specific, identifiable deficits, commonly in number combination fluency and in the cognitive processes needed for word problem solving, rather than a generalised inability to learn mathematics. Their intervention research suggests that when these gaps are directly targeted through structured, explicit teaching, students previously considered persistently low-achieving can make substantial gains, a useful reminder that a broad, discouraging pattern of forgetting is often a narrower, more addressable gap once correctly identified.
Barak Rosenshine’s synthesis of research on effective teaching adds a complementary explanation, and it underpins much of AERO’s guidance on explicit instruction. Reviewing previous learning at the start of a lesson, teaching in small steps with guided practice, and scaffolding difficult tasks can all help protect consolidation. Moving ahead before earlier material is secure is one of the more common ways apparent forgetting is unintentionally manufactured. No single explanation accounts for every instance on its own; together, cognitive load, an unconsolidated schema and limited retrieval opportunities offer a more useful starting point than assuming a student simply needs to try harder.
Where Intervention Should Begin
Given all of this, I think the most useful shift a school or teacher can make is remarkably simple to state, even though it takes discipline to practise consistently: ask what a student already understands, rather than what year level they are supposedly working at.
Year level tells us what a student is expected to know. It tells us almost nothing about what they actually know, which is precisely the information needed to plan effective teaching. Two Year 6 students who both perform poorly on a NAPLAN fractions item might need entirely different responses. One may have a shaky grasp of equivalence but a solid understanding of what a fraction represents. The other may never have developed a secure part-whole concept at all, and no amount of practice with equivalent fractions will help until that earlier gap is addressed.
NAPLAN is a standardised, summative assessment. It can flag that an area needs further investigation, but it was never designed to replace the tools teachers already use to build a fuller picture: classroom observation, targeted diagnostic assessment, conversations with students about how they solved a problem, analysis of the strategies and misconceptions visible in their working, curriculum-based assessment, and the formative checks that happen inside a lesson rather than months after it. Those sources of evidence answer a more useful question for planning what comes next: not simply how the student performed, but what they already understand, and what concept or prerequisite they are genuinely ready to learn next. In a landmark and still widely cited review of classroom assessment, the researchers Paul Black and Dylan Wiliam found substantial learning gains where teachers used this kind of ongoing, formative assessment to identify specific gaps and adjust teaching in response, rather than waiting for a summative result to arrive after the fact. A NAPLAN report can be a useful trigger for that investigation. It is not a substitute for it.
Effective numeracy intervention tends to share a number of features, drawing on AERO’s guidance on cognitive load and explicit instruction and on Fuchs and colleagues’ intervention research. It starts with a precise assessment of what a student currently understands and where the specific prerequisite gaps lie, rather than a general sense that a topic needs revisiting. Teaching is then explicit and carefully sequenced, moving through well-chosen worked examples with concrete and visual representations where they genuinely support the concept, rather than as decoration. Students need guided practice with frequent checks for understanding and corrective feedback, real opportunities to retrieve what they have learned, and cumulative review that keeps earlier knowledge active. Progress is monitored over time, teaching is adjusted based on how a student responds, and support gradually moves towards independent application, with enough practice to build genuine fluency.
What intervention should not mean is just as important. It is not simply assigning more worksheets, repeating the same explanation the same way, giving more test-style questions in the hope that repetition alone will close the gap, or moving a student back a full year level without first diagnosing where understanding actually breaks down. Handing a student concrete materials without explicit teaching around them, or teaching a procedure without meaning, are also unlikely to help on their own. Intervention that works is targeted to what a student currently understands, responsive to how they engage with each step, focused on the specific, identified gap rather than the topic in general, and adjusted as evidence accumulates. This is slower to set up than handing out another worksheet. It is also, according to the evidence, considerably more likely to work.
Evidence-Based Teaching and the I-CRAVE Maths® Methodology
Over some years of working with teachers and students, my colleagues and I have tried to bring together what this body of research consistently points to, into a structure workable for a classroom teacher every day. The I-CRAVE Maths® Methodology draws on several interconnected strands of evidence: diagnostic identification, concrete and visual representation, movement towards abstraction, mathematical language, explicit instruction, and the management of cognitive load through mastery and formative assessment. These are not separate boxes to tick. They work together, and explicit instruction in particular runs through every stage rather than sitting at one point in the process.
The sequence begins with Identify, the diagnostic step described above: establishing precisely what a student understands before deciding what to teach next, rather than assuming based on age or year level.
From there, the Concrete stage uses physical materials so that abstract ideas have something tangible to attach to before any symbol is introduced. This reflects the Concrete-Representational-Abstract, or CRA, sequence, for which there is good evidence in both general and special education contexts, as researchers such as Bradley Witzel have shown, though CRA is one evidence-informed sequence integrated within the broader methodology rather than another name for it. Teachers move between concrete, representational and abstract forms flexibly, based on the concept and how a student is responding, rather than applying a fixed sequence for a fixed number of lessons regardless of need. An older student who is still uncertain about a concept can benefit from concrete materials just as much as a younger one. The materials do not automatically produce understanding; they need to be mathematically accurate, explicitly connected to the written notation they represent, and gradually withdrawn as understanding becomes more secure.
The Representational stage introduces pictures, diagrams and visual models that maintain the structure of the concrete experience while moving towards abstraction. This prevents the common gap where a student can manipulate materials successfully but cannot yet connect that experience to a diagram or a number line, let alone to written notation.
Only once concrete and representational understanding is secure does the Abstract stage introduce formal symbols and procedures, so the notation has something meaningful to represent rather than being a set of rules memorised in isolation. Introducing abstraction well before a student is ready can force working memory to process symbols and concepts simultaneously, which is precisely the kind of overload cognitive load theory predicts will impede learning.
The Verbal stage asks students to explain their thinking in their own words. This matters, but a student’s explanation is best treated as one piece of evidence among several, alongside performance, representation and application, rather than as proof on its own that full understanding has been reached. A confident explanation can still contain a misconception, and a hesitant one can still reflect solid understanding from a student still building their mathematical vocabulary.
Explicit instruction runs through every stage rather than sitting at the end of it, and it is worth being clear about what this does and does not mean. It is not lecturing for the length of a lesson, a scripted routine delivered regardless of how students respond, rote memorisation, or the removal of discussion and problem solving. AERO describes explicit instruction as a systematic, engaging approach built around clear learning intentions, review of prerequisite knowledge, teacher modelling and worked examples, small instructional steps, guided practice, frequent checks for understanding, timely feedback, and a gradual release of responsibility towards independent, increasingly complex application. This reflects decades of underlying research, including Rosenshine’s principles of instruction and Anita Archer and Charles Hughes’s work on explicit teaching more broadly.
Mastery learning, woven through the sequence via ongoing formative checks, does not mean requiring perfect performance before a student moves on. It means ensuring the knowledge a coming lesson depends on is secure enough to carry that weight, not flawless, a principle traced back to Benjamin Bloom’s original model of mastery learning and revisited more recently by Thomas Guskey. Teachers still need to maintain appropriately high expectations, avoid holding students back unnecessarily once understanding is evident, revisit earlier knowledge through cumulative review, and differentiate support based on need, as AERO’s own guidance on mastery and application highlights. Because the sequence confirms understanding before building on it, students also tend to spend less time stuck in confusion or repeated failure, one of the more reliable ways to ease the mathematics anxiety discussed earlier in this article.
None of this is a shortcut, and it is not a guarantee. It is an attempt to apply, consistently and in a workable order, what research on learning and memory, both the international foundational work and its careful synthesis for Australian classrooms, has been telling educators for some time. The value of any methodology lies not in its name, but in whether it applies the evidence accurately and helps teachers respond to what students genuinely need.
Beyond the Score
A higher NAPLAN score should never be the goal in itself. Genuine mathematical understanding provides a stronger foundation for whatever assessment comes next, and it may contribute to improved performance over time, but it cannot guarantee a particular result for any individual student on any given occasion. What deep understanding more reliably changes is a student’s relationship with the subject. Confidence tends to grow when success comes from understanding rather than from remembering a fragile sequence of steps under time pressure. Secure understanding and appropriate problem-solving strategies are more likely to support that confidence when a student meets an unfamiliar question, though anxiety has several contributing causes and understanding alone will not remove it for every student. Knowledge is also more likely to last when it has been built into a connected schema rather than held briefly for one test, and a student who understands why a procedure works can adapt it to situations they have never seen before.
Every NAPLAN result tells a story. But it is only the beginning of an educational conversation, not the end of one. A result should prompt precise investigation, not a general instruction to practise harder. Students need secure conceptual understanding and procedural fluency, built through intervention that starts with what they already understand rather than their year level or a single score. Confidence grows through carefully sequenced learning that lets students experience real success, and lasting mathematical understanding cannot be built through fragile memorisation alone. The most important question a teacher or a school can ask is not how to improve next year’s score. It is what mathematical understanding this student already has, and what they genuinely need to learn next.
As we eagerly await the 2026 NAPLAN results, let's hope the results are different from last year. More importantly, let's remember that we already have a solution.
Continue the Conversation
If you’re looking for practical, evidence-based strategies to identify learning gaps, build conceptual understanding and deliver effective numeracy intervention, explore Maths Australia’s professional learning.
References:
Archer, A. L., & Hughes, C. A. (2011). Explicit instruction: Effective and efficient teaching. Guilford Press.
Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5), 181-185. https://doi.org/10.1111/1467-8721.00196
Australian Curriculum, Assessment and Reporting Authority. (2025). NAPLAN 2025 national results commentaries. https://dataandreporting.blob.core.windows.net/anrdataportal/ANR-Documents/NAP2025/2025%20NAPLAN%20National%20Results%20Commentary.pdf
Australian Curriculum, Assessment and Reporting Authority. (n.d.). F-10 curriculum: Mathematics. Retrieved July 2026, from https://www.australiancurriculum.edu.au/f-10-curriculum/learning-areas/mathematics/
Australian Education Research Organisation. (2023a). How students learn best: An overview of the evidence. https://www.edresearch.edu.au/research/research-reports/how-students-learn-best-overview-evidence
Australian Education Research Organisation. (2023b). Managing cognitive load optimises learning. https://www.edresearch.edu.au/summaries-explainers/explainers/managing-cognitive-load-optimises-learning
Australian Education Research Organisation. (2023c). Explicit instruction optimises learning. https://www.edresearch.edu.au/summaries-explainers/explainers/explicit-instruction-optimises-learning
Australian Education Research Organisation. (2024). Developing maths proficiency. https://www.edresearch.edu.au/summaries-explainers/explainers/developing-maths-proficiency
Australian Education Research Organisation. (2025a). Mastery and application. https://www.edresearch.edu.au/summaries-explainers/explainers/mastery-and-application
Australian Education Research Organisation. (2025b). Knowledge and memory. https://www.edresearch.edu.au/summaries-explainers/explainers/knowledge-and-memory
Australian Education Research Organisation. (2025c). Retention and recall. https://www.edresearch.edu.au/summaries-explainers/explainers/retention-and-recall
Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80(2), 139-148.
Bloom, B. S. (1968). Learning for mastery. Evaluation Comment, 1(2), 1-12.
Centre for Education Statistics and Evaluation. (2017). Cognitive load theory: Research that teachers really need to understand. NSW Department of Education. https://education.nsw.gov.au/about-us/educational-data/cese/publications/literature-reviews/cognitive-load-theory.html
Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24(1), 87-114. https://doi.org/10.1017/S0140525X01003922
Fuchs, L. S., Fuchs, D., Compton, D. L., Powell, S. R., Seethaler, P. M., Capizzi, A. M., Schatschneider, C., & Fletcher, J. M. (2006). The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology, 98(1), 29-43. https://doi.org/10.1037/0022-0663.98.1.29
Fuchs, L. S., Powell, S. R., Seethaler, P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D., Hamlett, C. L., & Zumeta, R. O. (2009). Remediating number combination and word problem deficits among students with mathematics difficulties: A randomized control trial. Journal of Educational Psychology, 101(3), 561-576. https://doi.org/10.1037/a0014701
Gathercole, S. E., & Alloway, T. P. (2008). Working memory and learning: A practical guide for teachers. Sage.
Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15. https://doi.org/10.1177/00222194040370010201
Geary, D. C., Hoard, M. K., Nugent, L., & Bailey, D. H. (2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five-year prospective study. Journal of Educational Psychology, 104(1), 206-223. https://doi.org/10.1037/a0025398
Guskey, T. R. (2007). Closing achievement gaps: Revisiting Benjamin S. Bloom’s “Learning for Mastery”. Journal of Advanced Academics, 19(1), 8-31. https://doi.org/10.4219/jaa-2007-704
National Assessment Program. (n.d.-a). What’s in the tests. Australian Curriculum, Assessment and Reporting Authority. Retrieved July 2026, from https://www.nap.edu.au/naplan/whats-in-the-tests
National Assessment Program. (n.d.-b). Proficiency level descriptions. Australian Curriculum, Assessment and Reporting Authority. Retrieved July 2026, from https://www.nap.edu.au/naplan/results-and-reports/proficiency-level-descriptions
Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (2013). Math anxiety, working memory, and math achievement in early elementary school. Journal of Cognition and Development, 14(2), 187-202. https://doi.org/10.1080/15248372.2012.664593
Rosenshine, B. (2012). Principles of instruction: Research-based strategies that all teachers should know. American Educator, 36(1), 12-19, 39.
Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257-285. https://doi.org/10.1207/s15516709cog1202_4
Willingham, D. T. (2009). Why don’t students like school? A cognitive scientist answers questions about how the mind works and what it means for the classroom. Jossey-Bass.
Witzel, B. S., Mercer, C. D., & Miller, M. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18(2), 121-131. https://doi.org/10.1111/1540-5826.00068