For years, maths education has relied on a simple formula: if a learner hasn’t mastered a concept, repeat it until they can.
As a science teacher and education leader, I know this approach does not work. Repetition creates short-term performance, but it rarely builds long-term understanding (Bjork & Bjork, 2011; Soderstrom & Bjork, 2015).
The real key is reinforcement, informed by cognitive science and evidence-based practice.
Reinforcement vs Repetition
Reinforcement strengthens retention and transfer through:
- Spaced practice – revisiting knowledge over time (Cepeda et al., 2006)
- Retrieval practice – actively recalling concepts (Roediger & Butler, 2011)
- Interleaving – mixing problem types to deepen understanding (Rohrer & Taylor, 2007)
Just as in science, where understanding why something works matters more than memorising a formula, in maths we want learners to grasp concepts, not just repeat procedures.
Implications for Maths at All Levels
Strong maths teaching blends procedural fluency with conceptual understanding (EEF, 2017, 2021). Leaders and teachers should ask:
- Are curriculum maps designed to reinforce learning over time, not just repeat it?
- Are teachers trained in evidence-based strategies, including retrieval, interleaving, and diagnostic assessment?
- Are interventions measured by retention and transfer, not only short-term fluency?
A Focus on Dyscalculia
For learners with dyscalculia, repetition can reinforce failure and anxiety (Butterworth, 2018). Evidence shows that structured, adaptive reinforcement improves outcomes (Dowker, 2019; Wilson et al., 2020).
Practical strategies include:
- Explicit instruction with visual and concrete scaffolds
- Short, frequent spaced retrieval practice
- Ongoing diagnostic assessment to guide adaptive reinforcement
The Leadership Shift
Repetition maintains the status quo. Reinforcement builds confident, capable mathematicians.
Applying a scientific lens, measuring outcomes, testing interventions, adapting methods, is not just good teaching; it is essential leadership.
When done right, reinforcement reduces maths anxiety, builds resilience, and opens life opportunities for all learners, including those with dyscalculia.
References
Bjork, R.A. & Bjork, E.L. (2011) ‘Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning’, Psychology and the Real World: Essays Illustrating Fundamental Contributions to Society, 2, pp. 59–68.
Butterworth, B. (2018) Dyscalculia: From Science to Education. London: Routledge.
Cepeda, N.J. et al. (2006) ‘Distributed practice in verbal recall tasks: A review and quantitative synthesis’, Psychological Bulletin, 132(3), pp. 354–380.
Dowker, A. (2019) Individual Differences in Arithmetic: Implications for Psychology, Neuroscience and Education. 2nd edn. London: Routledge.
Education Endowment Foundation (EEF) (2017) Improving Mathematics in Key Stages 2 and 3. London: EEF.
Education Endowment Foundation (EEF) (2021) Improving Mathematics in Early Years and Key Stage 1. London: EEF.
Roediger, H.L. & Butler, A.C. (2011) ‘The critical role of retrieval practice in long-term retention’, Trends in Cognitive Sciences, 15(1), pp. 20–27.
Rohrer, D. & Taylor, K. (2007) ‘The effects of overlearning and distributed practice on the retention of mathematics knowledge’, Applied Cognitive Psychology, 21(9), pp. 1209–1224.
Soderstrom, N.C. & Bjork, R.A. (2015) ‘Learning versus performance: An integrative review’, Perspectives on Psychological Science, 10(2), pp. 176–199.
Wilson, A.J. et al. (2020) ‘Interventions for children with mathematical difficulties: A review of the evidence’, Educational Psychology Review, 32, pp. 1–38.
Noor Esmail
Empowering Inclusive Maths Education | Director at JellyJames Publishing | NPQLTD-Qualified Leader Driving Innovation & Dyscalculia Awareness