In a world where mathematics often gets reduced to formulas and fast answers, it’s time we rethink how we help students truly learn maths. Decades of research in cognitive and learning sciences have converged on key strategies that deepen understanding, build long-term retention, and empower students to engage with mathematics meaningfully.

Among these evidence-based strategies, spaced practice, retrieval and interleaving stand out as particularly powerful. When integrated intentionally, they shift the classroom from one of short-term performance to long-term learning.

Spaced practice: Why forgetting can be good

One of the most consistent and powerful findings in learning science is the spacing effect. Rather than teaching a topic intensively for a short period (massed practice), spaced practice involves spreading learning over time. When students revisit concepts days or weeks after initial exposure, the brain is forced to work harder to retrieve and reconstruct understanding — leading to stronger, more durable memory.

This principle is well-established. In a 2006 meta-analysis, spacing out study sessions consistently improved retention across subjects and age groups. In mathematics, this might mean returning to concepts like fractions or algebraic manipulation multiple times over a term rather than completing one isolated unit.

Spacing works because a little forgetting requires effortful retrieval — a process that strengthens memory and understanding. Instead of seeing review as repetition, we can view it as retrieval-based reinforcement. A quick warm-up problem from two weeks ago may be more impactful than a full new lesson if it activates prior knowledge and reinforces connections.

Retrieval practice: Make it stick

Closely related to spaced practice is retrieval practice, or the act of recalling information from memory without prompts. Rather than re-reading notes or passively watching a worked example, students learn more when they try to recall and apply ideas on their own.

Karpicke and Blunt (2011) found that students who engaged in retrieval (e.g., solving problems from memory) outperformed those who used elaborative study methods like concept mapping. In the maths classroom, retrieval practice can take many forms: low-stakes quizzes, exit tickets, warm-up problems, or “brain dumps” where students explain a process from memory.

Retrieval works best when it is frequent, low-pressure, and paired with feedback. It also helps students become more metacognitive — aware of what they know and what they still need to work on.

Interleaving: Mixing it up

Traditional maths instruction often focuses on one type of problem at a time — 20 multiplication problems today, 20 fraction questions tomorrow. However, this can lead to superficial mastery that doesn’t transfer to unfamiliar contexts.

Interleaving — mixing different types of problems or topics in a single session — disrupts this pattern. It requires students to choose and apply the right strategy, rather than relying on context cues or rote methods.

Rohrer and Taylor (2007) found that interleaved practice significantly improved students’ ability to retain and transfer maths skills. Although students often feel they are learning less during interleaving, post-tests reveal the opposite — they’ve actually retained and understood more.

In practice, this might involve mixing geometry and measurement tasks, or combining different fraction operations in one session. It slows down performance in the short term but enhances understanding in the long term.

Putting it all together in the classroom

Integrating learning science into maths instruction can be relatively quick and easy to do. Here are practical ways to begin:

• Use weekly review problems that revisit earlier topics.
• Start lessons with retrieval tasks instead of re-teaching.
• Mix up problem types in worksheets and assessments.
  

These strategies can be transformative not just for test scores, but for how students see themselves as learners of mathematics.

Key learnings

Learning science is reshaping how we understand effective maths instruction. Spaced practice, retrieval and interleaving aren’t just academic jargon — they’re tools to help students learn better, retain more, and develop mathematical confidence.

By embracing these principles, we move away from a model of short-term performance and toward one of long-term understanding,one that prepares students not just for exams, but for real-world problem solving and lifelong learning.

How Instructive supports spaced practice

Instructive is built to integrate spaced practice into the learning experience seamlessly. By revisiting key concepts throughout the term and providing tailored, adaptive learning paths, Instructive ensures students engage with previously taught content regularly. Instructive helps students strengthen their long-term understanding by encouraging consistent retrieval and connection of concepts, making the spacing effect a natural part of their learning journey. This approach, combined with real-time data and personalised feedback, empowers students to retain key mathematical skills and build mastery over time.

If you’d like to see how Instructive can support spaced practice in your classroom, sign up for a free trial today.

Further Reading

Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. Psychological Bulletin, 132(3), 354–380. https://doi.org/10.1037/0033-2909.132.3.354

Carpenter, Shana & Pan, Steven & Butler, Andrew. (2022). The science of effective learning with a focus on spacing and retrieval practice. Nature Reviews Psychology. 1-16. 10.1038/s44159-022-00089-1.https://www.researchgate.net/publication/362093173_The_science_of_effective_learning_with_a_focus_on_spacing_and_retrieval_practice

Karpicke, J. D., & Blunt, J. R. (2011). Retrieval practice produces more learning than elaborate studying with concept mapping. Science, 331(6018), 772–775. https://doi.org/10.1126/science.1199327Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35(6), 481–498. https://doi.org/10.1007/s11251-007-9015-8