Spaced learning: the science behind the best math students

Your child spent an hour reviewing multiplication tables before the test. They got a good grade. 

But three weeks later, asked out of the blue, they can't remember a thing. You may be wondering if something is wrong.

Rest assured, nothing is wrong. It's just the brain working normally! 

And there is a simple method, backed by more than a century of neuroscience research, to get around the problem. It's called spaced learning.

What Ebbinghaus discovered in 1885

The German psychologist Hermann Ebbinghaus spent hours memorizing lists of meaningless syllables, then measured precisely how much he still remembered after different delays.

What he discovered changed the way we understand memory.

First, the forgetting curve: without review, we lose about half of what we have just learned within the next twenty minutes. The drop continues for the first few hours, then slows down. This isn't a flaw; it's how a normal brain sorts what is worth keeping from what isn't.

Second, and this is where it gets interesting: the same total study time produces radically different results depending on how it is spread out. Two hours of review in a single session are worth far less than two hours spread over several days. For the same amount of time, memory retains twice as much when learning is distributed.

What neuroscience explains

Why does it work? The answer lies in how the brain works during sleep.

When we learn something, the information is first stored in the hippocampus, a brain structure that works like a short-term buffer. At night, during sleep, this information is gradually transferred to the cortex, where it settles for the long term. This is called memory consolidation (Smolen, Zhang and Byrne, 2016).

This transfer takes time. If we reload the hippocampus with the same information before the first transfer is complete, we don't anchor it more firmly — we disrupt the process. On the other hand, if we wait for consolidation to be done before coming back to the concept, each review strengthens a trace that is already well established.

There is also a complementary mechanism: each time we retrieve information from memory, the trace becomes temporarily unstable, and it is in this moment of fragility that it can be strengthened. Spacing out reviews multiplies these opportunities for reconsolidation. That is why the effort of remembering works better than the effort of rereading.

What the research confirms in numbers

Spaced learning is not a teaching hunch. It is one of the best-documented phenomena in cognitive psychology.

The meta-analysis by Cepeda et al. (2006) analyzed 839 comparisons from 317 experiments. The verdict is clear: for the same study time, distributed practice outperforms massed practice by as much as a factor of two.

Their 2008 study of more than 1,350 subjects clarified a key point: the optimal interval between two reviews depends on how long you want to remember the information. To remember something for a week, an interval of one or two days is enough. To remember it for a year — the goal in math, where each concept is the foundation for the next — the interval should stretch to several weeks.

Why math in particular

Spaced learning is useful in every subject. But it is especially decisive in mathematics, for a simple reason: math is a cumulative subject.

What we learn in 3rd grade must still be available in 4th grade. What we learn in 4th grade must still be available in middle school. A concept that is poorly consolidated in elementary school doesn't disappear; it creates a gap that shows up later, when the stakes are higher and there is less time to catch up.

Studies focused on mathematics confirm this effect. Rohrer and Taylor (2007) compared two groups of students practicing geometry problems: one in a single massed session, the other in spaced sessions, with the same total time. Four weeks later, the spaced group scored twice as high.

Spacing isn't enough: the importance of interleaving

Spaced learning has a natural ally called interleaving.

The principle: rather than doing twenty exercises in a row on the same type of problem, we mix exercises of different kinds within the same session or homework. A fraction problem, then some mental math, then a geometry question, then a division.

It feels less effective at the time: students feel less in control because they can't settle into a routine. That is precisely why it works better. By alternating types of problems, students learn not only to carry out a procedure but to recognize when to use it. 

How Mathéo applies spaced learning

At Mathéo, spaced learning is at the heart of our teaching.

For each concept covered in class, we schedule several reviews spread out over time, calibrated to the child's age. The purpose of these review exercises is to reactivate the memory trace, not to explain the concept again.

How often concepts are reviewed depends on the student's age. A 1st grader will need to revisit what they have just learned sooner and more often than a 6th grader.