Published study- spaced mathematics practice improves test scores and reduces overconfidence

The literature on using the Spacing Effect to improve students’ retention of their learning is extensive and shows its benefit across a range of domains of learning. Rohrer & Taylor (2006) showed the Spacing Effect to be beneficial for learning specifically with mathematics-related content.

I have been fortunate to have the opportunity to work with Prof Doug Rohrer and Marissa Hartwig over the last few years and we have conducted a study (Emeny et al., 2021) which has recently been published in the Journal of Applied Cognitive Psychology. I write to share our findings with you in the hope that you find them useful for your own professional learning.

Our aims were:

• to investigate whether the Spacing Effect could be demonstrated in real secondary school classrooms, with typical secondary school students, using typical mathematics content taught in lessons. We wanted to conduct a published, controlled study that replicated as close as possible real-world classroom conditions
• to investigate whether spaced versus massed practice had an impact on how well students were able to predict the retention of their learning

There is a link to our full paper at the end of this post should you wish to dive into the details. For the benefit of the teacher reader looking for the main points only, I will summarise the key info below.

Method

We completed the experiment twice with Y7 students aged 11-12. 44 and 55 students participated in Experiments 1 and 2 respectively.

Each experiment consisted of two mixed-gender classes, A and B. In Experiment 1, Class A had significantly higher KS2 SAT maths scores than Class B. In Experiment 2 both classes had similar KS2 SAT maths scores.

The teaching materials used were based on two topics: Venn (Diagrams and Set Notation) and Permutations. These two topics were chosen very carefully and based on pilot studies. We wanted to ensure that their ‘difficulty to learn’ were a reasonable match to that encountered in usual Y7 classes, but we also needed to ensure that students had no prior knowledge of the topics before participating in the experiments. In mathematics, a subject where one topic often builds on another, this was a challenge!

Both classes were taught both Venns and Permutations. Students watched a video tutorial and then attempted 12 practice problems (with feedback being given after each one) completed either all in one session (massed condition) or in 3 sessions, each with 4 questions, separated by a 1 week spacing gap (spaced condition). After the final practice problem was completed, students had a 4 week gap and then took a test.

The study was ‘counterbalanced’ by ensuring that both classes studied in both conditions. I.e. if Class A did Venns spaced and Permutations massed then Class B did Permutations spaced and Venns massed. The results of all students in the spaced condition were compared with the results of all students in the massed condition.

At 3 points during the study of each topic students were asked to predict their score on the final test. This was done immediately after the final practice problem, immediately before the test and then immediately after the test.

Findings

In both experiments students scored higher on the final test when they studied in the spaced condition. These were statistically significant results and the ‘effect sizes’ were moderately large, 0.61 and 0.39 standard deviations in Experiment 1 and 2 respectively. The study showed that the Spacing Effect can be utilised in a close-to-real-world secondary school maths learning environment.

In both experiments, when in the spaced condition, students’ predictions of their test score were reasonably accurate whereas while in the massed condition they were overconfident, particularly the predictions made after the final practice problem and immediately before the test.

Within the context of the materials and methodology used in this experiment, studying in a spaced condition reduced students’ overconfidence. Whilst students were in the massed condition, they believed their learning was reasonably secure, only to find out it was not on the test 4 weeks’ later. The fluency achieved by completing a large number (12) of similar questions all in one practice session likely led students to an assumption that the fluency would be retained over time, which it was not (in relative terms).

What effect does thinking they have secured their learning on a topic after massed practice but then finding out later they were wrong have on students both in the short and long term? Is the overconfidence and subsequent correction a negative thing for students? Does spacing not only boost test scores, but lead to better self-awareness of how well students are learning too? These are interesting questions which could be investigated in future studies.

The Paper

Download the paper from my Research page.

References

Emeny, W.G., Hartwig, M.K. & Rohrer D. Spaced mathematics practice improves test scores and reduces overconfidence. Applied Cognitive Psychology, 35, 1082–1089

Rohrer, D., & Taylor, K. (2006). The effects of overlearning and distributed practice on the retention of mathematics knowledge. Applied Cognitive Psychology, 20, 1209-1224