It’s often useful to look back at older education research in order to look forward to what we should be doing in the classroom. Sure, studies need to be seen in the context of their time - for example, they may have had very small sample sizes - but revisiting influential work can really get you thinking about your practice.

Take, for instance, the study by Sweller et al (1982) that is a foundational text for cognitive load theory. In its simplest form, the first experiment resembles the numbers round on Countdown, but with restrictions. There is a target number that has to be obtained by making sums with mathematical operations. In this case, there is a start number and only two operations can be used: x3 (times three) and -69 (subtract 69).

For example, the initial number might be 60 and the final number 111. You can reach this by first multiplying by three and then subtracting 69. Or the initial number might be 35 and the final number 315, which would require you to multiply the start number by three twice.

Participants in the study were given different problems in a predefined order. The number of steps required to solve each problem was recorded, as was the amount of time it took each participant to solve them. These problems started off needing participants to apply the operations alternately (x3, followed by -69) in two, four, six and 10 steps. The final problem required participants to use the same operation twice.

The participants were split into two types of groups. One type, called “means-end”, simply had to find the solutions by trying. The other type, called “history-cued”, was presented with the solution to each problem immediately after solving it themselves, along with successful solutions from previous tasks. This group was also asked to memorise the sequence of steps that was required to solve all the problems.

Finally, as a post measurement, both groups got a complex task that required 10 alternating steps and a simple task that required two consecutive steps. It probably won’t surprise you that the “history-cued” group did the complex task much more efficiently than the “means-end” group. After all, the rule for success was primed into them.

Some people use this result to argue that “telling the rule” is superior to just trying. For this particular task, that’s true.

However, we hear less about how the groups fared on the simple task. The “history-cued” group actually did worse than the “means-end” group. This could have been caused by a so-called “Einstellung effect” that creates a fixed state of mind. Having primed participants so much for alternate sequences, those were the ones they kept on trying first, even for the simplest two-move tasks.

The number problems in this experiment are highly restricted but the study would suggest that the most effective solvers of such problems seem to be highly flexible in their strategies: they know their basic arithmetic skills but also have strategic insight.

The lesson here is to teach maths flexibly and not be wedded to one approach. By reading this “old” study, we can remind ourselves of this, and make sure that we understand the intricacies and nuances that underpin general statements that have been made about this work decades later.

There are plenty more gems like this in the archives out there, so get digging.

Christian Bokhove is associate professor in mathematics education at the University of Southampton and a specialist in research methodologies

This article originally appeared in the 22 October 2021 issue under the headline “Digging up old gems will help us sparkle in the future”