The Variability Effect: An instructional approach to enhance mathematics learning

Abstract

Based on cognitive load theory, the variability effect occurs when learners’ exposure to highly variable tasks results in better test performance. Using four randomised controlled trials in the area of secondary and tertiary mathematics instruction, the present study investigated the effects of variability, with an emphasis on levels of instructional guidance and levels of learner expertise. Experiments 1, 2 and 4 hypothesised that learners who study fully-guided worked examples will yield higher post-test performance scores, compared to learners who attempt unguided problem-solving tasks (Hypothesis 1); and learners who study high-variability worked examples will yield higher post-test performance scores, compared to learners who study low-variability worked examples, with no difference being generated under problem-solving conditions (Hypothesis 2). Hypothesis 1 was not supported in Experiments 1, 2 and 4, while Hypothesis 2 was supported only in Experiment 2. The variability effect that was produced in Experiment 2 led to further investigation in Experiment 3, where it was hypothesised that more-experienced learners (experts) would demonstrate the variability effect, and less-experienced learners (novices) would demonstrate a reverse variability effect. This hypothesis was supported, producing a classic expertise reversal effect. In addition, in all four experiments, learners’ cognitive load was evaluated by having each participant complete a subjective rating of difficulty scale upon completion of their learning tasks. The results supported the assumptions based on cognitive load theory: learners in the worked-examples groups experienced less cognitive load compared to the problem-solving groups (in Experiments 1, 2 and 4); novices experienced less cognitive load when solving low-variability problems compared to high-variability problems, and lower cognitive load was experienced by experts, compared to novices, for both high- and low-variability tasks (in Experiment 3); and cognitive load associated with the completion of high-variability tasks was higher compared to the completion of low-variability tasks (only in Experiment 4). Although it is well grounded in empirical evidence that learners should be provided with worked examples during the initial stages of learning, these results strongly suggest that learners should be initially presented with low-variability problems, and as their levels of knowledge advance, variability should increase.