The Boundary Condition: Before or After the Rule Is Available?

The two experiments in this study test a precise boundary in the choice between retrieval practice and worked examples: has the learner already been given the rule, or must they infer it during practice? That distinction lets us judge the earlier question about solving before instruction more carefully. The result is not a universal ranking; it is evidence that the same practice method can fit one cognitive demand and mismatch another.

The study used artificial language and mathematical rules so that prior subject knowledge would play a smaller role. Participants learned unfamiliar structures, practiced them through either retrieval practice or worked examples, and then faced new problems that required generalization. The crucial comparison was not only retrieval versus examples. It was how that comparison changed when initial instruction was present or absent, and when practice items were repeated or varied.

When the Rule Was Given First

In the first experiment, participants received initial instruction before the learning phase. Each rule was introduced with a definition and a simple example. The learning tasks then used artificial language and mathematical rules, and participants practiced through retrieval or worked examples. Item variability was assigned between participants: some repeatedly encountered the same item for a rule, while others encountered different items. Learning strategy was experienced within participants, so each person used both retrieval practice and worked examples across different materials.

The design matters because the initial instruction made the rules available before practice began. The practice phase still required learners to apply the rules, but it did not require them to discover from scratch what the rules were. The main demand was closer to retention and application: could learners bring the stated rule to mind and use it on a problem that was not simply the initial example?

Eighty adults took part, and two participants who did not complete the final test were excluded, leaving 78 participants. The final test measured generalization with new items. On that test, participants who engaged in retrieval practice performed significantly better than those who studied worked examples, F(1, 76) = 8.08, p = .006, partial η² = .10. This is a strategy effect under the experiment’s conditions; it does not mean that retrieval practice is always superior or that worked examples have no value.

The variability results are just as important as the strategy result. Participants who practiced with varied items and those who practiced with repeated items had similar final-test accuracy, F(1, 76) = 3.24, p = .076, partial η² = .04. The interaction between strategy and variability was also not significant, F(1, 76) = 0.02, p = .877, partial η² = .0003. In other words, the study did not find that variation changed the size of the retrieval advantage in this instructed condition.

The learning process was not cost-free. Retrieval practice required more learning time than studying worked examples, and that difference was larger when the practice items varied. Participants also improved more slowly during varied retrieval practice than during repeated retrieval. Those patterns suggest that variation increased processing demands during practice. Yet the slower and more effortful retrieval route still produced better final generalization than worked examples in this condition.