So: Should You Solve First or Study the Example First?

The answer to the title question is conditional: solve first when a designed attempt can help learners construct or expose a structure that later instruction will organize; study an example first when independent generation would overload the learner or when the needed procedure is not yet representable. Once the rule is available, retrieval practice with feedback is often the better next move, and meaningful variation becomes important when the goal is transfer across cases. The subject is not a permanent winner among methods, but the fit between a learner’s current representation, the task’s cognitive demand, and the evidence required at the end.

That answer is more useful than a slogan because it explains why the research can point in different directions without becoming incoherent. The order of activities changes what the learner is asked to do. Variation changes what the learner must compare. Feedback changes whether an error can be corrected. A responsible design keeps those variables visible instead of treating “problem solving,” “instruction,” “worked examples,” or “retrieval” as interchangeable labels for learning.

The Evidence Answers a Conditional Question

The broadest evidence in this series is a meta-analysis of problem solving followed by instruction, or PS-I, compared with instruction followed by problem solving, or I-PS. It included 53 studies and 166 comparisons. Across those comparisons, PS-I had a moderate average advantage, with Hedges’ g = 0.36 and a 95% confidence interval from 0.20 to 0.51. An estimate adjusted for possible publication bias was larger, Hedges’ g = 0.87, but that is an estimate of an underlying effect after an adjustment, not a universal replacement for the primary pooled result.

The first conclusion is therefore real but bounded: arranging an initial problem-solving experience before instruction can improve later learning on average. The word “can” carries the important qualification. The evidence also reports stronger effects when PS-I was implemented with high fidelity to Productive Failure principles, with effect sizes ranging from 0.37 to 0.58. That pattern suggests that implementation matters. It does not show that any difficult task, any period of confusion, or any request to “figure it out” will reproduce the result.

The same meta-analysis reports moderators. Student grade level, intervention time span, and whether a study was experimental or quasi-experimental contributed to PS-I efficacy. For younger learners in roughly grades two through five and for domain-general skills, the reported effect sizes instead favored I-PS. The available evidence does not turn those findings into a precise age cutoff or a universal rule about general skills. It does establish that the average PS-I result should be read through learner and task conditions.

The second source helps explain why a method ranking can shift when the learner’s starting state changes. In its first experiment, learners received initial instruction that presented the rules before practice. Retrieval practice then outperformed worked examples on the final generalization test, F(1, 76) = 8.08, p = .006, partial η² = .10. Variability did not produce a significant main effect, and it did not significantly interact with strategy. Retrieval practice took more learning time, especially with varied items, and varied practice slowed improvement during learning without improving final generalization in that instructed condition.

In the second experiment, the initial instruction was removed. Learners had to infer the rules during practice. Worked examples outperformed retrieval practice overall, F(1, 72) = 8.72, p = .004, partial η² = .11, and the strategy-by-variability interaction was significant, F(1, 72) = 4.78, p = .032, partial η² = .06. With repeated items, worked examples produced higher final generalization than retrieval practice: mean accuracy was .69 versus .49, with p < .001. With varied items, retrieval practice and worked examples were comparable: mean accuracy was .64 versus .67, p = .635. Varied retrieval also outperformed repeated retrieval, while varying worked examples did not improve their outcome in this experiment.

The two experiments reveal a change in the learner’s task. When initial instruction made the rule available, retrieval practice could strengthen access to a rule that learners were expected to apply. When initial instruction was absent, learners had to construct the rule while practicing. Repeated retrieval of one item offered little comparison for that induction.