Promoting lasting learning by combining spacing with worked examples

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Spacing the learning phases across multiple sessions instead of learning in only one session yields robust effects on retention when tested in the laboratory with simple learning material (e.g., word lists). However, the effect turned out to be less robust in real educational contexts involving coherent learning material, relevant for the curriculum. One explanation for this less robust effect is the limited, superficial elaboration of the learning content by the learners. The present project aims at investigating whether the spacing effect in real educational contexts can benefit from being combined with worked examples (and vice versa). Worked examples are a potent learning tool, involving a problem, the single solution steps, and the problem solution. Working through worked examples (combined with self-explanations) may stimulate a deeper, more elaborated processing. However, the long-term effects of worked examples on retention are hardly known yet. In the current project, we therefore investigate in the frame of three experiments within the field of mathematics learning in school whether the spacing of practice tasks yields enhances students’ lasting retention when being combined with worked examples—instead of simple problem solving tasks. The samples will comprise fourth Graders acquiring semi-written multiplication skills and eleventh Graders learning stochastics. We expect main effects of both spacing and worked examples and a multiplicative interaction effect when the two principles are combined. Moreover, we examine whether detecting errors in incorrect worked examples by the learners has a larger effect for lasting learning than being presented with worked examples that are already marked as correct or incorrect. Exploratorily, we additionally examine the impact of learners’ prior knowledge, their general mathematical achievement, and motivational aspects for the effects.