Do worked examples boost the spacing effect on lasting learning?

The acquisition of lasting knowledge that is accessible for a long time is an important educational goal. Spacing the learning or practice phase across multiple sessions fosters lasting learning, but the effect is less robust for complex material. We examined whether the meaningful elaboration of the learning material, evoked by means of self-explaining worked examples, contributes to a more robust spacing effect concerning the lasting learning in mathematics. Participants were fourth graders ( N = 213). Children received a formal instruction to long multiplication in school. Thereafter, they practiced the procedure either in a massed or a spaced manner, and either by pure problem solving or by additionally self-explaining worked examples in their regular math lessons. Time on task was held constant in all conditions. In a delayed test after eight weeks, children's procedural and conceptual knowledge was assessed. Their general math ability and their specific prior knowledge served as control variables. Contrary to our expectations, there was neither a main effect of worked examples nor of spacing, and no interaction emerged between the two variables. Exploratory analyses revealed the same results concerning the forgetting rate between the last practice set and the test. These null effects were confirmed by Bayesian analyses . Only children's general math ability and their prior knowledge predicted their test performance. The results suggest that the spacing effect in mathematics does not emerge reliably, even not when stimulated by worked examples. Further research on potential boundary conditions is required. • The spacing effect for complex learning material is not robust. • We combined spacing with worked examples to promote lasting learning in mathematics. • There were no main effects of spacing and worked examples and no interaction effect. • The null effects were confirmed by Bayesian analyses.