Microgenetic patterns of children's multiplication learning: confirming the overlapping waves model by latent growth modeling.

Variability in strategy selection is an important characteristic of learning new skills such as mathematical skills. Strategies gradually come and go during this development. In 1996, Siegler described this phenomenon as "overlapping waves." In the current microgenetic study, we attempted to model these overlapping waves statistically. In addition, we investigated whether development in strategy selection is related to development in accuracy and to what degree working memory is related to both. We expected that children with poor working memory are limited in their possibilities to make the associations that are necessary to progress to more mature strategies. This limitation would explain the often-found relationship between working memory and mathematical abilities. To this aim, the strategy selection and accuracy of 98 children who were learning single-digit multiplication was assessed eight times on a weekly basis. Using latent growth modeling for categorical data, we confirmed Siegler's hypothesis of overlapping waves. Moreover, both the intercepts and the slopes of strategy selection and accuracy were strongly interrelated. Finally, working memory predicted both strategy selection and accuracy, confirming that working memory is related to mathematical problem solving in two ways because it influences both the maturity of strategy choice and the probability of making procedural mistakes.