Fast and slow strategies in multiplication

In solving multiplication problems, children use both fast retrieval-based processes and slower computational processes. In the current study, we explore the possibility of disentangling these strategies using information contained in the observed response latencies using a method that is applicable in large data sets. We used a tree-based item response-modeling framework (De Boeck & Partchev, 2012) to investigate whether the proposed qualitative distinctions in fast and slow strategies can be detected. This so-called fast-slow model was applied to responses to a set of multiplication items, totalling more than 180,000 responses, collected in an online computer-adaptive training environment for mathematics. Parameters describing person characteristics (ability) and item characteristics (easiness) are estimated with the model. Both item and person characteristics differed between fast and slow processes and match predictions from substantive models of multiplication. Moreover, the parameters allowed us to describe the fast and slow strategies in more detail. Results emphasize the utility of the fast-slow model in the detection of strategies in multiplication but also in other areas of cognition and learning where strategies are expected.