An Adaptive Learning System for Stepwise Automatisation of Multiplication Facts in Primary Education

Abstract

We demonstrate an application for learning multiplication problems with an adaptive algorithm that is based on a computational cognitive model of the learner's memory. The application helps learners automatise multiplications through repeated practice over three levels of difficulty. In a naturalistic setting involving more than 500 primary school students (ages 6-10) who together recorded over 200,000 responses, we observed that performance improved as learners using the application progressed through the levels. A model-based analysis of performance revealed that learners' estimated speed of forgetting decreased from the second to the third level. This is consistent with a shift towards stronger declarative knowledge and/or more efficient computation procedures. The model also identified consistent differences in the difficulty of individual multiplication facts that persisted across levels. This study demonstrates the feasibility of using an adaptive fact learning application to help young learners automatise multiplication, an essential mathematical skill.