Cognitive interference in the learning of multiplication facts

Fluency with multiplication facts provides a strong foundation for future mathematics learning. Models of number fact storage and retrieval suggest that multiplication facts are stored in an associative network whereby neighbouring facts (e.g. 6 × 7 and 6 × 8) can interfere with one another. While existing theoretical models account for the skilled retrieval of number facts, an understanding of how interference develops during learning, and hence the need for inhibitory control during learning, is poor. In a pre-registered study, we tracked adults as they learnt a set of new multiplication facts and we monitored the interference between facts throughout their learning. Our findings are the first to show that interference emerges early in the learning process as individuals acquire knowledge of new facts. Moreover, interference does not decline as learning continues, even when retrieval accuracy is high and individuals are continuing to practice facts that they already know. These findings are consistent with theoretical assumptions and models of multiplication fact networks proposed by Ashcraft (1987), Campbell (1995) and De Visscher et al., (2016), but do not support the model proposed by Verguts & Fias (2005).