Learning multiplication facts: a study of children taught by discovery methods in England

The development of multiplication skills was examined in a group of children ages 8 to 12 years who were taught by discovery methods. Strategies used by the children included direct retrieval, retrieval + calculation, and counting-in-series. Repeated addition was not observed. Retrieval was the fastest and least error-prone strategy; counting-in-series was the slowest and most error prone. Children ages 8 and 9 years used mainly mixed strategies. Children ages 10 to 12 years used mainly retrieval or retrieval and calculation for low operands, but reverted to back-up strategies for high operands based on the strategies available for low operands. There was a general shift away from less effective strategies across ages 8 to 12 years but, by the end of the primary school (age 11 years), relatively few children used the most effective strategy of retrieval for all operands. The development of effective strategies was related to nonverbal reasoning ability and to working memory capacity. The results are considered with reference to experiential and pedagogical models of multiplication.