Abstract
The development of automaticity of number facts and computation skills is an important goal for all students in their primary school years given that they are inherent throughout the various mathematical domains. Crucially, when engaging in more advanced mathematical learning and problem solving tasks that require higher-order thinking, automaticity enables other cognitive conscious processes to take place simultaneously, easing the load on working memory. Given that problem solving occurs in working memory, and that working memory is limited in both time and capacity, automaticity allows conscious attention to be devoted to the purpose of the task rather than the minor elements, such as the recall of basic arithmetic facts.
This study employed an experimental design to assess the causal relationship of the intervention of automaticity training of multiplication facts and its impact on problem solving and student self-efficacy. The research involved 51 students from three classes at an Independent School in New Zealand. Data were obtained through pre- and post-test measures of the participants’ automaticity of multiplication facts and problem solving ability. Additionally, structured interviews were used as a means of capturing the students’ perceived problem solving capabilities pre- and post-intervention.
Findings from this study indicate that the intervention was successful in developing automaticity and problem solving ability. Of particular interest is that the class sessions focusing on the development of conceptual understanding were perhaps more effective than anticipated. Additionally, although the self-efficacy results indicated only modest gains, a key finding was that when students were confident in their ability to solve a problem, they tended to talk about the problem directly; when they were not confident about their ability, they tended to focus on themselves and not the problem.
A series of four case studies was conducted to supplement the quantitative data to offer insights into the quantitative results, providing an understanding of what influenced the various outcomes in this study. Some of the influencing factors uncovered included: life circumstances, individual characteristics (including specific learning difficulties), the language of the learner, and the impact of cultural contexts on learning. The significant finding is that a range of determinants had a subsequent impact on the participants overall outcomes.