Exploring the development of arithmetic fluency sub-classes from elementary to middle school

Fluency in mental arithmetic is regarded as a foundational math skill best measured as a single construct. Here we examine the benefits of distinguishing between standard and non-standard arithmetic problems in elementary and middle school students. Depending on the problem at hand, a student’s fluency may reflect reliance on fact retrieval versus computational processes. We used an accelerated longitudinal-design to study single-digit arithmetic problems that appear in a widely used 3-minute math fluency assessment across a large (n=914), diverse cohort of 3rd-8th grade students (ages 7-13 years). A novel tablet-based paradigm enabled us to aggregate performance across different problem types by labeling problems as belonging to the standard set of problems versus non-standard problems, typically excluded from research studies. Effects of problem class were evident across accuracy, response time, and combined responses per minute (RPM) metrics. The development of fluency with both classes of problems continued throughout the grade levels studied. The development of both types of problem showed sensitivity to grade effects, SES effects, and classroom context. Finally, we propose that differentiating inferential from recognition fluency is an initial step toward testing a proposed SIRPA (shift from inferential to recognition processes in arithmetic) model of mental arithmetic development.