Math fluency from elementary to middle school: differentiating recognition from inferential fluency

Fluency in mental arithmetic is often regarded as a foundational math skill best measured as a single construct. Here we examine the potential benefits of distinguishing between inferential fluency and recognition fluency in elementary and middle school students. Depending on the problem at hand, a student’s fluency may reflect reliance on inferential versus recognition processes. Here we studied single digit arithmetic problems that appear in a widely used 3-minute math fluency assessment across a large (n=914), diverse cohort of 3rd- 7th grade students. A novel tablet-based paradigm enabled us to aggregate performance across different problem types by devising a simple yet objective heuristic to designate problems as likely to draw upon recognition versus inferential fluency in this population. Effects of fluency type were evident across accuracy, response time, and combined responses per minute (RPM) metrics. A novel yet theoretically informative interaction emerged between fluency type and the operation effect. Both fluency types showed sensitivity to grade effects, SES effects, and global achievement levels on state-mandated math assessments. Inferential fluency proved to be a stronger predictor of global achievement than either recognition fluency or more traditional aggregate raw scores. Finally, we demonstrate how differentiating these two fluency types provides novel insights into how relationships between SES and global math achievement are mediated by both inferential and recognition fluency, but not equally. 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 math development.