Bridging gaps in math achievement: the role of number flexibility and groupitizing in the development of number sense

This study builds on the foundational work of Gray and Tall ( 1994 ) by replicating and extending their analysis of the number strategies that distinguish lower- and higher-achieving students in a contemporary, diverse US context, with an added focus on groupitizing. Mathematics education has long studied how children come to see quantities as structured, through conceptual subitizing and finger patterns; cognitive science has more recently measured this capacity as groupitizing. Bringing these conversations together, we test whether groupitizing’s association with achievement runs through students’ strategy use. Through cognitive interviews and dot enumeration tasks with students in grades 2–5, we examined how groupitizing—the perceptual and conceptual structuring of quantities into groups—relates to the use of flexible number strategies such as composition and decomposition. Results reveal that high-achieving students make greater use of flexible, relational strategies, while low-achieving students predominantly rely on counting approaches. Multivariate analyses show that groupitizing is a robust predictor of achievement status, with much of this association statistically accounted for by students’ number flexibility. These findings underscore the need for instructional practices that explicitly develop groupitizing and number flexibility, offering a pathway to address persistent achievement gaps and support students at risk for long-term mathematical difficulties.