Characterizing Mature Number Sense and Its Association To Other Constructs in Middle School Students

Improving children’s “number sense” has been a core component of recent mathematics curricular and instructional reforms (CCSS, 2010; NCTM, 2000, 2014) in the United States. Students with mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents, there is no systematic evidence on the state of US students’ mature number sense. Moreover, there is little evidence demonstrating that mature number sense is even a measurably distinct characteristic of mathematical cognition or that it is important for students’ grade-level mathematics achievement. One reason for slow progress is that the field currently lacks a rigorously validated measure of mature number sense that is both widely accepted and practical to use in classroom settings.

In this project, we aimed to address this issue and advance fundamental knowledge of mature number sense as a construct. Building off of initial work (Kirkland et al., 2020) to rigorously develop a practical measure of mature number sense with valid and reliable scores (AERA, APA, NCME, 2014), we first gathered additional convergent evidence of validity for our measure with students in grades 6-8. We compared middle school students’ (N = 40) scores on our measure with an established, though time-intensive, measure (Yang, 2019) and their strategy use during an in-depth interview of student thinking. We found scores on all three measures of mature number sense to be strongly related (r > 0.7). Then, using our developed measure, we analyzed 129 middle school students’ scores on our brief assessment of mature number sense and measures of several related constructs, including grade-level mathematics achievement and rational number knowledge. Through a series of analyses, we found evidence that mature number sense is measurably distinct from students’ rational number knowledge and is uniquely associated with their grade-level mathematics achievement.