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This Brief Report presents an example of assessment validation using an argument-based approach. The instrument we developed is a Brief Assessment of Students’ Mature Number Sense, which measures a central goal in mathematics education. We chose to develop this assessment to provide an efficient way to measure the effect of instructional practices designed to improve students’ number sense. Using an argument-based framework, we first identify our proposed interpretations and uses of student scores. We then outline our argument with three claims that provide evidence connecting students’ responses on the assessment with its intended uses. Finally, we highlight why using argument-based validation benefits measure developers as well as the broader mathematics education community. 

Students who exhibit mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly choose effective problem-solving strategies (McIntosh et al., 1997, https://ro.ecu.edu.au/ecuworks/6819). Due to its dispositional nature, mature number sense is typically measured through in-depth interviews or tests of strategy usage. Yet, the lack of an efficient, rigorously developed measure has made it difficult to collect systematic, replicable evidence on students’ mature number sense. To address this, we developed a brief assessment of mature number sense. The present study provides additional convergent evidence of validity for this measure with US students in grades 3-8 (8–14 years old). We compared middle school (N = 40) and upper elementary school (N = 41) scores from the brief assessment with an established, time-intensive measure (Yang, 2019, https://doi.org/10.1007/s10649-018-9874-8) and an in-depth interview of student strategy usage (Markovits & Sowder, 1994, https://doi.org/10.2307/749290). We found strong correlations (r > 0.7) across all three measures, and this held even when controlling for students’ arithmetic scores (pr > 0.6). Researchers and educators can now use the brief assessment to investigate students’ mathematical thinking and advance knowledge of a key aspect of mathematical cognition. 

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; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000), the association between students’ mature number sense and other important outcomes is not well specified. For example, how does students’ mature number sense relate to their grade-level mathematics achievement? We analyzed 153 upper elementary school students’ scores on measures of mature number sense, fraction and decimal knowledge, multiplication fluency, and grade-level mathematics achievement. We found mature number sense to be measurably distinct from their fraction and decimal knowledge and uniquely associated with students’ grade-level mathematics achievement.