Children's Multiplicative Reasoning: Differences Across Grade Level and Tasks for Multiplication and Division

ABSTRACT Multiplicative reasoning is a fundamental construct for children to engage meaningfully with multiplication and division. However, various reports suggest that elementary and middle school students in the United States lack the necessary multiplicative reasoning to engage in relevant topics. Moreover, these prior estimates vary considerably given they draw from relatively few schools. Furthermore, there is a substantial lack of scholarship on multidigit multiplication and division generally. The current study examined data from 1451 students across 57 teachers in 32 schools with the goal of examining what fourth, fifth, and sixth‐grade students' multiplicative reasoning was, whether there were differences across these grade levels, and if students' performance on multiplication and division tasks differed regarding their level of multiplicative reasoning. Results indicated that approximately half of fourth‐grade and over a quarter of fifth and sixth‐grade students lacked the necessary multiplicative reasoning to engage in partial products. While there were statistically significant differences between fourth‐grade and latter grades, there was no statistically significant difference in multiplicative reasoning between fifth and sixth‐grade students. Notably, students with such reasoning tended to perform better on multiplication and division tasks. Implications for research and practice are discussed.