Lessons Learned From Children’s Answers in Direct Modeling Strategies for Fraction Story Problems

• In Event: Elementary Students' Mathematical Cognition: Insights Into Estimation, Relational Reasoning, and Effective Feedback in Mathematics

Abstract

We explored 1726 direct modeling strategies for fraction story problems on a written assessment for grades 3–5. To provide insights into children’s emerging use of fractions in ways that connected with their sensemaking, we focused on how children expressed their answers based on valid models they created to solve problems. Analyses of correct answers revealed children’s use of both conventional and unconventional fraction notation. Analyses of incorrect answers revealed that children typically (over-)prioritized particular mathematical ideas—whole numbers, familiar fractions, counting totals, fraction rules, or descriptions of their models—to the exclusion of other ideas integral to answers. This landscape of answers showcases the complexity of expressing fractional answers and offers a pedagogical starting point for supporting children’s ideas.

Authors

• Victoria R. Jacobs, University of North Carolina - Greensboro

• Susan B. Empson, University of Missouri

• Katherine Collins, University of North Carolina - Greensboro