Mathematical Modeling in the Elementary Grades: Developing and Testing an Assessment

Erin E. Turner, Amy Roth McDuffie, Amy Been Bennett, Julia Aguirre, Mei Kuang Chen, Mary Q. Foote, James E. Smith

Research output: Contribution to journalArticlepeer-review


Mathematical modeling is a high-leverage topic, critical for college and career readiness, participation in STEM education, and civic engagement. Mathematical modeling involves connecting real-world situations, phenomenon, and/or data with mathematical models, and in this way applies across various STEM disciplines, including mathematics, engineering, and science. Although research has begun to explore mathematical modeling instruction in the elementary grades, questions remain about how to assess student learning at the elementary level. We addressed this need by designing an assessment of mathematical modeling competencies for students in grades 3 through 5. Informed by international research, our assessment includes a hybrid structure to assess mathematical modeling competencies holistically (as students engage in the complete modeling process) and atomistically (as students engage in different components of the modeling process, including making sense of phenomena and real-world situations, setting up and operating on mathematical models, and interpreting results in relation to the real-world context). We conducted student interviews, followed by two rounds of pilot testing to inform item development and ensure acceptable psychometric properties. The final assessment included 13 items (9 multiple choice, 3 open-response, and 1 complete modeling task). We describe our assessment development process, and provide sample assessment items and detailed coding rubrics. We summarize quantitative analyses which established high reliability and low standard error for our assessment, supporting its use for grades 3 to 5. Implications of our framework and assessment for mathematical modeling instruction and future research on STEM learning are discussed.

Original languageEnglish (US)
Pages (from-to)1387-1409
Number of pages23
JournalInternational Journal of Science and Mathematics Education
Issue number7
StatePublished - Oct 2022


  • Assessment of STEM competencies
  • Elementary grades
  • Mathematical modeling
  • Student learning

ASJC Scopus subject areas

  • Education
  • Mathematics(all)


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