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

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Abstract

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.

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Acknowledgements

This material is based upon work supported by the National Science Foundation under the EHR Core Research (ECR) Program, grant numbers 1561305, 1561304, 1561331, and 156274. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Authors and Affiliations

  1. Teaching, Learning and Sociocultural Studies Department, College of Education, University of Arizona, Tucson, AZ, USA

    Erin E. Turner, Mei-Kuang Chen & James E. Smith

  2. Department of Teaching and Learning, College of Education, Washington State University, Pullman, WA, USA

    Amy Roth McDuffie

  3. Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, USA

    Amy Been Bennett

  4. School of Education, University of Washington Tacoma, Tacoma, WA, USA

    Julia Aguirre

  5. Queens College, City University of New York, Flushing, NY, USA

    Mary Q. Foote

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  1. Erin E. Turner
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Correspondence to Erin E. Turner.

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Turner, E.E., Roth McDuffie, A., Bennett, A.B. et al. Mathematical Modeling in the Elementary Grades: Developing and Testing an Assessment. Int J of Sci and Math Educ 20, 1387–1409 (2022). https://doi.org/10.1007/s10763-021-10195-w

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