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Defining mathematical modeling for K-12 education

Groshong, Kimberly A
http://orcid.org/0000-0001-6657-8233
http://rave.ohiolink.edu/etdc/view?acc_num=osu1534374871189434

Abstract Details

2018, Doctor of Philosophy, Ohio State University, EDU Teaching and Learning.
This dissertation reports the research methodology and findings of three studies focused on mathematical modeling as a structured problem-solving process where the student translates relevant details from a situation, event, or phenomena in daily life into mathematical language with mathematically-defined structures and operations, which form the mathematical model. This model can be manipulated to yield a solution, description, explanation, or prediction, which are then interpreted within the context of the real-life event. Part of this process requires determining when the mathematical model can be adapted to new situations and identifying the model’s boundaries and limitations in providing descriptions, explanations, and predictions. Constructing, testing, and applying mathematical models meet the needs of science, technology, engineering, and mathematics (STEM) educational goals for advancing students’ knowledge and skills and for increasing students’ understanding of the world around them. To capture the complexities of mathematical modeling, this research defined the Systems Theory in Mathematical Modeling Education (STiMME) theoretical framework to investigate the interactions that influence students’ mathematical modeling experiences. Many stakeholders, e.g. researchers, educators, students, etc., work at various levels to deliver content standards, develop materials, implement lessons, engage in learning, and participate in a myriad of ways that affect outcomes. The STiMME framework probes these interrelated elements and their impact on students in hopes of revealing new ways of thinking about mathematical modeling teaching and learning practices and theories. This research defined three STiMME subsystems. The first study scrutinized 241 STEM literature artifacts distinguishing between models and representations, models and mathematical models, and modeling and mathematical modeling to yield definitions for laying a united foundation for investigating mathematical modeling teaching and learning in all STEM education subjects. Similarities in mathematical modeling, engineering and technology design, and scientific methodological processes were identified that may improve students’ transfer of knowledge and skills within different STEM courses. The second study scrutinized 342 resources to create a taxonomy for the 14 different types of mathematical models described in professional and educational writing. The final study examined student work from the same mathematical modeling activity presented in three math and physics classes to determine the impact that student question posing, tracking, and reviewing had on the types of mathematical models they constructed. The students asked exploratory, consolidating, clarifying, and elaborating questions. It was noted that students with more exposure to mathematical modeling activities and more experience with question strategies were able to construct more sophisticated mathematical models.
Patricia Brosnan (Committee Chair)
Theodore Chao (Committee Member)
Kathy Malone (Committee Member)
224 p.
Education; Educational Theory; Mathematics Education; Pedagogy; Science Education; Secondary Education; Systems Design
Mathematical modeling; STEM; education; definitions; systems theory; theoretical framework

Recommended Citations

Citations

  • Groshong, K. A. (2018). Defining mathematical modeling for K-12 education [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1534374871189434

    APA Style (7th edition)

  • Groshong, Kimberly. Defining mathematical modeling for K-12 education. 2018. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1534374871189434.

    MLA Style (8th edition)

  • Groshong, Kimberly. "Defining mathematical modeling for K-12 education." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1534374871189434

    Chicago Manual of Style (17th edition)

osu1534374871189434
2,861
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This open access ETD is published by The Ohio State University and OhioLINK.