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Toward a reconceptualization of model development from models-and-modeling perspective in mathematics education

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Abstract

Models-and-modeling perspective (MMP) is a problem-solving and learning perspective in mathematics education. Although modeling processes have been addressed widely in the international discussion on mathematical modeling, a homogeneous understanding has not been established yet. Hence, the field needs studies addressing the epistemological grounds of model development. Therefore, in this study, I aimed to scrutinize the latent aspects of modeling in MMP-based research. Based on the analysis of 143 chapter-sized documents, I aimed to articulate the characteristics of the modeling process and the models. The thematic analysis that was incorporated in document analysis revealed four latent aspects, namely, modeling (1) is a subjective and also inter- and intra-subjective process, (2) encompasses both structural and systematic properties, (3) produces models that are both implicit and explicit to a certain degree, and (4) culminates in an incomplete — but not inadequate — model. These aspects of model development led me to reconceptualize what a model conveys in MMP-based research and articulate the potential and limits of the models. This is particularly important for teachers and researchers in understanding what models indicate in relation to students’ ways of thinking, and such a systematic and analytical investigation can contribute to the scholarly conversation about modeling in the field of mathematics education.

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Notes

  1. Since the document analysis was held in 2019, the data corpus partially included the documents that were published in 2019.

  2. The keyword search in databases for years 2000–2019 resulted with 70 documents. During the initial data analysis phases, four additional documents that were cited by modeling researchers were identified as relevant. Therefore, these four additional documents two of which were published in 1990s, one document was in 1980s, and one in late 1970s were included in the data corpus.

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Acknowledgements

I would like to thank Emeritus Professor Richard Lesh, who developed the MMP with his colleagues and who contributed a lot to this document and thematic analysis by discussing each of the four aspects of the modeling presented in this study.

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  1. Mathematics and Science Education, Middle East Technical University, Ankara, Turkey

    Serife Sevinc

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Appendix. Thematic maps of the latent aspects of modeling from MMP

Appendix. Thematic maps of the latent aspects of modeling from MMP

Fig. 6
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Latent aspect #1 — inter/intra-subjective aspect of modeling

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Fig. 7
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Latent aspect #2 — structural and systemic aspect of modeling

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Fig. 8
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Latent aspect #3 — implicit and explicit aspects of models of modeling

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Fig. 9
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Latent aspect #4 — incomplete aspect of modeling

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Sevinc, S. Toward a reconceptualization of model development from models-and-modeling perspective in mathematics education. Educ Stud Math 109, 611–638 (2022). https://doi.org/10.1007/s10649-021-10096-3

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