Wilkerson, M. H., Bautista, A. Tobin, R., Cao, Y., & Brizuela, B. (In Press). More than meets the eye: Patterns and shifts in what middle school mathematics teachers describe as models. To appear in Journal of Mathematics Teacher Education.
Read the preprint manuscript here.
Though modeling is a popular topic in mathematics education, the field’s definition of model is diverse. Less is known about what teachers identify as mathematical models, even though it is teachers who ultimately enact modeling activities in the classroom. We asked nine middle school teachers with a variety of academic backgrounds and teaching experience to collect data related to one familiar physical phenomenon, cooling liquid. We then asked each to construct a model of that phenomenon, describe why it was a model, and identify whether a variety of artifacts representing the phenomenon also counted as models during a semi-structured interview. We sought to identify: What do mathematics teachers attend to when describing what constitutes a model? And, how do their attentions shift as they engage in different activities related to models? Using content analysis, we documented what features and purposes teachers attended to over the course of the interview. When constructing their own model, they focused on the visual form of the model and what quantitative information it should include. When deciding whether particular representational artifacts constituted models, they focused on how those representations reflected the system under study, and whether those representations could help to further understand the system. These findings suggest the teachers had multiple understandings of models, which were active at different times and reflected different perspectives toward modeling. This has implications for research, teacher education, and professional development.
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