The Emergence of Mathematical Modeling Competencies: An Investigation of Prospective Secondary Mathematics Teachers

Abstract

A study with prospective teachers without prior mathematical modeling experience sheds light on how their newly developed conceptual understanding of modeling manifested itself in their work on the final task of a modeling module within a pedagogy course in secondary mathematics curriculum and assessment. The main purpose of the module was to provide opportunity for the prospective teachers to experience the Common Core Mathematical Practice Model with Mathematics and begin to develop competency in modeling. Their work and reflections displayed a range of proficiency in several competencies associated with the modeling process. Examples of their work illustrating these ranges are provided. The prospective teachers expressed both struggle and rewards during the process, and reflected on challenges for teaching modeling. The results suggest that infusing modules in existing courses can be an effective way to elevate prospective teachers from unfamiliarity with modeling to noticeable levels of proficiency in various modeling sub-competencies.

Pre-service mathematics teachers’ professional modeling competencies: a comparative study between Germany, Mainland China, and Hong Kong

“…Therefore, they may know more about how specific modeling tasks should be analyzed compared to providing feedback. This explanation is supported by existing studies, which report PSTs' difficulties in suggesting alternative approaches (Anhalt et al, 2018).…”

“…Earlier studies have reported similar findings. For example, as noted above, PSTs were typically found to experience difficulties at some stages of the mathematical modeling cycle, particularly at the stages of interpreting and validating (Anhalt et al, 2018;Tan & Ang, 2013).…”

“…For example, Tan and Ang (2013) found that PSTs could interpret real-world situations and identify important quantities, but some teachers struggled to recognize the need to uncover relationships between variables and failed to interpret mathematical solutions in real situations or to validate their mathematical models. Anhalt et al (2018) also found that PSTs could make appropriate assumptions and simplifications and mathematize relevant quantities and their relations, but some participants showed low proficiency in interpreting Teaching Perspective (Explaining the adequacy of the task; choosing appropriate teaching approach) Fig. 1 Framework of professional mathematical modeling competences mathematical results in real-life contexts, and only half were able to suggest alternative approaches.…”

Mathematics Education as a Mathematician's Research Area: An Invitation for Collaboration

“…Another study (Anhalt, Cortez, & Been Bennett, 2018) focused on the particular competency of making appropriate assumptions to construct a model. We designed problems that required multiple assumptions and analyzed students' work and their reflections on their work to determine when during the modeling process assumptions were made.…”

“…Schematic of the progressive modeling cycle experienced by prospective teachers,Anhalt, Cortez, & Been Bennett, 2018. …”