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Abstract To effectively teach modeling, instructors need to select tasks that allow students to learn which mathematical operations are appropriate for modeling different scenarios. Naturally, instructors might select tasks using a priori task classification systems—ones that group real-world problems for a given operation based on mathematical formalisms (e.g., as reported by Vergnaud (in: Hiebert (ed) Number concepts and operations in the middle grades, National Council of Teachers of Mathematics, 1988). In this paper, we critique the robustness of a priori task classifications systems for guiding the selection of modeling tasks. We investigated the meanings undergraduate STEM majors attributed to multiplication while modeling a predator–prey system using differential equations. Through analysis of task-based clinical interviews with 23 participants, six distinct justifications forwhymultiplication was an appropriate operation for modeling the scenario were identified. These six justifications confirm that learners’ assimilation of scenarios to operations may differ from how educators classify problems using a priori classification schemes. Our findings challenge the use of a priori task classification systems for guiding the pedagogical selection of real-world scenarios to model because classifying real-world scenarios using a priori systems can overlook nuances in modelers’structuringandvalidating. We highlight the importance of these nuances for generating task trajectories that would leverage learners existing meanings for mathematical operations to build new associations between mathematical operations and novel problems. We end by suggesting a shift towards reasoning-based classification systems for selecting real-world scenarios to model—ones that are based on students reasoning about and within a scenario. 

This paper reports a study of 10 post-secondary STEM (Science, Technology, Engineering, Mathematics) instructors’ beliefs about mathematical modelling and the role of mathematics in STEM coursework. The participants were selected from STEM disciplines that are atypical to the literature base (e.g., anthropology and geography), in order to extend what is known about STEM instructors’ beliefs to other disciplines. We conducted episodic narrative interviews to hypothesize the genesis of participants’ most salient beliefs. We then conducted a cross-case synthesis to reflect on the similarities between our participants’ beliefs and findings previously reported in STEM education literature. Our participants held many beliefs in common with typical STEM instructors with regards to how they define modelling, the role of modelling in STE (Science, Technology, Engineering) courses, and their views of students as learners of mathematics and modelling. Our analysis suggests participants’ commitments within these categories are interdependent and arise from lived experiences. Additionally, participants within the same field held competing beliefs about modelling, suggesting that constituting ‘major’ as an independent variable in future research may not be straightforward