Abstract
While the culture of many mathematics departments inflects strongly towards STEM, most mathematics departments also offer a significant number of introductory courses intended for both STEM and non-STEM majors. We are a group of mathematicians who, in this work, examine the intent and goals of a university mathematics education for the non-STEM student. We engage in a community of inquiry to discuss how better to address the interests and experiences of our students, and conclude that centring the students’ point of view and decentring the professional mathematician’s point of view is potentially transformative in building resiliency and community. We propose a coordinate system to describe mathematical tasks, with a “contrived-authentic” axis, and a “clean-messy” axis. Finally, we elaborate on the value of the community of inquiry itself in developing our own philosophy and practice of teaching.
Résumé
Alors que la culture de nombreux départements de mathématiques se tourne de plus en plus vers les STEM, la plupart des départements de mathématiques offrent également un certain nombre de cours d'introduction destinés à la fois aux étudiants spécialisés en STEM et à ceux qui ne le sont pas. Nous sommes un groupe de mathématiciens qui, dans cette étude, examinons l'intention et les objectifs d'une formation universitaire en mathématiques à l’intention des étudiants non spécialisés en STEM. Nous participons à une communauté d'apprentissage pour traiter de la meilleure façon dont nous pouvons répondre aux intérêts et aux expériences de nos étudiants, et concluons que le fait de centrer le point de vue des étudiants, et de décentrer le point de vue des mathématiciens professionnels, peut transformer la communauté et accroitre sa résilience. Nous proposons un système de coordonnées pour décrire les tâches mathématiques, avec un axe « artificiel - authentique » et un axe « clair - désordonné ». Enfin, nous nous penchons sur la valeur de la communauté d'apprentissage en soi dans le développement de notre propre philosophie et de nos pratiques d'enseignement personnelles.
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Notes
The quadratic sequence {8,32,72,128,...} represents the number of tiles in the starblanket as the size of the starblanket increases, as shown below:
The sum of the terms in the sequence {1,2,3,4,3,2,1} represents the number of tiles in a single leaf of the starblanket on the right (above). ED’s students generally calculate these sums, and then multiply by 8, the total number of leaves.
In a follow-up discussion, ED proposed the following characterization: “messiness is proportional to the amount of time an expert [...] would have to spend to understand the situation; ‘messiness is proportional to time.’”
The species of authenticity used by the community of inquiry here is what Weiss, Herbst, and Chen label AMW, or “mathematics that is rooted in real world context” (p. 276), with the novel addition that the world in question ought to be the students’ world.
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Leung, FS., Radzimski, V. & Doolittle, E. Reimagining Authentic Mathematical Tasks for Non-STEM Majors. Can. J. Sci. Math. Techn. Educ. 20, 205–217 (2020). https://doi.org/10.1007/s42330-020-00084-9
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DOI: https://doi.org/10.1007/s42330-020-00084-9