Brandes, Hadas (2017) The Bare Necessities for Doing Undergraduate Multivariable Calculus. Masters thesis, Concordia University.
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Abstract
Students in two mathematics streams at Concordia University start their programs on similar footing in terms of pre-requisite courses; their paths soon split in the two directions set by the Pure and Applied Mathematics (MATH) courses and the Major in Mathematics and Statistics (MAST) courses. In particular, likely during their first year of studies, the students set out to take a two-term arrangement of Multivariable Calculus in the form of MAST 218 – 219 and MATH 264 – 265, respectively. There is an ongoing discussion about the distinction between the MAST and MATH courses, and how it is justified. This thesis seeks to address the matter by identifying the mathematics that is essential for students to learn in order to succeed in each of these courses. We apply the Anthropological Theory of the Didactic (ATD) in order to model the knowledge to be taught and to be learned in MAST 218 and MATH 264, as decreed by the curricular documents and course assessments. The ATD describes units of mathematical knowledge in terms of a practical block (tasks to be done and techniques to accomplish them) and a theoretical block that frames and justifies the practical block. We use these notions to model the knowledge to be taught and learned in each course and reflect on the implications of the inclusion and exclusion of certain units of knowledge in the minimal core of what students need to learn. Based on these models, we infer that the learning of Multivariable Calculus in both courses follows in a tradition observed in single-variable calculus courses, whereby students develop compartmentalized units of knowledge. That is, we find that it is necessary for students in MAST 218 and MATH 264 to specialize in techniques that apply to certain routine tasks, and to this end, it suffices to learn bits and pieces of theoretical knowledge that are not unified in a mathematically-informed way. We briefly consider potential implications of such learning in the wider context of the MATH and MAST programs.
| Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
|---|---|
| Item Type: | Thesis (Masters) |
| Authors: | Brandes, Hadas |
| Institution: | Concordia University |
| Degree Name: | M. Sc. |
| Program: | Mathematics |
| Date: | 1 September 2017 |
| Thesis Supervisor(s): | Hardy, Nadia |
| Keywords: | Anthropological Theory of the Didactic Multivariable Calculus |
| ID Code: | 983041 |
| Deposited By: | HADAS BRANDES |
| Deposited On: | 16 Nov 2017 17:33 |
| Last Modified: | 18 Jan 2018 17:56 |
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