Implicit Function Theorem: Students' autonomy in learning
Résumé
The Implicit Function Theorem is one of the rich theorems covered in multivariable calculus course with many applications and very limited lecturing time. In this paper we study the students’ perspective as part of the final step of didactic transposition from taught knowledge to learnt knowledge. As a general characteristic of education at the university level, the transposition to learnt knowledge includes significant students’ autonomy in learning, so with this pilot study we have studied the differences in students’ learnt knowledge and different perceptions of the value of the theorem. The interviews with three students show that concrete examples are meaningful and occupy their focus more than the proof of the theorem, while considering examples as applications provides motivation for theoretical knowledge, with limited study time leading to well-known effects of compartmentalization.
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