Fernando Hitt & Sarah Dufour
Introduction To Calculus Through An Open-Ended Task In The Context Of Speed: Representations And Actions By Students In Action
Keywords: Learning obstacles; mathematical modeling; differential calculus; potential and actual infinity; socially constructed representation.
Abstract: The first calculus course in the province of Quebec (Canada) is taught in the first year of college before university. Statistics show this course is the most difficult one at the collegial level for students and that it prompts many to drop out of school. In the past, among other problems in the learning of calculus, the following two were considered: one related to the need for students' skills to integrate pre-calculus topics and the other related to mathematical infinity, a concept essential to the concepts of limit, derivative, and integral. New trends in mathematical modeling (e.g. as in the Reform of Calculus in the USA and the STEM project) have introduced a new variable to the topic: the use of differential calculus in real contexts. In this paper, we outline students' learning obstacles that relate to mathematical modeling, to the integration of pre-calculus concepts, and to the concept of mathematical infinity. (Click here for article)