The first calculus course in the province of Quebec (Canada) is taught in the first year of college (17–18 year-old students) before university. Statistics show that this course is the most difficult one for students at the collegial level and that it prompts many to drop out of school. The literature has highlighted the cognitive problems students have with integrating concepts related to pre-calculus and their problems in learning calculus concepts related to infinity. In the current century, a new variable is added to the teaching of introductory calculus courses, namely, the introduction of situational problems as a way to generate new knowledge. This new approach to teaching is mainly related to modelling processes in the generation of knowledge. In this paper, we show the cognitive problems students have in learning calculus when solving situational problems. More precisely, we observe students’ mathematical activity as they solve an open-ended task related to speed. We analyze their use of different representations in the process of modelling the situation, the evolution of these representations when students work in a collaborative learning approach, and their construction of the concept of the derivative.

魁北克省（加拿大）的第一门微积分课程是在大学第一年（17至18岁的学生）上大学之前开设的。统计数据表明，对于高校学生来说，这门课程是最困难的课程，它促使许多人辍学。文献强调了学生在整合与预微积分有关的概念时存在的认知问题，以及他们在学习与无穷大有关的微积分概念时遇到的问题。在当前世纪，微积分入门课程的教学中增加了一个新变量，即引入情境问题以产生新知识。这种新的教学方法主要与知识生成过程中的建模过程有关。在本文中，我们展示了学生在解决情境问题时在学习微积分时遇到的认知问题。更确切地说，当学生解决与速度有关的开放性任务时，我们会观察他们的数学活动。我们在建模情况的过程中分析了他们对不同表示形式的使用，学生在协作学习方法中工作时这些表示形式的演变以及派生概念的构建。