Calculus is COOL – an ODE for practical demonstrations in calculus class
Most people consider the Fundamental Theorem of Calculus the crown jewel of single variable calculus. It’s hard to argue with them; the theorem captures the essence of calculus by marrying differentiation and integration in a (relatively) simple statement. However, I find that it’s at differential equations and modelling where the ideas and tools of calculus…
Read MoreTeaching practices to introduce limits of functions in the first year of university
Although lectures remain the dominant teaching method in higher education, their effectiveness in improving student understanding is widely questioned. Nevertheless, lectures provide teachers with an opportunity to build on students’ prior knowledge and introduce new concepts by using words, drawings and symbols. Lectures may also contain examples and prepare students for subsequent activities, such as…
Read MoreBrewing Alien Beer: Calculus Legacy as a Ludo-Didactical Experiment in a First-Year Engineering Calculus Course
Calculus is a foundational course in STEM programs, closely connected to various engineering disciplines, yet many first-year students experience this subject as abstract and demotivating. It often functions as a “gatekeeper course” hindering students’ motivation to continue. From this perspective, we redesigned the tutorials of a first-year calculus course with improved teaching philosophies, leading to…
Read MoreIntroducing students to mathematical problem solving – why and how?
Why problem solving? Students entering a university-level mathematics program often have a particular image of what mathematics is, shaped by their experiences in secondary school. Typically, this image is biased toward calculational skills—such as solving equations and manipulating formulas. Much of the practice they encountered in high school focused on training these skills. However, at…
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