CTM Conference 2025

Abstract: The usefulness of programming skills in mathematical teacher training is not universally recognized. In this talk I’ll give some theoretical arguments why computational thinking and mathematical thinking are closely intertwined. However, it is challenging to exploit this theoretical potential in courses of very limited teaching time. I will report on how I try to solve this dilemma in my courses. The core idea is to reduce the diversity of constructs in current programming languages to a necessary minimum so that a wide range of applications can be covered with just a few constructs, even if this often means that the programs are not very efficient from a CS perspective. Nevertheless, this concept makes it possible to cover everything from an introduction to programming to the basics of artificial intelligence in a two-hour course.

Abstract: Many engineering students lose motivation when mathematics is presented as a general tool; they also want to know where the tool is used. In the first-year mathematics courses at Aalborg University, we try to incorporate this by asking students to solve specific problems inspired by their own field of study. These problems are decided in collaboration with the individual engineering departments, and the students solve them in groups. This talk provides an insight into our experiences on how to implement this in practice: which problems are suitable, how difficult they can be, and which challenges are likely to occur in such a course restructuring.

Abstract: This talk is based on an ongoing initiative to teach mathematics to Master of Engineering students with the aim of obtaining a closer connection between mathematics and engineering subjects (teaching mathematics in context), and also with the aim of strengthening the computational aspects of mathematics. The initiative started as a project with a small number of study programmes involved and is now in the process of being scaled up to include all Master of Engineering students (ca. 1700) at NTNU. The ideas behind the contextualisation are anchored in the CDIO framework, advocating that mathematics should be presented in situations that the students recognise as important to them. In addition, the CDIO standard for Simulation-based mathematics is recognised, i.e., engineering programmes where the mathematics curriculum is infused with programming, numerical modelling and simulation. In the talk I will discuss opportunities and challenges involved when implementing a contextual approach to mathematics for engineering students, in particular on a large scale. Some examples of contextualisation used in the small-scale project will be presented. Part of the motivation behind the project was also to strengthen the relevance of mathematics. Some results from surveys capturing students' perceived relevance will be discussed.

Abstract: Feedback is a central factor in supporting students’ learning processes. In digital learning environments, informative tutoring feedback (ITF) strategies can be employed to support students with formative feedback without revealing correct solutions. Specifically for mathematical tasks, the ITF-strategy guiding feedback was conceptualized. It aims to provide learners with error-specific hints and otherwise offers them the possibility to solve tasks step-by-step. Initial studies on the use of guiding feedback have demonstrated positive cognitive, motivational, and metacognitive effects. However, findings also suggested that many students did not engage sufficiently with the feedback. To address this issue, this article proposes an optimization involving the integration of pedagogical agents to provide the feedback to students and the use of generative artificial intelligence (GenAI) to support the generation of error-specific information. This article introduces the conception of this optimized feedback strategy, explains its potential to enhance students’ engagement with feedback, and illustrates it through examples.