CTM Conference 2025

Abstract: Learning linear algebra is known to present significant challenges, and there are well-established proposals for overcoming these through the use of visualizations and dynamic geometry. I illustrate such approaches based on an introductory mathematics course for engineering students and on David Tall’s research into geometric and algebraic representation. I then discuss how these ideas can be extended to a professional development course, Mathematics and Computational Thinking, for upper-secondary school teachers. The key question is: Is it possible, in just one day, to give teachers—and by extension their students—a meaningful impression of what Singular Value Decomposition (SVD) is and how it can be applied?

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: What have I learnt from three years of teaching mathematics for ‘the technology studies of the future’? I share experiences of contextualization and computationally oriented teaching, with large-scale project work. This period has seen the arrival of large language models, so I’ll talk about the impact, limitations, and opportunities that they’ve brought.

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: At the Technical University of Denmark, we have just completed the second round of the major mandatory courses Math 1a and 1b. These courses constitute the mandatory mathematics teaching in all bachelor's programs. Despite being only 2 years old, they have already undergone major changes due to generative AI. I will talk about the problems that arose and how they have been tried to be remedied, as well as the changes we are making to next year's courses.

Abstract: This talk will present the author’s experience and conclusions concerning the use of AI-assisted tutoring and assessment in his MSc and BSc courses at the University of South-Eastern Norway, as well as his plans for the upcoming 2025/26 academic year. The author’s expectations regarding near-term AI developments in both areas (tutoring and assessment) will also be discussed. Experiments and data collection were carried out over the two last academic years using Copilot/ChatGPT and NotebookLM (and occasionally Claude). Experimental conditions varied over the course of this period due to the rapid transformation of the AI technological landscape, the evolving pedagogical goals and the resources made available to the students (ranging from free usage plans to university-supported OpenAI Plus accounts offered to all students).

Abstract: This work explores the feasibility of fully automated grading of advanced mathematics exam problems using state-of-the-art AI systems. We begin with a historical perspective on AI math-solving tools, from early applications like Photomath to recent reasoning-capable models such as ChatGPT-4o and ChatGPT-o1. Focusing on a real-world case study from the August 2024 Calculus 2 exam at Lund University, we demonstrate an end-to-end workflow: scanning handwritten student solutions, digitizing mathematical expressions, and applying AI to evaluate solutions according to a predefined grading rubric. We compare grading outputs from multiple AI models and analyze their strengths and weaknesses in handling multi-step solutions involving partial fractions, integration, and limit evaluation. Beyond grading accuracy, we discuss the broader educational implications, including potential integration into feedback loops, ethical considerations, and the challenges of scaling such systems for diverse problem types. This proof of concept highlights both the promise and the current limitations of AI as a reliable partner in mathematics education assessment.

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.