Related papers: The messages we send after we listen
It is rare to succeed in getting mathematics into ordinary conversation without meeting all kinds of reservations. In order to raise public awareness of mathematics effectively, it is necessary to modify such attitudes. In this paper, we…
We argue how AI can assist mathematics in three ways: theorem-proving, conjecture formulation, and language processing. Inspired by initial experiments in geometry and theoretical physics in 2017, we summarize how this emerging field has…
Large Language Model (LLM) simulations, where LLMs act as students with varying approaches to learning tasks, can support teachers' noticing of student thinking. However, simulations using zero- or few-shot prompting often yield inauthentic…
Children can take many paths to become scientists. But they undoubtedly include the following steps Play, play and play; Observe; Ask (themselves). In this paper I will talk about some of my experiences teaching girls and boys, teenagers…
Doing mathematics implies three levels of manipulation: manipulating the abstract, manipulating symbols and manipulating logic. Teaching mathematics therefore involves the teacher proposing situations in which pupils can explore a small…
Artificial Intelligence (AI) holds transformative potential in education, enabling personalized learning, enhancing inclusivity, and encouraging creativity and curiosity. In this paper, we explore how Large Language Models (LLMs) can act as…
In conversation, uptake happens when a speaker builds on the contribution of their interlocutor by, for example, acknowledging, repeating or reformulating what they have said. In education, teachers' uptake of student contributions has been…
In this paper, I explore what mathematical research can tell us about ourselves, and our role in the world, using examples from my own experience. The paper is a sequel to my piece "Mathematics is a Quest for Truth", published in the…
The growing ubiquity of artificial intelligence (AI), in particular large language models (LLMs), has profoundly altered the way in which learners gain knowledge and interact with learning material, with many claiming that AI positively…
The evolution of mathematics is shaped importantly by interestingness: researchers choose which problems to pursue, and students choose which problems to engage with, based on expectations of interest and challenge. As AI systems,…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
Math placement is a crucial step between admission and full engagement with the university for students in STEM majors. Students' placement experiences influence not only their mathematical entry point on their degree pathway, but their…
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
This essay, originally published in the Sept 1990 Notices of the AMS, discusses problems of our mathematical education system that often stem from widespread misconceptions by well-meaning people of the process of learning mathematics. The…
While Machine learning gives rise to astonishing results in automated systems, it is usually at the cost of large data requirements. This makes many successful algorithms from machine learning unsuitable for human-machine interaction, where…
Writing assignments in any mathematics course always present several challenges, particularly in lower-level classes where the students are not expecting to write more than a few words at a time. Developed based on strategies from several…
Conversational agents are becoming increasingly popular for supporting and facilitating learning. Conventional pedagogical agents are designed to play the role of human teachers by giving instructions to the students. In this paper, we…
This paper describes a collaboration between a mathematician and a compositionist who developed a sequence of collaborative writing assignments for calculus. This sequence of developmentally-appropriate assignments presents peer review as a…
Collaborative problem solving (CPS) is essential in mathematics education, fostering deeper learning through the exchange of ideas. Yet, classrooms often lack the resources, time, and peer dynamics needed to sustain productive CPS. Recent…
Email communication between instructors and students is ubiquitous, and it could be valuable to explore ways of testing out how to make email messages more impactful. This paper explores the design space of using emails to get students to…