Related papers: Engaging activities for teaching linear algebra
Introducing inner-city high school students to program design presents unique challenges. The typical assumptions of an introductory programming course, like students understand what variables and functions are, may not be safe. Therefore,…
In this note we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task-design that gives students the opportunity to conjecture, refute and prove. What is…
This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project…
When deploying autonomous agents in the real world, we need effective ways of communicating objectives to them. Traditional skill learning has revolved around reinforcement and imitation learning, each with rigid constraints on the format…
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…
Active learning in computer experiments aims at allocating resources in an intelligent manner based on the already observed data to satisfy certain objectives such as emulating or optimizing a computationally expensive function. There are…
Explanations have gained an increasing level of interest in the AI and Machine Learning (ML) communities in order to improve model transparency and allow users to form a mental model of a trained ML model. However, explanations can go…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
We present results and ideas on flexibility and its teaching for university mathematicians based on research and our experience in professional development programs. We believe this could provide food for thought for instructors of calculus…
This paper shares a classroom story from Fall 2022 to Spring 2025 about a learner centered routine in undergraduate mathematics. I use four steps: an opening question, a short mini lecture about meaning, structured small group work, and a…
This article contains a selection of problems from the American Mathematics Competitions.
Due to the remarkable language understanding and generation abilities of large language models (LLMs), their use in educational applications has been explored. However, little work has been done on investigating the pedagogical ability of…
This article describes the authors' teaching experience in flipping the class of a basic undergraduate mathematics course Introductory Linear Algebra. We utilize a full-featured free electronic textbook, online lecture notes, an intranet…
We discuss parallels between students and teachers in the process of pedagogical reform. Reform aims for students to develop their own process for becoming independent learners, and to gain personal ownership. Likewise teachers can develop…
This article proposes and discusses qualitatively the use of a didactic board game in Science Education for high school students. The game contemplates in an interdisciplinary way the areas of Physics, Biology, Chemistry and Astronomy and…
The present article is an empirical study that investigates the learning situation of linear algebra. Research was performed among 60 science and engineering students from different universities in Zhejiang, Jiangsu, Hubei, and Shandong who…
In upper-division undergraduate physics courses, it is desirable to give numerical problem-solving exercises integrated naturally into weekly problem sets. I explain a method for doing this that makes use of the built-in class structure of…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
Training examples are not all equally informative. Active learning strategies leverage this observation in order to massively reduce the number of examples that need to be labeled. We leverage the same observation to build a generic…
Randomized linear algebra (RLA) algorithms are a modern class of numerical linear algebra techniques that play an essential role in scientific computing and machine learning, with broad and growing adoption. However, their discovery remains…