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When a teacher provides examples for a student to study, these examples must be informative, enabling a student to progress from their current state toward a target concept or skill. Good teachers must therefore simultaneously infer what…
Presents a differentiated teaching proposal that allows the student to be the agent in the construction of knowledge, overcoming the difficulties that Mathematics presents. Aiming to understand how the use of statistical tools can…
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…
In parallel to the ever-growing usage of mechanized proofs in diverse areas of mathematics and computer science, proof assistants are used more and more for education. This paper surveys previous work related to the use of proof assistants…
This paper is one of a series in which elementary-education practice is analyzed by comparison with the history of mathematics, mathematical structure, modern practice, and (occasionally) cognitive neuroscience. The primary concerns are:…
The theme of the PME-48 conference, Making sure that mathematics education research reaches the classroom, highlights a key concern: not all mathematics education research informs classroom practice. This raises several fundamental…
Technology enables a more sustainable and universally accessible educational model. However, technology has brought a paradox into students' lives: it helps them engage in learning activities, but it is also a source of distraction. During…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
In their study of physics beyond the first year of University -- termed upper-division in the US, many of students' primary learning opportunities come from working long, complex back-of-the-book style problems, and from trying to develop…
Machine Learning (ML) techniques are encountered nowadays across disciplines, from social sciences, through natural sciences to engineering. The broad application of ML and the accelerated pace of its evolution lead to an increasing need…
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…
In this chapter, I discuss teaching mathematical tools specifically tailored for economics students. A typical one-semester course in this area seeks to blend a range of topics: from foundational elements of subjects such as linear algebra…
We describe our adventures in creating a new first-year course in Experimental Mathematics that uses active learning. We used a state-of-the-art facility, called The Western Active Learning Space, and got the students to "drive the…
Game-based technologies and mobile learning aids open up many opportunities for learners; however, evidence-based decisions on their appropriate use are necessary. This explorative study (N = 100) examines the role of game elements in…
Educators must make decisions about learner expectations and skills on which to focus when it comes to laboratory activities. There are various approaches but the general pattern is to encourage students to measure ordered pairs, plot a…
Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them…
Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think…
We assess the situation of our elementary Linear Algebra classes in the US holistically and through personal history recollections. Possible remedies for our elementary Linear Algebra's teaching problems are discussed and a change from…
Most introductory quantum physics instructors would agree that transitioning students from classical to quantum thinking is an important learning goal, but may disagree on whether or how this can be accomplished. Although (and perhaps…
What do we teach and what should we teach? An honest answer to this question is painful, very painful--what we teach lags decades behind what we practice. How can we reduce this `gap' to prepare a data science workforce of trained…