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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…

In this article, we suggest the use of Mathematical Relationships as a possible way to decrease the students' disinterest in Mathematics. First we made a consideration of the environment of the classroom from the perspective of teachers and…

A hallmark property of explainable AI models is the ability to teach other agents, communicating knowledge of how to perform a task. While Large Language Models perform complex reasoning by generating explanations for their predictions, it…

We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.

Drawing on the Data and Predictions strand of the Indicazioni Nazionali per il curricolo 2012, this study proposes a problem based instructional approach to the teaching of probability. More specifically, the study adopts a design based…

Good problems grab us. They invite us to find patterns, make conjectures, and prove-or perhaps disprove-a conjecture. When I first taught, I saw my work as tantalizing students with structures just beyond their reach, so that I could elicit…

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…

One can notice that quite often difference between so-called "standard students" and "gifted" ones is not because that first are less smart, but they have different "orientation", they consider subject as a collections of rules which should…

In this article, we identify the didactic conditions for learning mathematics in kindergarten. To do so, we rely on the framework of the theory of didactic situations (Brousseau, 1998) and the notion of problem-situation (Douady, 1984). We…

The school choice problem concerns the design and implementation of matching mechanisms that produce school assignments for students within a given public school district. In this note we define a simple student-optimal criterion that is…

This study discusses the opportunity to integrate tinkering, a constructionist practice, into formal education, highlighting its potential and challenges. We propose a model through which teachers can blend the open exploratory nature of…

Introductory algebra-based physics courses frequently feature multiple student major populations in the same course section, however, different majors' requirements may impact students' motivations towards different aspects of the course…

Debugging is often a challenging and infuriating experience for secondary school students learning their first text-based programming language. Many students resort to ineffective debugging strategies, making success with solving errors…

Numbers, both very large and very small, are crucially important for understanding the modern world. This paper assesses trials of a mathematics and physics module called Powers of the Universe in which arithmetic with extreme numbers…

First year calculus is often taught in a way that is very burdensome to the student. Students have to memorize a diversity of processes for essentially performing the same task. However, many calculus processes can be simplified and…

One of the grand challenges of Mathematics instruction is to provide students with problems that are both accessible and have a reasonably elegant solution. Instructors commonly resort to resources like course textbooks, online-learning…

Developing expert-like problem-solving skills is a central goal of undergraduate physics education. In this study, we investigate the impact of teaching explicit problem-solving frameworks, combined with deliberate practice, on students'…

Problem solving is central to physics instruction. Results from Physics Education Research (PER), however, demonstrate that traditional ways of teaching with problem solving are inefficient and ineffective for promoting true physics…

Students in introductory physics struggle with vector algebra and these challenges are often associated with contextual and representational features of the problems. Performance on problems about cross product direction is particularly…

This paper examines the initial beliefs held by elementary educators (n=11) and their students about teaching and learning quantum concepts at the elementary level. All teachers were participants in a grant-funded project focused on…