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Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification: that…
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…
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…
Understanding learners' understanding is a key requirement for an efficient design of teaching situations and learning environments, be they digital or not. This keynote outlines the modeling framework cK\cent (conception, knowing, concept)…
Given the profound and uncritiqued changes that have been implemented in Aotearoa New Zealand education since the 1990s, this paper provides a critical commentary on the characterising features of the New Zealand mathematics' curriculum in…
We present a research mathematician's perspective on current developments around in K-12 mathematics. We share activities, and highlight the different ways in which students' reasoning can progress, such as amount of abstraction,…
The purpose of this paper is to emphasize the role of language in the process of teaching and learning mathematics. We will begin with the definition of mathematics given by Cassiodorus (in its essential features repeated in Kolmogorov's…
"Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding, and you would not do it without some strong urge." [D. Ruelle]. We shall give some…
This paper lays out the current landscape of tools used in statistics education. In particular, it considers graphing calculators, spreadsheets, applets and microworlds, standalone educational software, statistical programming tools, tools…
With the rise of the popularity of Bayesian methods and accessible computer software, teaching and learning about Bayesian methods are expanding. However, most educational opportunities are geared toward statistics and data science students…
Momentum exists in the physics community for integrating computation into the undergraduate curriculum. One of many benefits would be preparation for computational research. Our investigation poses the question of which computational skills…
As educational settings increasingly integrate artificial intelligence (AI), understanding how AI tools identify -- and adapt their responses to -- varied educational contexts becomes paramount. This study examines conversational AI's…
Learning Spaces are certain set systems that are applied in the mathematical modeling of education. We propose a suitable compression (without loss of information) of such set systems to facilitate their logical and statistical analysis.…
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…
In recent years, computing has become an important part of the way we teach and learn physics. Teachers, both at high school and college levels, now use computational activities in many of their courses. Physics departments are offering…
We analyze a mathematical model to understand the dynamics of bullying in schools. The model considers a population divided into four groups: susceptible individuals, bullies, individuals exposed to bullying, and violent individuals.…
The widespread availability of generative artificial intelligence tools poses new challenges for school mathematics education, particularly regarding the formative role of traditional mathematical tasks. In post-AI educational contexts,…
A strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory.…
Statistics educators recommend teaching with real data with relevant contexts, but defining relevancy is challenging and varies by student. We investigated whether providing student choice of data context increases engagement through a…
We believe that economists have much to learn from educational research practices and related pedagogical innovations in other disciplines, in particular physics education. In this paper we identify three key features of physics education…