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Drawing inference from data is an important skill for students to understand their everyday life, so that the sampling distribution as a central topic in statistical inference is necessary to be learned by the students. However, little is…
Mathematical proofs should be paired with formal proofs, whenever feasible.
Developing expertise in physics entails learning to use mathematics effectively and efficiently as applied to the context of physical situations. Doing so involves coordinating a variety of concepts and skills including mathematical…
The concepts of the Coriolis and the centrifugal force are essential in various scientific fields and they are standard components of introductory physics lectures. In this paper we explore how students understand and apply concepts of…
Transformer-based language models have shown strong performance on an array of natural language understanding tasks. However, the question of how these models react to implicit meaning has been largely unexplored. We investigate this using…
We are convinced of the usefulness of sketches and diagrams during mathematical work but the observation is made in our practices that they are not spontaneously used by students. In order to study the understanding and use of sketches by…
This is the full version of a paper submitted to the Computability in Europe (CiE 2023) conference, with all proofs omitted there. In 2012 P. D. Azar and S. Micali introduced a new model of interactive proofs, called "Rational Interactive…
Questions of participant understanding of the nature of an activity have been addressed in anthropology and sociolinguistics with the concepts of frames and framing. For example, a student may frame a learning activity as an opportunity for…
We explore the Collatz conjecture and its variants through the lens of termination of string rewriting. We construct a rewriting system that simulates the iterated application of the Collatz function on strings corresponding to mixed…
Explication and reflection on expert vs. novice considerations within the problem-solving process characterize a cognitive apprenticeship approach for the development of expert-like problem solving practices. In the context of grading, a…
Reasoning models have achieved remarkable performance on tasks like math and logical reasoning thanks to their ability to search during reasoning. However, they still suffer from overthinking, often performing unnecessary reasoning steps…
This article reports the argumentation work of a group of trainee mathematics teachers in an experiment carried out in a virtual class (due to the emergence of COVID-19) during 2020. They worked with a task on fractions in an online…
In France, the first year of study at university is usually abbreviated L1 (for premiere annee de Licence). At Sorbonne Paris Nord University, we have been teaching an 18 hour introductory course in formal proofs to L1 students for 3 years.…
Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved…
This article investigates the sensemaking demonstrated in 6th grade students' written responses to a single question free response final exam for physics asking them to recount everything they learned over the course of the academic year.…
The reflection principle is the statement that if a sentence is provable then it is true. Reflection principles have been studied for first-order theories, but they also play an important role in propositional proof complexity. In this…
Instruction in quantum mechanics is becoming increasingly important as the field is not only a key part of modern physics research, but is also important for emerging technologies. However, many students regard quantum mechanics as a…
Deductive verification is an effective method to ensure that a given system exposes the intended behavior. In spite of its proven usefulness and feasibility in selected projects, deductive verification is still not a mainstream technique.…
Physics education research has probed for the relevance of physics in students' everyday lives. Attitudinal and epistemological surveys have asked students if they think of or use physics in their daily lives. We have previously documented…
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,…