Related papers: Teaching Proof to Future Mathematics Teachers in M…
We discuss two proof evaluation activities meant to promote the acquisition of learning behaviors of professional mathematics within an introductory undergraduate proof-writing course. These learning behaviors include the ability to read…
The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects.…
We discuss the idea that computers might soon help mathematicians to prove theorems in areas where they have not previously been useful. Furthermore we argue that these same computer tools will also help us in the communication and teaching…
Recent investigations have been carried out on critical analyses of beginning physics teachers confronted with questionable explanations. These studies raise the question of the choices made by teachers for their teaching once they have…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
This study aims to observe if the theorem prover Lean positively influences students' understanding of mathematical proving. To this end, we perform a pilot study concerning freshmen students at the University of Zurich (UZH). While doing…
The learning of mathematics starts early but remains far from any theoretical considerations: pupils' mathematical knowledge is first rooted in pragmatic evidence or conforms to procedures taught. However, learners develop a knowledge which…
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…
We discuss a practical method for assessing mathematical proof online. We examine the use of faded worked examples and reading comprehension questions to understand proof. By breaking down a given proof, we formulate a checklist that can be…
This book provides a comprehensive and accessible introduction to the emerging field of AI for mathematics. It covers the core principles and diverse applications of using artificial intelligence to advance mathematical research. Through…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
We present the Sequent Calculus Trainer, a tool that supports students in learning how to correctly construct proofs in the sequent calculus for first-order logic with equality. It is a proof assistant fostering the understanding of all the…
Asking questions is one of the most crucial pedagogical techniques used by teachers in class. It not only offers open-ended discussions between teachers and students to exchange ideas but also provokes deeper student thought and critical…
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…
Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often…
Mathematics is a mountain, but students need more than descriptions of the view: they need a trail they can actually walk. This paper presents the Math Teaching Atlas, a framework for mathematical exposition built around route units (single…
The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
"Math is not a spectator sport." "Lecturing is educational malpractice." Slogans like these rally some mathematicians to teach classes that feature "active learning", where lecturing is eschewed for student participation. Yet as much as I…
The flipped classroom technique has recently been a focus of attention for many math instructors and pedagogical researchers. Although research on the subject has greatly increased in recent years, it is still debated whether the flipped…