Related papers: The teaching of proof
The chapter supports educators and postgraduate students in understanding the role of simulation in software engineering research based on the authors' experience. This way, it includes a background positioning simulation-based studies in…
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…
The aim of this chapter is to identify and characterise the pedagogical model prescribed for this particular mathematics teaching delivered in post-primary vocational training. More specifically, the contribution investigates two major…
The article focuses on the differences in mathematics performance between girls and boys visible from the first four months of compulsory schooling in the French education system. The influence of gender stereotypes in the evaluation…
General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes "convincing evidence?" I will argue that, given the types of evidence that are currently…
The resources compiled in this document provide an approach to embed and teach Ethics in Mathematics at the undergraduate level. We provide mathematical exercises and homework problems that teach students ethical awareness and transferable…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
A brief account of some recent controversies about the teaching and learning of physics is presented. A shorter version of this outcome was accepted by The Physics Teacher, but publication is still pending.
Geometry is essentially a global language, which is fully understood in different times, countries and cultures. The proof of a geometric theorem (e.g. the Pythagorean Theorem) or a geometric construction (e.g. the construction of an…
In the article the problems of the systems of computer mathematics use as a tool for the students learning and research activities support are investigated. The promising ways of providing access to the mathematical software in the…
The example of the calculus is used to explain how simple, practical math was made enormously complex by imposing on it the Western religiously-colored notion of mathematics as "perfect". We describe a pedagogical experiment to make math…
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…
Mathematical proofs are a cornerstone of control theory, and it is important to get them right. Deduction systems can help with this by mechanically checking the proofs. However, the structure and level of detail at which a proof is…
Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic…
The import of Bell's Theorem is elucidated. The theorem's proof is illustrated both heuristically and in mathematical detail in a pedagogical fashion. In the same fashion, it is shown that the proof is correct mathematically, but it doesn't…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
An argument is presented that mathematics teachers would benefit from an ethics framework that allows them to reflect upon their position regarding the teaching of ethics within mathematics. We present such a framework, adapted from Chiodo…
The multi-layered nature of societal developments poses a challenge in the teaching and learning of history of mathematics. As an attempt to tackle this challenge we experimented with the use of Knowledge-Maps. The focus of our interest…
Experimental activities are an essential part of physics education. In addition to conveying scientific knowledge, they play a significant role in developing scientific literacy, inquiry skills, and critical thinking. In today's world,…
This chapter provides a hands-on tutorial on the important technique known as self-reducibility. Through a series of "Challenge Problems" that are theorems that the reader will---after being given definitions and tools---try to prove, the…