This article presents several mathematics problems on the same theme that can be used in class or for independent study. It is very difficult to show students how mathematics research is done by mathematicians, so the author first introduces a problem that can be tackled solely by arithmetic and then gives an idea of how a mathematician might…

This article recounts the life of mathematician Leonhard Euler and discusses the use of Graph Theory in student learning.

As a follow-up to their article, "Emojis and Their Place in the Mathematics Classroom" (EJ1358586), the authors examine how emojis can be used as bridging representations to support student understanding of proof and algebra in upper primary school. They take a problem from reSolve, Level 3, (AAMT, 2020), look at it from the perspective…

Duncan Symons and Derek Holton discuss the different types of mathematical reasoning and what each of these might look like in the classroom. By suggesting language that can be used to describe the different methods of reasoning, they hope to provide teachers with the tools they need to better recognise and assess student reasoning.

Here, we investigate what loci are produced when a square of side-length one is allowed to rotate around a square of side-length n, where n is a whole number. We find that if i = 1, 2, 3 or 4 (mod 4), the loci obtained for n [congruent to] i (mod 4) all have the same symmetry and we show how the perimeter of each class can be determined. We also…

Describes the Six Circle problem which consists of the numbers 1-6, six circles, and asks whether it is possible to put the numbers in the circles--which are configured in a triangle--so that the sums of the three numbers on either side are the same. (NB)

Discusses and presents examples of alternative styles of transmitting mathematical knowledge at the tertiary level, with a view to promoting debate on the issue. Emphasizes processes rather than skills, and considers problem solving and peer tutoring. (Author/ASK)

Describes the results of part of a study into mathematical problem solving in secondary schools. Concludes that positive results were achieved, in part, as a consequence of the time that was spent in problem-solving lessons which allowed students to practice reading and working with word problems and working on basic material, particularly…

Suggests six characteristics of mathematical play. Analyzes the problem-solving process for the Six Circles and observations of students solving calculator and integration problems in relation to theories of play and cognitive gain. Discusses some difficulties of implementing a 'play' approach in the classroom and proposes further research…

Here we give an example of a problem that could be beneficially investigated by AS/A level students. It is a geometry problem that they can profitably tackle by geometric (especially geometry software) and algebraic means. Such problems naturally lead students to the need for proof--an essential part of mathematics that is often lacking in current…

In a future that is likely to be increasingly dominated by new technology, it is important to consider what mathematics is and how it might be taught. This article discusses these and related issues in the context of both universities and schools.

Discusses a program in New Zealand to assist high school students who have an aptitude for mathematics. Uses the philosophy of extension and enrichment rather than acceleration and has a teaching emphasis of problem solving and the methodology of the research mathematician. (MKR)