This note outlines some connections between projective geometry and some designs used in clinical trials in the health sciences. The connections are not immediately obvious but they widen the scope for enrichment work at both the senior high school level and for capstone subjects at the undergraduate level.

This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…

The present paper describes beautiful conservation relations between areas formed by different geometrical shapes and area relations formed by algebraic functions. The conservation properties were investigated by students at an academic college of education using a computerized technological tool and were subsequently accompanied by justified…

The authors present mathematics problems related to the packaging of sporting goods which they used to motivate and engage their students in the USA. This article reports on a series of questions/problems that were explored in groups by the students in a college class designed for sophomores, as part of a program to prepare them to be teachers at…

This article suggests a tool for analysing diagrams in mathematical texts. The starting point for this tool is Halliday's Systemic Functional Grammar (SFG), which considered language as a social practice. Kress and Van Leeuwen (2006) applied Halliday's SFG to images, suggesting a grammar for reading images. Morgan (1996) adopted Halliday's SFG and…

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become "thinkable" the…

Sequences are an important topic--not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns…

We introduce a ruler and compass activity designed around Islamic Geometry and provide a detailed description of the various components of the activity along with ideas for students exhibitions in both digital and print form. In our experience, this activity helps students to "buy into" actively doing mathematics, making it an ideal…

Fragile understanding is where new learning begins. Students' understanding of new concepts is often shaky at first, when they have only had limited experiences with or single viewpoints on an idea. This is not inherently bad. Despite teachers' best efforts, students' tenuous grasp of mathematics concepts often falters with time or when presented…

According to Sinclair, Pimm, and Skelin (2012), the four big ideas of high school geometry are (1) diagrams; (2) variance and invariance; (3) definitions; and (4) proofs as the culmination of the proving process. On the first day of geometry class, Wayne Nirode began a multiday activity in which students were actively involved in working with…

This work covers a three-week program designed to provide undergraduate students with a background in structural chemistry and materials science. Sessions are based on the programming of regular polyhedra and their geometrical relationships by using an object-oriented language (i.e., POV-Ray). Three lectures introduce the basics of programming…

Partial Latin squares constitute an interesting approach to improve the teaching of different subjects in the mathematics classroom. This paper delves into this topic by introducing the use of a Dynamic Geometry System to deal with these combinatorial structures as a source of loci of points in the Euclidean plane. It is assumed to this end that…

Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are kept at a fairly elementary level, some, such as determining the safe domain, involve not so elementary…

Teachers and students had an unusual experience in 2020. Due to the outbreak of the COVID-19 pandemic, regular teaching and learning in schools were suspended in many countries. The prolonged school closure presented unprecedented challenges because all teaching and learning activities had to be converted to a fully online format. This article…

By having students practice constructing diagrams for geometric theorems, teachers can develop students' understanding of mathematical claims, vocabulary, and notation methods. This practice can also strengthen students' ability to interpret mathematical diagrams and recognize their limitations.