Most students can follow this simple procedure for division of fractions: "Ours is not to reason why, just invert and multiply." But how many really understand what division of fractions means--especially fraction division with respect to the meaning of the remainder. The purpose of this article is to provide an instructional method as a…

This article proposes a practical method of teaching the addition of unit fractions using a series of mirror equation experiments.

Suppose that there is an inexhaustible supply of $3 and $5 vouchers from the local supermarket. They may only be exchanged for items that cost an exact number of dollars made up from any combination of the vouchers. What is the highest amount not able to be obtained? This is an interesting problem in mathematical thinking and logic requiring only…

Selecting the "better" solution to a problem between the first one that comes to mind and the alternative that may follow is not a "fait-accompli". After all, is it better if it is more economical? Or is it better if it is more elegant? Moreover, taking shortcuts does not always lead to a shorter solution. Consider the simple…

This article presents some paper-folding activities for students to explore a different way to prove some of the angle properties in a circle.

This article gives an example for using Dynamic Geometry Software to encourage making conjectures, reasoning, and experiencing mathematics as a process.

Around 430 BCE it is reported that a typhoid epidemic carried off about a quarter of the population of Athens in ancient Greece. When the gods were asked what could be done to halt this raging epidemic, they apparently replied that the altar in the Temple of Apollo in Delios would have to be doubled in size. After several attempts to double the…

This article describes open-ended activities using digital technologies in secondary school mathematics classrooms that encourage novel investigation of science, technology, engineering and mathematics (STEM) concepts.

Students learn mathematics by solving problems. Mathematics textbooks are full of problems, and mathematics teachers use these problems to test students' understanding of mathematical concepts. This paper discusses how problem-solving skills can be fostered with a geometric tiling problem.

Context based learning (CBL) is a powerful tool that utilises areas of student interest framed in meaningful contexts to foster development of new skills and understanding. For middle school students, engineering activities that relate to real-world problems provide suitable CBL contexts for acquiring conceptual scientific and mathematical…

This article presents "The Two Children Problem," published by Martin Gardner, who wrote a famous and widely-read math puzzle column in the magazine "Scientific American," and a problem presented by puzzler Gary Foshee. This paper explains the paradox of Problems 2 and 3 and many other variations of the theme. Then the authors…

A mathematical mnemonic is a visual cue or verbal strategy that is used to aid initial memorisation and recall of a mathematical concept or procedure. Used wisely, mathematical mnemonics can benefit students' performance and understanding. Explorations into how mathematical mnemonics work can also offer students opportunities to engage in proof…

Southern Cross University (SCU) educators and local teachers have developed a five-lesson instructional sequence built around fluke identification as a way of resolving the question: How fast do humpback whales travel up the east coast of Australia?

It is hard to imagine that, eight hundred years on, the study of Fibonacci could affect the lives of teenagers in Australia. Or is it? A mathematics class of more able Year 9 students in a regional city of Western Australia feels that it has happened to them. Thirty-two students submitted a Fibonacci task as a mathematics assessment, with many of…

This article describes the implementation of a collaborative--competative pedagogy in a Year 10 class and the productive motivational outcomes that followed.