In addition to looking for applications that can be profitably examined algebraically, numerically and geometrically it is also helpful to use ideas that typical students might find interesting. Most secondary students are eager to obtain their driving license and part of becoming a good driver is understanding how long it takes to stop your…

In his recent article in this journal, John Gough (2004) concludes that the practical results of the considerable academic research undertaken at the University of Melbourne into the uses and impacts of graphics calculators and CAS (computer algebra systems) should be made more widely available in journals for teachers. This short article is…

Between the 17th and 19th centuries, the Japanese government closed its borders to the outside world in an attempt to become more powerful. Foreign books were banned, people could not travel, and foreigners were not allowed to enter the country. One result of this isolation was the flourishing of sangaku--wooden tablets inscribed with intricately…

This article presents two classroom episodes in which students were exposed to the value of asking questions and to the different roles played by proof in mathematics. The conversation in the two episodes is outlined in the article. The setting was a classroom of fifteen good high-school students, who were studying calculus. These episodes…

All students need some level of mathematics understanding for tertiary academic study (academic numeracy) and yet many preparatory and foundation programs for international students either include mathematics courses based on a school curriculum, or no mathematics at all. For the past fifteen years the University of Southern Queensland (USQ) has…

This article reports on the findings of a research project examining participant students' points of view on accelerated programs in mathematics from four state secondary schools in New Zealand. The four participant schools in this research offered a variety of different acceleration designs and philosophies and were different in size location,…

Perhaps next time teachers head towards the fundamental theorem of calculus in their classroom, they may wish to consider Fermat's technique of finding expressions for areas under curves, beautifully outlined in Boyer's History of Mathematics. Pierre de Fermat (1601-1665) developed some important results in the journey toward the discovery of the…

As time has progressed, the role of applied mathematics has become increasingly important. Indeed there are now more students enrolled in applied mathematics courses in senior high schools and colleges than in pure mathematics. Such courses become more relevant both to the student and to future employers, if the same constants and equations that…

It is always interesting to challenge more capable students with things that they have tended to take for granted. One area in particular that students often tend to overlook in their senior years concerns the important understandings associated with domains and ranges of functions. In this article, the author shares a few favourite questions that…

The trouble with mathematics is that it looks a little more logical and consistent than it is. Mathematics has a universally recognised exactitude. It also has an inexactitude that tends to remain concealed. This author contends that the trouble with mathematics is that it is neither structured, nor unstructured. It is nearly structured, but not…

Teachers are often faced with the difficulty of deciding exactly what problems the students are experiencing, and the extent to which students might understand "some of it". The one-on-one approach to helping students is most common, but very time consuming, and is an approach that may only serve to fix an immediate difficulty, perhaps by…

The Victorian Curriculum and Assessment Authority (VCAA) Computer Algebra System (CAS)Pilot study (2001-2005) is monitoring the use of CAS in senior secondary mathematics. This article explores the author's experiences in the CAS classroom and delineates changes in teaching style, as a result of the introduction of CAS into the senior mathematics…

The purpose of this article is to explore some research into teaching and learning algebra, and to consider related classroom issues. This leads to the development of diagnostic instruments that may be used by senior secondary teachers as students leave the middle years and embark on rigorous mathematical study. It also outlines an effective…

Despite the assurances of store employees, whenever a deal is on offer it always pays to apply a little logic (and mathematics) to see just how to use it most effectively. In this article, the author displays how to employ this technique by using the example of a shoe store that advertised "second pair half price" (with the fine print stating that…

There is an old joke that says that given the choice between eternal happiness and a ham sandwich, one should choose the ham sandwich. The proof is quite simple: (1) nothing is better than eternal happiness; (2) a ham sandwich is better than nothing; and therefore, it straightforwardly follows from (1) and (2) that (3) a ham sandwich is better…