Space-filling curves are related to fractals, in that they have self-similar patterns. Such space-filling curves were originally developed as conceptual mathematical "monsters", counter-examples to Weierstrassian and Reimannian treatments of calculus and continuity. These were curves that were everywhere-connected but nowhere-differentiable (or…

Almost every adult in Australia has played Noughts and Crosses at some time in their life--it is that sort of game, a universal classic. Very few Australian adults play Noughts and Crosses, adult against adult, unless they are bored, witless and cannot think of anything better to do. Adults stop playing this game. Many will say it is boring, while…

This article illustrates spatial thinking tasks through cube diagrams and drawings. The author talks about the pentacube diagram that is based on the principle that a vertical cube-edge is shown "vertically". The author describes how to extend isometric drawing to include triangular wedges that are made by slicing single cubes, bi-cubes,…

It is potentially arresting when a mathematical implication is offered in a non-mathematical book. This author contends that students are encouraged to develop mathematical thinking when they read mathematical challenges in books. Aspects of books such as time-lines, historical relationships, maps, journeys, cause-and-affect, deductive inference,…

This article presents situations involving perimeter, area, volume and mass, and the misconceptions often encountered with these measurements. The author suggests possible interventions that teachers can use to correct these misconceptions and help students to better understand these properties.

This article considers steps towards making a numeracy-across-the-curriculum policy. Numeracy means more than the kind of everyday arithmetic a person (a competent independent adult) needs to handle whole number (and simple decimal) calculations; e.g., money, time, and simple measurement. Importantly, aspects of numeracy arise in any everyday task…

Mathematics is like a language, although technically it is not a natural or informal human language, but a formal, that is, artificially constructed language. Importantly, educators use their natural everyday language to teach the formal language of mathematics. At times, however, instructors encounter problems when the technical words they use,…

Describes experiences and presents ideas to cope with students of lower ability and improve their self-esteem. (ASK)

Discuss from several perspectives the need for mathematics teachers to be up-to-date or innovative. (Contains 12 references.) (ASK)

Discusses ways of answering students' questions about when they will use the mathematics they learn in the classroom. Presents examples of the use of mathematical applications in real-life situations. (ASK)

Traditional mathematics curriculum is unsuitable for gifted children. Computing, statistics, operations research, and logic are suggested as suitable new topics. (MP)