Pattern generalising problems offer a very rich context for exploring relationships among quantities, expressing generality and representing the same relationship in different ways. Selecting appropriate tasks for students to work on in class is by no means a straightforward process, but there are ways to handle it. This article aims to explore…

This is the first of two articles which describe how to use "JavaSketchPad" to explore the centres of a triangle. This introductory exercise is suggested in the GSP "Workshop Guide". Students can use "JavaSketchPad Interactive Geometry" (JSP) at home at no cost. They are likely to impress their parents with their enthusiasm for geometry and all…

Engaging students with real-world activities can be effective in supporting the learning of mathematics, "whenever possible, real-world situations will provide a context for both introducing and applying geometric topics" (NCTM 1989). Tool making is a way to bring real-world mathematics into the classroom and using the tool is a way of taking…

In these days of financial turmoil, there is greater interest in depositing one's money in the bank--at least one might hope for greater interest. Banks and various trusts pay compound interest at regular intervals: this means that interest is paid not only on the original sum deposited, but also on previous interest payments. This article…

Learning about the area formulas provides many opportunities for students even at the beginning of junior secondary school to experience mathematical deduction. For example, in easy cases, students can put two triangles together to make a rectangle, and so deduce that the area of a triangle is half the area of a corresponding rectangle. They can…

It is instructive and interesting to find hidden numbers by using different positional numeration systems. Most of the present guessing techniques use the binary system expressed as less-than, greater-than or present-absent type information. This article describes how, by employing four cards having integers 1-64 written in different colours, one…

Studies have shown that students' understanding is typically analytic and not visual. Two possible reasons for this are when the analytic mode, instead of the graphic mode, is most frequently used in instruction or, when students or teachers hold the belief that mathematics consists simply of skillful manipulation of symbols and numbers. The…

A study was undertaken to implement a series of chance games and activities in a Year 7 classroom, and investigate the students' knowledge about probability concepts, as well as their attitudes to chance. Initially, the project involved selecting a set of appropriate learning activities to develop key probability concepts which are integral to the…

This article presents a hands-on experiment that covers many areas of high school mathematics. Included are the notions of patterns, proof, triangular numbers and various aspects of problem solving. The problem involves the arrangements of a school of fish using split peas or buttons to represent the fish. (Contains 4 figures.)

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,…

One of the best known numbers in mathematics is the number denoted by the symbol [pi]. This column describes activities that teachers can utilize to encourage students to explore the use of [pi] in one of the simplest of geometric figures: the circle.

The ability to discover, explore, describe and mathematise relationships between different concepts is at the heart of scientific work of professional mathematicians and scientists. At school level, however, helping students to link, differentiate or investigate the nature of relationships between mathematics concepts remains in the shadow of…

Inquiries into the state of mathematics and science education in Australia express the need to make the curriculum more relevant and meaningful to students' lives. However, such a vision requires that teachers understand how relevance can enter mathematics and science classrooms in meaningful and appropriate ways. This paper uses snippets from…

Understanding the concept of the sampling distribution of a statistic is essential for the understanding of inferential procedures. Unfortunately, this topic proves to be a stumbling block for students in introductory statistics classes. In efforts to aid students in their understanding of this concept, alternatives to a lecture-based mode of…

Tangrams have sometimes been used as an extension activity intended only to keep faster students busy while others finished essential desk-work. Without adequate introduction, many find that tangrams are just an open-ended form of a jigsaw puzzle. Happily teachers have discovered that games provide an effective introduction to a new topic. In the…