This article describes a lesson study on the area of a parallelogram for year 7 students. In Singapore, students in secondary schools are streamed into ability bands. Normal (Academic) is the label for the middle band. The teachers were convinced that Lesson Study provided a valuable platform for professional development. The authors followed the…

This article describes a unit of work that was designed for a Year 9 class of mixed ability and which involved the definition and measurement of angles, as well as the practical application of angle properties--such as complimentary angles and the relationships in a transversal. The unit considered the numeracy skills required to interpret a…

Circle Geometry, a senior mathematics topic, is often regarded as time-consuming and associated relational concepts difficult for students to grasp. Units of work that introduce students to circle geometry theorems are frequently described as a string of tedious constructions. This article explores teacher-designed dynamic geometry software…

There is much to be learned and pondered by reading "Proofs and Refutations" by Imre Lakatos (Lakatos, 1976). It highlights the importance of mathematical definitions, and how definitions evolve to capture the essence of the object they are defining. It also provides an exhilarating encounter with the ups and downs of the mathematical reasoning…

The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the formula b2 +…

In this article, the authors show how students can form familiar geometric figures on the calculator keypad and generate numbers that are all divisible by a common number. Students are intrigued by the results and want to know "why it works". The activities can be presented and students given an extended amount of time to think about them. As…

Spatial reasoning is a skill that needs to be developed in students as it is important in geometry for determining total surface areas and volumes of 3-dimensional shapes (Liedtke, 1995). Simply teaching children the formulae, in this case for finding total surface areas, can limit them in understanding mathematics conceptually (Bonotto, 2003).…

Padula, J. (2005) described how mathematics teachers can channel the passion of students interested in electronic music by teaching the mathematics that has been used to create it. She hypothesised that the study and enjoyment of music may help the study of mathematics since both mathematics and music are symbol systems and pattern (and its…

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…

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…

The number [pie] [approximately] 3.14159 is defined to be the ratio C/d of the circumference C to the diameter d of any given circle. In this article, the author looks at some surprising and unexpected places where [pie] occurs, and then thinks about some ways of remembering all those digits in the expansion of [pie].

Parabolic shapes are easy to find. Many homes outside the cable area have parabolic antennas to receive television transmissions from a satellite far out in space. Parabolic extrusions are used as reflectors behind fluorescent tubes and solar heated water pipes. Parabolic reflectors are used to build solar ovens, searchlights and radio telescopes.…

When the author first used "VisiCalc," the author thought it a very useful tool when he had the formulas. But how could he design a spreadsheet if there was no known formula for the quantities he was trying to predict? A few months later, the author relates he learned to use multiple linear regression software and suddenly it all clicked into…

A cube is a solid in three dimensions, with three mutually perpendicular right angles evident at the vertices. In this article, the author describes how to create a four-dimensional cube. Before searching this extra dimension, she first reviews what people know about zero, one, two, and three dimensions, and certain shapes in each of these. She…