Pattern generalisation has become an important feature of mathematics classrooms around the globe. Sometimes these activities focus purely on given numerical terms, but the use of pictorial or figural patterns is now becoming part of the standard repertoire for such generalisation exercises. From a pedagogic point of view, the investigation of…

The authors illustrate three basic types of reasoning used in mathematics by showing how they operate in practical and mathematical situations. The importance and function of the different types of reasoning in each situation is outlined. As a consequence the authors note that while introducing new techniques by example is good from a pedagogical…

The necessity of using inquiry-based learning (IBL) was recently recommended by studies and reports made for the European Commission. Several European projects are devoted to the widespread use of IBL methods. The effects of using IBL are studied worldwide. In the framework of the Seventh Framework Program (FP7) project PRIMAS, a series of…

Artificial satellites are easily observed most nights when the weather is fine. The website called "Heavens Above" at www.heavens-above.com will help locate these satellites flying over one's location. It also includes how bright they will appear. The direction of travel of each satellite in the night sky also indicates the type of satellite. For…

The authors have been conducting research with early career secondary mathematics teachers in metropolitan Sydney, focusing particularly on the professional experiences of student teachers. As part of the research, 12 supervising teachers were visited at their schools. Seven of them were interviewed individually about their role in developing the…

In this article, the authors present an approach to developing open-ended problems through capturing contextualised mathematics in photographs. They draw upon their research with the Problem Posing Research Project, a collaborative venture between an Australian and a Canadian university to broaden pre-service teachers pedagogical practices in the…

Principals are very aware that there is a great deal of competition in attracting qualified teachers of mathematics to their school, since there are just not enough qualified mathematics teachers out there. Recent studies of the qualifications of teachers in Australian schools have confirmed that there is a crisis in the supply of qualified…

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).…

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…

Calculus is a mathematical concept that is fundamental to how we understand the world around us. Whether it is in the world of technology, finance, astronomy, sociology, medicine, calculus in one form or another can be found. This brief article describes the origins of calculus in Greece, further developments by Newton and Leibniz, and the…

An event based on "find the rule" problems has been part of the University of Canberra Maths Day since 1985. In this paper, the authors describe the Swiss event, its context, its aims, its logistics, and gives examples of problems used in past events. The type of problems used, how they are used in an event at the maths day, and how the event…