Problematising the mathematics curriculum : some examples from Australia and Japan

Problem solving is often seen as being the core of mathematics. While there are many examples of teaching for and about problem solving, there are relatively few examples of teaching mathematical content through problem solving. This paper uses data from three, apparently quite different, mathematics lessons from Australia and Japan to explore different ways in which mathematics can be taught successfully through problem solving and to analyse some of the characteristics of such lessons. It also attempts to identify some of the supports and constraints for adopting a problem solving approach to the teaching of mathematics that exist in the quite different contexts of Japan and Australia.

Analyzing Australian middle years students' preferred mathematics classroom practices

The Middle Years of schooling have become an issue for mathematics teachers and educators, and calls for the reform of this period of schooling are frequent. However, the suggested reforms appear to be divided in their views of what would be best for these students. This paper provides a brief overview of what some Middle Years students say about their needs. Some 1500 students in the Middle Years of schooling (Years 5 to 9) were surveyed about their preferred mathematics classroom activities: the methods and results of the survey may be extremely relevant to those contemplating Middle Years reform.

Microworlds and mathematics: what shape is that?

The author provides ways to explore and use MicroWorlds to enhance mathematics teaching and learning. The procedures given randomly choose a shape from the specified list, draw the shape and require the user to type the name of the shape.

Using spreadsheets in chemical education to avoid symbolic mathematics.

Traditionally, quantum theory has traditionally relied heavily on the use of  mathematics. However, there is a significant cohort of students who are  weak in mathematics, for example, students who are majoring in   biochemistry, biological sciences, etc. This paper reports on the use of  spreadsheets to generate approximate numerical solutions and visual  (graphical) descriptions as a method of avoiding or minimizing symbolic  manipulations, mathematical derivations and numerical computation. A  specific example from quantum theory is provided. Some aspects of  educational pedagogy of spreadsheet usage are discussed.