Increasing access to mathematical thinking

The authors describe their current project that examines ways to maximise learning opportunities for students in upper primary and lower secondary mathematics classes. There are two aspects to the project: the type of tasks posed, and particularly ways to assist students experiencing difficulty with those tasks; and the steps that teachers can take to overcome structural barriers to mathematical learning by being explicit about classroom processes.

Re-thinking students 'at risk'

There are some students in the secondary schools who are considered to be 'at risk' and more likely to fail in the future simply because they do not accept traditional school-based modes of learning as being relevant. However, recent applied learning initiatives in the Victorian Certificate of Applied Learning (VCAL) have re-engaged many of these young people in schooling by treating them more like young adults and recognising that secondary schools must now cater for a greater diversity of career pathways.

The graphic calculator as a thinking tool : perspectives from the classroom

For over a decade, the graphic calculator has been promoted not only as a computational tool, but also as a thinking tool - for example, as an aid to enhance conceptual understanding, as a problem-solving tool and as a means of enabling students to engage in meaningful investigations. However, research studies focusing on these aspects have shown mixed results and have mostly focused on graphs and functions.

This paper reports on one aspect of a case study in a year 10 mathematics classroom - the role of the graphic calculator as a thinking tool. Data from observations of nine statistics lessons and interviews with the teacher and five students, are analysed from three perspective's: the teacher's intentions with respect to the use of the graphic calculator as a tool to promote conceptual understanding as opposed to procedural competence; the opportunities afforded during the lessons for student investigation; and students' views of how the graphic calculator enhanced conceptual understanding.

The results provide insights into ways in which students perceive the graphic calculator as promoting conceptual understanding, as well as some of the difficulties encountered in practice in a classroom where the teacher clearly intends to use the graphic calculator as a thinking tool.

Towards a framework for exploring children's analytical thinking and creativity in technology

Technology education provides children with opportunities to be creative as they engage in problem solving and make products that address human needs. When thinking creatively, children generate new ideas through remote associations and brainstorming and this type of thinking is enhanced when attention is allowed to wander in a relaxed and uncompetitive environment. Research shows that the two mental states (generative and nongenerative/analytical) cannot exist simultaneously (Howard-Jones 2002). It follows that at some point in the technological process a child’s generative mental state needs to give way to a nongenerative, analytical state so that the child can focus on analysing information. This research project aims to investigate the impact of analytical thinking on creativity in the context of technology education in young children.

Mathematical thinking: a screening profile for 'operations'

This paper comments on and adapts the screening profile developed from 'ACER Mathematics Profile Series (MAPS): Operations' (1977). A sample screening profile worksheet for 'Operations' is provided. This adaptation of the ACER MAPS Operations test may help teachers identify students who are able to use more advanced levels of mathematical thinking. Survey results may help form ability groups, deliver special needs curriculum materials, and guide students tackling the algebra curriculum.

Reflective thinking : turning a critical incident into a topic for research

Clinical nurses encounter critical incidents every day.  While these may be a source of frustration they also have the potential to be turned into research projects so that problems can be examined and others can learn from them.  This paper describes the reflective process used to generate a research project from a critical incident encountered in the clinical area.

Weighing it up : thinking about the implications of school based obesity prevention initiatives

In this paper we explore the tensions that exist between two health promotion discourses prevalent in school based Health Education. We use one example from a widely used curriculum resource and one classroom episode to explore discourses related to obesity prevention, often described as an obesity epidemic by media and health professionals alike. Our argument is that these discourses work to produce the 'unhealthy other' that everyone is then in danger of becoming and in the process produce moral judgements and reinforce stereotypes about overweight and obese people. In so doing they run counter to health education and other discourses that seek to promote self-esteem and body acceptance in students no matter what their shape and size.