G. Hilton1, A. Hilton2, S. Dole1, M. Goos1

1University of Queensland (AUSTRALIA)
2Aahrus University (DENMARK) / The University of Queensland (AUSTRALIA)
Proportional reasoning entails multiplicative relationships in situations of comparison. Successful proportional reasoners can recognise a proportional situation as distinct from a non-proportional one; they have a sense of co-variation and they have a range of strategies for solving proportional problems.
As educators we realise that teaching proportional reasoning cannot solely rely on asking students to complete symbolic and mechanical methods, such as the cross-product algorithm. To develop proportional reasoning, students must have regular opportunities to experience the underlying concepts. These concepts include foundational aspects of proportional reasoning, such as fractional thinking, multiplicative thinking (as opposed to additive), relative thinking (as opposed to absolute), as well as concepts of rate and scale.
As part of a large multi-state project in Australia to enhance middle years students' numeracy through a focus on proportional reasoning, 120 teachers participated in a series of professional learning workshops. These teachers generally reported feeling confident teaching the algorithmic aspects of proportional reasoning but a number of them specifically asked for assistance with the conceptual development of their students' proportional reasoning.
In response, the researchers developed a series of activities with the teachers, where digital cameras were used in the school environs to capture images that represented examples of proportional reasoning concepts. In small groups, the teachers moved around the school taking their photos and then reported back to the workshop, showing their images through a data projector while they explained the concepts they felt their images captured..
This presentation articulates the ways that the digital cameras were used by the teachers to capture and report on the proportional reasoning concepts, and their thoughts and aspirations as to how they would use the cameras to develop the proportional reasoning of their students.