Stimulating proportional reasoning through questions of finance and fairness

What could two people stand to gain from sharing a taxi ride? We aimed to explore the extent to which this challenging yet accessible financial context might stimulate students’ mathematical exploration of multiplicative thinking and proportional reasoning. Through teaching experiment methodology, data were collected from 37 Year 5 and 6 students (10–12 years of age) in suburban Melbourne. The findings reveal that the majority of the students had some intuitive understanding of how to solve a financial problem that involved rate, and at least half of them used either multiplicative thinking or proportional reasoning. While the study reported is small and cannot claim to be representative, the findings confirm that well-designed financial problems have the potential to unveil sophisticated mathematical understandings among primary school students. This research demonstrates what young adolescents can do prior to formal exposure to ratio and proportion as part of the curriculum.