Proportional reasoning in the laboratory: an intervention study in vocational education

Based on insights into the nature of vocational mathematical knowledge, we designed a computer tool with which students in laboratory schools at senior secondary vocational school level could develop a better proficiency in the proportional reasoning involved in dilution. We did so because we had identified computations of concentrations of chemical substances after dilution as a problematic area in the vocational education of laboratory technicians. Pre- and post-test results indeed show that 47 students aged 16-23 significantly improved their proportional reasoning in this domain with brief instruction time (50-90 min). Effect sizes were mostly large. The approach of using a visual tool that foregrounds mathematical aspects of laboratory work thus illustrates how vocational mathematical knowledge can be developed effectively and efficiently.