Educational Studies in Mathematics

, Volume 86, Issue 2, pp 211-221

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • Arthur BakkerAffiliated withFreudenthal Institute, Utrecht University Email author 
  • , Djonie GroenveldAffiliated withFreudenthal Institute, Utrecht University
  • , Monica WijersAffiliated withFreudenthal Institute, Utrecht University
  • , Sanne F. AkkermanAffiliated withFreudenthal Institute, Utrecht University
  • , Koeno P. E. GravemeijerAffiliated withEindhoven University of Technology


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.


Computer tool Janus-head nature of vocational mathematics Proportional reasoning Situated abstraction Hybridity Workplace mathematics