Proportional reasoning in the laboratory: an intervention study in vocational education
 Arthur Bakker,
 Djonie Groenveld,
 Monica Wijers,
 Sanne F. Akkerman,
 Koeno P. E. Gravemeijer
 … show all 5 hide
Abstract
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 posttest 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.
 Ainley, J, Pratt, D, Hansen, A (2006) Connecting engagement and focus in pedagogic task design. British Educational Research Journal 32: pp. 2136 CrossRef
 Akkerman, S. F., & Bakker, A. (2011). Crossing boundaries between school and work during apprenticeships. Vocations and Learning. doi:10.1007/s1218601190736.
 Bakker, A, Derry, J (2011) Lessons from inferentialism for statistics education. Mathematical Thinking and Learning 13: pp. 526 CrossRef
 Bakker, A, Hoyles, C, Kent, P, Noss, R (2006) Improving work processes by making the invisible visible. Journal of Education and Work 19: pp. 343361 CrossRef
 Bakker, A, Kent, P, Noss, R, Hoyles, C (2009) Alternative representations of statistical measures in computer tools to promote communication between employees in automotive manufacturing. Technology Innovations in Statistics Education 3: pp. 131
 BenChaim, D, Fey, JT, Fitzgerald, WM, Benedetto, C, Miller, J (1998) Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics 36: pp. 247273 CrossRef
 Coben, D (2003) Adult numeracy: Review of research and related literature. National Research and Development Centre for adult literacy and numeracy, London: NRDC
 Cohen, J (1992) A power primer. Psychological Bulletin 112: pp. 155159 CrossRef
 Landelijke kwalificaties MBO voor Analist [National qualifications MBO for lab technician]. COLO, Zoetermeer, The Netherlands
 Dierdorp, A, Bakker, A, Eijkelhof, HMC, Maanen, JA (2011) Authentic practices as contexts for learning to draw inferences beyond correlated data. Mathematical Thinking and Learning 13: pp. 132151 CrossRef
 Field, A (2005) Discovering statistics using SPSS. Sage, London
 Frick, RW (1998) Interpreting statistical testing: Process and propensity, not population and random sampling. Behavior Research Methods, Instruments, and Computers 30: pp. 527535 CrossRef
 Hoyles, C, Noss, R, Kent, P, Bakker, A (2010) Improving mathematics at work: The need for technomathematical literacies. Routledge, London
 Hutchins, E (1995) Cognition in the wild. MIT Press, Cambridge
 Mercer, N, Littleton, K (2007) Dialogue and the development of children’s thinking: A sociocultural approach. Routledge, London
 Nab, J, Pilot, A, Brinkkemper, S, Berge, H (2007) Authentic competencebased learning in university education in entrepreneurship. Utrecht University, Utrecht
 Noss, R, Hoyles, C (1996) Windows on mathematical meanings: Learning cultures and computers. Kluwer Academic Press, Dordrecht CrossRef
 Straesser, R Mathematical means and models from vocational contexts. A German perspective. In: Bessot, A, Ridgway, J eds. (2000) Education for mathematics in the workplace. Kluwer, Dordrecht, pp. 6580
 Tourniaire, F, Pulos, S (1985) Proportional reasoning: A review of the literature. Educational Studies in Mathematics 16: pp. 181204 CrossRef
 Van den Berg, N., & De Bruijn, E. (2009). Het glas vult zich. Kennis over de vormgeving en effecten van competentiegericht beroepsonderwijs; verslag van een review. [The glass is filling up. Knowledge about the design and effects of competencebased vocational education; A review study]. Amsterdam/’sHertogenbosch: ECBO.
 Merriënboer, JJG, Kirschner, PA (2007) Ten steps to complex learning: A systematic approach to fourcomponent instructional design. Erlbaum, New York
 Walter, JG, Hart, J (2009) Understanding the complexities of student motivations in mathematics learning. Journal of Mathematical Behavior 28: pp. 162170 CrossRef
 Wilkinson, L (1999) Statistical methods in psychology journals: Guidelines and explanations. American Psychologist 54: pp. 594604 CrossRef
 Williams, JS, Wake, GD (2007) Black boxes in workplace mathematics. Educational Studies in Mathematics 64: pp. 317343 CrossRef
 Title
 Proportional reasoning in the laboratory: an intervention study in vocational education
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Educational Studies in Mathematics
Volume 86, Issue 2 , pp 211221
 Cover Date
 20140601
 DOI
 10.1007/s106490129393y
 Print ISSN
 00131954
 Online ISSN
 15730816
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Computer tool
 Janushead nature of vocational mathematics
 Proportional reasoning
 Situated abstraction
 Hybridity
 Workplace mathematics
 Authors

 Arthur Bakker ^{(1)}
 Djonie Groenveld ^{(1)}
 Monica Wijers ^{(1)}
 Sanne F. Akkerman ^{(1)}
 Koeno P. E. Gravemeijer ^{(2)}
 Author Affiliations

 1. Freudenthal Institute, Utrecht University, Utrecht, Netherlands
 2. Eindhoven University of Technology, Eindhoven, Netherlands