# Preparing for workplace numeracy: a modelling perspective

- 569 Downloads
- 7 Citations

## Abstract

The starting point of this article is the question, “how might we inform an epistemology of numeracy from the point of view of better preparing young people for workplace competence?” To inform thinking illustrative data from two projects that researched into mathematics in workplace activity and the teaching and learning of modelling in the classroom is used albeit, by necessity, briefly. Analysis draws attention to the crucial role that understanding the structure of the contextual situation plays in developing a mathematical model of this. It is at this coupling of reality and mathematics that insight into, and understanding of, both mathematics and reality can be developed—or not. This important issue is illustrated with reference to two specific workplace situations that draw on understanding of fraction as gradient and explore how we might use a model of this to scaffold understanding of both reality and mathematics and how each might support the other. With a focus on model formulation during classroom activity attention is then drawn to how students tend to work towards reaching a solution to a particular problem with the consequence that their mathematical representation of the reality does not easily allow for consideration of variation of key factors. In conclusion a research agenda is proposed that seeks to inform an epistemology of numeracy by focussing on numerate activity at the nexus of reality and mathematics by (1) structuring mathematical knowledge using *mathematical* models that might be used to provide insight into a range of models of workplace realities, and (2) requiring student engagement with repeated use of models in ways that emphasise exploration of variability in key factors of the realities that the models represent.

## Keywords

Numeracy Workplace mathematics Modelling## References

- Ainley, J., Pratt, D., & Hansen, A. (2006). Connecting engagement and focus in pedagogic task design.
*British Educational Research Journal,**32*(1), 23–38.CrossRefGoogle Scholar - Bakker, A. (2014). Characterising and developing vocational mathematical knowledge.
*Educational Studies in Mathematics,**86*, 151–156. doi: 10.1007/s10649-014-9560-4.CrossRefGoogle Scholar - Bessot, A., & Ridgeway, J. (2000).
*Education and mathematics for the workplace*. Dordrecht: Kluwer.Google Scholar - Black, L., Williams, J., Hernandez-Martinez, P., Davis, P., Pampaka, M., & Wake, G. (2009). Developing a “leading identity”: The relationship between students’ mathematical identities and their career and higher education aspirations.
*Educational Studies in Mathematics,**73*(1), 55–72.CrossRefGoogle Scholar - Blomhöj, M., & Jensen, T. H. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning.
*Teaching Mathematics and Its Applications,**22*, 123–140. doi: 10.1093/teamat/22.3.123.CrossRefGoogle Scholar - Blum, W., & Leiß, D. (2007). How do students and teachers deal with mathematical modelling problems? The example “Filling up.” In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.),
*How do students and teachers deal with mathematical modelling problems? The example “Filling up”. Mathematical modelling (ICTMA 12): Education, engineering and economics.*Chichester: Horwood.Google Scholar - Blum, W., et al. (1996).
*Anwendungsbezüge im Mathematikunterricht—Trends und Perspektiven*. In G. Kadunz (Ed.), Trends und Perspektiven. Schriftenreihe Didaktik der Mathematik (vol. 23, pp. 15–38). Wien: Hölder-Pichler-Tempsky.Google Scholar - Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process.
*ZDM—The International Journal on Mathematics Education,**38*(2), 86–95.CrossRefGoogle Scholar - Burkhardt, H. (2013). Curriculum design and systemic change. In Y. Lee & G. Lappan (Eds.),
*Mathematics curriculum in school education*(Vol. 1). Berlin: Springer.Google Scholar - D’ Ambrosio, U. (2003). The role of mathematics in building a democratic society. In B. L. Madison & L. A. Steen (Eds.),
*Quantitative literacy: Why numeracy matters for schools and colleges*(pp. 235–238). Princeton: The National Council on Education and the Disciplines.Google Scholar - Damlamian, A., Rodrigues, J. F., & Sträßer, R. (2013).
*Educational interfaces between mathematics and industry: Report on an ICMI-ICIAM-study*(Vol. 16). New York: Springer.Google Scholar - Evans, J. (2000). The transfer of learning from school to work, not straightforward but not impossible either. In A. Bessot & J. Ridgeway (Eds.),
*Education for mathematics in the workplace*(pp. 5–16). Dordrecht: Kluwer.Google Scholar - FitzSimons, G. E. (2014). Commentary on vocational mathematics education: Where mathematics education confronts the realities of people’s work.
*Educational Studies in Mathematics,**86*, 291–305. doi: 10.1007/s10649-014-9556-0.CrossRefGoogle Scholar - Forman, S., & Steen, L. (2002). Making authentic mathematics work for all students. In
*Education for mathematics in the workplace*(pp. 115–126). doi: 10.1007/0-306-47226-0_10. - Foster, C., Wake, G., & Swan, M. (2014). Mathematical knowledge for teaching problem solving: Lessons from lesson study. In S. Oesterle, P. Liljedahl, C. Nicol, & D. Allan (Eds.),
*Proceedings of the joint meeting of PME 38 and PME-NA 36*(pp. 97–104). Vancouver: PME.Google Scholar - Freire, P. (1998).
*Pedagogy of freedom : ethics, democracy, and civic courage*. Lanham: Rowman & Littlefield.Google Scholar - Freudenthal, H. (1973).
*Mathematics as an educational task*. Dordrecht: Reidel.Google Scholar - Gal, I., & Tout, D. (2014).
*Comparison of PIAAC and PISA frameworks for numeracy and mathematical literacy*. OECD Education Working Papers, No. 102. Paris: OECD.Google Scholar - Goos, M., Geiger, V., & Dole, S. (2011). Teachers’ personal conceptions of numeracy. In
*Proceedings of the 35th conference of the international group for the psychology of mathematics education*(vol. 2, pp. 457–464).Google Scholar - Gutstein, E. (2006).
*Reading and writing the world with mathematics: Toward a pedagogy for social justice*. London: Taylor and Francis.Google Scholar - Hahn, C. (2011). Linking academic knowledge and professional experience in using statistics: a design experiment for business school students.
*Educational Studies in Mathematics,**86*(2), 239–251. doi: 10.1007/s10649-011-9363-9.CrossRefGoogle Scholar - Hoyles, C., Noss, R., Kent, P., & Bakker, A. (2010).
*Improving mathematics at work: The need for techno-mathematical literacies*. London: Routledge.Google Scholar - Jablonka, E. (2003).
*Mathematical literacy*. In A. J. Bishop et al. (Eds.), Second international handbook of mathematics education (pp. 75–102). Dordrecht: Kluwer Academic Publishers.Google Scholar - Kaiser-Meßmer, G. (1986).
*Anwendungen im Mathematikunterricht*. vol. 1—Theoretische Konzeptionen. Bad Salzdetfurth: Franzbecker.Google Scholar - Maaß, K. (2006). What are modelling competencies?
*ZDM—The International Journal on Mathematics Education,**38*, 113–142. doi: 10.1007/BF02655885.CrossRefGoogle Scholar - Madison, B. L., & Steen, L. A. (2003).
*Quantitative literacy: Why numeracy matters for schools and colleges.*In B. L. Madison, & L. A. Steen (Eds.). Princeton: The National Council on Education and the Disciplines.Google Scholar - Moschkovich, J. N. (2002). An introduction to examining everyday and academic mathematical Practices.
*Journal for Research in Mathematics Education. Monograph,**11*, 1–11. doi: 10.2307/749961.CrossRefGoogle Scholar - OECD. (2013).
*PISA 2012 assessment and analytical framework*-*mathematics, reading, science, problem solving and financial literacy*. doi: 10.1787/9789264190511-en. - Pollack, H. (1979). The interaction between mathematics and other school subjects. In UNESCO (Ed.),
*New trends in mathematics teaching IV*(pp. 232–248). Paris: UNSECO.Google Scholar - Pozzi, S., Noss, R., & Hoyles, C. (1998). Tools in practice, mathematics in use.
*Educational Studies in Mathematics,**36*(2), 105–122.CrossRefGoogle Scholar - Roth, W. M. (2012). Rules of bending, bending the rules: The geometry of electrical conduit bending in college and workplace.
*Educational Studies in Mathematics,**86*(2), 177–192. doi: 10.1007/s10649-011-9376-4.CrossRefGoogle Scholar - Skemp, R. R. (1978). Relational understanding and instrumental understanding.
*The Arithmetic Teacher,**26*, 9–15.Google Scholar - Skovsmose, O. (1994). Towards a critical mathematics education.
*Educational Studies in Mathematics,**27*, 35–57. doi: 10.1007/BF01284527.CrossRefGoogle Scholar - Stacey, K., & Turner, R. (2015).
*Assessing mathematical literacy*(pp. 217–306). New York: Springer.Google Scholar - Steen, L. A. (Ed.). (2001).
*Mathematics and democracy: The case for quantitative literacy.*Princeton: Woodrow Wilson Foundation. doi: 10.1111/j.1949-8594.1939.tb04037.x/abstract. - Strässer, R. (2007). Everyday instruments: On the use of mathematics. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.),
*Modelling and applications in mathematics education. The 14th ICMI study*(pp. 171–178). New York: Springer.CrossRefGoogle Scholar - Treffers, A. (1987).
*Three dimensions*. Dordrecht: D. Reidel.CrossRefGoogle Scholar - Triantafillou, C., & Potari, D. (2010). Mathematical practices in a technological workplace: The role of tools.
*Educational Studies in Mathematics,**74*, 275–294. doi: 10.1007/s10649-010-9237-6.CrossRefGoogle Scholar - Wake, G. (2007). Considering workplace practice from a mathematical modelling perspective. In Blum W., P. L. Galbraith, H. W. Henn, & N. M. (Eds.),
*Modelling and applications in mathematics education. The 14th ICMI study*(pp. 395–402). New York: Springer.Google Scholar - Wake, G. (2014). Making sense of and with mathematics: the interface between academic mathematics and mathematics in practice.
*Educational Studies in Mathematics,**86*(2), 271–290. doi: 10.1007/s10649-014-9540-8.CrossRefGoogle Scholar - Wake, G., Foster, C., & Swan, M. (2013). A theoretical lens on lesson study: Professional learning across boundaries. In A. M. Lindmeier & A. Heinze (Eds.),
*Proceedings of the 37th conference of the international group for the psychology of mathematics education*(pp. 369–376). Kiel: PME.Google Scholar - Wake, G., Foster, C., & Swan, M. (2014). Teacher knowledge for modelling and problem solving. In S. Poe (Ed.),
*Proceedings of the 8th British congress of mathematics education 2014*(pp. 335–342). British Society for Research into Learning Mathematics.Google Scholar - Wake, G., & Williams, J. (2000). Developing a new mathematics curriculum for post-compulsory education. In A. Bessot & J. Ridgeway (Eds.),
*Education for mathematics in the workplace*(pp. 167–180). Dordrecht: Kluwer Academic Publishers.Google Scholar - Wake, G., & Williams, J. (2001).
*Using college mathematics in understanding workplace practice summative report of research project funded by the Leverhulme Trust*. Manchester: The University of Manchester.Google Scholar - Wake, G. D., & Williams, J. S. (2003). Using workplace practice to inform curriculum change. In
*Mathematical modelling: a way of life (ICTMA 11)*(pp. 189–200). Chichester: Horwood.Google Scholar - Williams, J., & Wake, G. (2007). Black boxes in workplace mathematics.
*Educational Studies in Mathematics,**64*(3), 317–343.CrossRefGoogle Scholar