# Black Boxes in Workplace Mathematics

- 552 Downloads
- 47 Citations

## Abstract

We ground Cultural-Historical Activity Theory (CHAT) in studies of workplace practices from a mathematical point of view. We draw on multiple case study visits by college students and teacher-researchers to workplaces. By asking questions that ‘open boxes’, we ‘outsiders and boundary-crossers’ sought to expose contradictions between College and work, induce breakdowns and identify salient mathematics. Typically, we find that mathematical processes have been historically crystallised in ‘black boxes’ shaped by workplace cultures: its instruments, rules and divisions of labour tending to disguise or hide mathematics. These black boxes are of two kinds, signalling two key processes by which mathematics is put to work. The first involves automation, when the work of mathematics is crystallised in instruments, tools and routines: this process tends to distribute and hide mathematical work, but also evolves a distinct workplace ‘genre’ of mathematical practice. The second process involves sub-units of the community being protected from mathematics by a division of labour supported by communal rules, norms and expectations. These are often regulated by boundary objects that are the object of activity on one side of the boundary but serve as instruments of activity on the other side. We explain contradictions between workplace and College practices in analyses of the contrasting functions of the activity systems that structure them and that consequently provide for different genres and distributions of mathematics, and finally draw inferences for better alignment of College programmes with the needs of students.

## Keywords

black boxes case studies cultural – historical activity theory maths-in-work situated cognition transfer## Preview

Unable to display preview. Download preview PDF.

## References

- Bakhtin, M., Emerson, C. and Holquist, M.: 1986,
*Speech Genres and Other Late Essays*, (transl V.W. McGee), University of Texas Press, Austin.Google Scholar - Bakhtin, M.M.: 1981,
*The Dialogic Imagination: Four Essays*, University of Texas, Holquist, M. (ed.) Austin.Google Scholar - Bourdieu, P.: 1990,
*The Logic of Practice*, Polity Press, Oxford.Google Scholar - Chaiklin, S. and Lave, J.: 1993,
*Understanding Practice: Perspectives on Activity and Context*, Cambridge University Press, Cambridge, UK.Google Scholar - Cobb, P., Yackel, E. and McClain, K. (eds.): 2000,
*Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design*, Lawrence Erlbaum Associates, Mahwah, N.J.Google Scholar - Cole, M. and Engstrom, Y.: 1993, 'A cultural-historical approach to distributed cognition', in G. Solomon, (ed.),
*Distributed Cognitions: Psychological and Educational Considerations*, Cambridge University Press, Cambridge, pp. 1–46.Google Scholar - Engestrom, R.: 1995, 'Voice as communicative action',
*Mind, Culture and Activity*2(3), 192–214.Google Scholar - Engestrom, Y.: 1987,
*Learning by Expanding: An Activity-Theoretical Approach to Developmental Research*, Orienta-Konsultit, Helsinki.Google Scholar - Engestrom, Y.: 2003, 'Conceptualizing transfer: From standard notions to developmental perspectives', in T. Tuomi-Gröhn and Y. Engeström (eds.),
*Between School and Work: New Perspectives on Transfer and Boundary-Crossing*, Pergamon, Amsterdam/Oxford, pp. 19–38.Google Scholar - Engestrom, Y. and Cole, M.: 1997, 'Situated cognition in search of an agenda', in J.A. Whitson and D. Kirshner (eds.),
*Situated Cognition: Social, Semiotic, and Psychological Perspectives*, Lawrence Erlbaum Associates, Hillsdale, N.J., pp. 301–309.Google Scholar - Gee, J.P.: 1996,
*Social Linguistics and Literacies: Ideology in Discourses*, Taylor & Francis, London.Google Scholar - Gray, E.M. and Tall, D.O.: 1994, 'Duality, ambiguity, and flexibility: a 'proceptual' view of simple arithmetic',
*Journal for Research in Mathematics Education*25(2), 116–140.CrossRefGoogle Scholar - Hall, R.: 1999, 'Following mathematical practices in design-oriented work', in C. Hoyles et al., (eds.),
*Mathematics Education for the Twenty First Century*, Falmer Press, London.Google Scholar - Hoyles, C., Noss, R. and Pozzi, S.: 2001, 'Proportional Reasoning in Nursing Practice.',
*Journal for Research in Mathematics Education*32(1), 4–27.CrossRefGoogle Scholar - Hutchins, E.: 1995,
*Cognition in the Wild*, MIT Press, Cambridge, Mass.Google Scholar - Ilyenkov, E.V.: 1974, Activity and Knowledge, In
*Philosophy and Culture*, Moscow: Politizdat (1991).Google Scholar - Kirshner, D. and Whitson, J.A.: 1997,
*Situated Cognition: Social, Semiotic, and Psychological Perspectives*, Lawrence Erlbaum Associates, Hillsdale, N.J.Google Scholar - Latour, B.: 1987,
*Science in Action: How to Follow Scientists and Engineers Through Society,*Open University Press, Milton Keynes.Google Scholar - Latour, B.: 1993,
*We Have Never Been Modern,*Harvester Wheatsheaf, a divison of Simon & Schuster International Group, Hemel Hempstead, Herts.Google Scholar - Latour, B.: 1999,
*Pandora's Hope: Essays on the Reality of Science Studies,*Harvard University Press, Cambridge, Mass., London.Google Scholar - Latour, B.: 2000, When Things Strike Back – a possible contribution of Science Studies,
*British Journal of Sociology Special Millenium issue*'*Sociology Facing the New Millenium*'.Google Scholar - Lave, J. and Wenger, E.: 1991,
*Situated Learning: Legitimate Peripheral Participation*. Cambridge University Press, Cambridge, England.Google Scholar - Leontev, A.N.: 1978,
*Activity, Consciousness, and Personality (Transl. M.J. Hall),*Prentice-Hall, Englewood Cliffs, N.J.Google Scholar - Leontev, A.N.: 1981, 'Primaeval Collective Hunt', in
*Problems of the Development of Mind.*, Progress Publishers, Moscow, pp. 210–213.Google Scholar - Leverhulme Report: 2001,
*Using College Mathematics in Understanding Workplace practice: Summative Report of the Research Project Funded by the Leverhulme Trust*, Report by J.S. Williams and G.D. Wake, http://www.education.man.ac.uk/lta/publications/leverhulme_summary.htm - Nicol, C.: 2002, 'Where's the Math? Prospective teachers visit the workplace',
*Educational Studies in Mathematics*50, 289–309.CrossRefGoogle Scholar - Noss, R. and Hoyles, C.: 1996, 'The visibility of meanings: Modelling the mathematics of banking',
*International Journal of Computers for Mathematical Learning*1(1), 3–31.CrossRefGoogle Scholar - Noss, R., Hoyles, C. and Pozzi, S. 2002, 'Abstraction in Expertise: A Study of Nurses' Conceptions of Concentration',
*Journal for Research in Mathematics Education*33(3), 204–229Google Scholar - Pozzi, S., Noss, R. and Hoyles, C.: 1998, 'Tools in practice, mathematics in use',
*Educational Studies in Mathematics*36, 105–122.CrossRefGoogle Scholar - Riall, R. and Burghes, D.: 2000, 'Mathematical needs of young employees',
*Teaching Mathematics and its Applications*19(3), 104–113.CrossRefGoogle Scholar - Roth, W.-M.: 2002,
*Competent Workplace Mathematics: How Signs Become Transparent*, Paper presented to the American Educational Research Association, 2002.Google Scholar - Roth, W.-M. and Bowen, G.M.: 2001, 'Professionals read graphs: A semiotic analysis',
*Journal for Research in Mathematics Education*32, 150–194.CrossRefGoogle Scholar - Sfard, A.: 1991, 'On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin',
*Educational Studies in Mathematics*22, 1–36.CrossRefGoogle Scholar - Sfard, A. and Linchevski, L.: 1994, 'The gains and pitfalls of reification: the case of algebra
*Educational Studies in Mathematics*,' 26, 87–124.CrossRefGoogle Scholar - Straessar, R.: 2000, 'Mathematical means and models from vocational contexts – a German perspective', in A. Bessot and J. Ridgway (eds.),
*Education for Mathematics in the Workplace*, Kluwer, Dordrecht, Netherlands.Google Scholar - Vygotskii, L.S.: 1987, 'Thinking and speech', in R.W. Rieber et al. (eds.),
*The Collected Works of L.S. Vygotsky*, Plenum, New York.Google Scholar - Wake, G.D., Williams, J.S.: 2000,
*Can Workplace Practice Inform Design of Mathematics Curricula?*Paper presented to the International Congress of Mathematics Education, Tokyo, Japan,Google Scholar - Wake, G.D., Williams, J.S. and Haighton, J.: 2000, 'Spreadsheet Mathematics in College and in the Workplace: A Mediating Instrument?,'
*Proceedings of the Twenty-Fourth Conference of the International Group for the Psychology of Mathematics Education (PME)*, Hiroshima, Japan, PME.Google Scholar - Wake, G.D. and Williams, J.S.: 2001,
*Using College Mathematics in Understanding Workplace Practice. Summative Report of Research Project Funded by the Leverhulme Trust*, Manchester University, Manchester.Google Scholar - Wake, G.D. and Williams, J.S.: 2003, 'Using Workplace Practice to Inform Curriculum Change', in S.J. Lamon et al., (eds.),
*Mathematical Modelling: A Way of Life (ICTMA 11)*, Horwood, Chichester, pp. 189–200.Google Scholar - Wake, G.D., Haworth, A. and Nicholson, S: 2004, 'Applying mathematics in the post-16 curriculum: Teacher practices, student perspectives and emerging issues', in R. Barwell and O. McNamara,
*Research in Mathematics Education*Vol. 6.Google Scholar - Wertsch, J.V.: 1991,
*Voices of the Mind: A Sociocultural Approach to Mediated Action,*Harvester, London.Google Scholar - Whitson, J.A.: 1997, 'Cognition as a semiotic process: from situated mediation to critical reflective transcendence', in J.A. Whitson and D. Kirshner(eds.),
*Situated cognition: Social, Semiotic, and Psychological Perspectives*, Lawrence Erlbaum Associates, Mahwah, N.J., pp. 97–149.Google Scholar - Williams, J.S., Wake, G.D. and Jervis, A.: 1999, 'General mathematical competence in vocational education', in C. Hoyles, C. Morgan and G. Woodhouse(eds.)
*Mathematics Education for the 21st Century*. Falmer Press, London.Google Scholar - Williams, J.S. and Wake, G.D.: 2000, Daniel: A Student With Learning Difficulties in College but Competence in the Workplace?'
*Proceedings of the Twenty-Fourth Conference of the International Group for the Psychology of Mathematics Education*, Hiroshima, Japan, International Group for the Psychology of Mathematics Education.Google Scholar - Williams, J.S., Wake, G.D. and Boreham, N.C.: 2001, 'College mathematics and workplace practice: An activity theory perspective',
*Research in Mathematics Education*3, 69–84.CrossRefGoogle Scholar - Williams, J.S. and Wake, G.D.: 2002,
*Workplace Practice to College Mathematics: A Chain of Signs Linking Practices*, Paper presented to American educational Research Association, 2002.Google Scholar - Yin, R.K.: 2002, 3rd Edn,
*Case Study Research: Design and Methods,*SAGE Publications, London.Google Scholar