Studies of mathematics in workplaces 1996-98 Hoyles, Noss investment bank employees 1997-99 Hoyles, Noss, Pozzi nurses 1997-99 Hoyles, Noss, Pozzi pilots 2001-2 Kent, Noss engineers 2001-2 Hoyles, Wolf, Molyneux-Hodgson, Kent food processing, tourism,, health care...
2 starting points from preceding studies mathematics is quite different from school mathematics and is largely invisible pragmatic mental strategies little push for generality or appreciation of models high levels of error in p+p tests & high level of competence at work tools and artefacts shape activities in ways that only become visible at times of breakdowns to routine
5 Aims characterise the mathematical needs of employees in ICT-rich workplaces develop appropriate mathematical understandings through iterative (co-)design of learning opportunities Techno-mathematical Literacies at Work 2003-7 Funded by the Economic and Social Research Council, UK 2003-7
6 Techno-mathematical Literacies (TmL) TmL are new skills needed to be functional in IT-rich workplaces that are striving for improvements in efficiency and customer communication why literacies? why techno-mathematical?
7 Phase 2. Co-design with employer-partners using a cyclic approach of design, testing, analysis, revision Phase 1. Workplace ethnography: identification & characterisation of TmL Project methodology: two phases Each phase opened windows on how different communities made sense of critical elements of computer inputs & outputs & symbolic artefacts
8 Boundary objects & boundary crossing Boundary objects are artefacts that stand at interface between communities of practice satisfy the informational requirements of each where meanings are sources of debate so boundary crossing may not occur Symbolic artefacts as (potential) boundary objects
9 1: Financial Service Sector highly competitive market increasingly customer focused increasing complexity of products heavily dependent on computer systems invisibility of the model
10 TmL research in financial services 2 large pension/investment companies 1 specialist mortgage provider: current account mortgage (CAM)
11 Boundaries between different communities in finance industry Researchers customers sales IFAs call centre staff Actuaries
12 An example (1) of boundary object: pension statement
13 TmL in financial services understanding key variables (e.g. interest rates, admin fees) modelling these as relationships interpreting graphs (estimates and predictions)
14 Pseudo-mathematical labels Numbers as labels (number 27 bus): Credit card: 1.8% per month Mortgage: 5.9% per annum APR Graphs as qualitative diagrams rather than measured images of relationships
16 TEBOs in pensions modelling pension statement with spreadsheet management charges market value reduction compound interest tool explore present value of money with spreadsheet and interactive tool
18 2. Car Manufacturing observations of 1.practice & training in 2 large car factories 1.green belt SPC training
19 Boundaries between different communities in car factories researchers operators managers team leaders SPC department
symbolic artefact on shopfloor running out of time control vs specificationcontrol vs specification
21 X-bar: mean R-bar: mean range Control limits Cp = 1.96 Cpk = 1.50 Hartleys constants for SD estimation Information in corner
22 process capability indices one-number measures of how well the process is performing: your Cpk = 1.4 calculated from data, not from management employees can be beaten up for low Cpks most difficult part of training
23 Process capability measures Definitions of Cp and Cpk
TML needed understanding & reducing variation including knowing the difference between common and special cause variation, and how to respond noticing trends & patterns in processes graphing & interpreting time series data (control charts) including distinguishing mean versus target specification versus control limits control charts & one measure values Cp & Cpk were pseudo-mathematical
25 Irrelevant half of the C pk equation is greyed- out. Ratios now represented by moving coloured bars. boundary objecttechnologically-enhanced
USA Canada England Spain Germany Italy Turkey... worldwide disemination: out of control!
Findings current theories of workplace learning and training that recapitulate school mathematics are inadequate TmL are new skills in ICT-rich contexts TmL are rarely recognised by managers, or picked up on the job IT systems are based on models involving mathematics that is largely invisible Information often fails to fulfil its intended role as facilitating communication across community boundaries Symbolic informationis is often understood by employees as pseudo-mathematics exploit the complementary expertise of employees, employers and educators TmL requires engagement in authentic activities that embed work process models made more visible and manipulable through interactive software tools
Kent, P. (2009). "In the Workplace: Learning as articulation work, and doing articulation work to understand learning". In: Vavoula, G., Pachler, N., & Kukulska-Hulme, A. M. (Eds.) Researching Mobile Learning: Frameworks, Methods and Research Designs. New York: Peter Lang. 61-76. Bakker, A., Kent, P., Derry, J., Noss, R. & Hoyles, C. (2008). Statistical inference at work: Statistical process control as an example. Statistics Education Research Journal, 7, 2, 130- 145. Hoyles, C., Bakker, A., Kent, P., & Noss, R. (2007). Attributing meanings to representations of data: The case of statistical process control. Mathematical Thinking and Learning, 9, 4, 331-360. Hoyles, C., and Noss, R. (2007). "The meanings of statistical variation in the context of work". in Lesh, R., Hamilton, E. & Kaput, J. J. (Eds.), Foundations for the Future in Mathematics Education (pages 7-35). Mahwah, NJ: Lawrence Erlbaum Associates. Kent, P., Noss, R., Guile, D., Hoyles, C., & Bakker, A (2007). Characterizing the use of mathematical knowledge in boundary-crossing situations at work. Mind, Culture, and Activity 14, 1-2, 64-82. Noss, R., Bakker, A., Hoyles, C., & Kent, P. (2007). Situating graphs as workplace knowledge. Educational Studies in Mathematics, 65, 3, 367 - 384. Bakker, A., Hoyles, C., Kent, P., & Noss, R. (2006). "Improving work processes by making the invisible visible". Journal of Education and Work, 19, 4, 343-361.