along a dimension of required mathematics

1. Technology and automation in workplaces: who needs to know what, and how?Professor Richard NossInstitute of Education, University of London

2. along a dimension of required mathematics

3. Studies of mathematics in workplaces

4. 2 starting points from preceding studies

5. Techno-mathematical Literacies at Work 2003-7 • Aims • characterise the mathematical needs of employees in ICT-rich workplaces • develop appropriate mathematical understandings through iterative (co-)design of learning opportunities 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. 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 case study • 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 sales Actuaries call centre staff Researchers IFAs customers

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

15. technologically-enhanced boundary object

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 case study observations of • practice & training in 2 large car factories • “green belt” SPC training

19. Boundaries between different communities in car factories managers SPC department researchers team leaders operators

20. symbolic artefact on shopfloor control vs specification running out of time

21. Information in corner X-bar: mean R-bar: mean range Control limits Cp = 1.96 Cpk = 1.50 Hartley’s constants for SD estimation

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

24. control charts & one measure values Cp & Cpk were pseudo-mathematical 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

25. technologically-enhanced boundary object ‘Irrelevant’ half of the Cpk equation is greyed-out. Ratios now represented by moving coloured bars.

26. designing to understand

27. Findings

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