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Learning opportunities for Techno-mathematical Literacies in workplaces Phillip Kent, Arthur Bakker, Celia Hoyles, Richard Noss and Chand Bhinder London.

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Presentation on theme: "Learning opportunities for Techno-mathematical Literacies in workplaces Phillip Kent, Arthur Bakker, Celia Hoyles, Richard Noss and Chand Bhinder London."— Presentation transcript:

1 Learning opportunities for Techno-mathematical Literacies in workplaces Phillip Kent, Arthur Bakker, Celia Hoyles, Richard Noss and Chand Bhinder London Knowledge Lab - Institute of Education, University of London, UK Funded by

2 Outline Who we are Techno-mathematical Literacies (TmL) Boundary objects and boundary crossing Learning opportunities in Lifetime Pensions Ltd – Customer enquiry team Conclusions, Future developments

3 3 3.5 year research project (October 2003 – March 2007) Investigate the needs of employees in three industrial/ commercial sectors to have functional mathematical knowledge that is grounded in their workplace situations and in the technological artefacts that surround them Focus at the “intermediate skills” level (NVQ 2–3) – e.g. Sales agents or Customer enquiry agents in service industry, team leaders / first-level managers in manufacturing Explore implications of TmL for training practice by developing and testing flexible learning resources (“learning opportunities”) Techno-mathematical Literacies in the Workplace Project

4 4 Four sectors Packaging (relatively low-tech manufacturing) Automotive manufacturing (high-tech manufacturing) Pharmaceuticals manufacturing (very high-tech, and computerised) Financial services (highly computerised)

5 5 Techno-mathematical Literacies Needed to different degrees by workers at all levels more than a set of disconnected skills anchored in contexts of work understanding models – relationships, constraints, representations modifying models communicate mathematically-expressed decisions vertically, horizontally and outwards

6 6 Techno-mathematical Literacies “Post-Fordist” work organisation recognises the need for workers to be involved and informed about processes “Literacies”  the same sense that conventional literacy is understood as both a technology (of reading and writing) and the use of this technology to produce cultural forms (literature ). “Techno-mathematics”  broadly-defined and technologically-shaped mathematics – this can bring new “analytic power” to the workplace through “new media(-tion)” for the mathematical knowledge domain But mathematics has always been problematic: Formal and inaccessible TmL is a way of conceptualising mathematics for modern IT-based workplace practices

7 7 Project methodology: 2 phases Workplace ethnography: identification of TmL (3 or 4 companies per sector) “Learning opportunities” for TmL developed through design experiments

8 8 Developing learning opportunities Design experiments: Cycles of co-design, test, evaluate - in collaboration with the companies Learning/training as “boundary crossing” between researchers and workplace employees/managers/trainers Weave mathematical ideas into real situations using technology to support “constructionist” learning Mathematical artefacts become “boundary objects” for negotiation of meanings

9 9 Boundaries between different communities Maths Education Researchers Service team Managers Team manager Trainers

10 10 Boundary objects A boundary object serves to coordinate different perspectives of several communities of practice. Boundary objects are: flexible enough that different communities can use them effectively robust enough to maintain a common identity among those communities. Examples: medical claim forms [Wenger], pension statements sent to customers, mortgage illustrations

11 11 Boundary crossing Boundary crossing happens if boundary objects are used in ways that facilitate communication between and within communities Then, tacit knowledge and assumptions can be made more explicit and individuals from different communities can learn something new – both in the course of workplace practice, and in formal training A different way of framing the concept of “transfer” (cf. Tuomi-Gröhn & Engeström, 2003) More “symmetrical” and “democratic” – we are not trainers

12 12 TmL in financial services We are working with companies in areas of mortgages and life insurance/pensions We focus on two broad, common categories of TmL: appreciating models of financial products and their inter- related outputs reading graphs and being able to communicate the meanings of graphs in context


14 Case study: Lifetime Pensions Ltd Annual Pension Statement - An intended boundary object

15 Case study: Lifetime Pensions Ltd Actuary’s explanation of transfer value

16 Knowledge issues Answering customer enquiries presupposes that members of ET understand to some extent the mathematically-expressed artefacts which pass between ET and actuary/assistant, and between ET and customer ET knowledge is too fragmented: lack of organising models Intended boundary object does not function. Additional objects have to be brought in to support and allow only limited boundary crossing

17 Conclusions of ethnography at Lifetime Pensions Mathematical knowledge in boundary crossing situations Failure of the intended boundary object due to “skills gap” around TmL Workplace versus School mathematics At school, mathematics is sophisticated but simple in use, at work mathematics is simple but sophisticated in use. Employees have to “web” mathematical and contextual knowledge, producing meaning in activity. Legacy of mathematics avoidance – and a way forward Mathematics is “difficult” for employees and employers Missing language of description for the forms of mathematics required – we propose TmL Learning interventions based on boundary-crossing activity with mathematical artefacts drawn from the practice

18 Design guidelines for learning opportunities Boundary crossing: choose suitable artefacts that can mediate between employees – managers/trainers – researchers; understanding what is ‘behind the screen’ Modelling and structural reasoning: focus on mathematical relationships for bringing coherence to fragmented knowledge – eg. compound interest Software tools for reasoning: algebra ‘outsourced’ to the spreadsheet (constructionist approach) Surprise as motivation

19 Examples of learning opportunities for Lifetime Pensions New York shopping trip: “Warm up” and surprise Reconstructing a pension statement [so far 4 trials in 3 different companies]

20 New York Shopping Trip Camera priced $250 15% discount, 8% sales tax Customer objects: add the sales tax first so that the discount will be bigger Explain why the customer is right or wrong Warm-up: introduce the approach (discussion around mathematical artefacts, exploration of models of financial products) Surprise: theirs, and ours!

21 Annual Pension Statement Lower rate (5%) Mid rate (7%)Higher rate (9%) At age 60 your fund would be £31,000£41,900£55,600 This could buy a pension annuity of £838 pa£1,970 pa£3,780 pa OR A tax-free lump sum of £7,760£10,500£14,100 and a pension annuity of £629 pa£1,480 pa£2,840 pa Statement date: 24 April 2005 Date of birth: 19 April 1961 Pension age: 60 Your fund value at the statement date is: £14,223 No additional premiums to be paid Projected benefits at pension age:

22 Annual Pension Statement Use Excel to reconstruct pension statements Progressively open up the system “Black Box”: Add in complexity to the spreadsheet (no monthly premium  monthly premium  effects of inflation…) Focus on expressing mathematics correctly in the spreadsheet formulae (not in mathematical symbols) Then detailed calculations can be “outsourced” to the software

23 23 Current fund value: £ 14223.00 Year Interest Rate 5.00%7.00%9.00% Value Interest Earned Value Interest Earned Value Interest Earned 014,223.00711.1514,223.00995.6114,223.001,280.07 114,934.15746.7115,218.611,065.3015,503.071,395.28 215,680.86784.0416,283.911,139.8716,898.351,520.85 316,464.90823.2517,423.791,219.6718,419.201,657.73 417,288.15864.4118,643.451,305.0420,076.931,806.92 518,152.55907.6319,948.491,396.3921,883.851,969.55 619,060.18953.0121,344.891,494.1423,853.392,146.81 720,013.191,000.6622,839.031,598.7326,000.202,340.02 821,013.851,050.6924,437.761,710.6428,340.222,550.62 922,064.541,103.2326,148.411,830.3930,890.842,780.18 1023,167.771,158.3927,978.791,958.5233,671.013,030.39 1124,326.161,216.3129,937.312,095.6136,701.403,303.13 1225,542.461,277.1232,032.922,242.3040,004.533,600.41 1326,819.591,340.9834,275.232,399.2743,604.943,924.44 1428,160.571,408.0336,674.492,567.2147,529.384,277.64 1529,568.601,478.4339,241.712,746.9251,807.034,662.63 1631,047.0341,988.62 56,469.66 Annuity838.271973.473,783.47

24 24 Outcomes of three design cycles for learning opportunities Evidence of “transfer” of Excel knowledge: mainly for management statistics. Limited evidence of changed practice - but there is little scope for employees to change. “When on the phone talking to a customer about pension statements I had this Excel spreadsheet in my mind.” (mental model?) Learning opportunities have worked as intended

25 25 Outcomes of three design cycles for learning opportunities Generally increased confidence Boundary-crossing approach is appreciated: employees don’t like computer-based training; appreciate discussion with “trainers” that listen “With pension projections, to me they were just – someone gave you the figures over there and how they arrived at them was just magic! Now I can see what it is, it makes sense. It’s not just magic.”

26 26 Conclusions: A pedagogy for workplace learning? Business needs generally require employees to reason more effectively in workplace tasks by using mathematics Mathematical practices are changing through deployment of IT, not disappearing. “Maths avoidance” is a barrier to training. Learning opportunities for TmL promote situated modelling: context-based activities involve “making the invisible visible” through situated models and using these as basis for making business decisions – eg. in the work of the Customer Enquiry Team

27 27 Further research: Boundary crossing evolution With the companies: - fitting to the training and learning culture of the company - co-teaching with someone from the company or LOs as modules that can be taken off the shelf? With the sector: work with Skills Council to - “generalise” findings to other companies - get TmL on the agenda for future development of financial qualifications - sustain research beyond the project lifetime

28 28 Find out more Bakker, A., Kent, P., Hoyles, C., Noss, R. and Bhinder, C. (in press). “It’s not just magic!” Learning opportunities with spreadsheets in the financial sector. Proceedings of the British Society for Research into Learning Mathematics (February 2006) Kent, P., Noss, R., Guile, D., Hoyles, C., & Bakker, A. (in press). “Characterising the use of mathematical knowledge in boundary crossing situations at work”. To appear in Mind, Culture, and Activity, special issue on “Learning and Technology at Work” (edited by P. Kent, C. Hoyles, R. Noss, D. Guile & A. Bakker )

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