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MEP learning pack

Masters in Educational Practice: Numeracy learning pack

4

Contexts for learning and teaching

4.3

Issue of transfer and authentic contexts

Findings from a number of international research studies challenge the idea that the ‘basic’, ‘key’ or ‘essential skills’ of numeracy can be learnt separately and then applied unproblematically to any other academic or vocational area or everyday practice. (Lave, 1988; Harris, 2000; FitzSimons, 2005)

For example, Nunes et al. (1993) looked at how workers and students used informal ‘street maths’ and formal ‘school maths’ to tackle problems. They found that although there was some transfer of mathematical knowledge from one situation to another, everyday calculation knowledge learnt in one context did not help the subjects perform procedural context-free calculations of a similar nature. ‘Street maths’ did help in similar calculations in different contexts, but only when the contexts were meaningful to the subjects. The researchers concluded that the understanding of informal and formal types of calculation seemed to be entirely separate and were not used to support each other, i.e. transfer between ‘school’ and ‘street’ did not appear to take place.

If ‘transfer’ of skills and understanding is to be achieved, it is important to support learners (and teachers) to recognise both similarities and differences in the numeracy practices used within different contexts, for different purposes and by different ‘communities of practice’. 

Authentic contexts

Authentic situations embedded in ‘everyday’ life are more likely to have personal meaning for learners if they are linked to learner contexts. Gal (2000) identifies three different sorts of ‘authentic’ situations that might help teachers to develop numeracy-in-action activities with increasing complexity. 

Generative situations where learners count, quantify, compute, etc., manipulating numbers and generating responses, e.g. dealing with simple operations such as calculating a total price while shopping or measuring a shelf; dealing with multi-step operations embedded in text, such as completing an order form; and making reasonable decisions, such as choosing the cheapest mobile phone deal. Resulting responses have clear right or wrong answers.

Interpretative situations where learners make sense of verbal or text-based messages based on quantitative data but are not required to manipulate numbers, e.g. interpreting a chart in a newspaper or on the internet reporting youth crime statistics or reading a report of a survey on attitudes to smoking. The response expected in such situations is an opinion or as a result of critical questions that have no clear right or wrong answers.

Decisions situations where learners find and consider multiple pieces of information to determine a course of action, e.g. identifying ways to use limited resources, such as money and time, and choosing among alternatives. There is no correct answer in such situations, but the person may sacrifice precision or accuracy to save time, money or mental load when deciding on a response and may reach the response in an efficient or non-standard way.  

Activity 4.06

  1. Identify how Gal’s’ three ‘situations’ match the increasing complexity within the ‘Developing numerical reasoning’ strand of the National Literacy and Numeracy Framework (LNF) across the different year groups.
  2. Review three exemplar activities provided within the LNF from different year groups in terms of their ‘authenticity’ and ‘complexity’. (Remember that for a Year 8 learner, regular geography or PE lessons are as much a part of ‘everyday life’ as their ‘out-of-school’ activities.)
  3. Within your own subject area, identify at least one example of an authentic ‘generative’, ‘interpretative’ and ‘decision’ situation you could use to develop ‘numeracy-in-action’?

Topic 3 contains examples of how practitioners are developing approaches which provide learners with meaningful and authentic contexts that support numeracy learning and teaching.

References

FitzSimons, G. (2005) Numeracy and Australian Workplaces: findings and implications. Australian Senior Mathematics Journal, 19(2), pp.27–30

Gal, I. (2000) The numeracy challenge. In Gal, I. (Ed.), Adult Numeracy Development: Theory, research and practice (pp.9–31). Cresskill, N. J.: Hampton Press

Harris, M. (2000) Women, mathematics and work. In Coben, D. O’Donoghue, J. and FitzSimons,G. E. (Eds) Perspectives on Adults Learning Mathematics: Research and Practice. Dordrecht, Kluwer Academic Publishers

Lave, J. (1998) Cognition in Practice. Cambridge, CUP
Nunes, T., Schliemann, A. D. and Carraher, D. W. (1993) Street Mathematics and School Mathematics. Cambridge, CUP

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