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MEP learning pack

Masters in Educational Practice: Numeracy learning pack

4

Contexts for learning and teaching

4.1

Numeracy in a social context

The Welsh Government provides a definition of numeracy ‘in-action’ within a variety of social contexts:

Numeracy refers to the application of mathematical understanding in daily activities at school, at home, at work and in the community (Welsh Government, 2012)

Teachers using the National Literacy and Numeracy Framework (LNF) are developing ways to relate numeracy strands and elements within the framework to the application of numerical skills and reasoning within and across school curricula. Those working to support young people achieve Essential Skills Wales Application of Number qualifications are developing contextualised and embedded approaches to numeracy learning in a range of academic and vocational curricula.

It is often more challenging to identify explicit opportunities to share, value and build on the diverse range of formal and informal numeracy practice(s) learners engage in outside of school, college, work-based, community or other further education settings.

Numeracy practices

Bishop (1988) identified the following six ‘basic’ mathematical behaviours as occurring universally in all cultures. They provide some clues as to where to look (with colleagues, parents/carers and learners) for ‘daily activities’ involving numeracy practices both in and out of school.

  • Counting – what, how, and why we count – using a variety of counting systems in different contexts.
  • Locating – finding our way around, travelling without getting lost and relating objects to each other; developing and using different ways to code and symbolise our spatial environment.
  • Measuring – comparing, ordering and valuing; developing precision and systems of measuring units in relation to what society values.
  • Designing – creating objects and artefacts for various purposes in different contexts; modelling and constructing; using ideas of shape, size, scale, ratio, proportion and many other geometrical concepts.
  • Playing – creating and playing games; making and following rules; dealing with chance, risk and probability; logic and problem-solving; strategy and prediction.
  • Explaining – finding connections, generalising, predicting, abstracting.

Activity 4.01

  1. Reflect on when and how any of these behaviours or numeracy practices appear within your subject area. Think about contexts, purposes, tools, specialist words, people, activities, etc., associated with these.
  2. Reflect on when and how you undertake any of these behaviours or numeracy practices in your own life (in work and outside work). Again, think about the contexts, purposes, tools, key words, people, activities etc associated with these.

Learner contexts

Both the LNF and Essential Skills Wales standards identify required numeracy skills. Whole-school and further education curricula will provide many contexts for developing and embedding these across subject and extra-curricular areas, but learners also brings additional contexts. 

These include (and can be adapted to younger learner contexts):

  • domestic/home life
  • school life and training
  • leisure and interests
  • citizenship and community
  • enterprise activity and work life experience
  • using ICT in social roles – online shopping, banking, social media, etc. (Adapted from Adult Numeracy Core Curriculum, 2001)

Activity 4.02

  1. Think about what ‘numeracy in-action’ and being numerate might ‘look like’ for your learners within these different but inter-connected contexts.
  2. How could you work with learners, colleagues and parents/carers to make more meaningful links with learners’ diverse everyday numeracy practice(s)?
  3. How could you work with learners to help them make more meaningful links with their own numeracy practices in and out of school/college?
  4. Have you got maths eyes? (external link) Shows how communities in Ireland are discovering the mathematics that surround them and that they use every day. Are there any ideas here that you could adapt for your own learners?

Numeracy in-action

Research (Oughton, 2013; Gibney, 2013) shows that the way people carry out numeracy in everyday life outside of school or further education settings is often very different to the way mathematics and numeracy are taught in the classroom. Real life problems tend to be:

  • purposeful with meaningful outcomes
  • generated by individuals themselves
  • structured in terms of goals to be achieved, rather than mathematics involved 
  • often undertaken in collaboration other people in social situations, e.g. playing, cooking, constructing, shopping, designing
  • dependent on or shaped by particular tools or realia, e.g. mobile technologies, brochures, measuring devices, software packages and mobile apps.

This suggests that ‘numeracy in-action’ is something embedded in how we interact with purpose within our social world, rather than just a set of ‘stand-alone’ mathematical skills.

However, research (d’Abreu and Kline, 2003) also suggests that many learners regard practical numeracy skills as ‘just common sense’ and low status, whereas being competent in formal classroom mathematics is seen as high status and signifying ‘intelligence’. In addition, if numeracy teaching is solely related to functional purposes outside school or college, then learners will not be supported to access and achieve the formal mathematics and numeracy skills and qualifications required for many career paths and courses of further study. Swain et al (2005) also note from their research with older learners is that what makes a mathematics or numeracy task meaningful is the quality of an individual’s engagement with a problem rather than its utility or everydayness.

Funds of knowledge

A social practices view of numeracy does, however, provide opportunities to explore what ‘funds of knowledge’ learners already bring with them to school and college settings. This approach can help avoid a completely deficit view of learners’ numeracy, particularly in work with older children and young adults. The idea of ‘funds of knowledge’ which may not be reflected in formal qualifications or assessments was developed by Moll et al (1992) in their work with Mexican families living in Arizona. They discovered that households could draw on their own expertise and informal knowledge in a wide variety of fields. 

In relation to numeracy learning this might refer to our learners’:

  • knowledge, experiences, histories, identities, images of themselves
  • attitudes, dispositions, desires, values, beliefs, social and cultural relations
  • relationships  with learning, teachers and mathematics itself
  • numeracy practices beyond the classroom.

To get a qualification in numeracy, learners have to be able to switch from informal numeracy practices outside the classroom to the rules and processes of the formal numeracy practices inside the classroom (Street et al, 2005). Baker (2005) argues that if teachers and learners are more aware of their ‘funds of knowledge’, this can help to:

reveal conflicts and contrasts between formal numeracy practices in mathematics classrooms, numeracy practices in other subject classroom contexts and learners’ numeracy practices beyond the classroom
ensure learners' (and teachers’) ‘funds of knowledge’ become positive resources rather than problems to be overcome look at what a learner can do as a whole person, rather than simply trying to paste new skills onto old ones shape interactions with learners and help teachers to encourage learners to participate in the formal numeracy practices of the classroom develop a more balanced view of formal numeracy practices as dominant in the context of a formal qualification framework but not necessarily in other contexts.

Activity 4.03

A constructivist model of learning emphasises that we should build on what learners already know. Think of two learners you work with, perhaps one who is confident with mathematics and numeracy, and one who is less confident.

  1. What formal and informal ‘funds of knowledge’ does each bring with them to learning situations (e.g. qualities, skills, interests, enthusiasms, experiences, knowledge)?
  2. How might you and they ‘exploit’ these resources to support their numeracy learning within your subject area? Within the wider school or college community? At home?
  3. How do existing assessment arrangements help establish learners’ more informal ‘funds of knowledge’?

References

de Abreu, G. and Cline, T. (2003) School Mathematics and Cultural Knowledge Pedagogy. Culture and Society, 11(1), pp11–30. (online)

Baker, D. A. (1998) Numeracy as Social Practice; and adult education context in South Africa. Journal of Literacy and Numeracy Studies, 8(1) pp 37–50. Sydney, Australia.

Baker, D. (2005) Numeracy and ‘funds of knowledge’. Reflect, 3, pp16–19

Baker, D. and Rhodes, V. (2007) Making use of learners’ funds of knowledge for mathematics and numeracy: Improving Teaching and Learning of mathematics and numeracy in adult education. Research report. (online)

Bishop, A. J. (1988) Mathematical Enculturation: A Cultural Perspective on Mathematics Education. Dordrecht: D. Reidel.

DfEE (2001) Adult Numeracy Core Curriculum. London: DfEE. (online)

Oughton, H. (2013) ‘The social context of numeracy’, in G. Griffiths and R. Stone (eds) Teaching Adult Numeracy Principles and Practice. Berkshire: OUP, McGraw Hill.

Gibney, J. (2013) ‘Provoking mathematical thinking: numeracy teachers doing ‘realistic’ maths’, in G. Griffiths and R. Stone (Eds) Teaching Adult Numeracy Principles and Practice. Berkshire: OUP, McGraw Hill.

Moll, L. C., Amanti, C., Neff, D. and Gonzalez, N. (1992) Funds of Knowledge for teaching: Using a Qualitative Approach to Connect Homes and Classrooms. Theory into Practice, 31(2) pp 132–141.

Street B. V., Baker D. A., Tomlin A. (2005) Navigating Numeracies: Home/School Numeracy Practices. London: Kluwer.

Swain, J., Baker, E., Holder, D., Newmarch, B. and Coben, D. (2005) ‘Beyond the Daily Application’: Making Numeracy Teaching Meaningful to Adult Learners. London: NRDC. (online)

Useful links

  1. Watch a video clip (external link) which shows children, young people and their teachers talking about and developing their numeracy in a variety of contexts in Scottish schools and colleges.
  2. Listen to (external link) a group of parents and carers in Scotland talking about the importance of numeracy in life and how they believe it will impact on their children and young people.
  3. Listen to (external link) people in the workplace discussing the part numeracy plays in their jobs.
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