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Table of Contents:

The Final Framework:

  

Numeracy Definitions

Purpose: To suggest possible descriptive and normative orientations on adult numeracy.

References: 15, 16, 28, 32, 35, 38, 44, 51, 59, 82

  1. Descriptive/Normative Distinctions: [ from Tine Wedege, personal communication, 7/2/06]:

“‘Numeracy consists of functional mathematical skills and understanding that in principle all people need to have. … Numeracy changes in time and space along with social change and technological development’ [51, p. 5]. Here, adult numeracy is situated within a certain society and a certain culture at a certain stage of technological development. It is defined as functional skills and understanding ( i.e., competence) that is needed in society. Thus, the requirements from society, labour market, democracy etc., and the personal needs in relation to these requirements define adult numeracy.” This definition is descriptive as there is no prescription of what kind of mathematics that is needed.

  1. Numeracy encompasses the knowledge and skills required to effectively manage mathematical demands in personal, societal and work situations, in combination with the ability to accommodate and adjust flexibly to new demands in a continuously rapidly changing society that is highly dominated by quantitative information and technology. [38, p. 37]
  1. Numeracy draws upon foundations of mathematical knowledge developed by individuals over a lifetime of personal experience and enculturation, including formal education, to solve real problems in situations that are context-specific, requiring common sense, and are directed towards the achievement of specific and highly relevant goals. [28, 32]

 

  1. Which domain of adult numeracy is in focus and by whom?

Domain One numeracy may have low use value but high exchange value, yielding certificates tradeable on the labour market. It is useful for gaining access to institutions of modernity; based on the belief that to be numerate is beneficial both to the individual and to society. It is characterised by formalisation and standardisation of the curriculum, and technologisation, unitisation and commodification of learning and learning materials. It is competency-based and outcomes-focussed, with explicit equivalence with educational levels in schools.

Domain Two numeracy is about informal and non-standard mathematics practices and processes in adults’ lives, which may bear little relation to formal, taught mathematics. These practices which may be (dis)regarded as ‘just common sense’ by all concerned, ‘invisible’ mathematics; useful for doing and/or understanding. It has high use value but no exchange value beyond the community of practice in which it occurs. [15]

Normative Orientations [When we talk about numeracy teaching in formal education, we define the concept in a normative way through the curriculum.]

  1. Is the curriculum focus:
    1. solely on functional skills for everyday use?
    2. on (school) mathematics with applications, realistic or relevant, as context?
    3. on the integration of mathematics with the learner’s personal social, cultural, economic, emotional, etc., contexts? (Maguire & O’Donoghue, 2003)

 

  1. In developing numeracy, how does the learning activity address the dimensions of:
    1. using a variety of media, including written and oral information and communication, concrete materials, time, and processes (e.g., working with piles of soil or sand, areas of floors or land, distribution of work hours)?
    2. context:
      1. in the linguistic sense to help elucidate meaning, related to the task?
      2. in the situational sense (e.g., historical, social, cultural, or psychological relations) of something that has happened or is to be observed and considered (e.g., work, family, education, social & leisure time)?
    3. personal intentions, both conscious and unconscious(e.g., consider the various reasons for reading a newspaper article with quantitative information)?
    4. skills and understandings related to the other three dimensions,including the handling and sense of quantity and numbers (including estimation & approximation), dimension and form, patterns and relations, data and chance, and change? [51]

 

  1. How well does the activity develop mathematics literacy [or numerate behaviour] as an individual’s capacity, currently and in the future:
    1. to identify and understand (& even critique) the role that mathematics plays in the world from functional, aesthetic, and recreational perspectives?
    2. to make well-founded mathematical judgements and to engage in mathematics (i.e. mathematical thinking & doing) in a variety of ways that call for (critical) reflection and insight? [59]

 

  1. How well does the activity develop numerate behaviour in order for the individual to:
    1. manage a situation or solve a problem in a real context (e.g., personal everyday life, work, broader civic society, further learning situations)?
    2. respond to information assuming and/or containing mathematical ideas through interpreting, and possibly acting upon (including communicating to others)?

[NB The information may be represented in a range of ways such as objects and pictures, numbers and symbols, formulae, diagrams and maps, graphs, tables, texts.] [35]

 

  1. How well does the activity engender competence, confidence, and comfort with one’s judgements on:
    1. whether to use mathematics in a particular situation
    2. and if so, what mathematics to use, how to do it, what degree of accuracy [in number and in measurement of space & shape] is appropriate, and
    3. what the answer means in relation to the context? [16]

 

  1. Following the proposed UK definition of functional mathematics [see http://nationalstrategies.standards.dcsf.gov.uk/node/16057 ]:
    1. Will the learner develop sufficient understanding of a range of mathematical concepts and be able to know how and when to use them?
    2. Will they have the confidence and capability to use mathematics to solve problems embedded in increasingly complex settings and to use a range of tools, including ICT, as appropriate?
    3. In life and work, will the learner develop the analytical and reasoning skills to draw conclusions, justify how they are reached, and identify errors or inconsistencies?
    4. Will they also be able to validate and interpret results, to judge the limits of their validity and use them effectively and efficiently?

 

  1. Social and critical perspectives:
    1. To what extent is the numeracy task socially situated, incorporating personal reflection and social negotiation, uncovering assumptions and value systems, including whose interests are being served by any given representation of reality?
    2. How well does the activity develop a critical awareness (i.e., being able to situate, interpret, critique, use, and perhaps even create mathematics in context, taking into account all the mathematical as well as social and human complexities which come with that process)? [82]

 

  1. How are the inevitable tensions & contradictions within and between three types of numeracy knowledge as pedagogical content addressed:
    1. Visible numeracy (i.e., the kind of knowledge intended when using commonly accepted mathematical language and symbols to formulate mathematical relationships and to communicate these to others; e.g., counting, measuring)?
    2. Useable numeracy (i.e., the kind of numerical knowledge defined by its use in dealing with tasks and problems occurring in every day situations and the workplace)?
    3. Constructible numeracy (i.e., that kind of numeracy produced by an individual/social constructive process usually in a learning situation)? [44]