Defining ‘numeracy’ is more than just an academic exercise. Deciding what we mean by ‘numeracy’ has implications for what we think learners need to know and why; what we believe should be taught, how, where and when; how learners should be assessed; and what professional development teachers need (Hagedorn et al., 2003).

In practice, a range of terms are used to define what ‘numeracy’ is, including:

- basic computational arithmetic
- essential mathematics
- social mathematics
- survival skills for everyday life
- quantitative literacy
- mathematical literacy
- application of number
- functional mathematics
- mathemacy
- techno-mathematical literacy.

These descriptions reflect a range of personal abilities from basic skills to high level problem-solving and communication, and from little or no mathematics to quite advanced mathematics (O’Donoghue, 2002).

### Concepts of numeracy

In their work within adult mathematics and numeracy, Maguire and O’Donoghue (2002) offer a framework which organises concepts of numeracy along a continuum of increasing levels of sophistication.

1. Formative phase – numeracy is basic mathematics and arithmetic skills. It is normally assumed that these are acquired in childhood and are necessary for adults to function effectively in society. Evans (2000) calls this the ‘limited proficiency’ or 3Rs’ model of numeracy. Within this view, because the content is seen as ‘simple and functional’, learning numeracy may also be seen as easy. However, Brown et al. (2006) argue that in today’s workplace, individuals are increasingly required to make ‘sophisticated use of elementary mathematics’ and to perform quite complex analysis using relatively simple techniques, often supported by technology.

2. Mathematical phase – numeracy is ‘mathematics in context’ with explicit recognition of the importance of mathematics in everyday life (e.g. The Cockcroft Report definition). Numeracy within this phase often includes number, money and percentages; aspects of algebraic, geometric and statistical thinking; and problem-solving based on the mathematical demands of adult life. However, this idea of ‘numeracy-in-action’ is not straightforward given the very wide range of potential contexts and purposes, and the practical mathematical demands of school, college, work and everyday life which may require more than basic numeracy.

3. Integrative – numeracy is a multi-faceted, sophisticated idea that includes mathematics, communication, and cultural, social, emotional and personal aspects of each individual in context. According to Steen (1997), this sort of numeracy has a number of purposes and associations which are:

- practical – concerning mathematical and statistical skills that can be put into immediate use in the routine tasks of daily life
- civic – focus is on the benefits to society
- professional – because many jobs require mathematical skills
- recreational – appreciation of games, puzzles, sports, lotteries, and other leisure activities
- cultural – where mathematics is a universal part of human culture.

This integrative phase also includes critical concepts of numeracy such as those offered by Johnston (1995, p.34):

To be numerate is more than being able to manipulate numbers, or even being able to succeed in school or university mathematics. Numeracy is a critical awareness, which builds bridges between mathematics and the real world, with all its diversity . . . It is as important for an engineer to be numerate as it is for a primary school child, a parent, a car driver or gardener. The different contexts will require different mathematics to be activated and engaged in.

### Current situation

‘Integrative’ conceptions of numeracy that emphasise individuals becoming personally, technologically and socially numerate dominate almost all current thinking and policy making. These focus on conceptual understanding and the development of problem-solving and decision-making skills, rather than rule-based learning. The aim to help learners use mathematics knowledge and skills to meet real-life challenges and respond to the technological demands needed to ensure the economy has a workforce able to compete internationally. However, much mainstream practice still tends to reflect what Maguire and O’Donoghue (2000) describe as ‘formative’ and ‘mathematical’ approaches to numeracy.

# Activity 2.01

Look at the following definitions of numeracy found in:

- the Crowther report
- the Cockcroft report
- PISA
- the National Numeracy Programme in Wales
- your own responses to earlier activities.

- Where would each of these appear on Maguire and O’Donoghue’s ‘continuum of development’?
- Reflect on your experiences of current practice in supporting numeracy learning within your own teaching context on this continuum. Where would you place these on the ‘continuum of development’?

### Definitions of numeracy

Crowther (1959, par 401):

On the one hand is an understanding of the scientific approach to the study of phenomena – observation, hypothesis, experiment, verification. On the other hand is a need in the modern world to think quantitatively, to realise how far our problems are problems of degree even when they appear as problems of kind.

Cockcroft (1982, par 39):

We would wish ‘numerate’ to imply the possession of two attributes. The first of these is an ‘at-homeness’ with numbers and an ability to make use of mathematical skills which enable an individual to cope with the practical mathematical demands of his everyday life. The second is ability to have some appreciation and understanding of information which is presented in mathematical terms, for instance in graphs, charts or tables or by reference to percentage increase or decrease.

PISA (2002) defines **mathematical literacy** as:

. . . the capacity to identify, understand and engage in mathematics, and to make well-founded judgements about the role that mathematics plays in an individual’s current and future private life, occupational life, social life with peers and relatives, and life as a constructive, concerned and reflective citizen.

PISA (2012) defines **mathematical literacy** as:

. . . an individual’s capacity to formulate, employ, and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts, and tools to describe, explain, and predict phenomena. It assists individuals to recognise the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective citizens.

National Numeracy Programme (NNP) (2012) in Wales defines **numeracy** as:

. . . identifying and applying numerical reasoning skills in order to solve a problem, and carrying out the numerical procedures which enable people to work out and show their solutions.

### Glossary

**Critical numeracy** – ‘learners have the functional skills to participate fully in civic life e.g. interpreting advertising, understand financial information and government statistics, and take political and social action’ (Kerka, 1995).

**Techno-mathematical literacy** – combinations of mathematical and technological skills that people need, e.g. in workplaces.

### References

Brown, M., Coben D., Hodgen J., Stevenson I., and Venkatakrishnan H. (2006) ‘Functional Mathematics and its Assessment’ in Hewitt, Proceedings of the British Society for Research into Learning Mathematics. 26(1) February 2006 (online). (accessed 31 October 2013)

Condelli, L., Safford-Ramus, K., Sherman, R., Coben, D., Gal, I., and Hector-Mason, A. (2006) A Review of the Literature in Adult Numeracy: Research and conceptual issues. Washington, DC: American Institutes for Research (online). (accessed 31 October 2013)

Evans, J. (2000) Adults’ mathematical thinking and emotions: A study of numerate practices. London: Routledge/Falmer.

Hagedorn, L., Newlands, J., Blayney, I., & Bowles, A. (2003) Frameworks for adult numeracy education: A survey and discussion. Ontario, Canada: National Literacy Secretariat. Retrieved March 9, 2006, from the National Adult Literacy Database. (accessed 31 October 2013)

Johnston, B. (1994, Summer). ‘Critical numeracy?’ in Fine print, 16(4)

O’Donoghue, J. (2002) ‘Numeracy and Mathematics’, Irish math. Soc Bulletin, 48 pp. 47–55 (online). (accessed 31 October 2013)

Steen, L. A. (Ed) (1997) Why Numbers Count: Quantitative Literacy for Tomorrow’s America. New York, NY: The College Board.