Quantitatively literate citizens need to know more than formulas and equations. They need a predisposition to look at the world through mathematical eyes, to see the benefits (and risks) of thinking quantitatively about commonplace issues, and to approach complex problems with confidence in the value of careful reasoning. Quantitative literacy empowers people by giving them tools to think for themselves, to ask intelligent questions of experts, and to confront authority confidently. These are skills required to thrive in the modern world. (Quantitative Literacy Design Team 2001, p. 2)
Numeracyāsometimes referred to as quantitative literacyāis often interpreted narrowly as involving facility with numbers and computation performed with paper and pencil or āin the headā, and many people would regard reliance on an electronic calculator as evidence of innumeracy arising from lack of basic number skills. However, this kind of ābasic skillsā definition of numeracy is clearly outdated in the data-drenched, technology-rich world of the 21st century. The constant evolution of knowledge, social structures, work practices and new technologies requires a corresponding evolutionāor even revolutionāin the ways in which we think about numeracy.
This chapter encourages prospective and practising teachers to identify and refine their personal conception of numeracy. We begin by exploring the origins of numeracy as a concept and comparing some of the common definitions and terminologies for describing numeracy. Next, we look for examples of numeracy in a range of real-life contexts to highlight the important distinction between numeracy and mathematics. We then consider the impact of poor numeracy on young peopleās life chances to argue that numeracy education must be embedded in all subjects across the primary and secondary school curriculums. Finally, we find out how well prepared and confident teachers feel in taking on this task.
WHAT IS NUMERACY?
The idea of numeracy is a relatively recent one. The term was first introduced in the United Kingdom by the Crowther Report (Ministry of Education 1959) and was defined as the mirror image of literacy, but involving quantitative thinking. Another early definition proposed by the UK Cockcroft (1982) Report described ābeing numerateā as possessing an at-homeness with numbers and an ability to use mathematical skills to cope confidently with the practical demands of everyday life.
Review and reflect 1.1
- Before reading any further, write down your responses to the following prompts to capture your own ideas about numeracy.
- Numeracy involves ā¦
- A numerate person can ā¦
- A numerate person knows ā¦
- A numerate person is ā¦
- Compare your responses with those of a colleague and summarise any similarities or differences.
Teachersā conceptions of numeracy
We have carried out the āWhat is numeracy?ā task presented in Review and reflect 1.1 many times with primary school teachers, teachers of secondary school mathematics and teachers of other secondary school subjects. For the first group of teachers we worked with (see Goos, Geiger & Dole 2011), the most frequent responses to the prompt āNumeracy involves ā¦ā showed an appreciation of the role of context, with responses referring to āeveryday connectionsā and āapplication of mathematical processes in everyday practical situationsā. These teachers thought that numeracy also involved problem-solvingāfor example, āsolving problems in lifeā or āhaving a repertoire of strategiesā. When describing what āa numerate person canā do, the teachers typically wrote about mathematical skills such as āusing numbers to solve problemsā. But some also thought that a numerate person can āsort out how to transfer mathematical knowledge into real life situationsā and āuse problem solving skills to help them better understand some aspects of numeracyā. In deciding what āa numerate person knowsā, the teachers again commonly alluded to mathematical knowledge in the form of specific skills (e.g., āhow to convert currencyā), but some emphasised knowing mathematics that was appropriate to a particular task (āhow and when to use what skillā) or how to use mathematics in everyday life (āunderstand the odds of Melbourne Cup horsesā). Their responses to the prompt āA numerate person is ā¦ā again revealed an appreciation of contexts for numeracy (e.g., āsomeone who can use numeracy in everyday situationsā) as well as an emphasis on positive dispositions (e.g., āflexible in their mathematical thinking and confident to take learning risksā). Taken together, their responses suggested that this group of teachers understood numeracy as involving the confident application of mathematical knowledge, skills and problem-solving strategies across a range of everyday contexts.
Numeracy terminology and definitions
Although numeracy is a term used in many English-speaking countries, such as the United Kingdom, Ireland, Canada, South Africa, Australia and New Zealand, in the United States and elsewhere it is more common to speak of quantitative literacy or mathematical literacy. The Quantitative Literacy Design Team (2001) was formed by the US National Council on Education and the Disciplines to inquire into the meaning of numeracy in contemporary society. This team described quantitative literacy as āthe capacity to deal effectively with the quantitative aspects of lifeā (p. 6) and proposed that its elements included confidence with mathematics, appreciation of the nature and history of mathematics and its significance
Review and reflect 1.2
Numeracy is a term used mainly in English-speaking countries. Other countries in the world do not have a comparable term for numeracy or have simply adopted the PISA definition of mathematical literacy. Geiger, Goos and Forgaszās (2015) article presents a synthesis of international literature on the concept of numeracy.
- Read the article with a partner, paying particular attention to the sections on āUnderstandings of numeracyā and āFacets of numeracyā.
- Working individually, summarise the different ways in which numeracy is understood around the world.
- Compare your summary with your partnerās and with your responses to the Review and reflect 1.1 task.
for understanding issues in the public realm, logical thinking and decision-making, use of mathematics to solve practical everyday problems in different contexts, number sense and symbol sense, reasoning with data and the ability to draw on a range of prerequisite mathematical knowledge and tools. The Organisation for Economic Co-operation and Developmentās (OECD) Programme for International Student Assessment (PISA) offered a similarly expansive definition of mathematical literacy as āan individualās 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 judgements and decisions needed by constructive, engaged and reflective citizensā (OECD 2016, p. 65).
In Australia, educators and policy-makers have embraced a broad interpretation of numeracy similar to the OECDās definition of mathematical literacy. The definition adopted by a 1997 national numeracy conferenceāāTo be numerate is to use mathematics effectively to meet the general demands of life at home, in paid work, and for participation in community and civic lifeā (DEETYA 1997, p. 15)ābecame widely accepted in Australia and formed the basis for much numeracy-related research and curriculum development.
FINDING NUMERACY
The Australian description of numeracy highlights its role in helping people meet the general demands of life in three different contexts: home, work, and community and civic life. Teachers who are effective at developing their studentsā numeracy capabilities are also adept at recognising the numeracy demands of these everyday situationsāthey have cultivated the ability to see numeracy by asking questions about the world around them. What it means to see numeracy in this way is explored in the following examples.
At home
Many examples of numeracy in action can be found in the home. For example, cooking involves measurement of quantities and time (see Review and reflect 3.1); shopping requires the ability to compare prices and estimate value for money; playing team sports means keeping score and predicting the effect of different outcomes on an overall league table.
Review and reflect 1.3
A regular feature in a local newspaper invited readers to write to a well-known chef with questions about recipes. This readerās question, and the reply, caught our eye:
Q. I am planning to make a sma...