Numeracy Across the Curriculum

Research-based strategies for enhancing teaching and learning

Merrilyn Goos, Vince Geiger, Shelley Dole, Helen Forgasz, Anne Bennison

• Publisher: Routledge
• Year: 2020
• Print ISBN: 9780367718817
• eBook ISBN: 9781000246667
• Edition: 1
• Topic: Education
• Subtopic: Education General

Being numerate involves more than mastering basic mathematics. Numeracy connects the mathematics learned at school with out-of-school situations that require capabilities such as problem solving, critical judgment, and sense-making related to non-mathematical contexts. This book provides prospective and practising teachers with practical, research-based strategies for embedding numeracy across the primary and secondary school curriculum.

Based on the authors' ten-year research program, the text explains what numeracy is and how numeracy has developed as an educational goal. It describes in detail the five dimensions of the authors' model: attention to real-life contexts; application of mathematical knowledge; use of physical, representational and digital tools; the promotion of positive dispositions towards the use of mathematics to solve problems encountered in day-to-day life; and a critical orientation to interpreting mathematical results and making evidence-based judgements. There is guidance on how to embed numeracy across all subjects within the curriculum, how to assess numeracy learning and how to deal with challenges and dilemmas including working with discipline boundaries and developing support resources.

Featuring practical examples and case studies throughout, this book will build pre-service teacher confidence, demystify common misconceptions and grounds theory into practice in this vital area of student competency.

'The authors of this text are recognised authorities on numeracy. They have engaged heavily in numeracy research over many years and this text reflects the depth of their understanding and knowledge.' - Geoff Hilton, University of Queensland

1
Understanding numeracy

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)

Numeracy—sometimes referred to as quantitative literacy—is often interpreted narrowly as involving facility with numbers and computation performed with paper and pencil or ‘in the head’, 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 ‘basic skills’ 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 evolution—or even revolution—in 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 people’s 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 ‘being numerate’ 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

1. Before reading any further, write down your responses to the following prompts to capture your own ideas about numeracy.
   • Numeracy involves …
   • A numerate person can …
   • A numerate person knows …
   • A numerate person is …
2. Compare your responses with those of a colleague and summarise any similarities or differences.

Teachers’ conceptions of numeracy

We have carried out the ‘What is numeracy?’ 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 ‘Numeracy involves …’ showed an appreciation of the role of context, with responses referring to ‘everyday connections’ and ‘application of mathematical processes in everyday practical situations’. These teachers thought that numeracy also involved problem-solving—for example, ‘solving problems in life’ or ‘having a repertoire of strategies’. When describing what ‘a numerate person can’ do, the teachers typically wrote about mathematical skills such as ‘using numbers to solve problems’. But some also thought that a numerate person can ‘sort out how to transfer mathematical knowledge into real life situations’ and ‘use problem solving skills to help them better understand some aspects of numeracy’. In deciding what ‘a numerate person knows’, the teachers again commonly alluded to mathematical knowledge in the form of specific skills (e.g., ‘how to convert currency’), but some emphasised knowing mathematics that was appropriate to a particular task (‘how and when to use what skill’) or how to use mathematics in everyday life (‘understand the odds of Melbourne Cup horses’). Their responses to the prompt ‘A numerate person is …’ again revealed an appreciation of contexts for numeracy (e.g., ‘someone who can use numeracy in everyday situations’) as well as an emphasis on positive dispositions (e.g., ‘flexible in their mathematical thinking and confident to take learning risks’). 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 ‘the capacity to deal effectively with the quantitative aspects of life’ (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 Forgasz’s (2015) article presents a synthesis of international literature on the concept of numeracy.

1. Read the article with a partner, paying particular attention to the sections on ‘Understandings of numeracy’ and ‘Facets of numeracy’.
2. Working individually, summarise the different ways in which numeracy is understood around the world.
3. Compare your summary with your partner’s 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 Development’s (OECD) Programme for International Student Assessment (PISA) offered a similarly expansive definition of 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 judgements and decisions needed by constructive, engaged and reflective citizens’ (OECD 2016, p. 65).

In Australia, educators and policy-makers have embraced a broad interpretation of numeracy similar to the OECD’s definition of mathematical literacy. The definition adopted by a 1997 national numeracy conference—‘To 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 life’ (DEETYA 1997, p. 15)—became 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 students’ numeracy capabilities are also adept at recognising the numeracy demands of these everyday situations—they 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 reader’s question, and the reply, caught our eye:

Q. I am planning to make a sma...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• CONTENTS
• About the authors
• List of figures, tables and case studies
• Chapter 1 Understanding numeracy
• Chapter 2 Towards numeracy across the curriculum
• Chapter 3 Numeracy in the 21st century
• Chapter 4 Numeracy demands
• Chapter 5 Numeracy opportunities
• Chapter 6 Planning for numeracy across the curriculum
• Chapter 7 Whole-school approaches to numeracy
• Chapter 8 Assessing numeracy learning
• Chapter 9 Challenges in enhancing numeracy
• Acknowledgements
• References
• Index