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MathsWorks for Teachers SerieseditorDavid Leigh-Lancaster
Foundation Numeracy in Context
David Tout and Gary Motteram
Foundation Numeracy in Contextdescribes an approach to teaching mathematics
based on applied and contextual learning principles.This means that the teaching and
learning of mathematics proceeds from a contextual,task-based and investigative
point of view—where the mathematics involved is developed from a modelled situation
or practical task.Practical investigations and projects are principle vehicles for student
learning in such an approach.
This text is written for teachers working with students who have become disengaged
from learning mathematics during the middle to latter years of secondary schooling,
and will likely have had limited success with mathematics.The approach used will be
helpful for teachers of students who need a practical rather than formal mathematical
background for their everyday life skills and further education,training or career
aspirations.The text illustrates how this approach works through some sample contexts
such as cars and driving,sport,cooking and catering,and draws together mathematics
from the areas of number,measurement,space,data and statistics,and algebra.
Series overview
MathsWorks for Teachershas been developed to provide a coherent and contemporary
framework for conceptualising and implementing aspects of middle and senior
mathematics curricula.
Titles in the series are:
Functional Equations
David Leigh-Lancaster
Contemporary Calculus
Michael Evans
Matrices
Pam Norton
Foundation Numeracy
in Context
David Tout & Gary Motteram
Data Analysis
Applications
Kay Lipson
Complex Numbers
and Vectors
Les Evans
Foundation Numeracy
in Context
David Tout and Gary Motteram
MathsWorks for Teachers
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First published 2006
by ACER Press
Australian Council for Educational Research Ltd
19 Prospect Hill Road, Camberwell, Victoria, 3124
Copyright © 2006 Dave Tout, Gary Motteram, David Leigh-Lancaster
All rights reserved. Except under the conditions described in the Copyright Act 1968 of
Australia and subsequent amendments, no part of this publication may be reproduced, stored
in a retrieval system or transmitted in any form or by any means, electronic, mechanical,
photocopying, recording or otherwise, without the written permission of the publishers.
Edited by Ruth Siems Editorial Services
Cover design by FOUNDRY Typography, Design & Visual Dialogue
Text design by Robert Klinkhamer
Typeset by Desktop Concepts P/L, Melbourne
Printed by Shannon Books Pty Ltd
National Library of Australia Cataloguing-in-Publication data:
Tout, Dave, 1950– .
Foundation numeracy in context.
ISBN 0 86431 516 3.
1. Numeracy. I. Motteram, Gary. II. Title.
(Series: MathsWorks for Teachers).
372.72044
Visit our website: www.acerpress.com.au
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C O N T E N T S
Introduction vii
About the authors viii
1
Teaching mathematics in context 1
Introduction 1
Why do we need a different approach? 2
Connections 4
Teaching in context and applied learning 10
So what does this mean for classroom practice? 12
Covering mathematics curriculum content and
designing a program 16
Does it work? 17
Conclusion 19
2
Designing teaching programs 23
Introduction 23
How to plan 23
The teacher role 30
Information and communication technology (ICT) 33
3
Making meaning 35
Introduction 35
Mathematics areas covered 37
Some examples of using texts 42
Possible starting points 46
Resources 48
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Contents
4
Driving away 50
Introduction 50
Mathematics areas covered 50
Possible starting points 52
Example of mathematics skills covered 56
Resources 59
5
Making algebra work 61
Introduction 61
A common approach to teaching algebra at school 62
Introducing and connecting with algebra 63
Mathematics areas covered 64
Extensions 66
Resources 69
6
Cooking mathematics up 72
Introduction 72
Mathematics areas covered 72
Possible starting points 74
Example of mathematics skills covered 78
Resources 82
7
A sporting opportunity 84
Introduction 84
Mathematics areas covered 85
Possible starting points 88
Examples of negotiated investigations 92
Resources 97
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Contents
8
Curriculum connections 99
Appendices 105
A Planning grid 105
B Possible contexts 107
C Sample brainstorm 110
D Mathematics skills example 111
E Resources 112
F Contract for the outline of the investigation 117
G Sample worksheets 118
Notes 144
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I N T R O D U C T I O N
MathsWorks is a series of teacher texts covering various areas of study and
topics relevant to senior secondary mathematics courses. The series has been
specifically developed for teachers to cover helpful mathematical background,
and is written in an informal discussion style.
The series consists of six titles:
(cid:127) An Introduction to Functional Equations
(cid:127) Contemporary Calculus
(cid:127) Matrices
(cid:127) Data Analysis Applications
(cid:127) Foundation Numeracy in Context
(cid:127) Complex Numbers and Vectors
Each text includes historical and background material; discussion of key
concepts, skills and processes; commentary on teaching and learning
approaches; comprehensive illustrative examples with related tables, graphs
and diagrams throughout; references for each chapter (text and web-based);
student activities and sample solution notes; and a bibliography.
The use of technology is incorporated as applicable in each text, and a
general curriculum link between chapters of each text and Australian state
and territory as well as and selected overseas courses is provided.
A Notes section has been provided at the end of the text for teachers to
include their own comments, annotations and observations. It could also be
used to record additional resources, references and websites.
vii
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A B O U T T H E A U T H O R S
David Tout is one of the most experienced adult numeracy educators in
Australia. He is particularly interested in language and mathematics, and
making mathematics relevant, interesting and fun for all students particularly
those students who are disengaged from the subject. David has written a wide
range of teaching, curriculum, assessment and professional development
materials and resources, and has presented on a wide range of topics at
numerous local, regional, national and international conferences and events,
including in Sweden, Japan, Spain, the Netherlands, the USA, Canada and
the UK.
Gary Motteram has over 25 years of classroom teaching experience. He has a
particular interest in developing programs to support numeracy development
in vocational and real-world contexts. Gary has contributed to curriculum and
policy development at local and state levels and has provided professional
development activities for teachers on the incorporation of learning
technologies in classrooms.
viii
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1
CHAPTER
T E A C H I N G M AT H E M AT I C S I N
C O N T E X T
INTRODUCTION
This text describes an approach to teaching mathematics based on applied or
contextualised learning principles. This approach means that teachers teach
mathematics from a contextual and task-based or investigative point of view,
one where mathematics is developed from an actual or modelled situation or
task in which the mathematics is embedded. Investigations and projects are
used as vehicles for learning. Teachers are encouraged to take into account
students’ interests and knowledge, and their own informal ways of doing
mathematics, allowing the understandings and strategies learnt in and out of
school to serve as valid resources.
While primarily targeted at teachers of students who have become
disengaged and/or disenfranchised from learning mathematics successfully
during the middle to latter years of secondary schooling, this approach is also
suitable for students who don’t need formal mathematics as part of their
further education, training or career aspirations. Often these two groups
overlap. Taking an applied learning approach with an emphasis on problem
solving can enable most students to succeed and progress, with students able
to work from the same starting point but then proceed in different directions,
learning and applying different mathematical skills to varying levels of
sophistication. It can be used to engage and motivate students in order for all
of them to succeed in learning and applying mathematics to whatever level
they are capable of—it does not have to be just for students who are
considered to be unsuccessful at mathematics. It will support students to
become numerate and engaged citizens who are capable of using, transferring
and adapting their mathematical knowledge and skills in this era of life-long
learning and change.
1
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