Teaching Mathematics in Primary Schools

by Dole, Shelley; Jorgensen, Robyn

• ISBN13: 9781741757231
• ISBN10: 1741757231
• Edition: 2nd
• Format: Paperback
• Copyright: 2011-07-01
• Publisher: Allen & Unwin

Summary

'Every chapter reeks of intellectual integrity, a strong knowledge of pertinent research literatures, and the wisdom of practice.' - Professor Ken Clements, co-founder of the Mathematics Education Research Group of Australasia 'This is an outstanding book: it should be high on the list of any primary school teacherAEs set of references and a required text for pre-service teachers.' - Kath Truran in Australian Primary Mathematics Classroom Teaching Mathematics in Primary Schools moves beyond traditional lock-step approaches to teaching mathematics to emphasise how students can learn to think mathematically in the new times of globalisation and a technology-rich society. Based on current international research, the book focuses on learning outcomes and the general principles that underlie educational practices rather than any specific curriculum. Current approaches to mathematics education are explained and critiqued, and insights into why some students have difficulties with mathematics are provided. Teachers are shown how to encourage their students to develop deep learning in mathematics, and to relate mathematics to the rest of the curriculum. The authors firstly examine the philosophy behind mathematics and its impact on curriculum design, the history of learning outcomes, and theories on how students learn mathematics. They then present the key areas of mathematics teaching in detail: number, chance and data, measurement, space, and algebra. In each area, the emphasis is on problem-solving. Finally, they discuss practical classroom issues such as the trend towards developing students' capacity to think mathematically, broad approaches to teaching mathematics, planning for a whole school approach to mathematics, diversity and access, and assessment, reporting and evaluation. New material on numeracy, early numbers and fractions has been added to this second edition. It also includes new material on teaching mathematics in the middle years of schooling. With practical activities that can be implemented in the classroom, this book is an invaluable resource for students and teachers.

Author Biography

Shelley Dole (Author) : Robyn Jorgensen (Author) : Robyn Jorgensen (formerly Zevenbergen) is Professor of Education at Griffith University. Shelley Dole is Senior Lecturer in Mathematics Education at the University of Queensland.

Table of Contents

About this book	p. xi
About the authors	p. xiv
The changing face of school mathematics	p. l
Mathematics education and society	p. 1
Teaching mathematics in modern society	p. 2
Mathematics classrooms	p. 3
New models of teaching mathematics	p. 4
Content and pedagogy	p. 6
What is mathematics?	p. 8
Where does mathematics come from?	p. 11
The mathematics curriculum	p. 12
Integrating curriculum	p. 17
Integrating mathematics with other curriculum areas	p. 18
Numeracy	p. 19
Review Questions	p. 20
Further reading	p. 20
References	p. 21
Theories of learning mathematics	p. 23
Why study theories of learning mathematics?	p. 23
Cognitive theories	p. 24
Sociocultural theories: The influence of Vygotsky	p. 27
Socially critical theories	p. 28
Modern society	p. 29
Theory into practice	p. 31
Review questions	p. 32
Further reading	p. 32
References	p. 32
Language and mathematics	p. 34
The language of mathematics	p. 34
Word problems	p. 39
Language error analysis	p. 43
Mathematical literacies	p. 44
Making pedagogy explicit	p. 45
Review questions	p. 46
Further reading	p. 46
References	p. 47
Diversity and equity	p. 49
Equity and equality	p. 50
Cognitive models of difference	p. 51
Social models of difference	p. 52
Teachers' beliefs	p. 53
Home-school differences	p. 55
Knowledge and world-views	p. 58
Implications for school mathematics	p. 60
Review questions	p. 62
Further reading	p. 63
References	p. 63
Planning for teaching	p. 65
Planning	p. 66
Why plan?	p. 67
Planning: What do I want to teach?	p. 68
Teaching: How will I teach?	p. 73
Evaluating teaching: How will I know whether it has been a success?	p. 76
Planning the learning environment	p. 77
Planning for substantive learning	p. 81
Review questions	p. 82
Further reading	p. 82
References	p. 82
Assessment	p. 84
Why assess?	p. 84
Models of assessment	p. 88
What to assess	p. 90
Planning assessment	p. 92
Assessment tools	p. 94
Student writing	p. 104
Tests	p. 105
Rubrics	p. 106
Opening up assessment	p. 107
Communicating results	p. 109
Review questions	p. 110
Further reading	p. 111
References	p. 111
Working mathematically	p. 113
Working and thinking mathematically	p. 113
Problem-solving	p. 115
Problem-posing	p. 122
Technology for thinking mathematically	p. 122
Making connections	p. 124
Communicating mathematically	p. 125
Review questions	p. 128
Further reading	p. 128
References	p. 128
Early number	p. 130
Number sense	p. 130
Pre-number	p. 132
Subitising: Group recognition	p. 133
Counting	p. 134
Conservation of number	p. 137
Number benchmarks	p. 141
Types of numbers	p. 143
Numeration and place value	p. 145
Addition and subtraction	p. 154
Multiplication and division	p. 156
Review questions	p. 158
Further reading	p. 159
References	p. 159
Basic facts and mental computation	p. 161
Working flexibly with number	p. 162
Basic facts of addition	p. 164
Basic facts of subtraction	p. 174
Addition and subtraction: Mental computation	p. 174
Basic facts of multiplication	p. 175
Basic facts of division	p. 183
Mental computation and estimation	p. 184
Promoting mental computation in the middle years	p. 187
Review questions	p. 188
Further reading	p. 189
References	p. 189
Written algorithms	p. 192
The value of concrete materials	p. 193
Principles for using concrete materials	p. 194
The addition algorithm	p. 194
The subtraction algorithm	p. 197
The multiplication algorithm	p. 201
The division algorithm	p. 209
Teaching written algorithms in the middle years	p. 213
Summary	p. 214
Review questions	p. 214
Further reading	p. 215
References	p. 215
Rational number	p. 216
Common and decimal fractions	p. 216
Whole number and rational number connections	p. 217
Fractions	p. 218
Decimals	p. 229
Ratio and proportion	p. 234
Promoting language and mental images of ratio and proportion	p. 239
Rate	p. 245
Per cent	p. 247
Teaching rational number in the middle years	p. 254
Summary	p. 255
Review questions	p. 255
Further reading	p. 255
References	p. 256
Patterns and algebra	p. 258
Patterning	p. 259
Number, arithmetic and algebra	p. 267
The importance of algebra in the primary school	p. 271
Teaching algebra in the middle years	p. 272
Review questions	p. 272
Further reading	p. 273
References	p. 273
Measurement	p. 275
What is measurement?	p. 275
Teaching measurement	p. 281
Length	p. 289
Area	p. 291
Volume and capacity	p. 293
Mass	p. 295
Time	p. 296
Temperature	p. 300
Money	p. 300
Making connections between sub-strands	p. 301
Teaching measurement in the middle years	p. 304
Review questions	p. 305
Further reading	p. 306
References	p. 306
Chance and data	p. 307
What are chance and data?	p. 307
Teaching chance	p. 310
Data collection, representation and interpretation	p. 317
Measures of central tendency	p. 329
Statistical literacy: Interpretation of data representations	p. 331
Teaching notes for graphing	p. 332
Teaching chance and data in the middle years	p. 335
Review questions	p. 337
Further reading	p. 337
References	p. 338
Space	p. 339
Topics in the space strand	p. 340
Visualisation	p. 340
The van Hiele levels of geometric thinking	p. 341
Teaching notes	p. 343
Spatial concepts: Early activities	p. 344
Shape and structure	p. 345
Transformation and symmetry	p. 352
Location and arrangement	p. 361
Teaching space in the middle years	p. 367
Review questions	p. 368
Further reading	p. 369
References	p. 370
Index	p. 373
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