Understanding and teaching primary mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London ; New York
Routledge, Taylor & Francis Group
2021
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| Ausgabe: | Fourth edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xx, 327 Seiten Illustrationen 26 cm |
| ISBN: | 9780367332051 9780367332044 |
Internformat
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Datensatz im Suchindex
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| adam_text | Preface to the fourth edition Acknowledgements Chapter 1 ! Chapter 2 1 ! Chapter 3 xiii xx Teaching and learning primary mathematics 1 ì i Introduction Starting point Why is mathematical subject knowledge important? What is good mathematical subject knowledge? What makes a good teacher of mathematics? How will this book develop my subject knowledge? A framework for teaching mathematics Foundations for learning mathematics 1 2 3 4 5 6 Organisation of the book The companion website Summary 7 8 9 11 11 What should 1 know? What do 1 know? 13 ! Introduction Starting point Auditing your current knowledge Summary Going further 13 13 14 23 24 Recent developments in mathematics teaching: teaching for mastery 25 ¡ Introduction 25 A history of teaching for mastery From the research 25 26 f vii
Contents Developing teaching for mastery in your classroom Chapter 4 Summary Going further 28 36 36 Problem solving using mathematics 39 Introduction Progression in problem solving using mathematics 39 42 44 Big ideas Teaching points Summary Reflections on this chapter Going further 49 59 60 62 62 63 64 64 Self-audit 66 Counting: place value; fractions, decimals and percentages 68 Introduction 68 Starting point Progression in counting; place value; fractions, decimals, percentages; and proportionality Big ideas Teaching points In practice Rationale and evaluation Observing counting and understanding number Assessing counting and understanding number A cross-curricular project involving counting and understanding number Summary Reflections on this chapter Going further Self-audit 69 In practice Rationale and evaluation Assessing problem solving using mathematics Cross-curricular teaching of problem solving ! Chapter 5 1! 1 viii 70 72 82 98 1OO 10O 101 102 102 103 103 105
Contents Chapter 6 Knowing and using number facts 108 ! 1 Introduction Starting point Progression in knowing and using number facts Big ideas Teaching points 108 109 111 113 119 125 127 In practice Rationale and evaluation Observing the teaching of knowing and using number facts Assessing knowing and using number facts Cross-curricular teaching of knowing and using number facts Summary ! Chapter 7 128 129 Reflections on this chapter Going further Self-audit 130 131 132 Calculation: addition, subtraction, multiplication and division 133 ! Introduction Starting point Progression in calculation Big ideas Teaching points In practice Rationale and evaluation Observing the teaching of calculation Assessing calculation Cross-curricular teaching of calculation Summary 1 ! Chapter 8 127 128 133 134 137 139 160 165 166 167 167 168 168 Reflections on this chapter Going further Self-audit 169 169 171 Algebra 172 ì 1 Introduction Starting point 172 173 ix
Contents ! Chapter 9 ¡ Progression in algebra 175 Big idea Using Cuisenaire rods to develop algebraic thinking 177 Teaching points 182 In practice 186 Rationale and evaluation 186 Observing algebra 188 Assessing algebra 189 Cross-curricular teaching of algebra 189 Summary 189 Reflections on this chapter 190 Going further 190 Self-audit 191 Geometry: properties of shapes; position and direction 193 I Introduction 193 Starting point 193 Progression in geometry 198 Big ideas 200 Teaching points 206 In practice 215 Rationale and evaluation 216 Observing geometry 217 Assessing geometry 217 Cross-curricular teaching of geometry Summary 218 Reflections on this chapter 220 Going further 221 Self-audit 222 ! Chapter 10 Measurement x 180 219 223 Introduction 223 Starting point 224 Progression in measuring Big ideas 225 228
Contents Teaching points In practice Rationale and evaluation Observing teaching measurement Assessing understanding of measurement Cross-curricular teaching of measurement Summary Reflections on this chapter Going further Self-audit Chapter 11 Statistics and handling data Introduction Starting point Progression in statistics and handling data Big ideas Teaching points In practice Rationale and evaluation Observing the teaching of statistics and handling data Assessing knowledge of statistics and handling data Cross-curricular teaching of statistics and handling data Summary Reflections on this chapter Going further Self-audit Chapter 12 Teaching and learning mathematics in the early years Introduction Starting point Problem solving, reasoning and numeracy Young children learning number Young children learning measures Young children learning shape and space Young children learning algebra 229 236 238 239 240 240 241 241 242 242 244 ! 1 244 245 246 248 254 259 260 261 261 262 262 263 263 264 265 i 265 267 269 271 275 277 280
Contents Creating a mathematically rich environment 282 Assessment in the early years 284 Observing teaching in the early years 286 Summary Reflections on this chapter 287 Going further 287 Chapter 13 Issues of inclusion 289 Introduction 289 Starting point 290 Children with special educational needs 293 Children learning English as an Additional Language (EAL) Children with social, emotional and mental health needs 294 296 Children with autism 297 Children with Developmental Coordination Disorder (DCD or dyspraxia) 298 Children with dyslexia 299 Children with dyscalculia 300 Children who are gifted and talented 300 Multicultural and anti-racist approaches 302 Observing inclusive mathematics teaching 304 Summary 304 Reflections on this chapter 305 Going further 305 Chapter 14 ICT and the use of calculators in teaching and learning mathematics xii 287 307 Introduction 307 Starting point 307 Progression in using calculators 309 The appropriate use of personal computers and other devices 313 Summary 316 Reflections on this chapter Going further 316 Glossary Index 318 323 317
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| adam_txt |
Preface to the fourth edition Acknowledgements Chapter 1 ! Chapter 2 1 ! Chapter 3 xiii xx Teaching and learning primary mathematics 1 ì i Introduction Starting point Why is mathematical subject knowledge important? What is good mathematical subject knowledge? What makes a good teacher of mathematics? How will this book develop my subject knowledge? A framework for teaching mathematics Foundations for learning mathematics 1 2 3 4 5 6 Organisation of the book The companion website Summary 7 8 9 11 11 What should 1 know? What do 1 know? 13 ! Introduction Starting point Auditing your current knowledge Summary Going further 13 13 14 23 24 Recent developments in mathematics teaching: teaching for mastery 25 ¡ Introduction 25 A history of teaching for mastery From the research 25 26 f vii
Contents Developing teaching for mastery in your classroom Chapter 4 Summary Going further 28 36 36 Problem solving using mathematics 39 Introduction Progression in problem solving using mathematics 39 42 44 Big ideas Teaching points Summary Reflections on this chapter Going further 49 59 60 62 62 63 64 64 Self-audit 66 Counting: place value; fractions, decimals and percentages 68 Introduction 68 Starting point Progression in counting; place value; fractions, decimals, percentages; and proportionality Big ideas Teaching points In practice Rationale and evaluation Observing counting and understanding number Assessing counting and understanding number A cross-curricular project involving counting and understanding number Summary Reflections on this chapter Going further Self-audit 69 In practice Rationale and evaluation Assessing problem solving using mathematics Cross-curricular teaching of problem solving ! Chapter 5 1! 1 viii 70 72 82 98 1OO 10O 101 102 102 103 103 105
Contents Chapter 6 Knowing and using number facts 108 ! 1 Introduction Starting point Progression in knowing and using number facts Big ideas Teaching points 108 109 111 113 119 125 127 In practice Rationale and evaluation Observing the teaching of knowing and using number facts Assessing knowing and using number facts Cross-curricular teaching of knowing and using number facts Summary ! Chapter 7 128 129 Reflections on this chapter Going further Self-audit 130 131 132 Calculation: addition, subtraction, multiplication and division 133 ! Introduction Starting point Progression in calculation Big ideas Teaching points In practice Rationale and evaluation Observing the teaching of calculation Assessing calculation Cross-curricular teaching of calculation Summary 1 ! Chapter 8 127 128 133 134 137 139 160 165 166 167 167 168 168 Reflections on this chapter Going further Self-audit 169 169 171 Algebra 172 ì 1 Introduction Starting point 172 173 ix
Contents ! Chapter 9 ¡ Progression in algebra 175 Big idea Using Cuisenaire rods to develop algebraic thinking 177 Teaching points 182 In practice 186 Rationale and evaluation 186 Observing algebra 188 Assessing algebra 189 Cross-curricular teaching of algebra 189 Summary 189 Reflections on this chapter 190 Going further 190 Self-audit 191 Geometry: properties of shapes; position and direction 193 I Introduction 193 Starting point 193 Progression in geometry 198 Big ideas 200 Teaching points 206 In practice 215 Rationale and evaluation 216 Observing geometry 217 Assessing geometry 217 Cross-curricular teaching of geometry Summary 218 Reflections on this chapter 220 Going further 221 Self-audit 222 ! Chapter 10 Measurement x 180 219 223 Introduction 223 Starting point 224 Progression in measuring Big ideas 225 228
Contents Teaching points In practice Rationale and evaluation Observing teaching measurement Assessing understanding of measurement Cross-curricular teaching of measurement Summary Reflections on this chapter Going further Self-audit Chapter 11 Statistics and handling data Introduction Starting point Progression in statistics and handling data Big ideas Teaching points In practice Rationale and evaluation Observing the teaching of statistics and handling data Assessing knowledge of statistics and handling data Cross-curricular teaching of statistics and handling data Summary Reflections on this chapter Going further Self-audit Chapter 12 Teaching and learning mathematics in the early years Introduction Starting point Problem solving, reasoning and numeracy Young children learning number Young children learning measures Young children learning shape and space Young children learning algebra 229 236 238 239 240 240 241 241 242 242 244 ! 1 244 245 246 248 254 259 260 261 261 262 262 263 263 264 265 i 265 267 269 271 275 277 280
Contents Creating a mathematically rich environment 282 Assessment in the early years 284 Observing teaching in the early years 286 Summary Reflections on this chapter 287 Going further 287 Chapter 13 Issues of inclusion 289 Introduction 289 Starting point 290 Children with special educational needs 293 Children learning English as an Additional Language (EAL) Children with social, emotional and mental health needs 294 296 Children with autism 297 Children with Developmental Coordination Disorder (DCD or dyspraxia) 298 Children with dyslexia 299 Children with dyscalculia 300 Children who are gifted and talented 300 Multicultural and anti-racist approaches 302 Observing inclusive mathematics teaching 304 Summary 304 Reflections on this chapter 305 Going further 305 Chapter 14 ICT and the use of calculators in teaching and learning mathematics xii 287 307 Introduction 307 Starting point 307 Progression in using calculators 309 The appropriate use of personal computers and other devices 313 Summary 316 Reflections on this chapter Going further 316 Glossary Index 318 323 317 |
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| spellingShingle | Cotton, Tony 19XX- Understanding and teaching primary mathematics Mathematics / Study and teaching (Elementary) Mathematics / Study and teaching (Elementary) fast Mathematik Grundschule (DE-588)4022349-8 gnd Mathematikunterricht (DE-588)4037949-8 gnd |
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| title_fullStr | Understanding and teaching primary mathematics Tony Cotton |
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| title_short | Understanding and teaching primary mathematics |
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