Modelling and Applications in Mathematics Education - The 14th ICMI Study

Modelling and Applications in Mathematics Education - The 14th ICMI Study

von: Peter L. Galbraith, Hans-Wolfgang Henn, Mogens Niss

Springer-Verlag, 2007

ISBN: 9780387298221 , 524 Seiten

Format: PDF

Kopierschutz: Wasserzeichen

Windows PC,Mac OSX Apple iPad, Android Tablet PC's

Preis: 130,89 EUR

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Modelling and Applications in Mathematics Education - The 14th ICMI Study


 

TABLE OF CONTENTS

6

PREFACE

12

INTRODUCTION

16

Part 1 INTRODUCTION

17

PLENARIES

47

Chapter 2.1 LESS CHALK, LESS WORDS, LESS SYMBOLS... MORE OBJECTS, MORE CONTEXT, MORE ACTIONS

48

Chapter 2.2 WHAT'S ALL THE FUSS ABOUT COMPETENCIES?

58

Chapter 2.3 A THEORY OF MATHEMATICAL MODELLING IN TECHNOLOGICAL SETTINGS

70

Chapter 2.4 WHAT KNOWLEDGE DO TEACHERS NEED FOR TEACHING MATHEMATICS THROUGH APPLICATIONS AND MODELLING?

82

Chapter 2.5 BEYOND THE LOW HANGING FRUIT

92

Chapter 2.6 MODELLING FOR LIFE: MATHEMATICS AND CHILDREN'S EXPERIENCE

102

Chapter 2.7 MODELLING IN LOWER SECONDARY MATHEMATICS CLASSROOM - PROBLEMS AND OPPORTUNITIES

112

Chapter 2.8 MATHEMATICAL MODELLING - A CONVERSATION WITH HENRY POLLAK

122

ISSUES IN APPLICATIONS AND MODELLING

134

Section 3.1 EPISTEMOLOGY AND MODELLING

135

Chapter 3.1.0 EPISTEMOLOGY AND MODELLING - OVERVIEW

136

Chapter 3.1.1 MODELLING BODY MOTION: AN APPROACH TO FUNCTIONS USING MEASURING INSTRUMENTS

140

Chapter 3.1.2 EMERGENT MODELLING AS A PRECURSOR TO MATHEMATICAL MODELLING

148

Chapter 3.1.3 PROVING AND MODELLING

156

Chapter 3.1.4 A DEVELOPMENTAL APPROACH FOR SUPPORTING THE EPISTEMOLOGY OF MODELING

164

Chapter 3.1.5 WHAT IS DISTINCTIVE IN ( OUR VIEWS ABOUT) MODELS & MODELLING PERSPECTIVES ON MATHEMATICS PROBLEM SOLVING, LEARNING, AND TEACHING?

172

Chapter 3.1.6 EVERYDAY INSTRUMENTS: ON THE USE OF MATHEMATICS

182

Section 3.2 AUTHENTICITY AND GOALS

190

Chapter 3.2.0 AUTHENTICITY AND GOALS - OVERVIEW

191

Chapter 3.2.1 HOW TO REPLACE WORD PROBLEMS WITH ACTIVITIES OF REALISTIC MATHEMATICAL MODELLING

195

Chapter 3.2.2 THE RELEVANCE OF MODELLING AND APPLICATIONS: RELEVANT TO WHOM AND FOR WHAT PURPOSE?

203

Chapter 3.2.3 FEATURES AND IMPACT OF THE AUTHENTI-CITY OF APPLIED MATHEMATICAL SCHOOL TASKS

211

Chapter 3.2.4 ELEMENTARY MODELLING IN MATHEMATICSLESSONS: THE INTERPLAY BETWEEN "REAL-WORLD" KNOWLEDGE AND "MATHEMATICAL STRUCTURES"

219

Section 3.3 MODELLING COMPETENCIES

227

Chapter 3.3.0 MODELLING COMPETENCIES - OVERVIEW

228

Chapter 3.3.1 LEVELS OF MODELLING COMPETENCIES

234

Chapter 3.3.2 MODELLING BOTH COMPLEXITY AND ABSTRACTION: A PARADOX?

242

Chapter 3.3.3 STUDYING AND REMEDYING STUDENTS' MODELLING COMPETENCIES: ROUTINE BEHAVIOUR OR ADAPTIVE EXPERTISE

250

Chapter 3.3.4 ASSESSING THE " PHASES" OF MATHEMATICAL MODELLING

258

Chapter 3.3.5 THE ARITHMETIC OPERATIONS AS MATHEMATICAL MODELS

266

Section 3.4 APPLICATIONS & MODELLING FOR MATHEMATICS

274

Chapter 3.4.0 APPLICATIONS AND MODELLING FOR MATHEMATICS - OVERVIEW

275

Chapter 3.4.1 THE ROLES OF MODELLING IN LEARNING MATHEMATICS

283

Chapter 3.4.2 DEVELOPING MATHEMATICAL LITERACY

293

Chapter 3.4.3 CLASSROOM ACTIVITIES AND THE TEACHER

303

Chapter 3.4.4 USES OF TECHNOLOGIES IN LEARNING MATHEMATICS THROUGH MODELLING

317

Section 3.5 MODELLING PEDAGOGY

327

Chapter 3.5.0 MODELLING PEDAGOGY - OVERVIEW

328

Chapter 3.5.1 MATHEMATICAL MODELLING IN HIGH SCHOOL MATHEMATICS: TEACHERS' THINKING AND PRACTICE

332

Chapter 3.5.2 MATHEMATICAL MODELLING IN TEACHER EDUCATION - NECESSITY OR UNNECESSARILY

340

Chapter 3.5.3 BUILDING CONCEPTS AND CONCEPTIONS IN TECHNOLOGY-BASED OPEN LEARNING ENVIRONMENTS

348

Chapter 3.5.4 TOWARDS A WIDER IMPLEMENTATION OF MATHEMATICAL MODELLING AT UPPER SECONDARY AND TERTIARY LEVELS

356

Chapter 3.5.5 HOW MIGHT WE SHARE MODELS THROUGH COOPERATIVE MATHEMATICAL MODELLING? FOCUS ON SITUATIONS BASED ON INDIVIDUAL EXPERIENCES

364

Section 3.6 IMPLEMENTATION AND PRACTICE

372

Chapter 3.6.0 IMPLEMENTATION AND PRACTICE - OVERVIEW

373

Chapter 3.6.1 SOME CONDITIONS FOR MODELLING TO EXIST IN MATHEMATICS CLASSROOMS

377

Chapter 3.6.2 PICTURE ( IM)PERFECT MATHEMATICS!

385

Chapter 3.6.3 LEARNING MATHEMATICAL MODELLING - FROM THE PERSPECTIVE OF PROBABILITY AND STATISTICS EDUCATION

393

Chapter 3.6.4 CONSIDERING WORKPLACE ACTIVITY FROM A MATHEMATICAL MODELLING PERSPECTIVE

401

Section 3.7 ASSESSMENT AND EVALUATION

409

Chapter 3.7.0 ASSESSMENT AND EVALUATION - OVERVIEW

410

Chapter 3.7.1 MODELLING BASED PROJECT EXAMINATION

414

Chapter 3.7.2 MATHEMATICAL MODELLING AND APPLICATIONS: ABILITY AND COMPETENCE FRAMEWORKS

422

Chapter 3.7.3 "TO MODEL, OR TO LET THEM MODEL?" THAT IS THE QUESTION!

430

Chapter 3.7.4 MODELLING AND APPLICATIONS IN PISA

438

Chapter 3.7.5 ASSESSMENT OF APPLIED MATHEMATICS AND MODELLING: USING A LABORATORY LIKE ENVIRONMENT

446

EDUCATIONAL LEVELS

454

Chapter 4.1 MODELLING AND APPLICATIONS IN PRIMARY EDUCATION

455

Chapter 4.2 POSSIBILITIES FOR, AND OBSTACLES TO TEACHING APPLICATIONS AND MODELLING IN THE LOWER SECONDARY LEVELS

461

Chapter 4.3 UPPER SECONDARY PERSPECTIVES ON APPLICATIONS AND MODELLING

467

Chapter 4.4 TEACHING APPLICATIONS AND MODELLING AT TERTIARY LEVEL

473

Chapter 4.5 MODELLING IN TEACHER EDUCATION

479

CASES IN APPLICATIONS AND MODELLING

487

Chapter 5.1 MOVING THE CONTEXT OF MODELLING TO THE FOREFRONT: PRESERVICE TEACHERS' INVESTIGATIONS OF EQUITY IN TESTING

488

Chapter 5.2 MODELLING IN ONTARIO: SUCCESS IN MOVING ALONG THE CONTINUUM

494

Chapter 5.3 IMPLEMENTATION CASE STUDY: SUSTAINING CURRICULUM CHANGE

500

Chapter 5.4 MATHEMATICAL MODELLING OF SOCIAL ISSUES IN SCHOOL MATHEMATICS IN SOUTH AFRICA

506

BIBLIOGRAPHY

514

INDEX

520