Suchen und Finden
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
Preis: 106,99 EUR
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
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