: Werner Blum, Peter L. Galbraith, Hans-Wolfgang Henn, Mogens Niss
: Peter L. Galbraith, Hans-Wolfgang Henn, Mogens Niss
: Modelling and Applications in Mathematics Education The 14th ICMI Study
: Springer-Verlag
: 9780387298221
: 1
: CHF 100.50
:
: Schulpädagogik, Didaktik, Methodik
: English
: 524
: Wasserzeichen
: PC/MAC/eReader/Tablet
: PDF

The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.
TABLE OF CONTENTS6
PREFACE12
INTRODUCTION16
Part 1 INTRODUCTION17
PLENARIES47
Chapter 2.1 LESS CHALK, LESS WORDS, LESS SYMBOLS... MORE OBJECTS, MORE CONTEXT, MORE ACTIONS48
Chapter 2.2 WHAT'S ALL THE FUSS ABOUT COMPETENCIES?58
Chapter 2.3 A THEORY OF MATHEMATICAL MODELLING IN TECHNOLOGICAL SETTINGS70
Chapter 2.4 WHAT KNOWLEDGE DO TEACHERS NEED FOR TEACHING MATHEMATICS THROUGH APPLICATIONS AND MODELLING?82
Chapter 2.5 BEYOND THE LOW HANGING FRUIT92
Chapter 2.6 MODELLING FOR LIFE: MATHEMATICS AND CHILDREN'S EXPERIENCE102
Chapter 2.7 MODELLING IN LOWER SECONDARY MATHEMATICS CLASSROOM - PROBLEMS AND OPPORTUNITIES112
Chapter 2.8 MATHEMATICAL MODELLING - A CONVERSATION WITH HENRY POLLAK122
ISSUES IN APPLICATIONS AND MODELLING134
Section 3.1 EPISTEMOLOGY AND MODELLING135
Chapter 3.1.0 EPISTEMOLOGY AND MODELLING - OVERVIEW136
Chapter 3.1.1 MODELLING BODY MOTION: AN APPROACH TO FUNCTIONS USING MEASURING INSTRUMENTS140
Chapter 3.1.2 EMERGENT MODELLING AS A PRECURSOR TO MATHEMATICAL MODELLING148
Chapter 3.1.3 PROVING AND MODELLING156
Chapter 3.1.4 A DEVELOPMENTAL APPROACH FOR SUPPORTING THE EPISTEMOLOGY OF MODELING164
Chapter 3.1.5 WHAT IS DISTINCTIVE IN ( OUR VIEWS ABOUT) MODELS164
172164
Chapter 3.1.6 EVERYDAY INSTRUMENTS: ON THE USE OF MATHEMATICS182
Section 3.2 AUTHENTICITY AND GOALS190
Chapter 3.2.0 AUTHENTICITY AND GOALS - OVERVIEW191
Chapter 3.2.1 HOW TO REPLACE WORD PROBLEMS WITH ACTIVITIES OF REALISTIC MATHEMATICAL MODELLING195
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 TASKS211
Chapter 3.2.4 ELEMENTARY MODELLING IN MATHEMATICSLESSONS: THE INTERPLAY BETWEEN211
Chapter 3.2.4 ELEMENTARY MODELLING IN MATHEMATICSLESSONS: THE INTERPLAY BETWEEN211
Chapter 3.2.4 ELEMENTARY MODELLING IN MATHEMATICSLESSONS: THE INTERPLAY BETWEEN211
Chapter 3.2.4 ELEMENTARY MODELLING IN MATHEMATICSLESSONS: THE INTERPLAY BETWEEN211
219211
Section 3.3 MODELLING COMPETENCIES227
Chapter 3.3.0 MODELLING COMPETENCIES - OVERVIEW228
Chapter 3.3.1 LEVELS OF MODELLING COMPETENCIES234
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 EXPERTISE250
Chapter 3.3.4 ASSESSING THE250
Chapter 3.3.4 ASSESSING THE250
258250
Chapter 3.3.5 THE ARITHMETIC OPERATIONS AS MATHEMATICAL MODELS266
Section 3.4 APPLICATIONS266
274266
Chapter 3.4.0 APPLICATIONS AND MODELLING FOR MATHEMATICS - OVERVIEW275
Chapter 3.4.1 THE ROLES OF MODELLING IN LEARNING MATHEMATICS283
Chapter 3.4.2 DEVELOPING MATHEMATICAL LITERACY293
Chapter 3.4.3 CLASSROOM ACTIVITIES AND THE TEACHER303
Chapter 3.4.4 USES OF TECHNOLOGIES IN LEARNING MATHEMATICS THROUGH MODELLING317
Section 3.5 MODELLING PEDAGOGY327
Chapter 3.5.0 MODELLING PEDAGOGY - OVERVIEW328
Chapter 3.5.1 MATHEMATICAL MODELLING IN HIGH SCHOOL MATHEMATICS: TEACHERS' THINKING AND PRACTICE332
Chapter 3.5.2 MATHEMATICAL MODELLING IN TEACHER EDUCATION - NECESSITY OR UNNECESSARILY340
Chapter 3.5.3 BUILDING CONCEPTS AND CONCEPTIONS IN TECHNOLOGY-BASED OPEN LEARNING ENVIRONMENTS348
Chapter 3.5.4 TOWARDS A WIDER IMPLEMENTATION OF MATHEMATICAL MODELLING AT UPPER SECONDARY AND TERTIARY LEVELS356
Chapter 3.5.5 HOW MIGHT WE SHARE MODELS THROUGH COOPERATIVE MATHEMATICAL MODELLING? FOCUS ON SITUATIONS BASED ON INDIVIDUAL EXPERIENCES364
Section 3.6 IMPLEMENTATION AND PRACTICE372
Chapter 3.6.0 IMPLEMENTATION AND PRACTICE - OVERVIEW373
Chapter 3.6.1 SOME CONDITIONS FOR MODELLING TO EXIST IN MATHEMATICS CLASSROOMS377
Chapter 3.6.2 PICTURE ( IM)PERFECT MATHEMATICS!385
Chapter 3.6.3 LEARNING MATHEMATICAL MODELLING - FROM THE PERSPECTIVE OF PROBABILITY AND STATISTICS EDUCATION393
Chapter 3.6.4 CONSIDERING WORKPLACE ACTIVITY FROM A MATHEMATICAL MODELLING PERSPECTIVE401
Section 3.7 ASSESSMENT AND EVALUATION409
Chapter 3.7.0 ASSESSMENT AND EVALUATION - OVERVIEW410
Chapter 3.7.1 MODELLING BASED PROJECT EXAMINATION414
Chapter 3.7.2 MATHEMATICAL MODELLING AND APPLICATIONS: ABILITY AND COMPETENCE FRAMEWORKS422
Chapter 3.7.3422
Chapter 3.7.3422
430422
Chapter 3.7.4 MODELLING AND APPLICATIONS IN PISA438
Chapter 3.7.5 ASSESSMENT OF APPLIED MATHEMATICS AND MODELLING: USING A LABORATORY LIKE ENVIRONMENT446
EDUCATIONAL LEVELS454
Chapter 4.1 MODELLING AND APPLICATIONS IN PRIMARY EDUCATION455
Chapter 4.2 POSSIBILITIES FOR, AND OBSTACLES TO TEACHING APPLICATIONS AND MODELLING IN THE LOWER SECONDARY LEVELS461
Chapter 4.3 UPPER SECONDARY PERSPECTIVES ON APPLICATIONS AND MODELLING467
Chapter 4.4 TEACHING APPLICATIONS AND MODELLING AT TERTIARY LEVEL473
Chapter 4.5 MODELLING IN TEACHER EDUCATION479
CASES IN APPLICATIONS AND MODELLING487
Chapter 5.1 MOVING THE CONTEXT OF MODELLING TO THE FOREFRONT: PRESERVICE TEACHERS' INVESTIGATIONS OF EQUITY IN TESTING488
Chapter 5.2 MODELLING IN ONTARIO: SUCCESS IN MOVING ALONG THE CONTINUUM494
Chapter 5.3 IMPLEMENTATION CASE STUDY: SUSTAINING CURRICULUM CHANGE500
Chapter 5.4 MATHEMATICAL MODELLING OF SOCIAL ISSUES IN SCHOOL MATHEMATICS IN SOUTH AFRICA506
BIBLIOGRAPHY514
INDEX520