Modelling and Applications in Mathematics Education (eBook)
XIV, 524 Seiten
Springer US (Verlag)
978-0-387-29822-1 (ISBN)
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.
Among the themes that have been central to mathematics education dur- ing the last 30 years are those of mathematical modelling and applications of mathematics to extra-mathematical fields. More generally we refer to these as relations between mathematics and the extra-mathematical world (some- times also called the "e;real world"e;) or preferably, according to Henry PoUak, the "e;rest of the world"e;. That applications and modelling have been important themes in mathematics education can be inferred from the wealth of litera- ture on these topics, including material generated from a multitude of na- tional and international conferences. In particular let us mention firstly the ICMEs (the International Congresses on Mathematical Education), with their regular working or topic groups and lectures on applications and modelling; and secondly the series of ICTMAs (the International Conferences on the Teaching of Mathematical Modelling and Applications) which have been held biennially since 1983. Their Proceedings and Survey Lectures, have addressed the state-of-the-art at the relevant time, and contain many exam- ples, studies, conceptual contributions and resources involving relations between the real world and mathematics, for all levels of the educational system. In curricula and textbooks we find today many more references to real world phenomena and problems than, say, twenty years ago.
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?
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
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
| Erscheint lt. Verlag | 5.12.2007 |
|---|---|
| Reihe/Serie | New ICMI Study Series |
| Zusatzinfo | XIV, 524 p. |
| Verlagsort | New York |
| Sprache | englisch |
| Themenwelt | Geisteswissenschaften |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Sozialwissenschaften ► Pädagogik ► Erwachsenenbildung | |
| Sozialwissenschaften ► Pädagogik ► Schulpädagogik / Grundschule | |
| Technik | |
| Schlagworte | Evaluation • ICMI • Mathematics • mathematics education • Modelling • NISS • Statistics |
| ISBN-10 | 0-387-29822-3 / 0387298223 |
| ISBN-13 | 978-0-387-29822-1 / 9780387298221 |
| Haben Sie eine Frage zum Produkt? |
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