Werner Blum, Peter L. Galbraith, Hans-Wolfgang Henn, Mogens NissSpringer-Verlag | 2006 | 515 páginas | 22 MB
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Referência em: MathEduc
The overall goal of Modelling and Applications in Mathematics Education is to provide a comprehensive overview of the state-of-the-art in the field of modelling and applications in mathematics education. Key issues are dealt with, among which are the following:
Epistemology and the relationships between mathematics and the "rest of the world"; the meaning of mathematical modelling and its process components; the respect in which the distinction between pure mathematics and applications of mathematics make sense
Authenticity and Goals dealing with modelling and applications in mathematics teaching; appropriate balance between modelling activities and other mathematical activities; the role that authentic problem situations play in modelling and applications activities
Modelling Competencies: characterizing how a student's modelling competency can be characterized; identifiable sub-competencies, and the ways they constitute a general modelling competency; developing competency over time
Mathematical Competencies: identifying the most important mathematical competencies that students should acquire, and how modelling and applications activities can contribute toward building up these competencies; the meaning of "Mathematical Literacy" in relation to modelling
Modelling Pedagogy: appropriate pedagogical principles and strategies for the development of modelling courses and their teaching; the role of technology in the teaching of modelling and applications
Implementation and Practice: the role of modelling and applications in everyday mathematics teaching; major impediments and obstacles; advancing the use of modelling examples in everyday classrooms; documenting successful implementation of modelling in mathematics teaching
Assessment and Evaluation: assessment modes that capture the essential components of modelling competency; modes available for modelling and applications courses and curricula; appropriate strategies to implement new assessment and evaluation modes in practice
The contributing authors are eminent members of the mathematics education community. Modelling and Applications in Mathematics Education will be of special interest to mathematics educators, teacher educators, researchers, education administrators, curriculum developers and student teachers.
PREFACE xi
1 INTRODUCTION 1
1 MOGENS NISS, WERNER BLUM & PETER GALBRAITH 3
Introduction
2 PLENARIES 33
2.1 CLAUDI ALSINA 35
Less chalk, less words, less symbols ... more objects, more context, more actions
2.2 MORTEN BLOMH0J & TOMAS HOJGAARD JENSEN 45
What's all the fuss about competencies?
2.3 JERE CONFREY & ALAN MALONEY 57
A theory of mathematical modelling in technological settings
2.4 HELEN M. DOERR 69
What knowledge do teachers need for teaching mathematics through applications and modelling?
2.5 PETER GALBRAITH 79
Beyond the low hanging fruit
2.6 BRIAN GREER, LIEVEN VERSCHAFFEL & 89
SWAPNA MUKHOPADHYAY
Modelling for life: Mathematics and children's experience
2.7 GABRIELE KAISER & KATJA MAASS 99
Modelling in lower secondary mathematics classroom - problems and opportunities
2.8 HENRY POLLAK 109
Mathematical modelling - A conversation with Henry Pollak
3 ISSUES IN APPLICATIONS AND MODELLING 121
3.1 EPISTEMOLOGY AND MODELLING 123
3.1.0 JERECONFREY 125
Epistemology and modelling - overview
3.1.1 FERDINANDO ARZARELLO, GIOVANNI PEZZI & ORNELLA ROBUTTI
Modelling body motion: An approach to functions using measuring instruments
3.1.2 KOENO GRAVEMEIJER 137
Emergent modelling as a precursor to mathematical modelling
3.1.3 GILA HANNA & HANS NIELS JAHNKE 145
Proving and modelling
3.1.4 RICHARD LEHRER & LEONA SCHAUBLE 153
A developmental approach for supporting the epistemology of modelling
3.1.5 RICHARD LESH & CAROLINE YOON 161
What is distinctive in (our views about) models and modelling perspectives on mathematics problem solving, learning, and teaching?
3.1.6 RUDOLF STRASSER 171
Everyday instruments: On the use of mathematics
3.2 AUTHENTICITY AND GOALS 179
3.2.0 PETER GALBRAITH 181
Authenticity and Goals - overview
3.2.1 CINZIA BONOTTO 185
How to replace word problems with activities of realistic mathematical modelling
3.2.2 EVA JABLONKA 193
The relevance of modelling and applications: Relevant to whom and for what purpose?
3.2.3 TORULF PALM 201
Features and impact of the authenticity of appHed mathematical school tasks
3.2.4 RALPH SCHWARZKOPF 209
Elementary modelling in mathematics lessons: The interplay between "real-world" knowledge and "mathematical structures"
3.3 MODELLING COMPETENCIES 217
3.3.0 BRIAN GREER & LiEVEN VERSCHAFFEL 219
Modelling compentencies - overview
3.3.1 HERBERT HENNING & MIKE KEUNE 225
Levels of modelling competencies
3.3.2 MIHAELA SINGER 233
Modelling both complexity and abstraction: A paradox?
3.3.3 DIRK DE BOCK, WIM VAN DOOREN & DIRK JANSSENS 241
Studying and remedying students' modelling competencies: Routine behaviour or adaptive expertise
3.3.4 KEN HOUSTON 249
Assessing the "phases" of mathematical modelling
3.3.5 ZALMAN USISKIN 257
The arithmetic operations as mathematical models
3.4 APPLICATIONS & MODELLING FOR MATHEMATICS 265
3.4.0 ERIC MULLER & HUGH BURKHARDT 267
Applications and modelling for mathematics - overview
3.4.1 MALCOLM SWAN, ROSS TURNER & CAROLINE YOON, WITH ERIC MULLER
The roles of modelling in learning mathematics
3.4.2 LYNN ARTHUR STEEN & Ross TURNER WITH HUGH BURKHARDT
Developing mathematical literacy
3.4.3 S0REN ANTONIUS , CHRIS HAINES, THOMAS HOJGAARD JENSEN & MOGENS NiSS WITH HUGH BURKHARDT
Classroom activities and the teacher
3.4.4 DANIEL PEAD & BILL RALPH WITH ERIC MULLER 309
Uses of technologies in learning mathematics through modelling
3.5 MODELLING PEDAGOGY 319
3.5.0 HANS-WOLFGANG HENN 321
Modelling pedagogy - overview
3.5.1 OLIVE CHAPMAN 325
Mathematical modelling in high school mathematics: Teachers' thinking an practise
3.5.2 THOMAS LINGEFJARD 333
Mathematical modelling in teacher education - necessity or unnecessarily
3.5.3 STEPHAN HUSSMANN 341
Building concepts and conceptions in technology-based open learning environments
3.5.4 DJORDJE KADIJEVICH 349
Towards a wider implementation of mathematical modelling
at upper secondary and tertiary levels
3.5.5 AKIO MATSUZAKI 357
How might we share models through cooperative mathematical modelling? Focus on situations based on individual experiences
3.6 IMPLEMENTATION AND PRACTICE 365
3.6.0 THOMAS LINGEFJARD 367
Implementation and Practice - overview
3.6.1 MICHELE ARTAUD 371
Some conditions for modelling to exist in mathematics classrooms
3.6.2 WILFRIED HERGET & MARLENE TORRES-SKOUMAL 379
Picture (im)perfect mathematics!
3.6.3 EWALAKOMA 387
Learning mathematical modelling - from the perspective of probability and statistics education
3.6.4 GEOFF WAKE 395
Considering workplace activity from a mathematical modelling perspective
3.7 ASSESSMENT AND EVALUATION 403
3.7.0 PETER GALBRAITH 405
Assessment and evaluation - overview
3.7.1 S0REN ANTONIUS 409
Modelling based project examination
3.7.2 CHRISTOPHER HAINES & ROSALIND CROUCH 417
Mathematical modelling and applications: Ability and competence frameworks
3.7.3 JERRY LEGE 425
"To model, or to let them model?" That is the question!
3.7.4 Ross TURNER 433
Modelling and applications in PISA
3.7.5 PAULINE Vos 441
Assessment of applied mathematics and modelling: Using a laboratory-like environment
4 EDUCATIONAL LEVELS 449
4.1 MARIA SALETT BIEMBENGUT 451
Modelling and applications in primary education
4.2 TOSHIKAZUIKEDA 457
Possibilities for, and obstacles to teaching applications and modelling in the lower secondary levels
4.3 GLORIA STILLMAN 463
Upper secondary perspectives on applications and Modelling
4.4 CLAUDI ALSINA 469
Teaching applications and modelling at tertiary level
4.5 THOMAS LINGEFJARD 475
Modelling in teacher education
5 CASES IN APPLICATIONS AND MODELLING 483
5.1 KATIE MAKAR & JERE CONFREY 485
Moving the context of modelling to the forefront: Preservice teachers' investigations of equity in testing
5.2 CHRISTINE SUURTAMM & GEOFFREY ROULET 491
Modelling in Ontario: Success in moving along the continuum
5.3 GLORIA STILLMAN 497
Implementation case study: Sustaining curriculum change
5.4 CYRIL JULIE & ViMOLAN MUDALY 503
Mathematical modelling of social issues in school mathematics in South Africa
BIBLIOGRAPHY 511
INDEX 519
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