Modelling And Applications in Mathematics Education

by Blum, Werner; Galbraith, Peter L.; Henn, Hans-Wolfgang; Niss, Mogens

• ISBN13: 9780387298207
• ISBN10: 0387298207
• Format: Hardcover
• Copyright: 2006-12-30
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Preface	xi
Introduction	1	(32)
Introduction	3	(30)
Mogens Niss
Werner Blum
Peter Galbraith
Plenaries	33	(88)
Less chalk, less words, less symbols . . . more objects, more context, more actions	35	(10)
Claudi Alsina
What's all the fuss about competencies?	45	(12)
Morten Blomhøj
Tomas Højgaard Jensen
A theory of mathematical modelling in technological settings	57	(12)
Jere Confrey
Alan Maloney
What knowledge do teachers need for teaching mathematics through applications and modelling?	69	(10)
Helen M. Doerr
Beyond the low hanging fruit	79	(10)
Peter Galbraith
Modelling for life: Mathematics and children's experience	89	(10)
Brian Greer
Lieven Verschaffel
Swapna Mukhopadhyay
Modelling in lower secondary mathematics classroom -- problems and opportunities	99	(10)
Gabriele Kaiser
Katja Maass
Mathematical modelling -- A conversation with Henry Pollak	109	(12)
Henry Pollak
Issues in Applications and Modelling	121	(328)
Epistemology and Modelling	123	(56)
Epistemology and modelling -- overview	125	(4)
Jere Confrey
Modelling body motion: An approach to functions using measuring instruments	129	(8)
Ferdinando Arzarello
Giovanni Pezzi
Ornella Robutti
Emergent modelling as a precursor to mathematical modelling	137	(8)
Koeno Gravemeijer
Proving and modelling	145	(8)
Gila Hanna
Hans Niels Jahnke
A developmental approach for supporting the epistemology of modelling	153	(8)
Richard Lehrer
Leona Schauble
What is distinctive in (our views about) models and modelling perspectives on mathematics problem solving, learning, and teaching?	161	(10)
Richard Lesh
Caroline Yoon
Everyday instruments: On the use of mathematics	171	(8)
Rudolf Strasser
Authenticity and Goals	179	(38)
Authenticity and Goals -- overview	181	(4)
Peter Galbraith
How to replace word problems with activities of realistic mathematical modelling	185	(8)
Cinzia Bonotto
The relevance of modelling and applications: Relevant to whom and for what purpose?	193	(8)
Eva Jablonka
Features and impact of the authenticity of applied mathematical school tasks	201	(8)
Torulf Palm
Elementary modelling in mathematics lessons: The interplay between ``real-world'' knowledge and ``mathematical structures''	209	(8)
Ralph Schwarzkopf
Modelling Competencies	217	(48)
Modelling compentencies -- overview	219	(6)
Brian Greer
Lieven Verschaffel
Levels of modelling competencies	225	(8)
Herbert Henning
Mike Keune
Modelling both complexity and abstraction: A paradox?	233	(8)
Mihaela Singer
Studying and remedying students' modelling competencies: Routine behaviour or adaptive expertise	241	(8)
Dirk De Bock
Wim Van Dooren
Dirk Janssens
Assessing the ``phases'' of mathematical modelling	249	(8)
Ken Houston
The arithmetic operations as mathematical models	257	(8)
Zalman Usiskin
Applications & Modelling for Mathematics	265	(54)
Applications and modelling for mathematics -- overview	267	(8)
Eric Muller
Hugh Burkhardt
The roles of modelling in learning mathematics	275	(10)
Malcolm Swan
Ross Turner
Caroline Yoon
Eric Muller
Developing mathematical literacy	285	(10)
Lynn Arthur Steen
Ross Turner
Hugh Burkhardt
Classroom activities and the teacher	295	(14)
Søren Antonius
Chris Haines
Thomas Højgaard Jensen
Mogens Niss
Hugh Burkhardt
Uses of technologies in learning mathematics through modelling	309	(10)
Daniel Pead
Bill Ralph
Eric Muller
Modelling Pedagogy	319	(46)
Modelling pedagogy -- overview	321	(4)
Hans-Wolfgang Henn
Mathematical modelling in high school mathematics: Teachers' thinking an practise	325	(8)
Olive Chapman
Mathematical modelling in teacher education -- necessity or unnecessarily	333	(8)
Thomas Lingefjard
Building concepts and conceptions in technology-based open learning environments	341	(8)
Stephan Hussmann
Towards a wider implementation of mathematical modelling at upper secondary and tertiary levels	349	(8)
Djordje Kadijevich
How might we share models through cooperative mathematical modelling? Focus on situations based on individual experiences	357	(8)
Akio Matsuzaki
Implementation and Practice	365	(38)
Implementation and Practice -- overview	367	(4)
Thomas Lingefjard
Some conditions for modelling to exist in mathematics classrooms	371	(8)
Michele Artaud
Picture (im)perfect mathematics!	379	(8)
Wilfried Herget
Marlene Torres-Skoumal
Learning mathematical modelling -- from the perspective of probability and statistics education	387	(8)
Ewa Lakoma
Considering workplace activity from a mathematical modelling perspective	395	(8)
Geoff Wake
Assessment and Evaluation	403	(46)
Assessment and evaluation -- overview	405	(4)
Peter Galbraith
Modelling based project examination	409	(8)
Søren Antionius
Mathematical modelling and applications: Ability and competence frameworks	417	(8)
Christopher Haines
Rosalind Crouch
``To model, or to let them model?'' That is the question!	425	(8)
Jerry Lege
Modelling and applications in PISA	433	(8)
Ross Turner
Assessment of applied mathematics and modelling: Using a laboratory-like environment	441	(8)
Pauline Vos
Educational Levels	449	(34)
Modelling and applications in primary education	451	(6)
Maria Salett Biembengut
Possibilities for, and obstacles to teaching applications and modelling in the lower secondary levels	457	(6)
Toshikazu Ikeda
Upper secondary perspectives on applications and Modelling	463	(6)
Gloria Stillman
Teaching applications and modelling at tertiary level	469	(6)
Claudi Alsina
Modelling in teacher education	475	(8)
Thomas Lingefjard
Cases in Applications and Modelling	483	(28)
Moving the context of modelling to the forefront: Preservice teachers' investigations of equity in testing	485	(6)
Katie Makar
Jere Confrey
Modelling in Ontario: Success in moving along the continuum	491	(6)
Christine Suurtamm
Geoffrey Roulet
Implementation case study: Sustaining curriculum change	497	(6)
Gloria Stillman
Mathematical modelling of social issues in school mathematics in South Africa	503	(8)
Cyril Julie
Vimolan Mudaly
Bibliography	511	(8)
Index	519