Interdisciplinarity, Creativity, and Learning: Mathematics with Literature, Paradoxes, History, Technology, and Modeling

(Montana mathematics enthusiast,  7)

Bharath Sriraman, Viktor Freiman e Nicole Lirette-Pitre 

Information Age Publishing | 2009 | 261 páginas | rar - pdf | 2,7 Mb

link (password: matav)

A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education Series Editor Bharath Sriraman, The University of Montana Interdisciplinarity is increasingly viewed as a necessary ingredient in the training of future oriented 21st century disciplines that rely on both analytic and synthetic abilities across disciplines. Nearly every curricular document or vision statement of schools and universities include a call for promoting creativity in students. Yet the construct of creativity and giftedness across disciplines remains elusive in the sense that the prototypical examples of such work come from eminent scientists, artists and mathematicians, and little if any work has been conducted with non-eminent individuals. This monograph is an attempt to fill this gap by putting forth the view that interdisciplinarity and creativity are related constructs, and that the cultivation of domain general creativity is possible. Mathematics has historically been anchored to numerous disciplines like theology, natural philosophy, culture and art, allowing for a flexibility of thought that is difficult to cultivate in other disciplines. In this monograph, the numerous chapters from Australia, U.S.A., Canada, Cyprus, Denmark and Japan provide a compelling illustration of the intricate connection of mathematics with literature, paradoxes, history, technology and modeling, thus serving as a conduit for interdisciplinarity, creativity and learning to occur.

ContentsSection I Interdisciplinarity in Mathematics and Literature
1 The Interdisciplinary Nature of Inductive Processes in Forming Generalizations.... 3
Bharath Sriraman and Harry Adrian
2 The Existential Void in Learning: Juxtaposing Mathematics and Literature.... 13
Bharath Sriraman and Harry Adrian
3 Mathematics and Literature: Synonyms, Antonyms or the Perfect Amalgam?...... 31
Bharath Sriraman
4 Mathematics and Literature (The Sequel): Imagination as a Pathway to Advanced Mathematical Ideas and Philosophy..... 41
Bharath Sriraman
Section II Mathematics and Paradoxes 
5 1 or 0?: Cantorian Conundrums in the Contemporary Classroom.... 55
Bharath Sriraman and Libby Knott
6 Understanding Mathematics through Resolution of Paradoxes...... 61
Margo Kondratieva
7 Mathematical Paradoxes as Pathways into Beliefs and Polymathy.... 75
Bharath Sriraman
Section II I Geometry and History
8 Voronoi Diagrams.... 97
Michael Mumm
9 An In-Depth Investigation of the Divine Ratio.... 109
Birch Fett
10 Cyclide Manipulation........ 133
Akihiro Matsuura
Section IV Interdisciplinarity and Modeling
11 Modeling Interdisciplinary Activities Involving Mathematics and Philosophy... 147
Steffen M. Iversen
12 Integrating Engineering Education within the Elementary and Middle School Mathematics Curriculum.... 165
Lyn D. English and Nicholas G. Mousoulides
13 Mathematical Modelling in the Early School Years........... 177
Lyn D. English and James J. Watters
Section V Technology and the NET Generation
14 Connected Giftedness: Mathematical Problem Solving by Means of a Web Technology: Case of the CASMI Project...... 205
Viktor Freiman and Nicole Lirette-Pitre
15 Teaching and Learning for the Net Generation: A Robotic-Based Learning Approach....217
Samuel Blanchard
16 Does Technology Help Building More Creative Mathematical Environments?... 233
Dominic Manuel

Mathematical Interest Theory

Leslie Vaaler e James Daniel

Mathematical Association of America | 2008 -2ª edição | 493 páginas | rar - pdf | 2 Mb

link (password : matav)

Mathematical Interest Theory gives an introduction of how investments grow over time. This is done in a mathematically precise manner. The emphasis is on practical applications that give the reader a concrete understanding of why the various relationships should be true. Among the modern financial topics introduced are: arbitrage, options, futures, and swaps. The content of the book, along with an understanding of probability, will provide a solid foundation for readers embarking on actuarial careers. On the other hand, Mathematical Interest Theory is written for anyone who has a strong high-school algebra background and is interested in being an informed borrower or investor. The content is suitable for a mid-level or upper-level undergraduate course or a beginning graduate course. Mathematical Interest Theory includes more than 240 carefully worked examples. There are over 430 problems, and numerical answers are included in an appendix. A companion student solution manual has detailed solutions to the odd-numbered problems. Most of the examples involve computation, and detailed instruction is provided on how to the Texas Instruments BA II Plus and BA II Plus Professional calculators can be used to efficiently solve the problems. This is important for readers wishing to pass the SOA/CAS joint financial mathematics exam FM/2. However, this part of the book can be skipped without disturbing the flow of the exposition

Contents
An introduction to the Texas Instruments BA II Plus
The growth of money
Equations of value and yield rates
Annuities (annuities certain)
Annuities with different payment and conversion periods
Loan repayment
Bonds
Stocks and financial markets
Arbitrage, term structure of interest rates, and derivatives
Interest rate sensitivity.

Educational Interfaces between Mathematics and Industry: Report on an ICMI-ICIAM-Study

Alain Damlamian, José Francisco Rodrigues e Rudolf Sträßer

New ICMI studies series, v.16.

Springer | 2013 | 451 páginas | rar - pdf | 4 Mb

link (password : matav)

This book is the “Study Book” of ICMI-Study no. 20, which was run in cooperation with the International Congress on Industry and Applied Mathematics (ICIAM). The editors were the co-chairs of the study (Damlamian, Straesser) and the organiser of the Study Conference (Rodrigues). The text contains a comprehensive report on the findings of the Study Conference, original plenary presentations of the Study Conference, reports on the Working Groups and selected papers from all over world. This content was selected by the editors as especially pertinent to the study each individual chapter represents a significant contribution to current research.

Contents

Part I Discussion Document and Study Report

Discussion Document. . . . . . 3

The International Programme Committee

Report on the Study . . .  . . . 17

Alain Damlamian, José Francisco Rodrigues and Rudolf Sträßer

Part II Plenary and Invited Lectures

Getting Math off the Ground: Applied Mathematics at Boeing . . 27

Stephen P. Keeler and Thomas A. Grandine

Mathematics in the Workplace: Issues and Challenges . . . .. . . 43

Celia Hoyles, Richard Noss, Phillip Kent and Arthur Bakker

Mathematical Modeling Education is the Most Important Educational Interface Between Mathematics and Industry . . . 51

Tatsien Li

Models for Industrial Problems: How to Find and How to Use them—in Industry and in Education . . . . . . .  . 59

Helmut Neunzert

Interfacing Education and Research with Mathematics for Industry: The Endeavor in Japan. 77

Masato Wakayama

Part III WG Education/Training with Industry Participation

Education/Training with Industry Participation . . . . 95

Gail FitzSimons and Tom Mitsui

How it is Possible to Make Real-World Mathematics More Visible: Some Results from Two Italian Projects  . . 109

Cinzia Bonotto

The Project ‘‘Ways to More MINT-Graduates’’ of the Bavarian Business Association (vbw) with Focus on the M (=Mathematics) at the University of Augsburg, Germany . . 119

Matthias Brandl

Mathematics in a Safety–Critical Work Context: The Case of Numeracy for Nursing . 127

Diana Coben and Meriel Hutton

Linking Professional Experiences with Academic Knowledge: The Construction of Statistical Concepts by Sale Manager Apprentices . . 137

Corinne Hahn

Learning Conversation in Mathematics Practice School–Industry Partnerships as Arena for Teacher Education . . 147

Gert Monstad Hana, Ragnhild Hansen, Marit Johnsen-Høines, Inger Elin Lilland and Toril Eskeland Rangnes

The Threefold Dilemma of Missing Coherence: Bridging the Artificial Reef Between the Mainland and Some Isolated Islands. . 57

Guenter Törner, Volker Grotensohn and Bettina Roesken

The Project ‘‘Mathe-Meister’’: A Mathematical Self Assessment Centre with Diagnostic Feedback for Vocational Trainees . . . 165

Kathrin Winter

Part IV WG University and Academic Technical/Vocational Education

University and Academic Technical/Vocational Education . . .  . 173

Nilima Nigam and José Francisco Rodrigues

Mathematics for Engineering and Engineering for Mathematics . .185

Miquel Alberti Palmer, Sergio Amat, Sonia Busquier, Pilar Romero and Juan Tejada

Laboratory for Computational Mathematics: An Interface Between Academia and Industry 199

A. Araújo, S. Barbeiro and J. A. Ferreira

Improving the Industrial/Mathematics Interface.. . 205

Jean P. F. Charpin and Stephen B. G. O’Brien

Two Masters on ‘Mathematics for Industry’ at the Universities of Paris and of Pau . 213

Edwige Godlewski, M. Madaune-Tort and S. Dossou-Gbete

Mathematics in Industry and Teachers’ Training . .  223

Matti Heilio

Interfaces Between Mathematics and Industry and the Use of Technology in Mathematics Education in India  . 229

Ajit Kumar

Modeling Modeling: Developing Habits of Mathematical Minds . . 237

John A. Pelesko, Jinfa Cai and Louis F. Rossi

The Evolution of Graduate Applied Math Courses in the Institute of Mathematics, University of the Philippines. . 247

Carlene P. C. Pilar-Arceo and Jose Maria L. Escaner IV

The Vertical Integration of Industrial Mathematics, the WPI Experience  . 253

Bogdan Vernescu

Part V WG Education in Schools

Educational Interfaces Between Mathematics and Industry at School Level . . 263

Gabriele Kaiser, Henk van der Kooij and Geoff Wake

Mathematical Applications, Modelling and Technology as Windows into Industry Based Mathematical Practice .  . 271

Vince Geiger

Mathematics Education and the Information Society . . . 279

Koeno Gravemeijer

Authentic Complex Modelling Problems in Mathematics Education . . 287

Gabriele Kaiser, Martin Bracke, Simone Göttlich and Christine Kaland

Embedding Authentic Real World Tasks into Secondary Mathematics Curricula .. 299

Gloria Stillman and K. E. D. Ng

Drawing on Understanding of Workplace Practice to Inform Design of General Mathematics Curricula .  . 309

Geoff Wake

Part VI WG Mathematics-Industry Communication

Communication and Collaboration. . .. . 319

Solomon Garfunkel, Rolf Jeltsch and Nilima Nigam

Engineering, Mathematics Communication, and Education: Reflections on a Personal Experience . . . 333

Jorge Buescu

A View on Mathematical Discourse in Research and Development . . . 341

Vasco Alexander Schmidt

Using Popular Science in a Mathematical Modeling Course  . . 351

Burt S. Tilley

Part VII WG Technology Issues

Technology Issues . .  . 359

Helmer Aslaksen and Fadil Santosa

Tackling the Challenges of Computational Mathematics Education of Engineers . . 365

France Caron and André Garon

Integrating Computational Modelling in Science, Technology, Engineering, and Mathematics Education.. . 375

Rui Gomes Neves, Jorge Carvalho Silva and Vítor Duarte Teodoro

Incorporating the Ideas and Methods of Mathematical Modeling into Calculus Teaching .385

Qixiao Ye

Part VIII WG the Mathematics-Industry Interface

The Mathematics–Industry Interface . . 397

Jofré Alejandro and Lutz-Westphal Brigitte

Part IX Selected Papers Linked to More than One Working Group 

Inappropriate Use of Spreadsheets in the Finance Industry . . . . 403

Djordje M. Kadijevich

MITACS Accelerate: A Case Study of a Successful Industrial Research Internship Program . . . 413

Sarah Petersen and Marsh Rebeccah

A Meta-analysis by Mathematics Teachers of the GIFT Program Using Success Case Methodology . . . 421

Richard Millman, Meltem Alemdar and Bonnie Harris

Cultivating an Interface Through Collaborative Research Between Engineers in Nippon Steel & Sumitomo Metal and Mathematicians in University . . . 427

Junichi Nakagawa and Masahiro Yamamoto

An Introduction to CUMCM: China/Contemporary Undergraduate Mathematical Contest in Modeling . . 435

Jinxing Xie

Part X Conclusion

Conclusion on Educational Interfaces Between Mathematics and Industry. . . . . 447

Alain Damlamian, José Francisco Rodrigues and Rudolf Sträßer

Index . . . 453

Mathematical Modelling: A Way Of Life - Ictma 11

S J Lamon, W A Parker e S K Houston

Woodhead Publishing |  2003 | páginas | 278 páginas | pdf | 17 Mb

link

Mathematical modelling is often spoken of as a way of life, referring to habits of mind and to dependence on the power of mathematics to describe, explain, predict and control real phenomena. This book aims to encourage teachers to provide opportunities for students to model a variety of real phenomena appropriately matched to students' mathematical backgrounds and interests from early stages of mathematical education. Habits, misconceptions, and mindsets about mathematics can present obstacles to university students' acceptance of a ''models-and-modelling perspective'' at this stage of mathematics education. Without prior experience in building, interpreting and applying mathematical models, many students may never come to view and regard modelling as a way of life. The book records presentations at the ICTMA 11 conference held in Milwaukee, Wisconsin in 2003.

• Examines mathematical modelling as a way of life, referring to habits of mind and dependence on the power of mathematics to describe, explain, predict and control real phenomena

• Encourages teachers to provide students with opportunities to model a variety of real phenomena appropriately matched to students' mathematical backgrounds and interests from early stages of mathematical education

• Records presentations at the ICTMA 11 conference held in Milwaukee, Wisconsin in 2003

Table of Contents
ICTMA Publications
Preface
Section A: Modelling in the Elementary School Mathematical Modelling With Young Learners
Lyn English, Queensland University of Technology, Australia
2 Modelling in Elementary School: Helping Young Students to See the World Mathematically
Susan 1. Lamon, Marquette University, USA
Section B: Modelling with Middle and Secondary Students
3 How Mathematizing Reality is Different from Realizing Mathematics 37
Richard A. Lesh, Purdue University, USA
4 Environmental Problems and Mathematical Modelling 53
Akira Yanagirnoto, Tennoji Jr. & Sf. High School; Osaka Kyoiku University, Japan
5 Three Interacting Dimensions in the Development of Mathematical Knowledge 61
Guadalupe Carmona, Purdue University, USA
6 Working and Learning in the Real World: A Mathematics Education
Project in Baden-Wuerttemberg 71
Hans-Wolfgang Henn, University of Dortmund, Germany
7 Powerful Modelling Tools for High School Algebra Students 81
Susan J. Lamon, Marquette University, USA
Section C: Post Secondary Modelling
8 Solving Problems: Perchance to Dream 97
Stephen 1. Merrill, Marquette University, US
9 Formal Systems of Logic as Models for Building the Reasoning Skills of Upper Secondary School Teachers 107
Paola Forcheri, Istituto di Matematica Applicata e Tecnologie Infonnatiche del CNR, Italy
Paolo Gentilini, Istituto di Matematica Applicata e Tecnologie Infonnatiche del CNR, Italy; Ligurian Regional Institute of Educational Research, Italy
10 Learning Mathematics Using Dynamic Geometry Tools 119
Thomas Lingefjard & Mikael Holmquist, Goteborg University, Sweden
II Modelling Search Algorithms 127
Albert Fassler, Hochschule fuer Technik und Architektur Biel/Bienne, Switzerland
12 Mathematical Modelling in a Differential Geometry Course 133
Adolf Riede, University of Heidelberg, Germany
13 Defending the Faith: Modelling to Increase the Accountability of Organisational Leadership 143
Peter Galbraith, University of Queensland, Australia
Section D: Research
14 Assessing Modelling SkiIls 155
Ken Houston & Neville Neill, University of Ulster, N. Ireland
15 Assessing the Impact of Teaching Mathematical Modelling: Some Implications 165
John Izard, RMIT, Australia Chris Haines, City University, U.K Ros Crouch, University of Hertfordshire, U.K Ken Houston, University of Ulster, N. Ireland NeviIle NeiIl, University of Ulster, N. Ireland
16 Towards Constructing a Measure of the Complexity of Application Tasks 179
Gloria Stillman, University of Melbourne, Australia Peter Galbraith, University of Queensland, Australia
17 Using Workplace Practice to Inform Curriculum Change 189
Geoff Wake & Julian Williams, University of Manchester, UK
18 Comparing an Analytical Approach and a Constructive Approach to Modelling 201
Toshikazu Ikeda, Yokohama National University, Japan Max Stephens, University of Melbourne, Australia
Section E: Perspectives
19 The Place of Mathematical Modelling in Mathematics Education 215
Michael J. Hamson, (Formerly) Glasgow Caledonian University, UK
20 What is Mathematical Modelling? 227
Jonei Cerqueira Barbosa, Faculdade Integrada da Bahia e Faculdades Jorge Amado, Brazil
21 Beyond the Real World: How Mathematical Models Produce Reality 235
Susana Carreira, Universidade do Algarve; Universidade de Lisboa-eIEFUL, Portugal
22 Reconnecting Mind and World: Enacting a (New) Way of Life 245
Stephen R. Campbell, Simon Fraser University, Canada; University of California, Irvine, U.S.A.
23 ICTMA: The First 20 Years 255
Ken Houston, University of Ulster, N. Ireland

Teaching Mathematical Modelling: Connecting to Research and Practice

(International Perspectives on the Teaching and Learning of Mathematical Modelling)

 Gloria Ann Stillman, Gabriele Kaiser, Werner Blum e Jill P. Brown

 Springer | 2013 | 612 páginas | pdf  | 9 Mb

link

This book provides readers with an overview of recent international research and developments in the teaching and learning of modelling and applications from a variety of theoretical and practical perspectives. There is a strong focus on pedagogical issues for teaching and learning of modelling as well as research into teaching and practice. The teaching of applications of mathematics and mathematical modelling from the early years through primary and secondary school and at tertiary level is rising in prominence in many parts of the world commensurate with an ever-increasing usage of mathematics in business, the environment, industry and everyday life. The authors are all members of the International Community of Teachers of Mathematical Modelling and Applications and important researchers in mathematics education and mathematics. The book will be of interest to teachers, practitioners and researchers in universities, polytechnics, teacher education, curriculum and policy

Contents
1 Mathematical Modelling: Connecting to Teaching and Research Practices – The Impact of Globalisation.... 1
Gloria Ann Stillman, Gabriele Kaiser, Werner Blum, and Jill P. Brown
Part I Innovative Practices in Modelling Education Research and Teaching
2 From Conference to Community: An ICTMA Journey—The Ken Houston Inaugural Lecture .... 27
Peter Galbraith
3 Modelling from the Perspective of Commognition – An Emerging Framework..... 47
Jonas Bergman Ärlebäck and Peter Frejd
4 Should Interpretation Systems Be Considered to Be Models if They Only Function Implicitly?.... 57
Rita Borromeo Ferri and Richard Lesh
5 Mathematical Modelling, Mathematical Content and Tensions in Discourses ...... 67
Andréia Maria Pereira de Oliveira and Jonei Cerqueira Barbosa
6 Ethnomodelling as a Methodology for Ethnomathematics ...... 77
Milton Rosa and Daniel Clark Orey
7 Dual Modelling Cycle Framework for Responding to the Diversities of Modellers..... 89
Akihiko Saeki and Akio Matsuzaki
8 The Eyes to See: Theoretical Lenses for Mathematical Modelling Research...... 101
Nils Buchholtz
9 Strässer’s Didactic Tetrahedron as a Basis for Theorising Mathematical Modelling Activity Within Social Contexts.... 107
Vince Geiger
10 Ethnomodelling as a Research Lens on Ethnomathematics and Modelling ..... 117
Milton Rosa and Daniel Clark Orey
Part II Research into, or Evaluation of, Teaching Practice
11 Real-Life Modelling Within a Traditional Curriculum: Lessons from a Singapore Experience .... 131
Ang Keng Cheng
12 Students’ Mathematical Learning in Modelling Activities ..... 141
Morten Blomhøj and Tinne Hoff Kjeldsen
13 Students’ Designing an Ideal Tourism Route as Mathematical Modelling .... 153
Chan Chun Ming Eric
14 Comparison of Mathematical Modelling Skills of Secondary and Tertiary Students .... 165
Juntao Fu and Jinxing Xie
15 Taking Advantage of Incidental School Events to Engage with the Applications of Mathematics: The Case of Surviving the Reconstruction........ 175
Vince Geiger, Merrilyn Goos, and Shelley Dole
16 The Development of Modelling Competencies by Year 9 Students: Effects of a Modelling Project..... 185
Susanne Grünewald
17 Evidence of a Dual Modelling Cycle: Through a Teaching Practice Example for Pre service Teachers..... 195
Akio Matsuzaki and Akihiko Saeki
18 Considering Multiple Solutions for Modelling Problems – Design and First Results from the MultiMa-Project.... 207
Stanislaw Schukajlow and André Krug
19 Challenges in Modelling Challenges: Intents and Purposes ... 217
Gloria Ann Stillman, Jill P. Brown, and Peter Galbraith
20 Mathematical Modelling of a Real-World Problem: The Decreasing Number of Bluefi n Tuna ... 229
Akira Yanagimoto and Noboru Yoshimura
21 Mathematical Modelling of a Social Problem: Pension Tax Issues .... 241
Noboru Yoshimura and Akira Yanagimoto
Part III Pedagogical Issues for Teaching and Learning
22 Pedagogical Refl ections on the Role of Modelling in Mathematics Instruction ..... 255
Toshikazu Ikeda
23 Complex Modelling Problems in Co-operative, Self-Directed Learning Environments ..... 277
Gabriele Kaiser and Peter Stender
24 Inducting Year 6 Students into “A Culture of Mathematising as a Practice” ..... 295
Jill P. Brown
25 A Whole Week of Modelling – Examples and Experiences of Modelling for Students in Mathematics Education.... 307
Nils Buchholtz and Sarah Mesrogli
26 Teachers’ Self-Perceptions of Their Pedagogical Content Knowledge Related to Modelling – An Empirical Study with Austrian Teachers ...... 317
Sebastian Kuntze, Hans-Stefan Siller, and Christiane Vogl
27 A Cross-Sectional Study About Modelling Competency in Secondary School .... 327
Matthias Ludwig and Xenia-Rosemarie Reit
28 Teacher Readiness in Mathematical Modelling: Are There Differences Between Pre-service and In-Service Teachers?... 339
Kit Ee Dawn Ng
29 Exploring the Relationship Between Mathematical Modelling and Classroom Discourse .... 349
Trevor Redmond, Raymond Brown, and Joanne Sheehy
30 The Role of Textbooks in Developing a Socio- critical Perspective on Mathematical Modelling in Secondary Classrooms ... 361
Gloria Ann Stillman, Jill P. Brown, Rhonda Faragher, Vince Geiger, and Peter Galbraith
31 Pre-service Secondary School Teachers’ Knowledge in Mathematical Modelling – A Case Study .... 373
Tan Liang Soon and Ang Keng Cheng
32 How Students Connect Descriptions of Real- World Situations to Mathematical Models in Different Representational Modes .. 385
Wim Van Dooren, Dirk De Bock, and Lieven Verschaffel
33 Pre-service Teacher Learning for Mathematical Modelling ..... 395
Mark Winter and Hamsa Venka
34 Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: Conceptions of Mathematical Modelling ....... 405
Chan Chun Ming Eric
35 Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: Problem Posing and Task Design .... 415
Lee Ngan Hoe
36 Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: A Framework for Facilitation....... 427
Kit Ee Dawn Ng
37 Teacher Professional Development on Mathematical Modelling: Initial Perspectives from Singapore .... 437
Vince Geiger
Part IV Influences of Technologies
38 Reality Based Test Tasks with Digital Tools at Lower Secondary ....... 445
Gilbert Greefrath and Michael Rieß
39 On Comparing Mathematical Models and Pedagogical Learning ....... 457
Janeen Lamb and Jana Visnovska
Part V Assessment in Schools
40 Formative Assessment in Everyday Teaching of Mathematical Modelling: Implementation of Written and Oral Feedback to Competency- Oriented Tasks...... 469
Michael Besser, Werner Blum, and Malte Klimczak
41 Assessment of Modelling in Mathematics Examination Papers: Ready-Made Models and Reproductive Mathematising ....... 479
Pauline Vos
Part VI Applicability at Different Levels of Schooling, Vocational Education, and in Tertiary Education
42 Complex Modelling in the Primary and Middle School Years: An Interdisciplinary Approach ..... 491
Lyn D. English
43 Modelling in Brazilian Mathematics Teacher Education Courses ...... 507
Maria Salett Biembengut
44 The Development of Mathematical Concept Knowledge and of the Ability to Use This Concept to Create a Model ... 517
César Cristóbal-Escalante and Verónica Vargas-Alejo
45 Problem Posing: A Possible Pathway to Mathematical Modelling ..... 527
Ann Downton
46 A Study of the Effectiveness of Mathematical Modelling of Home Delivery Packaging on Year 12 Students’ Function Education .. 537
Tetsushi Kawasaki and Yoshiki Nisawa
47 How to Introduce Mathematical Modelling in Industrial Design Education? ...... 551
Geert Langereis, Jun Hu, and Loe Feijs
48 Rationality of Practice and Mathematical Modelling – On Connections, Conflicts, and Codifications ....... 563
Lars Mouwitz
49 Extending Model Eliciting Activities (MEAs) Beyond Mathematics Curricula in Universities .... 573
Mark Schofield
50 Building Awareness of Mathematical Modelling in Teacher Education: A Case Study in Indonesia ...... 583
Wanty Widjaja
Part VII Modelling and Applications in Business and the Lived Environment
51 Mathematics and the Pharmacokinetics of Alcohol ...... 597
Michael Jennings and Peter Adams
52 Beyond the Modelling Process: An Example to Study the Logistic Model of Customer Lifetime Value in Business Marketing ...... 607
Issic K.C. Leung

Mathematical Modelling in Education and Culture: ICTMA 10

(Mathematics & Applications)

Q.X. Ye, Werner Blum, S.K. Houston e Q.Y. Jiang

Woodhead Publishing |2003 | 341 páginas | pdf

link

The mathematical modelling movement in mathematics education at school and university level has been influencing curricula for about 25 years. Lecturers will find useful material to enhance their teaching and extracurricular activities and educators will find innovative ideas to inform their course design and focus their research, while students will find interesting problems to explore.

Table of Contents
Preface X
Section A - Research in Teaching, Learning and Assessment
1 Context in application and modelling - an empirical approach
Andreas Busse' and Gabriele Kaise
2 Mathematical modelling as pedagogy: Impact of an immersion programme
Trudy Dunne' and Peter Galbraith2
3 Using ideas from physics in teaching mathematical proofs
Gila Hanna' and Hans Niels Jahnke
4 Deconstructing mathematical modelling: Approaches to problem solving
Christopher Haines’, Rosalind Crouch’ and Andrew Fitzharris’
5 Investigating students’ modelling skills
Ken Houston and Neville Neil
6 “How to model mathematically” table and its applications
Wang Geng
Section B - Mathematical Modelling Competitions
7 New applications of the mathematics A-lympiad
Dkdk de Haan
8 Mathematics contest in modelling: Problems from practice
Shang Shouting, Zheng Tong and Shang Wei
Section C - Using Technology in the Teaching of Modelling
9 Modelling and spreadsheet calculation 101
Mike Keune’ and Herbert Henning’
10 Technology-enriched classrooms: Some implications for teaching applications and modelling
Peter Galbraith, Peter Renshaw, Merrilyn Goos and Vince Geiger
11 Choosing and using technology for secondary mathematical modelling tasks: Choosing the right peg for the right hole
Vince Geiger, Peter Galbraith, Peter Renshaw and Merrilyn Goos
Section D - Models for Use in Teaching
12 Groups, symmetry and symmetry breaking
Albert Fassler
13 The rainbow: f'rom myth to model
Hans- Wolfgang Henn
14 Teaching inverse problems in undergraduate level mathematics, modelling and applied mathematics courses
Fengshan Liu
15 Bezier curves and surfaces in the classroom
Baoswan Dzung Wong
Section E - Teacher Education
16 A mathematical modelling course for pre-service secondary school mathematics teachers
Zhonghong Jiang, Edwin McClintock and George 0 'Brien
17 Mathematical modelling in teacher education
Mikael Holmquist and Thomas LingeJard
18 Two modelling topics in teacher education and training 209
Ado y Riede
Section F - Innovative Modelling Courses
19 The knowledge and implementation for the course of mathematical experiment
Zhao Jing, Jiang Jihong, Dan Qi and Fu Shilu
20 Teaching patterns of mathematical application and modelling in high school
Tang Anhua, Sui Lili and Wang Xiaodan
21 Mathematical experiment course: Teaching mode and its practice
Qiongsun Liu, Shanqiang Ren, Li Fu and Qu Gong
22 The mathematical modelling - orientated teaching method of elicitation
Ruiping Hu and Shuxia Zhang
23 Teaching and assessment of mathematical modelling in community colleges
Lu Xiuyan, Mo Jingiing and Lu Keqiang
24 The role of mathematical experiment in mathematics teaching
Jinyuan-Li
25 Theory and practice in teaching of mathematical modelling at high school level
Qiu Jinjia

Modelling and Mathematics Education: ICTMA 9: Applications in Science and Technology

J.F. Matos, S.K. Houston, Werner Blum e S.P. Carreira

Woodhead Publishing | 2002 | 433 páginas | PDF | 25 Mb

link

The articles included in this book are from the ICTMA 9 conference held in Lisbon, attended by delegates from about 30 countries. This work records the 1999 Lisbon Conference of ICTMA. It contains the selected and edited content of the conference and makes a significant contribution to mathematical modelling which is the significant investigative preliminary to all scientific and technological applications from machinery to satellites and docking of space-ships.

Contents
Preface ix
Section A. Mathematical modelling revisited
1 Enacting possible worlds: Making sense of (human) nature
Stephen R Campbell
2 The mountain is the utility - On the metaphorical nature of mathematical models
Susana Carreira
3 The theory of multiple intelligences and mathematical modelling
S Kenneth Houston
4 Modelling modelling: Where is the centre of gravity of-for-when teaching modelling?
John Mason
5 Fact, fiction, fiddle - Three types of models
Allan Tarp
6 Issues and problems of research on the teaching and leaming of applications and modelling
Mogens Niss
Section B. Mathematical aspects of modelling
7 Mathematical modelling by means of functional equations: The missing link in the leaming of functions
Claudi Alsina
8 Applications of simultaneous iteration
Neville T Neil
9 On the derivative of nondifferentiable fimctions
Miguel Ramos
10 Mathematics before or through applications. Top-down and bottom-up understandings of linear and exponential functions
Allan Tarp
Section C. Mathematical modelling and technology
Formulating and assessing a mathematical modelling problem in a technological environment
Roger Brown
The graphics calculator and mathematical modelling - Creating an integrated learning environment
Milton Fuller
Mobile classroom - A school project focussing on modelling
Hans- Wolfgang Henn
What should be asked of a computer program for mathematical modelling in primary/lower secondary school?
Inge B Larsen
Modelling and algebra: How ‘pure’ shall we be?
Henk van der Kooij
Section D. Mathematical modelling in higher education
16 Mathematical modelling in pre-service teacher education
Jonei Cerqueira Barbosa
17 Mathematical modelling in calculus courses
Jussara de Loiola Aratijo and Josk Antbnio Salvador
18 Mathematical modelling and technology in teacher education - Visions and reality
Thomas Lingejard and Mikael Holmquist
19 Modelling optimisation problems: From simple to realistic 216
Margarida P Mello and Sandra A Santos
20 Role of mathematical modelling and applications in university mathematics service courses: An across countries study
Sergiy Klymchuk and Tatyana Zverkova
21 A mathematics curriculum for undergraduate courses based on mathematical modelling and computer science
Regina Helena Franchi
22 Mathematical applications and modelling: A case study involving first year higher education students
Fernanda Tavares
23 Mathematical modelling with environmental students
Mike Hamson
24 Exploring different approaches to mathematical modelling in engineering calculus courses
Maria Ines Cavallaro and Marta Anaya
25 From mathematical modelling to mathematical experiments
Qiyuan Jiang
Section E. Pedagogical issues in mathematical modelling
26 Modelling: Good problems - not only a question of (good) taste
Eva Jablonka
27 Assumptions and context: Pursuing their role in modelling activity
P. Galbraith and G. Stillman
28 The effect of task organisation on classroom modelling activities 311
Iben Maj Christiansen
Aiming for success: Modelling sports problems with an aiming theme
Trevor Gethins
Context orientated teaching
Klaoudatos Nikos and Papastavridis Stavros
Enculturation in mathematical modelling
Susan J Lamon
Conceptual and procedural demands embedded in modelling tasks
Peter Galbraith and Christopher Haines
Mathematical modelling by the pupils themselves - Possibilities and limitations in school-leaving examination papers
Wolfiam Eid
Understanding students’ modelling skills
Christopher Haines, Rosalind Crouch and John Davies
The effects of students’ discussion in mathematical modelling
Toshikazu Ikeda and Max Stephens
Critical evaluation of models in relation to the modelling process
Iben Maj Christiansen
Mathematics of traffic safety - Composite real mathematics approach
Akira Yanagimoto and Noboru Yoshimura
Trigonometry with reference to modern land surveying techniques in maths lessons

Katja MaaJ

Mathematical Modelling Education, Engineering And Economics

ICTMA 12

Christopher Haines, Peter Galbraith, Werner Blum e Sanowar Khan

Woodhead Publishing | 2007 | 511 páginas | rar - pdf | 63,6 Mb

link (password: matav)

This book continues the ICTMA tradition of influencing teaching and learning in the application of mathematical modelling. Each chapter shows how real life problems can be discussed during university lectures, in school classrooms and industrial research. International experts contribute their knowledge and experience by providing analysis, insight and comment whilst tackling large and complex problems by applying mathematical modelling. This book covers the proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications.

• Covers the proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications
• Continues the ICTMA tradition of influencing teaching and learning in the application of mathematical modelling
• Shows how real life problems can be discussed during university lectures, in school classrooms and industrial research

TABLE OF CONTENTS

Preface v

MODEL TRANSITIONS IN A REAL WORLD v

ICTMA12 - THE CONFERENCE vii

ICTMA xi

ICTMA Books xii

Acknowledgements xiii

Section 1: Models and Modelling in Reality 1

1.1 Communicating big themes in applied mathematics 2

Julian Hunt FRS, University College, London, UK

1.2 Economic modelling: Theory, reality, uncertainty and 25

decision-making

Kate Barker, Bank of England, UK

Section 2: Modelling Constructs in Education 43

2.1 Dreaming a 'possible dream': More windmills to conquer 44

Peter Galbraith, University of Queensland, Australia

2.2 Modelling in class: What do we want the students 63

to learn?

Katja Maaß, University of Education, Freiburg, Germany

2.3 Learning by constructing and sharing models 79

Celia Hoyles and Richard Noss, Institute of Education, University of London, UK

Section 3: Recognising Modelling Competencies 89

3.1 Exemplar models: Expert-novice student behaviours 90

Rosalind Crouch, University of Hertfordshire

and Christopher Haines, City University, London, UK

3.2 A teaching experiment in mathematical modelling 101

Toshikazu Ikeda, Yokohama National University, Japan

Max Stephens, University of Melbourne, Australia

and Akio Matsuzaki, Tsukuba University, Japan

3.3 Modelling and modelling competencies in school 110

Gabriele Kaiser, University of Hamburg, Germany

3.4    Exploring university students' competencies in modelling 120

France Caron and Jacques Bélair, Université de Montréal, Canada

3.5 Facilitating middle secondary modelling competencies 130

Peter Galbraith, University of Queensland, Australia

Gloria Stillman and Jill Brown, University of Melbourne

and Ian Edwards, Luther College, Melbourne, Australia

3.6 Assessing mathematical modelling competency 141

Tomas Højgaard Jensen, The Danish University of Education, Denmark

3.7 A stochastic model for the modelling process 149

Michael Voskoglou, Higher Technological Educational Institute, Patras, Greece

3.8 Assessing progress in mathematical modelling 158

John Izard, RMIT University, Melbourne, Australia

3.9 An introduction to CUMCM

Qiyuan Jiang and Jinxing Xie, Tsinghua University, China 168

and Qixiao Ye, Beijing Institute of Technology, China

Section 4: Everyday Aspects of Modelling 'Literacy' 176

4.1 Functional mathematics and teaching modelling 177

Hugh Burkhardt, University of Nottingham, UK

4.2 Modelling and the critical use of mathematics 187

Jussara de Loiola Araújo, Universidade Federal de Minas Gerais (UFMG), Brazil

4.3 Learners’ context preferences and mathematical literacy 195

Cyril Julie, University of the Western Cape, South Africa

4.4 ‘Real world’ interactions for adult basic numeracy tutors 203

Yvonne Hillier, City University, London, UK

4.5 Math modelling: What skills do employers want in industry? 212

ManMohan Sodhi and Byung-Gak Son, City University, London, UK

Section 5: Cognitive Perspectives on Modelling 221

5.1 How do students and teachers deal with modelling problems? 222

Werner Blum and Dominik Leiß, University of Kassel, Germany

5.2    Teacher-student interactions in mathematical modelling 232

Jonei Cerqueira Barbosa, State University of Feira de Santana, Brazil

5.3 Mathematical modelling: A teachers' training study 241

José Ortiz, University of Carabobo, Venezuela,

Luis Rico and Enrique Castro, University of Granada, Spain

5.4 Mathematics in the physical sciences: Multiple perspectives 250

Geoff Wake and Graham Hardy, University of Manchester, UK

5.5 Modelling problems from a cognitive perspective 260

Rita Borromeo Ferri, University of Hamburg, Germany

5.6 An explorative study on realistic mathematical modelling 271

Cinzia Bonotto, University of Padova, Italy

5.7 Student reasoning when models and reality conflict 281

Jerry Legé, California State University, Fullerton, USA

5.8 The concept of the derivative in modelling and applications 288

Gerrit Roorda, Pauline Vos and Martin Goedhart,        University of Groningen, The Netherlands

5.9 Inequalities as modelling tools in computing applications 294

Sergei Abramovich, State University of New York at Potsdam, USA

Section 6: The Practice of Modelling 303

6.1 Integration of energy issues in mathematics classrooms 304

Astrid Brinkmann, Berufskolleg Iserlohn, University of Dortmund

and Klaus Brinkmann, University of Trier, Umwelt Campus, Birkenfeld, Germany

6.2   Models of ecology in teaching engineering mathematics 314

Norbert Gruenwald and Gabriele Sauerbier,

Wismar University of Technology, Germany,

Tatyana Zverkova, Odessa National University, Ukraine

and Sergiy Klymchuk, Auckland University of Technology, New Zealand

6.3 Modelling as an integrated part of the class on calculus 323

Adolf Johannes Riede, Ruprecht-Karls-Universität, Heidelberg, Germany

6.4 Case study: Leak detection in a pipeline 332

Andrei Kolyshkin, Riga Technical University, Latvia

6.5 Discrete and continuous models for the evolution of 340

lizard populations

Michael Jones and Arup Mukherjee, Montclair State University, New Jersey, USA

6.6 Modelling and problem solving in billiards 349

Burkhard Alpers,  Aalen University of Applied Sciences: Germany

6.7 The lottery of Casanova 359

Hans-Wolfgang Henn and Andreas Büchter, University of Dortmund, Germany

6.8 Model transitions in the real world: The Catwalk problem 368

Thomas Lingefjärd and Mikael Holmquist, Gothenburg University, Sweden

6.9 Fractal image compression 377

Franceso Leonetti, University of L’Aquila, Italy

6.10 Modelling heat flow in work rolls 386

Leticia Corral, Instituto Tecnológico de Cd. Cuauhtémoc, Chihuahua, Mexico,

Rafael Colás, UANL, San Nicolás de los Garza, Mexico and Antonino Hernández,
        Centro de Investigación en Materiales

Avanzados, Chihuahua, México

6.11 Applications of modelling in engineering and technology 395

Sanowar Khan, Kenneth Grattan and Ludwik Finkelstein,  City University, London, UK

Section 7: Behaviours in Engineering and Applications 405

7.1 Mathematics in architecture education 406

Igor Verner and Sarah Maor,  Technion – Israel Institute of Technology

7.2 Modelling in Engineering: Advantages and difficulties 415

Maria Salett Biembengut and Nelson Hein, Universidade Regional de Blumenau, Brazil

7.3 Modelling: Difficulties for novice engineering students 424

Marta Anaya, María Inés Cavallaro and María Cristina Domínguez,

University of Buenos Aires, Argentina

7.4 Integration of applications in the Technion calculus course 433

Shuki Aroshas, Igor Verner and Abraham Berman,        Technion – Israel Institute of Technology

7.5 Mathematical modelling modules for calculus teaching 443

Qiyuan Jiang and Jinxing Xie, Tsinghua University, China

and Qixiao Ye, Beijing Institute of Technology, China

7.6 An experimental approach to teaching modelling 451

Ken Houston and Mark McCartney, University of Ulster, UK

7.7 Modelling for pre-service teachers 458

Susann Mathews and Michelle Reed, Wright State University, Dayton, Ohio, USA

7.8 The Finnish Network for mathematical modelling 465

          Robert Piché, Seppo Pohjolainen, Kari Suomela, Kirsi Silius and
         Anne-Maritta  Tervakari, Tampere University of Technology, Finland

7.9 Learning environment through modelling and computing 473

Regina Lino Franchi, Methodist University of Piracicaba, Brazil

7.10 Modelling is for reasoning 480

Luís Soares Barbosa and Maria Helena Martinho, Minho University, Braga, Portugal

Authors’ contact email addresses 490