The Mathematics Education into the 21st Century Project
University of Applied Sciences, Dresden
Proceedings of the 10th International Conference
“Models in Developing Mathematics Education”
September 11-17, 2009
Dresden, Saxony, Germany
Editors: Ludwig Paditz & Alan Rogerson
CASIO www.casio-europe.com Autograph www.autograph-maths.com
Dynatech www.dynatech.de VON ARDENNE www.vonardenne.biz
Printing supported by the Dresden University of Applied Sciences
ISBN Number 83-919465-9-2
All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright holder.
The Mathematics Education into the 21st Century Project wishes to thank for their support:
Saxony Ministry of Education
Saxony Ministry of Science and the Arts
Dresden University of Applied Sciences (HTW)
The Institute for Educational Progress (IQB) Berlin
Dresden University of Technology (TU)
Gesellschaft für Didaktik der Mathematik (GDM)
MUED, DQME II, MAV, MERGA, Wholemovement
The Hong Kong Institute of Education
ALMA Teacher Training Centre, Poland
International Program Committee
Dr. Alan Rogerson, Coordinator of the Mathematics in Society Project (Poland).
Prof. Dr. Fayez Mina, Professor Emeritus, Ain Shams University (Egypt).
Prof. Khaled Abuloum, University of Jordan (Jordan).
Prof. Roberto Baldino, UNESP (Brazil).
Dr. Andy Begg, Auckland University of Technology (New Zealand).
Dr. Donna F. Berlin, The Ohio State University (USA).
Prof. Dr. Werner Blum, University of Kassel (Germany).
Prof. Ubiratan D'Ambrosio, Campinas/UNICAMP (Brazil).
Prof. Bruno D'Amore, University of Bologna (Italy).
Prof. Dr. Tilak de Alwis,
Louisiana University (USA).
Prof. Dr. William Ebeid, Emeritus Professor, Ain Shams University (Egypt).
Prof. Paul Ernest, University of Exeter (UK).
Prof. Dr. Gabriele Kaiser, Hamburg University (Germany).
Dr. Madeleine J. Long, Hunter College, City University of New York (USA).
Prof. Nicolina Malara, University of Modena (Italy).
Prof. Dr. M. Ali M. Nassar, Institute of National Planning (Egypt).
Prof. Lionel Pereira Mendoza, Educational Consultant (Canada).
Prof. Angela Pesci, University of Pavia (Italy).
Prof. Medhat Rahim, Lakehead University, Faculty of Education (Canada).
Prof. Filippo Spagnolo, University of Palermo, Sicily (Italy).
Prof. Dr. Alicia Villar Icasuriaga, IPA, Montevideo (Uruguay).
Dr. Arthur L. White, The Ohio State University ( USA).
Prof. Wacek Zawadowski, Siedlce University (Poland).
Local Organizing Committee
Prof. Dr. Ludwig Paditz, Dresden University of Applied Sciences.
Dr. Rainer Heinrich, Ministry of Education of Saxony.
Dr. Stefan Deschauer, Dresden
University of Technology.
Prof. Dr. Michael Jung, Dresden University of Applied Sciences.
Prof. Dr. Claus Lange, Dresden University of Applied Sciences.
Prof. Dr. Klaus Neumann, Dresden University of Applied Sciences.
Prof. Dr. Wolfgang Preuß, Dresden University of Applied Sciences.
Prof. Dr. Matthias Richter, Dresden University of Applied Sciences.
Prof. Dr. Margit Voigt, Dresden University of Applied Sciences.
Prof. Dr. Matthias Weber, Dresden University of Applied Sciences.
Dr. Hans-Dieter Dahlke, Dresden University of Applied Sciences.
Dr. Martina Timmler, Dresden University of Applied Sciences.
This volume contains the papers presented at the International Conference on “Models in Developing Mathematics Education” held from September 11-17, 2009 at The University of Applied Sciences, Dresden, Germany. The Conference was organized jointly by The University of Applied Sciences and The Mathematics Education into the 21st Century Project - a non-commercial international educational project founded in 1986. The Mathematics Education into the 21st Century Project is dedicated to the improvement of mathematics education world-wide through the publication and dissemination of innovative ideas. Many prominent mathematics educators have supported and contributed to the project, including the late Hans Freudental, Andrejs Dunkels and Hilary Shuard, as well as Bruce Meserve and Marilyn Suydam, Alan Osborne and Margaret Kasten, Mogens Niss, Tibor Nemetz, Ubi D’Ambrosio, Brian Wilson, Tatsuro Miwa, Henry Pollack, Werner Blum, Roberto Baldino, Waclaw Zawadowski, and many others throughout the world. Information on our project and its future work can be found on Our Project Home Page http://math.unipa.it/~grim/21project.htm
It has been our pleasure to edit all of the papers for these Proceedings. Not all papers are about research in mathematics education, a number of them report on innovative experiences in the classroom and on new technology. We believe that “mathematics education” is fundamentally a “practicum” and in order to be “successful” all new materials, new ideas and new research must be tested and implemented in the classroom, the real “chalk face” of our discipline, and of our profession as mathematics educators. These Proceedings begin with a Plenary Paper and then the contributions of the Principal Authors in alphabetical name order. We sincerely thank all of the contributors for their time and creative effort. It is clear from the variety and quality of the papers that the conference has attracted many innovative mathematics educators from around the world. These Proceedings will therefore be useful in reviewing past work and looking ahead to the future. For further information about the work of our Project, please email firstname.lastname@example.org
We wish to thank especially Fayez Mina and Rainer Heinrich for all their support and hard work without which this conference, and these Proceedings, would not have been possible. A special thanks are also due to all our very generous major sponsors, the Saxony Ministries of Education and Science & the Arts and the City of Dresden.
Keynote Plenary Address
Language and Mathematics: A Model for Mathematics in the 21st Century
Proofs and "Puzzles"
Buma Abramovitz, Miryam Berezina, Abraham Berman & Ludmila Shvartsman 5
Some Initiatives in Calculus Teaching
Buma Abramovitz, Miryam Berezina, Abraham Berman & Ludmila Shvartsman 10
A Study On Problem Posing-Solving in the Taxicab Geometry and Applying Simcity Computer Game
Tuba Ada & Aytaç Kurtuluş 15
An innovative model for developing critical thinking skills through mathematical education
Einav Aizikovitsh & Miriam Amit 19
The “Kidumatica” project - for the promotion of talented students from underprivileged backgrounds
Miriam Amit 23
How do rabbits help to integrate teaching of mathematics and informatics?
Agnis Andžāns & Laila Rācene 28
Conjecturing (and Proving) in Dynamic Geometry after an Introduction of the Dragging Schemes
Anna Baccaglini-Frank 31
Mathematics brought to life by the Millennium Mathematics Project
Nadia Baker 37
Pre-service teachers’ mathematics profiles and the influence thereof on their instructional behaviour
The Relationship between Didactics and Classroom Management: Towards New Tools for the Training of Math Teachers
Beaudoin & Catherine
Astrid Beckmann 47
Rescuing Statistics from the Mathematicians
Mike Bedwell 52
Presentation of the Digital School Journal Revista Escolar de la Olimpiada Iberoamericana de Matemática, Sponsored by the O.E.I. Organización de Estados Iberoamericanos para la Educación, la Ciencia y la Cultura
Francisco Bellot-Rosado 56
In what case is it possible to speak about Mathematical capability among pre-school children?
Anna V. Beloshistaya 57
Maria Salett Biembengut 60
How to increase the understanding of differentials by using the Casio-calculator model 9860 G I/II to solve differential equations
Bjřrn Bjřrneng 64
Origami-Mathematics Lessons: Researching its Impact and Influence on Mathematical Knowledge and Spatial Ability of Students
Norma Boakes 69
Josef Böhm 74
Innovations in Educational Research and Teaching of Experimental Calculus
Horacio E. Bosch, Claudia Guzner, Mercedes S. Bergero,
Mario A. Di Blasi, Adriana Schilardi & Leonor Carvajal 78
The Best of Both Worlds: Teaching Middle School and College Mathematics
Daniel J. Brahier 83
Language and Number Values: The Influence of the Explicitness of Number Names on Children’s Understanding of Place Value
Sandra Browning 86
Integrating Technology into the Mathematics Classroom: Instructional Design and Lesson Conversion
Marcia M. Burrell & Clayton Cohn 90
Gail Burrill 95
Presentations Using Autograph
Douglas Butler 100
Elementary Teacher Candidates’ Understanding of Rational Numbers: An International Perspective
Rose Elaine Carbone 101
Use and misuse of quantitative and graphical Information in Statistics. An Approach in Teaching
Lucette Carter & Cécile Hardouin 106
Cheng Chun Chor-Litwin 111
How Involving Secondary Students in the Assessment Process Transforms a Culture of Failure in Mathematics to a Culture of Accountability, Self-Efficacy and Success in Mathematics Student Action Plans, Assessment, and Cultural Shift
Katharine W. Clemmer 116
An Alternate Route to Urban Mathematics Teaching: The NYC Teaching Fellows Program
Laurel A. Cooley 120
Analyzing the effects of a linguistic approach to the teaching of algebra: students tell “stories of development” revealing new competencies and conceptions
Annalisa Cusi 124
Localization of Learning Objects in Mathematics
Valentina Dagiene & Inga Zilinskiene 129
Large-Scale Assessment as a Tool for Monitoring Learning and Teaching: The Case of Flanders, Belgium
Erik De Corte, Rianne Janssen & Lieven Verschaffel 134
Connections between Mathematics and Arts & Culture: An exploratory Study with Teachers in a South African school
Joseph Dhlamini 139
Mathematical Competitions for University Students
Alexander Domoshnitsky & Roman Yavich 143
Internet Mathematical Olympiads
Alexander Domoshnitsky & Roman Yavich 146
Essential Ingredients that form the basis for Mathematical Learning: What has 20 years of teaching mathematics to teenagers taught me?
Ruth J. Duffield 149
Exploring mathematical identity as a tool for self-reflection amongst pre-service primary school teachers: “I think you have to be able to explain something in about 100 different ways”
Patricia Eaton & Maurice OReilly 153
Recognising Torres Strait Islander Women’s Knowledges in their Children’s Mathematics Education
Bronwyn Ewing 157
Proportional Reasoning Models in Developing Mathematics Education Curricula for Prospective Elementary School Teachers
Beverly J. Ferrucci & Jack Carter 162
Modelling in Mathematics and Informatics: How Should the Elevators Travel so that Chaos Will Stop?
Andreas Filler 166
Ajda Fošner 172
Mathematics Professional Learning Communities: Opportunities and Challenges in an Elementary School Context
Douglas Franks 176
Impact on Student Achievement of Teacher Participation in K-8 Mathematics Professional Development
Todd Frauenholtz & Derek F. Webb 180
One mathematical formula in the science textbook: looking into innovative potential of interdisciplinary mathematics teaching
Viktor Freiman 184
The Role of the Music to Learn Geometrical Transformations
Daniela Galante 189
A Cross-Cultural Comparison of Algebra 1 Students’ Achievement
Sofokli Garo 195
Can Early Algebra lead non-proficient students to a better arithmetical understanding?
Sandra Gerhard 199
Problems to put students in a role close to a mathematical researcher
Nicolas Giroud 202
Toward Calculus via Real-time Measurements
Tine Golež 204
Problem Fields in Elementary Arithmetic
Günter Graumann 209
Disrupting linear models of mathematics teaching|learning
Barbara Graves & Christine Suurtamm 215
Modelling tasks for learning, teaching, testing and researching
Gilbert Greefrath 219
May Hamdan 223
Each and Every Student: The Stamford, Connecticut Model for Change in Mathematics
Mona Hanna, Carrie Chiappetta 227
Folding the circle in half is a text book of information
Bradford Hansen-Smith 231
CAS and calculation competence of students
Dr. Rainer Heinrich 235
Using Data Modeling at the Elementary Level to Make Sense of Doing Mathematics and Science
Marjorie Henningsen & Nisreen Ibrahim 239
The use of notebooks in mathematics instruction: What is manageable? What should be avoided? A field report after 10 years of CAS-application.
Peter Hofbauer 242
Marilyn Holmes 246
Modelling the Transition from Secondary to Tertiary Mathematics Education: Teacher and Lecturer Perspectives
Ye Yoon Hong, Suzanne Kerr, Sergiy Klymchuk, Johanna McHardy,
Priscilla Murphy, Sue Spencer, Mike Thomas & Peter Watson 250
Linking Teachers and Mathematicians: The AWM Teacher Partnership Program
Pao-sheng Hsu, Suzanne Lenhart & Erica Voolich 255
Project work Is the Legacy of Ancient Greece and Rome really the Cradle of European Civilization?
Darka Hvastija & Jasna Kos 259
A Model to Develop Mathematics Education: Modify the Public Traditional Perceptions of Mathematics-Case of UAE Schools’ Principals
Hanan Innabi 262
A Four Phase Model for Predicting the Probabilistic Situation of Compound Events
Irma Jan & Miriam Amit 267
From a textbook to an e-learning course (E-learning or e-book?)
Antonín Jančařík & Jarmila Novotná 272
Reflections on an Initiative to Improve Junior Secondary School Pupils’ Understanding of Number
Noel Johnston 277
‘Pushing for Privileged
Passage’: A study of a charter school working to step back from tracking
Tina Louise Johnston 282
Veselin Jungic, Deborah Kent & Petra Menz 287
Nakhshin A. Karim 291
Individual Approaches in Rich Learning Situations Material-based Learning with Pinboards
Does the parameter represent a fundamental concept of linear algebra?
Stefan-Harald Kaufmann 300
Media as a Means to Develop
Students’ Statistical Concepts
Marian Kemp 302
A program for reducing teacher's resistance to changes in curriculum in centralized education systems. An experience on changes of mathematics text books in Iran based on distinction results
Zohreh Ketabdar 307
Professional Development for Mathematics Teachers Through Lesson Study
Azimeh Sadat Khakbaz 312
Nanad Kishore & Ramesh Chandra 317
for harnessing the Internet
in mathematics education
Barry Kissane 319
and number theory
in the classroom -- Contribution of cryptography to mathematics teaching
Katharina Klembalski 323
Using History to Teach Mathematics
Jacqui Klowss 328
The use of technology to motivate, to present and to deepen the comprehension of math
Damjan Kobal 331
Koreňová L., Dillingerová M., Vankúš P., Židová D 333
Workshop: Some interesting math problems for high school students solved by graphic calculators CASIO
Koreňová L., Židová D 335
internships of prospective mathematics teachers – a model for
exchange between theory and practice using the triple coaching approach
Sebastian Kuntze, Anke Wagner & Claudia Wörn 336
The influence of localization and materialization of mathematics activities on the indigenous first grade students’ learning effects: Two assessment results
Li Tsung Wen Kuo, Wei-Hao Cheng & Chih-Chen Kao 341
Interactive PDF Documents in Math Education. Focused on Tests for Differential Equations
Silvie Kuráňová 347
Helping a Young Child Connect Fact Family Addition and Subtraction using Tools
Terri L. Kurz, H. Bahadir Yanik & Jorge Garcia 353
Shi-Pui Kwan & Ka-Luen Cheung 358
Elementary Students’ Construction of Proportional Reasoning Problems: Using Writing to Generalize Conceptual Understanding in Mathematics
Millard Lamm & David K. Pugalee 364
How to teach modeling in mathematics classrooms? The implementation of modeling tasks. Comparing learning arrangements and teacher methods with respect to student’s activities
A Collaborative Model for Calculus Reform—A Preliminary Report
Po-Hung Liu, Ching-Ching Lin, Tung-Shyan Chen, Yen-Tung Chung,
Chiu-Hsiung Liao, Pi-Chuan Lin, Hwai-En Tseng & Ruey-Maw Chen 372
in the North Carolina
Mathematics Curriculum: A Comparative Study, 1920s, 1930’s with 2003
Corey Lock & David Pugalee 376
Bridging the gap between technology design and school practice: a specific experiment within the ReMath Project
Laura Maffei 378
The Effect of Rephrasing Word Problems on the Achievements of Arab Students in Mathematics
Asad Mahajne & Miriam Amit 383
Radley Kebarapetse Mahlobo 386
Mathematics and Mathematics Education Development in Finland: the impact of curriculum changes on IEA, IMO and PISA results
George Malaty 390
class practice to improve
student’s attitude towards mathematics
Maria Flavia Mammana & Mario Pennisi 395
Stefanie Meier 399
Paper&Pencil Skills in the 21st Century, a Dichotomy?
Hartwig Meissner & Annabella Diephaus 404
How to Solve It
Luigi Menna 409
for tests and A-levels using
Heidi Metzger-Schuhäker 413
Models of Mathematics Curriculum Development in Egypt
Fayez M. Mina 417
Laurenţiu Modan 420
Vivekanand Mohan-Ram 423
Exploring the mathematics that children read in the world: A case study of Grade 8 learners in a South African School
Lesego Brenda Mokotedi 427
On Teaching Quality Improvement of a Mathematical Topic Using Artificial Neural Networks Modeling (With a Case Study)
Hassan. M. Mustafa & Ayoub Al-Hamadi 431
New Forms of Assessment in the South African Curriculum Assessment Guidelines: What Powers do Teachers Hold?
Willy Mwakapenda 436
Investigating Elementary Teachers’ Mathematical Knowledge for Teaching Geometry: The Case of Classification of Quadrilaterals
Dicky Ng 440
Mathematics Teacher TPACK Standards and Revising Teacher Preparation
Margaret Niess 445
Balancing the Use of Technology and Traditional Approaches in Teaching Mathematics within Business Courses
Mehryar Nooriafshar 450
Chapter-spanning Review: Teaching Method for Networking in Math Lessons
Swetlana Nordheimer 454
Application of Mathematics – From Diagnostics to Innovations
Reinhard Oldenburg 459
From Physical Model To Proof For Understanding Via DGS: Interplay Among Environments
Iman M. Osta 464
Using ClassPad-technology in the education of students of electrical engineering (Fourier- and Laplace-Transformation)
Ludwig Paditz 469
Reflective practices – a means to instil a deep learning approach to mathematics or another time consuming fad? Work-in-progress.
Mandy Parnell 475
Discussion of different teaching
strategies adopted during a Statistics tutorial
Vasos Pavlika 477
The Learning of Mathematics for Limited English Proficient Learners: Preparation of Doctoral Level Candidates
Theresa Perez & David K. Pugalee 481
Cooperative Learning and Peer Tutoring to Promote Students’ Mathematics Education
Angela Pesci 486
Building leadership capacity in the development and sharing of mathematics learning resources, across disciplines, across universities
Anne L. Porter 491
Medhat H. Rahim & Radcliffe Siddo 496
Clearness as a Principle of the Teaching of Mathematics
Ildar S. Safuanov & Irina G. Shamsutdinova 501
Creative mathematical activity of the students in the Model of Differentiated Teaching in Russian Federation
Ildar S. Safuanov & Valery A. Gusev 505
Innovations in Podcasting and Screencasting Course Materials To Bring Mathematics to Life
Paula Savich & Sandra Pierce 509
Concept Literacy in Mathematics and Science: experiences with the development and use of a multilingual resource book in Xhosa, Zulu, English and Afrikaans in South Africa
Marc Schäfer 512
Single Sex Mathematics Classes: A Critical Analysis of the Impact at a Secondary School
Angelique Seifert & David K. Pugalee 517
Visual Modeling of Integrated Constructs in Mathematics As the Base of Future Teacher Creativity
Eugeny Smirnov, Sergei Burukhin & Irina Smirnova 520
Using Technology to Discover and Explore Linear Functions and Encourage Linear Modeling
Tanja Soucie, Nikol Radović , Renata Svedrec & Helena Car 524
Virtual Manipulatives: Design-based Countermeasures to Selected Potential Hazards
William R. Speer 526
Teaching for the objectification of the Pythagorean Theorem
Panagiotis Spyrou 530
education reform: The
role of coherence within the complexity of change
Christine Suurtamm & Barbara Graves 535
Mathematics games: Time wasters or time well spent?
Paul Swan and Linda Marshall 540
On Evaluation Problem of the Quality of Educational Models
Vladimir A. Testov 545
How Can a System with no Public Exams be Fair?
Kerry J Thomas 548
Teaching Mathematics in Eniaio Lykeio (Unified Upper-Secondary Education) with the use of New Technologies
Eleni Tsami 554
Math lessons for the thinking classrooms
Ariana-Stanca Văcăreţu 559
Rüdiger Vernay Please Note Page 335
Michael Gr. Voskoglou 565
Developing explanatory competencies in teacher education
Anke Wagner, Claudia Wörn & Sebastian Kuntze 570
Mathematical Skills, and Future Success through Implementation of Novel
Mathematics Bridge Course for High School Seniors and Post-secondary
Derek Webb, Glen Richgels, Marty J. Wolf, Todd Frauenholtz &
Ann Hougen 575
Family Maths and Complexity Theory
Paul Webb & Pam Austin 579
Mathematics from an
Advanced Standpoint and Elementary Views on Advanced Mathematics
Ysette Weiss-Pidstrygach 584
Michelle H. Wilkerson-Jerde & Uri Wilensky 587
Algebraic Thinking- More to Do with Why, Than X and Y
Windsor W.J.J 592
A New Pedagogical Model for Teaching Arithmetic.
David Womack 596
Solids of Revolution – from the Integration of a
Function to the Modelling of a Problem
help of CAS and GeoGebra
Otto Wurnig 600
A way of computer use in mathematics teaching -The effectiveness that visualization brings-
Shuichi Yamamoto & Naonori Ishii 606
physical experiments in
mathematics lessons to introduce mathematical concepts
Simon Zell 611
Hypothesis Aided Approach to the Instruction of the Limit of a Function
Ivan Mezník 615
Using Digital Video to Strengthen Student Learning of Mathematics
Virginia (Ginny) Keen
Photos of the participants in Dresden
Working Group Reports
1. Technology: A summary of themes and key ideas discussed*
Barry Kissane, Mehryar Noorisfshar & Naikshin Karim
2. Comparative Education
Willy Mwakpenda, Bronwyn Ewing, Ariana Vacaretu
4. Teacher Education and Development
Marjorie Henningsen, Arjorie Henningsen, Beverly Ferrucci, Angela Pesci
5. „Problem Solving“
6. Applications and Statistics
Members: Ivan Meznik, Gail Burrill & Viktor Freiman