**
The Mathematics
Education into the 21 ^{st} Century Project **

**
**

**
**

** University
of Applied Sciences, Dresden**

** **

** ** Proceedings
of the 10^{th} 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

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
21 ^{st} 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

Major Sponsors

International Program Committee

** **

**Chairmen**

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,
Southeastern
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**

**Chairman**

Prof. Dr. Ludwig Paditz, Dresden University of Applied Sciences.

**Vice-Chairman**

Dr. Rainer Heinrich, Ministry of Education of Saxony.

Prof.
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 alan@rogerson.pol.pl

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 21 ^{st}
Century**

**
David K. Pugalee (IQB Visiting Professor)****
**1

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

** **

**Workshop Summary**

**Mathematics
brought to life by the Millennium Mathematics Project**

Nadia Baker 37

Hayley
Barnes
39

Michel
Beaudoin & Catherine
Lanaris
43

Astrid Beckmann 47

** **

**Rescuing**
**Statistics from the Mathematicians**

Mike Bedwell 52

** **

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

Bjørn Bjørneng 64

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

Sandra Browning 86

Integrating Technology into the Mathematics Classroom: Instructional Design and Lesson Conversion

Marcia M. Burrell & Clayton Cohn 90

Gail Burrill 95

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

Katharine W. Clemmer 116

**
An Alternate Route to Urban Mathematics Teaching: The
NYC
Teaching Fellows Program
**

Laurel A. Cooley 120

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

Joseph Dhlamini 139

**
Mathematical Competitions for University Students**

Alexander Domoshnitsky & Roman Yavich 143

** **

**Internet
Mathematical Olympiads**

Alexander Domoshnitsky & Roman Yavich 146

** **

Ruth J. Duffield 149

Patricia Eaton & Maurice OReilly 153

**
Recognising
Torres Strait Islander
Women’s Knowledges in their Children’s Mathematics Education**

Bronwyn Ewing 157

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

Douglas Franks 176

**Impact
on
Student Achievement of Teacher Participation in K-8 Mathematics
Professional
Development**

Todd Frauenholtz & Derek F. Webb 180

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

Peter Hofbauer 242

Marilyn Holmes 246

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

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

**
Preventing
‘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**

Michael
Katzenbach
296

**Does
the
parameter represent a fundamental concept of linear algebra?**

Stefan-Harald Kaufmann 300

**
Using the
Media as a Means to Develop
Students’ Statistical Concepts **

Marian Kemp
302

Zohreh Ketabdar 307

**Professional
Development for Mathematics Teachers Through Lesson Study**

Azimeh Sadat Khakbaz 312

** **

Nanad Kishore & Ramesh Chandra 317

** **

**
Models
for harnessing the Internet
in mathematics education
**Barry
Kissane
319

**
Cryptography
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

** **

**
Accompanying
“in-service teaching”
internships of prospective mathematics teachers – a model for
encouraging
exchange between theory and practice using the triple coaching approach
**

Sebastian Kuntze,
Anke Wagner & Claudia
Wörn
336

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

Millard Lamm & David K. Pugalee 364

**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

**
Changes
in the North Carolina
Mathematics Curriculum: A Comparative Study, 1920s, 1930’s with 2003
**
Corey Lock &
David Pugalee
376

** **

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

George Malaty 390

**
A
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

Luigi Menna 409

**
Tasks
for tests and A-levels using
CAS**

Heidi
Metzger-Schuhäker
413

**Models of
Mathematics Curriculum Development in Egypt**

Fayez M. Mina 417

Laurenţiu Modan 420

Vivekanand Mohan-Ram 423

Lesego Brenda Mokotedi 427

Hassan. M. Mustafa
&`
Ayoub
Al-Hamadi
431`

** **

Willy Mwakapenda 436

Dicky Ng 440

** **

**Mathematics
Teacher TPACK Standards and Revising Teacher Preparation**

Margaret Niess 445

Mehryar Nooriafshar 450

**Chapter-spanning
Review:
Teaching Method for Networking in Math Lessons**

Swetlana Nordheimer 454

**
Students’
knowledge of
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

Ludwig Paditz 469

Mandy Parnell 475

**
A
Discussion of different teaching
strategies adopted during a Statistics tutorial**

Vasos
Pavlika
477

Theresa Perez & David K. Pugalee 481

**Cooperative
Learning and Peer Tutoring to Promote Students’ Mathematics Education**

Angela Pesci 486

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

** **

Ildar S. Safuanov & Valery A. Gusev 505

** **

** **

**
Innovations
in Podcasting and
Screencasting Course Materials To Bring Mathematics to Life**

Paula Savich & Sandra Pierce 509

** **

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

**
Mathematics
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

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

**
Improving
Student Interest,
Mathematical Skills, and Future Success through Implementation of Novel
Mathematics Bridge Course for High School Seniors and Post-secondary
Students**

Derek Webb,
Glen Richgels, Marty J. Wolf, Todd Frauenholtz &

Ann Hougen 575

**Family
Maths and
Complexity Theory**

Paul Webb & Pam Austin 579

**
Elementary
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
given
Function** **to the Modelling of a Problem
with the
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

**
Using
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**

**
**

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“**

Günter Graumann

**6.
****Applications and
Statistics**

Members: Ivan Meznik, Gail Burrill & Viktor Freiman