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

Major Sponsors

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 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.

Foreword

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 DAmbrosio, 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 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.

Presented Papers

Keynote Plenary Address

Language and Mathematics: A Model for Mathematics in the 21^st Century

David K. Pugalee (IQB Visiting Professor) 1

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 Andāns & 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

Pre-service teachers mathematics profiles and the influence thereof on their instructional behaviour

Hayley Barnes 39

The Relationship between Didactics and Classroom Management: Towards New Tools for the Training of Math Teachers

Michel Beaudoin & Catherine Lanaris 43

Learning Mathematics through Scientific Contents and Methods

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

Possibilities and Challenges of Mathematical Modeling in Teachers Formation

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

Bjørn Bjørneng 64

Origami-Mathematics Lessons: Researching its Impact and Influence on Mathematical Knowledge and Spatial Ability of Students

Norma Boakes 69

Linking Geometry, Algebra and Calculus with GeoGebra

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 Childrens Understanding of Place Value

Sandra Browning 86

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

Marcia M. Burrell & Clayton Cohn 90

The Role of Dynamic Interactive Technology in Teaching and Learning Statistics

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

Basic knowledge and Basic Ability: A Model in Mathematics Teaching in China

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 Womens Knowledges in their Childrens 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

Matrices and Routing

Ajda Foner 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 Gole 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

Transcribing an Animation: The case of the Riemann Sums

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

Community Engagement: Home School Partnership

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

Preventing Pushing for Privileged Passage: A study of a charter school working to step back from tracking
Tina Louise Johnston 282

Creating and Utilizing Online Assignments in a Calculus Class

Veselin Jungic, Deborah Kent & Petra Menz 287

Understanding Quadratic Functions Using Real World Problems and IT

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

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

An Apt Perspective of Analysis

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

Experience with solving real-life math problems in DQME II project

Koreňová L., Dillingerová M., Vankú P., idová D 333

Workshop: Some interesting math problems for high school students solved by graphic calculators CASIO

Koreňová L., idová 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

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

The van Hiele Phases of Learning in studying Cube Dissection

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 students activities

Céline Liedmann 368

A Collaborative Model for Calculus ReformA 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, 1930s 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

Open-Ended Approach To Teaching And Learning Of High School Mathematics

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

A class practice to improve students attitude towards mathematics
Maria Flavia Mammana & Mario Pennisi 395

Identifying Modelling Tasks

Stefanie Meier 399

Paper&Pencil Skills in the 21st Century, a Dichotomy?

Hartwig Meissner & Annabella Diephaus 404

How to Solve It

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

To Teach Combinatirics, Using Selected Problems

Laurenţiu Modan 420

Modelling Geometric Concepts Via Pop-Up Engineering

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

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

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

A 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

The use of visualization for learning and teaching mathematics

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

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

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

Good classroom practice how a new journal supports this

Rüdiger Vernay Please Note Page 335

A Stochastic Model for the Process of Learning

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

DeltaTick: Applying Calculus to the Real World through Behavioral Modeling

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

Papers Accepted for the Proceedings but not Presented at the Conference

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

George Malaty, Miriam Amit, Filippo Spagnolo And Franco Favilli

3. Innovation Working Group

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