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

**
The University
of North Carolina Charlotte**

Mathematics Education in a Global Community

**Editors**

**
David K. Pugalee, Alan Rogerson &
Amélie
Schinck**

** **

**
Sep 7-12, 2007**

**
Major Sponsors
**

**
CASIO,
Autograph, Charlotte Regional Visitors Authority **

**
**

**
Printing
supported by the Center for Mathematics, Science & Technology Education, UNCC**

**
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:**

**
Wholemovement, The Hong Kong
Institute of Education**

**
ALMA Teacher Training Centre,
Poland**

**
**

**
Major Sponsors**

**
**

**
Autograph**

ISBN Number 83-919465-8-4

**
**

**
International Program Committee**

**Chairman
**Dr. Alan Rogerson,
International Coordinator of the Mathematics in Society Project (Poland).

Prof Khaled Abuloum, University of Jordan (Jordan).

Professor Roberto Baldino, UNESP (Brazil).

Dr. Andy Begg , University of Waikato (New Zealand).

Dr. Donna F. Berlin, The Ohio State University (USA)

Prof. Dr. Werner Blum, University of Kassel (Germany).

Professor Ubiratan D'Ambrosio, Campinas/UNICAMP, (Brazil).

Professor Bruno D'Amore, University of Bologna (Italy).

Professor Dr.
Tilak de Alwis, Southeastern Louisiana University (USA)

Prof Dr William Ebeid, Emeritus Professor, Faculty of Education, Ain Shams
University (Egypt).

Professor 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 Dr Fayez Mina, Faculty of Education, Ain Shams University (Egypt).

Prof Nicolina Malara, University of Modena (Italy)

Prof Dr M. Ali M. Nassar, Director of Planning Center, Institute of National Planning (Egypt).

Professor Lionel Pereira Mendoza, Associate Professor, NIE (Singapore).

Professor Angela Pesci, University of Pavia (Italy)

Prof. Medhat Rahim, Lakehead University, Faculty of Education (Canada).

Professor Filippo Spagnolo, University of Palermo, Sicily, (Italy).

Professor Dr. Alicia Villar Icasuriaga, IPA, Montevideo, (Uruguay)

Dr. Arthur L. White, The Ohio State University ( USA)

Professor. Wacek Zawadowski, Siedlce University (Poland).

**
Local Organizing Committee**

**Chairman**:
Associate Professor Dr. David K. Pugalee, (dkpugale@email.uncc.edu)

Sally Adkin, North Carolina School of Science and Mathematics (adkin@ncssm.edu)

Laura Brinker, University of South Carolina (LBrinker@gwm.sc.edu)

Vic Cifarelli, University of North Carolina Charlotte (vvcifare@email.uncc.edu)

Dr. Beth Costner, Winthrop University (costnerb@winthrop.edu)

Cos D Fi, University of North Carolina at Greensboro (cdfi@uncg.edu)

Patsy (Patricia) Douville, University of North Carolina Charlotte (pdouvill@email.uncc.edu)

Susan Friel, University of North Carolina at Chapel Hill (sfriel@email.unc.edu)

Adam Harbaugh, University of North Carolina Charlotte (apharbau@email.uncc.edu)

Timothy Hendrix, Meredith College (Hendrixt@meredith.edu)

Karen Hollenbrands, North Carolina State University (karen_hollebrands@ncsu.edu)

Corey Lock, University of North Carolina Charlotte (crlock@email.uncc.edu)

Carol Malloy, UNC Chapel Hill (cmalloy@email.unc.edu)

Henry Neale, Charlotte Country Day School/UNC Charlotte (henry.neale@charlottecountryday.org

Drew Polly, University of North Carolina Charlotte (abpolly@uncc.edu)

Ron Preston, East Carolina University (PRESTONR@MAIL.ECU.EDU)

Sid Rachlin, Association of Mathematics Teacher Eductors, President, (rachlins@ecu.edu)

David Royster, Director, Center for Mathematics, Science & Technology Education, UNCC, (droyster@email.uncc.edu)

Norma Royster, Cabarrus County Schools/UNC Charlotte(nroyster@cabarrus.k12.nc.us)

Bill Scott, Charlotte-Mecklenburg Schools (bill.scott@cms.k12.nc.us)

Olof Steinthorsdottir, University of North Carolina at Chapel Hill (steintho@email.unc.edu)

Hollylynne Stohl Lee, North Carolina State University (Hollylynne@ncsu.edu )

This volume contains the
papers presented at the International Conference on **
Mathematics Education in a Global Community **
held from September 7-12, 2007 at The University of North
Carolina Charlotte
http://www.uncc.edu and
the Hilton Charlotte University Place Hotel
www.charlotteuniversity.hilton.com

**Project Home Page**
which leads directly to the Charlotte Conference First** **Announcement
pdf:** **
http://math.unipa.it/~grim/21project.htm

http://math.unipa.it/~grim/21_malasya_2005.doc - Malaysia 2005 Conference

http://math.unipa.it/~grim/21project.htm
- Our Project Home Page

http://math.unipa.it/~grim/egypt.pdf - Egypt Conference site

http://math.unipa.it/~grim/jourdain - Jordan conference site

http://math.unipa.it/~grim/cairms - Australia conference site

http://math.unipa.it/~grim/palermo2002 - Sicily Conference site

http://dipmat.math.unipa.it/~grim/21_project/21_brno_03.htm - Brno Conference site

http://math.unipa.it/~grim/21_project/21_ciechocinek_04.htm - Ciechocinek Conference site

Filippo Spagnolo, of Palermo University, is webmaster for the above sites. Felix Rieper has compiled at: http://www.ph-heidelberg.de/wp/filler/ciecho04/index.htm, a photo album of the Ciechocinek Conference.Krys Bestry is webmaster for our Polish Superkurs Home Page and National Planning Meetings webpage www.cdnalma.poznan.pl (in Polish - but with pictures!) See also: http://www.vsg.edu.au/egypt99/ for more information about our project and its work. For the Brno conference see http://www.math.muni.cz/matheduconf.sept2003.

It has been our pleasure to read all of the papers and to edit them 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 so 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 the Plenary Papers and otherwise contain contributions mostly in alphabetical order of the Principal Presenters. 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 arogerson@inetia.pl

Alan Rogerson, Amélie Schinck & David Pugalee

** **

**
Plenaries**

CLASSROOM GADGETS

- NOW WHAT?

Douglas Butler

Director, iCT Training Centre (Oundle
School), Peterborough, UK

Email:
debutler@argonet.co.uk

Web:
www.tsm-resources.com

**
Douglas Butler Plenary Address
**

**
**The
Malaysian Experience

Noor Azlan Ahmad Zanzali

Universiti Teknologi Malaysia azanzali@utm.my

** **
Mohammed Fdhle Ali Ahmed

** **

** **
Renu Ahuja

** **

**
Translations towards connected mathematics (Workshop)**

Mark Applebaum & Roza Leikin

**
The Family
Maths Programme, Developing Inquiry-based Teaching**

Pam Austin & Paul Webb

Anna Baccaglini-Frank & Al Cuoco

**
Theory Practice
Service Learning in a Statistics Class**

Evelyn C. Bailey

**
Improve Mathematics
Education – Teach Mathematics as an Experimental Science**

Peter Baptist

Candace Barriteau Phaire

Virginia Bastable

**
The Effects of the
Use of Explicit Number Names on Mathematical Understanding and Performance**

** **
Judith E. Beauford & Sandra Browning

Stephanie L. Behm & Gwendolyn M. Lloyd

Valerie Bell, Sarah Ives, Gemma Mojica & Ryan C. Smith

**
Mathematics
Education Issues in post-Soviet Kazakhstan:An International Perspective**

Zaur Berkaliev

**
Using a Cultural
Context to Integrate Mathematics and Science Education**

Donna F. Berlin

**
Developing Algebraic
Habits of Mind from the Context of Computer Science (Workshop)**

Phyllis Bolin & Connie H. Yarema

Christine Browning and Gina Garza-Kling

**
Using Statistics to
Improve Education: A Dilemma**

Gail Burrill

**
Mathematical
Relations in Architecture and Spatial Design**

Jane Burry

**
Giving All Students a
Voice in the Elementary Mathematics Classroom**

Megan Burton

**Making the new MS Office 2007
Mathematically Friendly**

Douglas Butler

**
Fun with Autograph for the youngsters (Workshop for teachers of years 7-10) **

Douglas Butler

**Pushing the boundaries with Autograph
(Workshop for teachers of years 11-12)**

Douglas Butler

**
Relational Notation & Mapping
Structures: A Data Analysis Framework**

Günhan Caglayan

Bernardo Camou

**
What are students thinking as they
solve open-ended mathematics problems?**

Mary Margaret Capraro, Robert M. Capraro & Victor V. Cifarelli

R. Elaine Carbone & P. Eaton

** **Nancy Cerezo,
Sylvia Rockwell, Carol Walker, Valerie Wright & Monika Vo

**
Power Series Explorations In
Precalculus**

Ken Collins

**
In what sense is it true to claim
that mathematics is culture-free?**

David M. Davison

**
Investigating Social and Individual
aspects in Teachers’ approaches to Mathematical Problem Solving**

Erik De Corte, Fien Depaepe & Lieven Verschaffel

**
"Workshop of Mathematical Talent", a
Wonderful Educational Experience**

Fernando de la Cueva Landa & Elena Gil Clemente

**
Proof in Dynamic Geometry: More than
Verification**

Michael de Villiers

**
Preparing Teachers for Democratic
Mathematics Education**

Mark Ellis & Carol E. Malloy

**
Development and Validation of the
Calculus Concept Inventory**

Jerome Epstein

**
The Integrated Laboratory Program for
Cognitive Development**

Jerome Epstein

**
Community engagement: Talking about
Mahematics**

Bronwyn Ewing

**
Participation and Non-Participation
in Mathematics Classrooms**

Bronwyn Ewing

**
**

**
Discovering functional and dynamic
aspects of parametric equations by creating computer animations**

Andreas Filler

**
Retaining Beginning Mathematics
Teachers in the United States**

Molly H. Fisher

**
Math in a Zoo < – > Math in the Wild **

Gary Flewelling

Douglas Franks, Michael McCabe & Barbara Olmsted

Viktor Freiman, Nicole Lirette-Pitre, Dominic Manuel, Sylvie Blain, Marcia Cormier, Carole Essiembre & Jacinthe Beauchamp

**
Building a Virtual Community of
Problem Solvers: The CASMI project (Workshop)**

Viktor Freiman, Nicole Lirette-Pitre, Dominic Manuel

**
Knots and Soap Film Minimal Surfaces**

Nat Friedman

**
Using the ClassPad as a Dynamic
Learning Environment to Teach Mathematics (Workshop)**

Hideshi Fukaya & Diane Whitfield

**
A Quest for Understanding
Understanding in Mathematics Learning: Examining Theories of Learning**

Kgomotso Gertrude Garegae

**Negotiating a Problem-Solving
Teaching Approach Model: Exploring Ideas(Workshop)**.

Kgomotso Gertrude Garegae

Barbara Garii & Marcia M. Burrell

**
Developing Calculus
Concepts through Applications Related to NASA’s Space Exploration Program**

Chris Giersch, Josephine Letts & David K. Pugalee

**
Different
representations of functions in a dynamic geometry environment **

Gunnar Gjone

**
Dynamic
Geometry with ClassPad and ClassPad Manager (Workshop)**

Gunnar Gjone

**
Affective Pathways and Structures in
Urban Student's Mathematical Learning**

Gerald A. Goldin, Yakov M. Epstein & Roberta Y. Schorr

**
Using 3D Computer Graphics Multimedia
to Motivate Teachers’ Learning of Geometry and Pedagogy**

Tracy Goodson-Espy, Kathleen Lynch-Davis, Samuel L. Espy, Pamela Schram

& Art Quickenton

**
Laplace transform to students of
engineering **

V.R.Lakshmi Gorty

**
Where the Gold is: Data Mining and
Improving the Curriculum in the 21 ^{st} Century**

Deborah J. Gougeon

**
Preparing Qualified Middle School
Mathematics Teachers**

Sharon M. Gronberg

May Hamdan

**
What is the future of Wholemovement
in the development of Mathematics Education?**

Bradford Hansen-Smith

**
A Descriptive Analysis of Secondary
Mathematics Students’ Formal **

**Report Writing**

Adam P. Harbaugh, David K. Pugalee, and Margaret Adams

**
Including Awareness of Assessment
Issues in Teacher Content Preparation**

Judith H. Hector

**
A non-standard course for future High
School mathematics teachers**

Michel Helfgott

Mark H. Holmes

Hanan Innabi

Sarah Ives

**
Using Inspiration 6® in
Introductory Statistics: A Preliminary Report**

Alisa Izumi

**
Mathematical Modeling with NetLogo:
Cognitive Demand and Fidelity**

Iris DeLoach Johnson

Julie P. Jones & Paul J. Riccomini

**
Mathematics Language Skills of Second
Year Analysis Students**

** **
Tangül Kabael &Aynur Özdaş

**
Teaching linear equations using
mathematica at senior secondary school level.**

Luckson M. Kaino

**
Quantitative Reasoning Applications
and Modelling in The Real World at Zayed University**

Nakhshin Karim

**
Penpals, Children's Books, and
Learning Mathematics**

Virginia (Ginny) Keen

**
The Effect of Using Prediction
Questions in the Middle School Algebra Classroom**

Ok-Kyeong Kim & Lisa Kasmer

**
Using a
Touchscreen Calculator in a Calculus Course to obtain Multiple Representations
of Functions
**Benjamin G. Klein

**
n-ary
Relation Operations on Databases**

Miloš Koch & Ivan Mezník

**
Teachers’ Perceptions of a Learning
Community**

Na-Young Kwon

**
The Use of Research-Based Methods and
Materials for Preparing to Teach Mathematics with Technology **

Hollylynne Stohl Lee, Karen F. Hollebrands & P. Holt Wilson

**
Developing Algebra Concepts through
Applications Related to NASA’s Space Exploration Program**

Josephine Letts, Chris Giersch, NASA & David K. Pugalee

**
Technology for Pre-service Teachers**

N. Leveille

**
Mathematics at Distance Education for
Students in Prison**

Genoveva Leví, Eduardo Ramos, María Pilar González & Luis Tejero

**
A Sustained Professional Development
Partnership in an Urban Middle School**

Cathy Liebars

**
Help for the Mathematics Learning
Slump**

Madeleine J. Long & Jeanne Weiler

**
Developing Innovative Technology
Based Mathematics Learning Resources **

Conrad Lotze

**PISA
Results and School Mathematics in Finland: strengths, weaknesses and future**

George Malaty

**
Mathematics Education Program in
Malaysian Universities: Curriculum Emphasis and Preparedness of Students to
Become Teachers **

Aida Suraya Md.Yunus, Ramlah Hamzah & Habsah Ismail

**
Helping Students Understand Technical
Calculus via an Online Learning Supplement and Group Learning**

David A. Miller

**
The Use of Writing to Teach and Learn
Mathematics: Results of Research Testify to Benefits**

L. Diane Miller

Fayez M. Mina

**
Impact on the implementation of
bilingualism in science and mathematics in Malaysian school system.**

Mohini Mohamed

**
The Growth of the Dynamic Figural
Concept – Sense-Making Strategies Applied to Conceptions of Shape**

Doris J. Mohr, Crystal Walcott & Signe Kastberg

Mogege Mosimege

**
Calculators: A Tool to Develop
Number Sense for Pre-Service Elementary Teachers (Workshop)**

Stuart Moskowitz

**
Outdoor Mathematical Experiences:
Constructivism, Connections, and Health (Workshop)**

Meg Moss

**
Keeping all Students on the Learning Path**

Judy Mousley, Peter Sullivan & Robyn Zevenbergen

Willy Mwakapenda**
**

** **

**
The Inequity Of Mathematics Education
In The United States**

Karen S. Norwood

Stacie S. Nunes

**
Teaching and Learning Mathematics:
Student Reflection Adds a New Dimension **

Victor U. Odafe

John Olive & Günhan Çaglayan

**
A Cognitive Gap between Formal
Arithmetic and Visual Representation in Fractional Operations**

Nevin Orhun

**
The Relationship between Learning
Styles and Achievement in Physics **

**Course and Calculus Course**

Önder Orhun & Nevin Orhun

**Using the ClassPad300Plus in Analysis
to Solve a System of Linear Differential Equations**

Ludwig Paditz

Ludwig Paditz

**
A Mathematical Problem Solving
Process Model of Thai Gifted Students**

Supattra Pativisan & Margaret L. Niess

**
Success Starts at Home - An
educational partnership**

Maria-Joao Peres

**
Mathematical Understanding: Analyzing Student
Thought Processes while Completing Mathematical Tasks**

Drew Polly, Corey Lock & Barbara Bissell

Drew Polly

**
Through the Eye of the Camera: A
Teacher’s View of Video-Conferencing**

Tom Potter

**
Tablet PCs and Web-based Interaction
in the Mathematics Classroom**

M. Reba

**
Fractions Without Pain! (Workshop)**

Hugo Rodriguez

**
Online Mathematics courses: A New
Paradigm in teaching and learning**

Behnaz Rouhani

**
Developing the Deductive Reasoning of BS
Mathematics Students**

Marliza E. Rubenecia

**Origami,
Papierfalten, Papiroflexia: Paper Folding in Mathematics Education**

R. Alan Russell

**Investigating Properties of Isosceles
Trapezoids with the GSP: The case of a Pre-service Teacher**

Adalira Sáenz-Ludlow & Anna Athanasopoulou

**
Increasing Accessibility of Multiplication
Facts with Large Factors and Products**

Lynnea C. Salvo

**
The Cultural and Language Challenges
in Teaching Saudi Arabian Students, in the English Language, the Mathematics
Needed in Order to be Successful in the Degree Programs of Engineering,
Computer Technology and Business Management.**

John E. Sasser & Raja Clouse

**
Structures, Journeys, and Tools:
Using Metaphors to Unpack Student Beliefs about Mathematics**

Amélie G. Schinck, Henry W. Neale, Jr., David K. Pugalee & Victor V. Cifarelli

Kathryn G. Shafer

**
Creative Thinking in Problem Solving**

A G (Tony) Shannon

**
Project M ^{3}: Mentoring
Mathematical Minds (Workshop)**

Linda Jensen Sheffield

Ryan Smith, Karen Hollebrands, Kathleen Iwancio & Irina Kogan

**
Critical Mathematics Pedagogy:
Transforming Teachers’ Practices**

David W. Stinson, Carla R. Bidwell, Christopher C. Jett, Ginny C. Powell &

Mary M. Thurman

**
Spreadsheet Investigations in Modular
Arithmetic**

Steve Sugden

Éva Szeredi and Katalin Fried

Hussein Tahir

Martha Tapia

Sylvia Taube & Bill Jasper

**
The Effects of Participating in
Lesson Studies on Practices of Teaching Mathematics**

Agnes Tuska & Rajee Amarasinghe

**
Second Chance in Mathematics
Education**

Ariana-Stanca Văcăreţu

**
Understanding Probability Using
Algebra**

Natalya Vinogradova

**
Frameworks for Improving Mathematical
Sophistication and Teaching Philosophies**

Gideon Weinstein

An Attempt to Integrate Mathematics Across Different Curriculum Areas at Lower Secondary Level

Ian Willson

**
The Role of
Representations in Growth of Understanding in Pattern-Finding Tasks**

P. Holt Wilson & Catherine C. Stein

Encouraging Technology and Hands On Science: A School System Model for Systemic
Change in Science Education

Danae’ Wirth

** **

**
A Continuum of Secondary Mathematics
Teacher Leadership**

Jan A. Yow

**
An
Analysis of Reformatting Curriculum and Instruction in the Calculus Sequence
**Mary Zachary & Sherry Biggers

Working Groups:

**
Learning and Problem Solving Working Group:
Erik de Corte, George
Malaty & Ginny Keen**

**
Working Group
n.6, Rich Learning Tasks: Gary Flewelling, Henry Kepner, Bronwyn Ewing**

**
Working Group
3, Teacher Education: Agnes Tuska**