The
Mathematics Education into the 21st 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 21st 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. The Conference was organized jointly by The University of North Carolina Charlotte 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 the following webpages.
Project Home Page which leads directly to the Charlotte Conference First Announcement pdf: 21project.htm
21_malasya_2005.doc - Malaysia 2005 Conference
21project.htm
- Our Project Home Page
egypt.pdf - Egypt Conference site
jourdain - Jordan conference site
cairms - Australia conference site
palermo2002 - Sicily Conference site
http://dipmat.sites.unipa.it/grim/21_project/21_brno_03.htm - Brno Conference site
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
WELL
WE'VE GOT ALL THESE 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 NASAs 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 21st 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
Milo 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 NASAs 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 Teachers 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 M3: 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