The Mathematics Education into the 21st Century Project


The University of North Carolina Charlotte



Proceedings of the Ninth International Conference


Mathematics Education in a Global Community


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





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,  (

Sally Adkin, North Carolina School of Science and Mathematics (

Laura Brinker, University of South Carolina (

Vic Cifarelli, University of North Carolina Charlotte (

Dr. Beth Costner, Winthrop University (

Cos D Fi, University of North Carolina at Greensboro (

Patsy (Patricia) Douville,  University of North Carolina Charlotte (

Susan Friel, University of North Carolina at Chapel Hill (

Adam Harbaugh, University of North Carolina Charlotte (

Timothy Hendrix, Meredith College (

Karen Hollenbrands, North Carolina State University (

Corey Lock, University of North Carolina Charlotte (

Carol Malloy, UNC Chapel Hill (

Henry Neale, Charlotte Country Day School/UNC Charlotte (

Drew Polly, University of North Carolina Charlotte (

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

Sid Rachlin, Association of Mathematics Teacher Eductors, President, (

David Royster, Director, Center for Mathematics, Science & Technology Education, UNCC, (

Norma Royster, Cabarrus County Schools/UNC Charlotte(

Bill Scott, Charlotte-Mecklenburg Schools (

Olof Steinthorsdottir, University of North Carolina at Chapel Hill (

Hollylynne Stohl Lee, North Carolina State University ( )




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 and the Hilton Charlotte University Place Hotel 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 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 the following webpages.

Project Home Page which leads directly to the Charlotte Conference First Announcement pdf:  - Malaysia 2005 Conference  - Our Project Home Page  - Egypt Conference site  - Jordan conference site  - Australia conference site  - Sicily Conference site  - Brno Conference site  - Ciechocinek Conference site

Filippo Spagnolo, of Palermo University, is webmaster for the above sites. Felix Rieper has compiled at:, a photo album of the Ciechocinek Conference.Krys Bestry is webmaster for our Polish Superkurs Home Page and National Planning Meetings webpage   (in Polish - but with pictures!)  See also:  for more information about our project and its work. For the Brno conference see


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


Alan Rogerson, Amélie Schinck & David Pugalee




Text Box:


Douglas Butler

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

Douglas Butler Plenary Address






Continuing issues in

mathematics education

 The Malaysian ExperienceText Box:  


Noor Azlan Ahmad Zanzali

Universiti Teknologi Malaysia




Presented Papers


Evaluation of The learning achievement levels of pupils in the  5th  class in Primary  School in Mathematics

            Mohammed   Fdhle Ali Ahmed


Professional Competence in Teaching of Mathematics in Selected High Schools of India and U.S.: The Interplay of Cognition, Conceptions, and Context

            Renu Ahuja


Translations towards connected mathematics (Workshop)

            Mark Applebaum & Roza Leikin


The Family Maths Programme, Developing Inquiry-based Teaching

            Pam Austin & Paul Webb


The CME Project

            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


Video Games and Mathematics Education: Studying Commercial Sports Video Games to Identify the Potential for Learning and Thinking About Mathematics

            Candace Barriteau Phaire


Reasoning Algebraically about Operations: Developing early algebraic thinking by examining the generalizations that underlie young student’s mathematical thinking.  What do teachers and those who prepare teachers need to understand?

            Virginia Bastable


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

            Judith E. Beauford & Sandra Browning


Student Teachers’ Experiences with Mathematics Curriculum Materials: Issues of Autonomy and Teacher Learning

            Stephanie L. Behm & Gwendolyn M. Lloyd


Growth of Mathematical Understanding Through Pattern Finding Viewed through Coactions and Conversions

            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


“Big-screen” technology for little hands: incorporating graphing calculators in the elementary/middle school mathematics curriculum (Workshop)

            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


Tackling Epistemological  Problems (TEP) A didactical engineering to break through the amazing world of regular polyhedra (Workshop)

Bernardo Camou


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

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


Findings from Two Countries Regarding Prospective Teachers’ Knowledge of Addition and Division of Fractions

            R. Elaine Carbone & P. Eaton


I Think I Can, I Think I Can:  Impacting Pre-service Teachers’ Dispositions toward Mathematics (Workshop)

            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


Extending Pre-Service Teacher Education through an Interdisciplinary Mathematics, Health and Technology Approach.

            Douglas Franks, Michael McCabe & Barbara Olmsted


Impact of individual laptop use on middle school mathematics teaching and learning: implementation of problem based learning scenarios

            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


Mathematics in the Middle: Enhancing Teachers’ Understanding of the Interplay Between “School Math” and Professional Uses of Mathematics

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 21st Century

            Deborah J. Gougeon


Preparing Qualified Middle School Mathematics Teachers

            Sharon M. Gronberg


Concentration or Lack of it

            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


Project CSUMS at Rensselaer

            Mark H. Holmes


Mathematics Education Candidates’ Orientations toward the Infusion Approach in Teaching Mathematics and Thinking Skills

            Hanan Innabi


The Relationship between Preservice Teachers’ Conceptions of Randomness and their Pedagogical Content Knowledge of Probability

            Sarah Ives


Using Inspiration 6® in Introductory Statistics:  A Preliminary Report

Alisa Izumi


Mathematical Modeling with NetLogo: Cognitive Demand and Fidelity

            Iris DeLoach Johnson



Effective Organization of Instructional Time in a Content Mastery: Math Resource Room for Students with Learning Disabilities

            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


Authentic Values and Coping with some Paradigm Shifts as Determinants of Mathematics Education in a Global Community

            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


Indigenous Mathematical Knowledge at South African Cultural Villages: Opportunities for Integration in Mathematics Classrooms

            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


A contextualised approach towards making connections between mathematics and other school curriculum disciplines

Willy Mwakapenda


The Inequity Of Mathematics Education In The United States

            Karen S. Norwood


Designing a Program to Support Underrepresented (UREP) Students in Mathematics and Computer Science (Workshop)

            Stacie S. Nunes

Teaching and Learning Mathematics: Student Reflection Adds a New Dimension

            Victor U. Odafe


8th Grade Students' Understanding of Slope and its Antcedents in a Learning Situtaion based on Quantitative Reasoning

            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


Using the ClassPad300Plus in Statistics to Draw Step Functions and to Compute their Quantiles (Workshop)

            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


Examining the influence of learner-centered professional development on elementary mathematics' teachers enacted and espoused practices

            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


The Modern Geometry Course Works Overtime:  Preservice Teachers Learn Content and Technological Pedagogical Content Knowledge with Geometer’s Sketchpad.

            Kathryn G. Shafer


Creative Thinking in Problem Solving

            A G (Tony) Shannon


Project M3: Mentoring Mathematical Minds (Workshop)

            Linda Jensen Sheffield


The Affects of a Dynamic Program for Geometry on College Students’ Understandings of Properties of Quadrilaterals in the Poincaré Disk Model

            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


Non-verbal arithmetic

            Éva Szeredi and Katalin Fried


A New Approach to Conics

            Hussein Tahir


Let’s Do Math with Technology

            Martha Tapia


A Program that Promotes Responsive Mathematics Teaching for English Language Learners in Gr. 6-12 Classrooms

            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 n 5, Comparative Education, Social and Equity Issues: Noor Azlan Ahmad Zanzali, Amelie Schinck, Adam Harbaugh


Working Group 3, Teacher Education: Agnes Tuska


Report from the working group on Applications and Statistics: Ivan Meznik, Gail Burril  & Willy Mwakapenda


Summary of the Technology Working Group, Examples, Issues, Next Steps: Iris DeLoach Johnson, Ludwig Paditz, and Douglas Butler