The Mathematics Enthusiast Volume 5 Number 1 Article 18 1-2008 TME Volume 5, Number 1 Follow this and additional works at: https://scholarworks.umt.edu/tme Part of the Mathematics Commons Let us know how access to this document benefits ou.y Recommended Citation (2008) "TME Volume 5, Number 1," The Mathematics Enthusiast: Vol. 5 : No. 1 , Article 18. Available at: https://scholarworks.umt.edu/tme/vol5/iss1/18 This Full Volume is brought to you for free and open access by ScholarWorks at University of Montana. It has been accepted for inclusion in The Mathematics Enthusiast by an authorized editor of ScholarWorks at University of Montana. For more information, please contact [email protected]. The Montana Mathematics Enthusiast ISSN 1551-3440 VOL5.NO.1. JANUARY 2008, pp.1-166 Editor-in-Chief Bharath Sriraman, The University of Montana Associate Editors: Lyn D. English, Queensland University of Technology, Australia Claus Michelsen, University of Southern Denmark, Denmark Brian Greer, Portland State University Luis Moreno-Armella, University of Massachusetts-Dartmouth International Editorial Advisory Board Miriam Amit, Ben-Gurion University of the Negev, Israel. Ziya Argun, Gazi University, Turkey. Ahmet Arikan, Gazi University, Turkey. Astrid Beckmann, University of Education, Schwäbisch Gmünd, Germany. John Berry, University of Plymouth,UK. Morten Blomhøj, Roskilde University, Denmark. Robert Carson, Montana State University- Bozeman, USA. Mohan Chinnappan, University of Wollongong, Australia. Constantinos Christou, University of Cyprus, Cyprus. Bettina Dahl Søndergaard, University of Aarhus, Denmark. Helen Doerr, Syracuse University, USA. Ted Eisenberg, Ben-Gurion University of the Negev, Israel. Paul Ernest, University of Exeter, UK. Viktor Freiman, Université de Moncton, Canada. Fulvia Furinghetti, Università di Genova, Italy Eric Gutstein, University of Illinois-Chicago, USA. Marja van den Heuvel-Panhuizen, University of Utrecht, The Netherlands. Gabriele Kaiser, University of Hamburg, Germany. Libby Knott,The University of Montana, USA. Tinne Hoff Kjeldsen, Roskilde University, Denmark. Jean-Baptiste Lagrange, IUFM-Reims, France. Stephen Lerman, London South Bank University, UK. Frank Lester, Indiana University, USA. Richard Lesh, Indiana University, USA. Michael Mitchelmore, Macquarie University, Australia. Nicholas Mousoulides, University of Cyprus, Cyprus. Swapna Mukhopadhyay, Portland State University, USA. Norma Presmeg, Illinois State University, USA. Gudbjorg Palsdottir,Iceland University of Education, Iceland. João Pedro da Ponte, University of Lisbon, Portugal Michael Pyryt, University of Calgary, Canada. Demetra Pitta Pantazi, University of Cyprus, Cyprus. Linda Sheffield, Northern Kentucky University, USA. Olof Bjorg Steinthorsdottir, University of North Carolina- Chapel Hill, USA. Günter Törner, University of Duisburg-Essen, Germany. Renuka Vithal, University of KwaZulu-Natal, South Africa. Dirk Wessels, UNISA, South Africa. Nurit Zehavi, The Weizmann Institute of Science, Rehovot, Israel. The Montana Mathematics Enthusiast is an eclectic internationally circulated peer reviewed journal which focuses on mathematics content, mathematics education research, innovation, interdisciplinary issues and pedagogy. The journal is published by Information Age Publishing and the electronic version is hosted jointly by IAP and the Department of Mathematical Sciences- The University of Montana, on behalf of MCTM. Articles appearing in the journal address issues related to mathematical thinking, teaching and learning at all levels. The focus includes specific mathematics content and advances in that area accessible to readers, as well as political, social and cultural issues related to mathematics education. Journal articles cover a wide spectrum of topics such as mathematics content (including advanced mathematics), educational studies related to mathematics, and reports of innovative pedagogical practices with the hope of stimulating dialogue between pre-service and practicing teachers, university educators and mathematicians. The journal is interested in research based articles as well as historical, philosophical, political, cross-cultural and systems perspectives on mathematics content, its teaching and learning. The journal also includes a monograph series on special topics of interest to the community of readers The journal is accessed from 102+ countries and its readers include students of mathematics, future and practicing teachers, mathematicians, cognitive psychologists, critical theorists, mathematics/science educators, historians and philosophers of mathematics and science as well as those who pursue mathematics recreationally. The 40 member editorial board reflects this diversity. The journal exists to create a forum for argumentative and critical positions on mathematics education, and especially welcomes articles which challenge commonly held assumptions about the nature and purpose of mathematics and mathematics education. Reactions or commentaries on previously published articles are welcomed. Manuscripts are to be submitted in electronic format to the editor in APA style. The typical time period from submission to publication is 8-11 months. Please visit the journal website at http://www.montanamath.org/TMME Indexing Information Australian Education Index (For Australian authors); EBSCO Products (Academic Search Complete); EDNA; Directory of Open Access Journals (DOAJ); PsycINFO (the APA Index); MathDI/MathEDUC (FiZ Karlsruhe); Journals in Higher Education (JIHE); Ulrich’s Periodicals Directory; ZDM THE MONTANA MATHEMATICS ENTHUSIAST ISSN 1551-3440 Vol.5, No.1, January 2008, pp.1-166 TABLE OF CONTENTS 0. Bharath Sriraman EDITORIAL: Expanding spheres of influence- the zenith, the nadir and everything in-between .....................................................................................................................................................................pp.1-2 FORUM: ETHICS AND VALUES IN MATHEMATICS, TEACHING & LEARNING 1. Ted Eisenberg (Israel) Flaws and Idiosyncrasies in Mathematicians: Food for the Classroom..........................................pp.3-14 REACTIONS TO EISENBERG 2. Wolff-Michael Roth (Canada) Historical Tidbits, the Shoah, and the Teaching of Mathematics..................................................pp.15-28 3. Brian Greer (Portland, USA) Comments provoked by "Flaws and idiosyncrasies in mathematicians: Food for the classroom?" ………………………………………………………………………………………...........pp.29-34 4. Renuka Vithal (South Africa) Critique on Eisenberg’s article.............................................................................................................pp.35-36 REJOINDER BY EISENBERG 5. Ted Eisenberg (Israel) Reaction to the Reactors…………………………...………........................................................pp.37-44 SURREJOINDER BY GREER 6. Brian Greer (Portland, USA) Final comments on Eisenberg's paper...............................................................................................pp.45-46 OTHER PERPSECTIVES 7. Alan Bishop (Australia) Values in Mathematics and Science Education: similarities and differences...............................pp.47-58 8. Kurt Stemhagen (Virginia, USA) Doin’ the Math: On Meaningful Mathematics-Ethics Connections.............................................pp.59-66 i FEATURE ARTICLES 9. Murad Jurdak (Lebanon) The Action Map as a Tool for Assessing Situated Mathematical Problem Solving Performance...........................................................................................................................................pp.67-78 10. M.K Akinsola (Botswana) Relationship of some psychological variables in predicting problem solving ability of in-service mathematics teachers..........................................................................................................................pp.79-100 11. Kristin Umland (New Mexico, USA) A reflection on mathematical cognition: how far have we come and where are we going? ....................................................................................................................................................pp.101-116 12. Yuichi Handa (California, USA) Reflections upon Teaching a Poorly-Conceived Lesson.............................................................pp.117-124 13. Jaehoon Yim, Sanghun Song, Jiwon Kim (South Korea) Mathematically gifted elementary students' revisiting of Euler's polyhedron theorem..........pp.125-142 Montana Feature Article 14. David M. Davison and Johanna E. Mitchell (Montana, USA) How is Mathematics Education Philosophy Reflected in the Math Wars?..............................pp.143-154 MATHEMATICS FOR THE CLASSROOM 15. Sue Waring (UK) Teaching Proof at KS4 .....................................................................................................................pp.155-162 16. Steve Humble (UK) Consecutive numbers.......................................................................................................................pp.163-166 ii EDITORIAL: Expanding spheres of influence- the zenith, the nadir and everything in-between Bharath Sriraman The University of Montana The Montana Mathematics Enthusiast has now entered its fifth year in existence. The changes the journal has been through since its inception has been healthy, especially it’s ever increasing sphere of influence in the intellectual community. Being a meticulous keeper of journal records, I have watched with both awe and enthusiasm (no-pun