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Proceedings of the 2Nd International Symposium on Mathematics and Its Connections to the Arts and Sciences (MACAS2), Odense Edited by Bharath Sriraman, Claus Michelsen, Astrid Beckmann & Viktor Freiman Proceedings of the 2nd International Symposium on Mathematics and its Connections to the Arts and Sciences (MACAS2), Odense Centre for Science and Mathematics Education, University of Southern Denmark Volume 4 • 2008 Volume 4 Sriraman, Bharath; Michelsen, Claus; Beckmann, Astrid; Freiman, Viktor (eds.) Proceedings of the 2nd International Symposium on Mathematics and its Connections to the Arts and Sciences (MACAS2), Odense © 2008 Centre for Science and Mathematics Education, University of Southern Denmark Printed in Denmark, by Print & Sign, Odense ISBN 978-87-92321-04-6 Published by Centre for Science and Mathematics Education Syddansk Universitet Campusvej 55 5230 Odense M Denmark www.sdu.dk/namadi PROCEEDINGS OF MACAS2 SECOND INTERNATIONAL SYMPOSIUM ON MATHEMATICS AND ITS CONNECTIONS TO THE ARTS AND SCIENCES, ODENSE, DENMARK EDITED BY BHARATH SRIRAMAN, The University of Montana CLAUS MICHELSEN, University of Southern Denmark ASTRID BECKMANN, University of Education- Schwäbisch Gmünd VIKTOR FREIMAN, Université de Moncton TABLE OF CONTENTS 1. Bharath Sriraman, Claus Michelsen, Astrid Beckmann & Viktor Freiman INTERDISCIPLINARITY IN MATHEMATICS, SCIENCE AND ARTS: STATE OF THE ART..........................................................................................................................………...….....pp.1-4 PLENARY PAPERS 2. Lyn D. English (Australia) MATHEMATICAL MODELING: LINKING MATHEMATICS, SCIENCE AND ARTS IN THE PRIMARY CURRICULUM……………………....…...............................................….pp.5-36 3. Michiel Doorman & Koeno Gravemeijer (Netherlands) LEARNING MATHEMATICS THROUGH APPLICATIONS BY EMERGENT MODELING: THE CASE OF SLOPE AND VELOCITY…………………...……….pp.37-56 4. Swapna Mukhopadhyay (USA) THE DECORATIVE IMPULSE: ETHNOMATHEMATICS AND TLINGIT BASKETRY …………………………………………………………………………………………pp.57-74 5. Norma Presmeg (USA) MATHEMATICS EDUCATION RESEARCH EMBRACING ARTS AND SCIENCES ………………………………………………………………………………...………..pp.75-88 i SYMPOSIUM PAPERS 6. Claus Jensen (Denmark) THE GEOMETRY OF 17TH CENTURY DUTCH PERSPECTIVE BOXES……pp.89-106 7. Damjan Kobal (Slovenia) THE ARITHMETIC MEAN AND CAR DIFFERENTIAL………………………..pp.107-116 8. Franka Miriam Brückler,Vladimir Stilinović (Croatia) GRAPH THEORY AS A METHOD OF IMPROVING CHEMISTRY AND MATHEMATICS CURRICULA …………………………………………..…….....pp. 117- 126 9. Bharath Sriraman(USA) MATHEMATICAL PARADOXES AS PATHWAYS INTO BELIEFS AND POLYMATHY ……………………………………………………………………..……..……..........pp.127-142 10. Brian Greer (USA) MASS KILLINGS: THE COMMUNICATION OF OUTRAGE ………...………...pp.143-154 11. Herbert Gerstberger (Germany) “GOOD THEORY” FOR “GOOD PRACTICE” AND VICE VERSA IN THE COMBINATION OF SCIENCE, ART AND TEACHING…………………...……pp.155-164 12. Steffen M. Iversen (Denmark) MODEL ELICITING ACTIVITIES REVISITED – A REPORT FROM A CASE STUDY OF THE PENALTY THROW PROBLEM…………………………………………..…pp.165-172 13. Stinne Hørup Hansen (Denmark) CHALLENGES FOR INTERDISCIPLINARY TEACHING OF MATHEMATICS AND THE SCIENCES IN UPPER SECONDARY SCHOOL…………………..…..……pp.173-180 14. Thilo Hoefer (Germany) FERMAT MEETS PYTHAGORAS……………………………………………....…pp.181-186 15. Astrid Beckmann (Germany) MATHEMATICAL LITERACY - THROUGH SCIENTIFIC THEMES AND METHODS ..................................................................................................................................pp.187-196 ii 16. Heinz Schumann (Germany) INTERACTIVE MODELING IN VIRTUAL SPACE: OBJECTS OF CONCRETE ART ........................................................................................................................................................pp.197-208 17. Viktor Freiman , Nicole Lirette-Pitre , Dominic Manuel (Canada) BUILDING A VIRTUAL LEARNING COMMUNITY OF PROBLEM SOLVERS: EXAMPLE OF CASMI COMMUNITY………………………………………..…..pp. 209-222 18. Jessica Carter (Denmark) VISUALIZATION AND UNDERSTANDING IN MATHEMATICS …….…...….pp.223-232 19. Gesche Pospiech (Germany) MATHEMATICAL CONSTRUCTS IN THE PHYSICAL REALITY………..……pp. 233-240 20. Randy Taylor & Steve Krevisky (USA) USING MATHEMATICS AND STATISTICS TO ANALYZE WHO ARE THE GREAT SLUGGERS IN BASEBALL………………………………………………........….pp. 241-244 21. Marina Rugelj, Tine Golež (Slovenia) GIVING SENSE TO THE MATH FORMULA………………………………...….pp. 245-254 22. Annica Andersson (Sweden) A CULTURAL VISIT IN MATHEMATICS EDUCATION………………...……...pp.255-264 23. Wolfgang Mueckenheim (Germany) THE INFINITE IN SCIENCES AND ARTS…………………………………..…...pp.265-272 24. Claus Michelsen (Denmark) PROMOTING STUDENTS´ INTERESTS IN MATHEMATICS AND SCIENCE THROUGH INTERDISCIPLINARY INSTRUCTION...................................................pp.273-284 25. Mette Andresen & Lena Lindenskov (Denmark) MULTIDISCIPLINARY PROJECTS IN UPPER SECONDARY SCHOOL- NEW ROLES FOR MATHEMATICS?..........................................................................................................pp. 285-292 iii 26. Tine Golež (Slovenia) COOPERATION BETWEEN MATHEMATICS AND PHYSICS TEACHING – THE CASE OF HORIZONTAL LAUNCH..............................................................................................pp.293-298 iv GROUP PICTURE OF PARTICIPANTS v vi INTERDISCIPLINARITY IN MATHEMATICS, SCIENCE AND ARTS: STATE OF THE ART Bharath Sriraman, The University of Montana Claus Michelsen, University of Southern Denmark Astrid Beckmann, University of Education- Schwäbisch Gmünd Viktor Freiman, Université de Moncton The Second International Symposium on Mathematics and its Connections to the Arts and Sciences (MACAS2) was held in Odense at the University of Southern Denmark, May 29-31, 2007, organized by Claus Michelsen (Univ. of Southern Denmark), Bharath Sriraman (Univ. of Montana) and Prof. Astrid Beckmann (Univ. of Education- Schwäbisch Gmünd). We took a leadership role in organizing this professional group at the conclusion of the 10th International Congress in Mathematics Education in Copenhagen in 2004 where we were part of a topics study group on this domain. MACAS2 attracted 45 participants from 15 different countries. These participants included math, science and art educators; physicists; historians and philosophers of mathematics and science, as well as some local classroom teachers. Four plenary lectures were delivered on the theme of the Symposium. In addition 21 papers were presented in an interactive atmosphere. These proceedings include the extended versions of all the papers presented at Odense. Several excursions were planned for the participants to expose them to Odense, the birthplace of Hans Christian Andersen, as well as the island of Fyn which is known as the garden of Denmark. Our long term goal is to build our interdisciplinary network by finding and sharing the best experiences; creating new collaborations; conducting new studies; reflecting on commonalities and differences – multidisciplinary, multicultural and divergent approaches to content, teaching and learning. Plans are already being made to hold the 3rd MACAS Symposium in Moncton, Canada in 2009 to be hosted by Viktor Freiman. The papers in these proceedings are very diverse in nature. Some papers are theoretical musings on the relationship between mathematics, science and arts. However there are clear strands within which the papers could be clustered. Some focus on the role of mathematical modeling in fostering an interdisciplinary approach towards the learning of mathematics, others highlight the important role that art can play in helping students appreciate the interplay between mathematics and arts, as well as in the communication of unspeakable outrages occurring in the world today. Several papers address curricular initiatives aimed at integrating science and mathematics. Last but not least, the necessity to include cultural and ethnomathematical dimensions into the teaching of mathematics is also addressed in two papers. Today’s young learners have borne not only the fruits of enormous progress of science and technology that marked the 20th century but also the challenges surrounding complex and ill- defined real life problems that remain unsolved. Moreover, issues humanity faces such as climate change, health, environment, overpopulation, and so on are so complex that these problems can not be solved by a single person or even a single discipline. An interdisciplinary approach to teaching and learning is thus a key element for any successful educational enterprise which aims to prepare future generations to deal with the increasing complexity and B.Sriraman, C.Michelsen, A. Beckmann & V. Freiman (Eds). (2008). Proceedings of the Second International Symposium on Mathematics and its Connections to the Arts and Sciences (MACAS2). CentreUniversity for Science of Southern and MathematicsDenmark Press, Education, pp.1-4 pp. 1-4 Sriraman, Michelsen, Beckmann & Freiman interconnectivity of our world. After two Symposia we have established a core group of researchers who share a vision of integrating the arts, mathematics, and the sciences in the school and university curricula by engaging in joint interdisciplinary projects. The four authors are consolidating efforts at collecting research evidence based on similar classroom experiments involving interdisciplinary problem solving in the school curriculum at different sites (Canada, USA, Denmark and Germany). In the USA, several models of connected and integrated mathematics curriculum have been implemented and evaluated by researches. Standard concepts of mathematics curriculum have been applied to the solving of real-life problems
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