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  • INTRODUCTION The symposium series MACAS, Mathematics and its Connections to the Arts and Sciences, was founded in 2005 by Astrid Bechmann, University of Education Schwäbsich Gmünd, Bharath Sriraman, The University of Montana and Claus Michelsen, University of Southern Denmark as an outcome of the continued collaboration between some participants of Topic Study Group 21 at the 10th International Congress of Mathematics Education (ICME-10), held in Copenhagen in July 2004 (Anaya & Michelsen 2005, 2008). The first MACAS symposium was held in 2005 at the University of Education Schwäbsich Gmünd, Germany (Beckmann, Michelsen & Sriraman 2005). Subsequent MACASmeetings were held at University of Southern Denmark in Odense, Denmark in 2007 (Sriraman, Michelsen, Beckmann & Freiman 2008), and at University of Moncton, Canada in 2009 (Sriraman & Freiman 2011). For its 10th anniversary in 2015 MACAS turned back to University of Education Schwäbsich Gmünd (Beckmann, Freiman & Michelsen 2016) and in 2017 it returned to Denmark, this time at Danish School of Education, Aarhus University in Copenhagen. Mathematics is part of almost every aspect of everyday life, and the society consumes a lot of mathematics. Across regions, nations, and continents mathematics plays a central role in educational systems from kindergarten to lifelong learning. Mathematics plays an increasingly important part in many scientific disciplines like the physical, the engineering, the biological sciences, information science, economics, sociology, linguistics and dozens of other disciplines as well, although the way in which mathematics is involved in them varies considerably with the discipline. The vision which the MACAS-initiative is based upon is to develop a holistic approach to education that combines various disciplines in a single curriculum – an approach first suggested by renaissance philosophers. According to this philosophical notion, the aim is to educate students by enabling them to pursue diverse fields of inquiry while at the same time exploring the aesthetic and scientific connections between the arts and science. In view of the challenges of the 21st century, a modern approach to education with a focus on multi- and interdisciplinary is more important than ever. The field of mathematics assumes a key role in this approach as it is connected to all other disciplines and can serve as a bridge between them. This is the approach of MACAS – Mathematics and its Connections to the Arts and Sciences. The MACAS 2017 symposium took place at Danish School of Education, Aarhus University in Copenhagen 27 - 29 June 2017. It included 42 participants from Canada, China, Denmark, Faroe Islands, Germany, Mexico, Russia, Sweden, Switzerland, Ukraine and United Kingdom interested in connections between mathematics and the arts and. The following areas were in focus at the symposium: • Theoretical investigation of the relation between mathematics, arts and science • Curricular approaches to integrate mathematics and science • The importance of mathematical modelling and interdisciplinary for studying and learning mathematics • The importance of arts and humanities for the understanding of the connections between arts, humanities and mathematics in ordinary everyday situations • Intercultural dimensions of studying mathematics These proceedings collect papers corresponding to the plenary lectures and presentations given at MACAS 2017 symposium. The proceedings present 19 peer reviewed papers. The papers are very diverse in nature reflecting the fact that impacts of mathematics can spread very in many cases. However, this diversity points at the need for a community-wide effort to rethink the mathematics education at all levels. Ideas, experiences, conceptual frameworks, and theories to connect mathematics education to the arts and sciences need to be improved to meet the challenges and opportunities of the future. From the symposium’s plenary sections, the paper by Annie Savard (Canada) discusses how critical thinking using mathematics might support the decisionmaking process from an ethnomathematical perspective. Jens Højgaard Jensen(Denmark) shares his reflections about the distinction between theory-derived mathematical models and ad-hoc mathematical models as a way to help ordinary people, not to distinguish between trustworthy and non-trustworthy models, but to distinguish between the different qualities of the evaluation proses behind different sorts of models. A third plenary (without proceedings paper) was given by Paul Ernest (UK) on the topic of "Mathematics, Beauty and Art" in which he addressed the questions what beauty in mathematics is and what dimensions of mathematical beauty that can be distinguished? Provisional answers to these questions were given, and mathematical beauty was illustrated by means of an example from visual art. Since beauty is shared by both mathematics and art, Ernest also asked the question of what parallels, including similarities and differences, that can be drawn between mathematics and art? Two papers have focus on geometrical objects. Hans Walser (Switzerland) comes across different aspects of equivalence by dissection: Variations on the theorem of Pythagoras, differences between methods and creativity, symmetry, optimizing, rational and irrational rectangles, color and esthetics. The paper of Gao Shuzhu, Chen Weiwei and Zheng Qian (China) explains the volume of a cone by the concept of a centroid. A group of papers address the connections between mathematics and the subjects of natural sciences. Thomas Højgaard and Jan Sølberg (Denmark)present a two-dimensional model to ensure that students acquire competencies that transcend traditional subjects. The paper by Martin Niss (Denmark) focuses on how the how the students’ ability to perform the mathematization process can be trained by using so-called unformalized physics problems. The paper by Claus Michelsen (Denmark) reports about an in-service teacher program aimed at enabling teachers to implement interdisciplinary instructional sequences in mathematics and biology in their daily classroom practices. Simon Zell (Germany) discusses different approaches for models of interdisciplinary teaching and presents his own model “Mathematics and Science under one roof”. Topics related to technology in mathematics are addressed in the papers by LeBlanc, Freiman and Furlong (Canada) with focus on emerging mathematical connections when students are learning in school makerspaces and students’ motivation for learning mathematics when technology-based games are integrated within the classroom. Several papers address the connections between mathematics and literature, music and arts. Starting out with G. H. Hardy’s aesthetic arguments for the value of pure mathematics the paper by Uffe Thomas Jankvist, Helle Rørbech & Jesper Bremholm (Denmark) points out didactic potentials in an interdisciplinary approach to beauty and aesthetics within the context of mid-20th century ways of thinking and understanding mathematics and literature. Irina Golovacheva, Alexandre Stroev, Mikhail Zhuravlev and Polina de Mauny (Russia) analyze the structure at the artistic space of two world-famous masochistic novellas by mathematical modeling. The paper by Lina Medina Ibarra, Avenilde Romo-Vázquez & Mario Sánchez Aguilar (Mexico) presents an activity centered on an analysis of the story of Jorge Luis Borges “The library of Babel” from a literary as well as from a mathematical point of view. Hans Peter Nutzinger (Germany) shares the idea that music is a way of learning about patterning and thereby about mathematics. The use of terahertz electromagnetic oscillations in art expertise and public art technologies is analyzed in the paper by Darya Yeryomka (Ukraine). Giftedness, creativity and aesthetic are explored in three papers. Peter Weng and Uffe Jankvist (Denmark) address the problem of many teachers not being equipped for engaging in dialogue with gifted students and thus not being able to facilitate their mathematical learning in a productive and efficient manner. Lena Lindenskov (Denmark) presents the “Seven keys” model as a theoretical background for combining aesthetic aspect of mathematics research and mathematics learning. In the paper by Lisser Rye Ejersbo (Denmark) three cases are presented to discuss how to make mathematics a creative subject. Finally, Maria Kirstine Østergaard (Denmark) argues that it is essential to focus on the development of students’ beliefs in mathematics education, particularly about mathematics as a discipline, in order to enhance the students’ apprehension of the role and use of mathematics in the world and to emphasize the interdisciplinary possibilities of mathematics. The overall success of the MACAS 2017 Symposium was a result of a very productive scientific work magnificently supported by the great enthusiasm, devotion and hospitality of the local organizing team lead by Professor, Dr. Uffe Jankvist promotes for the continuation of the MACAS symposia in the coming years. The 6th one is planned in 2019 in Montreal, Canada.

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Author:Claus Michelsen, Astrid Beckmann, Viktor Freiman, Uffe Thomas Jankvist
Publisher:Laboratorium for Sammenhængende Undervisnings og Læring (LSUL)
Place of publication:Syddansk Universitet Campusvej 55 5230 Odense M Denmark
Document Type:Conference Proceeding
Year of Completion:2018
Date of first Publication:2018/12/18
Release Date:2018/12/18
First Page:2
Last Page:228
To order the print edition:1658526724
Institutes:Fakultät II
DDC class:500 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):License LogoVeröffentlichungsvertrag mit Print-on-Demand