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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.
Abstract
This study sought to explore the views and perceptions of education stakeholders (i.e. teachers, heads of schools and curriculum specialists) on the integration of environmental education into primary education curricula in Tanzania. The study also sought for stakeholders’ views and perceptions to explain why EE has not been a successful story despite having been integrated in schools for decades. Empirical studies by Kimaryo (2011) and Mtaita (2007) discovered that although EE was included in Tanzanian primary schools since 1960’s and was even stressed in the policy of education in 1990’s; yet, the condition of environment has rather deteriorated.
Studies that have been conducted in this field, mainly explained the success or failure of EE implementation basing on teachers and students as key agents, thus capturing a narrow view to explain the phenomenon. As argued by Klitgaard (1973) in the theory of diffusion of innovations in education, success or failure of educational innovations and reforms cannot be a priori attributed to only one part of the educational system. He says educational systems operate in a chain of command where different actors and levels of authorities need to function properly and collaborate with other levels so as to ensure successful implementation of change and reforms in curriculum. For this reason, this study involved the curriculum specialists and heads of schools besides teachers. Moreover, none of the studies has explored how the school theory promotes or hinders the integration of EE into the curriculum.
The study attempted to answer the following four questions:
Which views and perceptions do teachers have on the environment, environmental changes and challenges?
How do teachers perceive EE integration, content adequacy and relevance; And which instructional methods and resources do they use in integrating EE content into their subject curriculum?
How do teachers perceive their motivation and professional development on environmental education issues?
How do heads of schools and curriculum specialists perceive EE integration, and how do they motivate teachers to successfully integrate EE into their teaching?
The study is qualitative in nature, employing research techniques such as interviews and document analysis to answer the inquiry. Data was obtained from five primary schools’ teachers, heads of schools and curriculum specialists with a total of 30 participants taking part in the study. Grounded theory and thematic strategies were employed in data analysis.
The findings from teachers revealed that environmental changes and challenges are mainly seen as anthropogenic. The issue of climate change was a concern for a majority of participants. Awareness of the concept of ‘pillars of sustainability’ (i.e. ecology, economy and culture) is generally low and their balance is perceived impossible without addressing the poverty issue. Teachers’ competence and motivation are low due to lack of resources and professional training, large class sizes and work load as well as lack of government priority on environmental issues. Moreover, results revealed that EE goals and principles are incompatible with the traditional role and goals of schooling, and as EE is not a subject in itself, it is marginalized in teaching. Findings from heads of schools and curriculum
specialists confirmed most of the findings from teachers, and acknowledged that very little support for teachers to implement EE was provided. In general, results concluded that there was no perspective for effective implementation of EE in the near future, unless there is due priority given from top authorities downwards.
The study recommends capacity building of teachers as well as involvement in planning and development for curricula reforms. Government priority on environmental issues is insisted on and urged to set concrete criteria for EE competence assessment in curricula. To ensure environmental sustainability the government should keep striving to fight poverty. Lastly the study proposes a model to improve the implementation of EE in primary schools. The findings of this study hold imperative implications for the government through the Ministry of Education and Vocational Training in Tanzania, curriculum specialists, and heads of schools as well as teachers as they are key players in determining the success or failure of educational innovations and reforms.