Crossing Boundaries in Mathematical Modelling and Applications Educational Research and Practice

This chapter gives an overview on the current state-of-the-art on the teaching and learning of mathematical modelling and applications and its contribution to educational research and practice which is reflected in the various contributions in this book. Several chapter authors use the opportunity to strengthen and build our research practices by reaching out to others in educational research, beyond the boundaries of our community, and those in fields other than education. By researchers recognising boundaries in applications and modelling research that limit our vision and what we are currently able to do, a more entrepreneurial view of research groups could lead to the brokerage of knowledge in multidisciplinary or multi-community teams to work on some of the more perplexing research questions that have faced our research community. Fluid social alliances in research groups that coalesce and then disperse could result in a much wider dissemination of knowledge both to, and from, our community in the future.

[1]  Susan Leigh Star,et al.  Institutional Ecology, `Translations' and Boundary Objects: Amateurs and Professionals in Berkeley's Museum of Vertebrate Zoology, 1907-39 , 1989 .

[2]  Mette Andresen,et al.  Modelling Chemical Equilibrium in School Mathematics with Technology , 2011 .

[3]  Robyn Levenia Zevenbergen,et al.  The Contexts of mathematics tasks and the context of the classroom: Are we including all students? , 2003 .

[4]  Wajeeh M. Daher,et al.  PRE-SERVICE TEACHERS’ MODELLING PROCESSES THROUGH ENGAGEMENT WITH MODEL ELICITING ACTIVITIES WITH A TECHNOLOGICAL TOOL , 2015 .

[5]  Maria Meletiou-Mavrotheris,et al.  Mobile technologies in the service of students’ learning of mathematics: the example of game application A.L.E.X. in the context of a primary school in Cyprus , 2015, Mathematics Education Research Journal.

[6]  Lyn D. English,et al.  STEM education K-12: perspectives on integration , 2016, International Journal of STEM Education.

[7]  James J. Gibson,et al.  The Ecological Approach to Visual Perception: Classic Edition , 2014 .

[8]  Gabriele Kaiser,et al.  Complex Modelling Problems in Co-operative, Self-Directed Learning Environments , 2013 .

[9]  E. Silver.  On Mathematical Problem Posing. , 1994 .

[10]  Hugh Burkhardt.  Curriculum Design and Systemic Change , 2014 .

[11]  Miroslav Lovric,et al.  Tensions Between Mathematics and Science Disciplines: Creative Opportunities to Enrich Teaching Mathematics and Science , 2017 .

[12]  Peter Galbraith,et al.  Modelling and Applications in Mathematics Education , 2007 .

[13]  Gilbert Greefrath,et al.  Teaching and Learning Mathematical Modelling: Approaches and Developments from German Speaking Countries , 2016 .

[14]  Milton Rosa,et al.  Ethnomodelling as a Research Lens on Ethnomathematics and Modelling , 2013 .

[15]  Roy D. Pea,et al.  The Social and Technological Dimensions of Scaffolding and Related Theoretical Concepts for Learning, Education, and Human Activity , 2004, The Journal of the Learning Sciences.

[16]  Gail E. FitzSimons,et al.  Education/Training with Industry Participation , 2013 .

[17]  Y. Engeström,et al.  Polycontextuality and Boundary Crossing in Expert Cognition: Learning and Problem Solving in Complex Work Activities. , 1995 .

[18]  Gilbert Greefrath,et al.  Teaching and Learning Mathematical Modelling , 2016 .

[19]  A. Sfard.  Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing , 2008 .

[20]  Gilbert Greefrath,et al.  MATHEMATICAL MODELLING IN CLASS REGARDING TO TECHNOLOGY , 2009 .

[21]  Werner Blum,et al.  How do Students and Teachers Deal with Modelling Problems , 2007 .

[22]  Morten Blomhøj,et al.  Developing mathematical modelling competence: conceptual clarification and educational planning , 2003 .

[23]  Christer Bergsten,et al.  On the Use of Realistic Fermi Problems in Introducing Mathematical Modelling in Upper Secondary Mathematics , 2013 .

[24]  Neil Mercer,et al.  Explaining the dialogic processes of teaching and learning: The value and potential of sociocultural theory , 2012 .

[25]  S. L. Star,et al.  This is Not a Boundary Object: Reflections on the Origin of a Concept , 2010 .

[26]  Sanjay Jain,et al.  Towards a Better Understanding of Incremental Learning , 2006, ALT.

[27]  Milton Rosa,et al.  Ethnomodelling as a Methodology for Ethnomathematics , 2013 .

[28]  Gabriele Kaiser,et al.  Modelling Competencies: Past Development and Further Perspectives , 2015 .

[29]  Andreas Busse.  Upper Secondary Students’ Handling of Real-World Contexts , 2011 .

[30]  Akio Matsuzaki.  Using Response Analysis Mapping to Display Modellers’ Mathematical Modelling Progress , 2011 .

[31]  Uffe Thomas Jankvist,et al.  Problem solving in the borderland between mathematics and physics , 2017 .

[32]  Akihiko Saeki,et al.  Evidence of a Dual Modelling Cycle: Through a Teaching Practice Example for Pre-service Teachers , 2013 .

[33]  James Garraway.  Knowledge boundaries and boundary-crossing in the design of work-responsive university curricula , 2010 .

[34]  Peter Frejd,et al.  Modelling from the Perspective of Commognition – An Emerging Framework , 2013 .

[35]  Ian Huntley,et al.  Mathematical Modelling: Methodology, Models, and Micros , 1986 .

[36]  Lyn D. English,et al.  Problem solving in a 21st century mathematics curriculum , 2016 .

[37]  Peter Galbraith,et al.  A framework for success in implementing mathematical modelling in the secondary classroom , 2007 .

[38]  Mark N. Hoover,et al.  Principles for Developing Thought-Revealing Activities for Students and Teachers , 2000 .

[39]  Klaus Brinkmann,et al.  Integration of Energy Issues in Mathematics Classrooms , 2007 .

[40]  Dirk De Bock,et al.  Students' Overreliance on Linearity in Economic Thinking: An Exploratory Study at the Tertiary Level , 2014 .

[41]  Y. Engeström.  Expansive learning at work: Toward an activity theoretical reconceptualization. , 2001 .

[42]  Deborah K. LaPointe.  Will Games and Emerging Technologies Influence the Learning Landscape , 2008 .

[43]  Richard Lesh,et al.  Problem Solving, Modeling, and Local Conceptual Development , 2003 .

[44]  N. Calder,et al.  Mathematics education and mobile technologies , 2016 .

[45]  N. Hatton,et al.  Reflection in teacher education: Towards definition and implementation , 1995 .