Introduction to the papers of TWG17: Theoretical perspectives and approaches in mathematics education research

Abstract : Line of thought of the previous working groups in CERME5 to CERME9 Since CERME4 in 2005, theoretical approaches and perspectives have been the topic of an ongoing CERME working group. The idea of the networking of theories emerged at CERME 4 and was explored in the subsequent conferences. At CERME 5 (Arzarello et al., 2007), the diversity of theories in the field of mathematics education was regarded as a source of richness, and the networking of theories as a multi-theoretical approach which preserves theoretical identity but also while allowing to bridge the boundaries of theories for a better understanding of teaching and learning. Thereby, the effort was made to make hidden assumptions and relationships of theoretical approaches visible. Principles and heuristics of handling the diversity of theories in empirical research were explored as a new possibility to better grasp the complexity of empirical situations of teaching and learning mathematics, such as the interplay between the individual and the social. Typical heuristics to network theories were to relate different approaches based on research: bottom-up on the one hand and starting from theoretical views top-down on the other, but also mixed types were presented. One interesting result was that not only theoretical principles may be hidden in the use of theories but also the view on the nature of mathematics can be an implicit but relevant feature in the specific theoretical approach. The central theme of TWG 9 of CERME 6 (Prediger et al., 2010) was investigating how the use of networking strategies may lead to a more comprehensive understanding of the empirical world, what kind of limits have to be faced, and what kind of difficulties have to be considered. In this respect, the questions of commensurability and complementarity of theories came into play. (2008) as a triad of principles, methodologies and research questions built as a cultural entity of research practice in the semiosphere, a cultural-semiotic space of research as activities, was applied to structure the way networking strategies were used as guiding heuristics which link different aspects of theories. Examples showed that through the networking of theories new questions of balance can be posed, concepts at the boundary of theories may become relevant to solve problems, and theoretically-in and zooming-can be a strategy when theories of different grain size are coordinated. The discussion in this TWG was captured by a dynamic view on theory as a living entity embedded in the researchers social, cultural and institutional heritage (Prediger et al., 2010, p. 1533).
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Angelika Bikner-Ahsbahs, Arthur Bakker, Mariam Haspekian, Mirko Maracci. Introduction to the papers of TWG17: Theoretical perspectives and approaches in mathematics education research. Tenth Congress of the European Society for Research in Mathematics Education (CERME10), European Society for Research in Mathematics Education, Feb 2017, Dublin, Ireland. https://www.researchgate.net/publication/322539757_Tenth_Congress_of_the_European_Society_for_Research_in_Mathematics_Education_CERME10. ⟨hal-01689161⟩

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