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Starting points for dealing with the diversity of theories. (English)
Bikner-Ahsbahs, Angelika (ed.) et al., Networking of theories as a research practice in mathematics education. Authored by the networking theories group. Cham: Springer (ISBN 978-3-319-05388-2/hbk; 978-3-319-05389-9/ebook). Advances in Mathematics Education, 3-12 (2014).
Summary: This chapter presents the main ideas and constructs of the book and uses the triplet (system of principles, methodologies, set of paradigmatic questions) for describing the theories involved. In Part II (Chapters 3, 4, 5, 6, and 7 [{\it F. Arzarello} and {\it C. Sabena}, ibid., 31‒45 (2014; ME 2014f.00295); {\it M. Artigue} et al., ibid., 47‒65 (2014; ME 2014f.00296); {\it M. Bosch} and {\it J. Gascon}, ibid., 67‒83 (2014; ME 2014f.00297); {\it T. Dreyfus} and {\it I. Kidron}, ibid., 85‒96 (2014; ME 2014f.00298); {\it A. Bikner-Ahsbahs} and {\it S. Halverscheid}, ibid., 97‒113 (2014; ME 2014f.00299)]), the diversity of five theoretical approaches is presented; these approaches are compared and systematically put into a dialogue throughout the book. In Part III (Chapters 9, 10, 11, and 12 [{\it T. Dreyfus} et al., ibid., 127‒151 (2014; ME 2014f.00301); {\it I. Kidron} et al., ibid., 153‒177 (2014; ME 2014f.00302); {\it C. Sabena} et al., ibid., 179‒200 (2014; ME 2014f.00303); {\it A. Bikner-Ahsbahs} et al., ibid., 201‒221 (2014; ME 2014f.00304)]), four case studies of networking practices between these approaches show how this dialogue can take place. Chapter 8 [{\it S. Prediger} and {\it A. Bikner-Ahsbahs}, ibid., 117‒125 (2014; ME 2014f.00300)] and Part IV (Chapters 13, 14, 15, 16, and 17 [{\it S. Halverscheid}, ibid., 225‒233 (2014; ME 2014f.00305); {\it A. Bikner-Ahsbahs} and {\it S. Prediger}, ibid., 235‒247 (2014; ME 2014f.00306); {\it M. Artigue} and {\it M. Bosch}, ibid., 249‒265 (2014; ME 2014f.00307); {\it K. Ruthven}, ibid., 267‒279 (2014; ME 2014f.00308); {\it L. Radford}, ibid., 281‒286 (2014; ME 2014f.00309)]) provide methodological discussions and reflections on the presented networking practices.
Classification: D20
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