Diversity of theories in mathematics education—How can we deal with it?

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The Ethics of Being and Knowing: Towards a Cultural Theory of Learning (2008, background): “3 For some recent discussions on these differences see e.g. Bikner-Ahsbahs and Prediger (2006), Cobb (2007), Lerman (2006), Lester (2005), Niss (1999), Radford (2008b, 2008c), Silver and Herbst (2007), and Sriraman and English (2005).”
Networking strategies and methods for connecting theoretical approaches: first steps towards a conceptual framework (2008, methodology): “As already emphasized in Bikner-Ahsbahs & Prediger (2006) , it is important not to synthesize different parts of incompatible theories into arbitrary patchwork-theories.”
Connecting theories in mathematics education: challenges and possibilities (2008, background): “In the first part, drawing explicitly and implicitly on some previous ideas and discussions (e.g., Bikner-Ahsbahs & Prediger, 2006; Cobb, 2007; Lerman, 2006; Lester, 2005; Niss, 1999; Silver & Herbst, 2007; Sriraman & English, 2005), I argued for the need to create ‘‘topics’’ or ‘‘plots’’ in the…”
Networking of Theories—An Approach for Exploiting the Diversity of Theoretical Approaches (2010, background): “…for quality of theories, e.g. • their potential contribution to design activities and their research background (Cobb, 2007) • validity versus relevance (Gellert, 2008) • other criteria like degree of maturity, explicitness, empirical scope, connectivity (see Bikner-Ahsbahs & Prediger, 2006) • ….”