Providing cognitively activating learning opportunities in the mathematics classroom is essential for instructional quality (Clausen, Reusser & Klieme, 2003) and the development of competencies of students (Stigler & Hiebert, 1999; OECD, 2003). In particular, teachers can create cognitively activating and conceptually rich learning opportunities by an awareness of ‘Big Ideas’ in mathematics, i.e. of overarching concepts that cross-link mathematical contents. An emphasis on such overarching concepts is also a goal shared by the aims of national standards in many European countries and beyond (Office of Qualifications and Examinations Regulation, 2002; AECC, 2008; KMK, 2003; NCTM, 2000). As examples of mathematical ‘Big Ideas’ in the classroom, we are referring to such overarching concepts as: linking multiple perspectives, rather than seeing mathematical contents only in one way, reflecting on infinity, rather than emphasising merely procedures for calculating; identifying conjectures, arguments and proofs, not merely supporting calculation techniques (cf. Kuntze, Lerman, et al., accepted).

A prerequisite for improving instructional quality according to this approach is professional knowledge related to such overarching concepts, namely mathematical content knowledge and corresponding pedagogical content knowledge (Shulman, 1986).

However, in many European countries sufficiently deep content knowledge in mathematics is not made available in pre-service teacher training. This might be a key inhibiting factor for facilitating an overarching understanding of mathematics in the mathematics classroom and for fostering mathematical competency beyond the emphasis of technical routines. Moreover, empirical research into professional knowledge about overarching concepts relevant for mathematics instruction is scarce.

Responding to this need, the tri-national and EU-funded project ABCmaths (“Awareness of Big Ideas in Mathematics Classrooms”, www.abcmaths.net) joins the perspectives and methodological approaches of British, German and Austrian researchers and aims to identify professional development needs of mathematics teachers on the base of a shared theoretical framework. Further, research in ABCmaths focuses on the description of developments in the professional knowledge of participants of teacher education activities in the partner countries.

For the research in ABCmaths, we use a theoretical model of professional knowledge (Kuntze & Kurz-Milcke, 2010) that combines the distinction of domains of professional knowledge by Shulman (1986; cf. Ball, Thames & Phelps, 2008 for the possibility of refinement into sub-domains) as well as the additional dimension of a spectrum between declarative and procedural knowledge on the one hand and convictions/beliefs on the other (e.g. Pajares, 1992) with levels of globality of professional knowledge (Törner, 2002), which take into account that professional knowledge is often organised episodically (Leinhardt & Greeno, 1986; Bromme, 2001). Professional knowledge related to overarching concepts can connect different components of professional knowledge and support its coherence.

The symposium gives an overview on the theoretical and methodological approaches of ABCmaths and presents both quantitative and qualitative empirical findings from studies with in-service and pre-service teachers from the UK, Germany and Austria. Three empirical papers bring together the perspectives of the above-mentioned countries and a fourth, theoretical presentation locates the importance of an emphasis on overarching concepts in a wider educational context framing mathematics classrooms.