Frameworks for analysing the expertise that underpins successful integration of digital technologies into everyday teaching practice

Although the uptake of digital technologies in mathematics teaching continues to be inhibited by factors such as poor resourcing of schools, limited recognition in curricula, and lack of acceptance in examinations, such barriers are slowly diminishing. This brings to the fore what is perhaps the most crucial influence on the successful integration of digital technologies into everyday teaching practice: relevant expertise on the part of the teacher. This paper will examine three contemporary frameworks for analysing such expertise, and explore commonalities, complementarities and contrasts between them: the Technological, Pedagogical and Content Knowledge (TPACK) framework (Koehler & Mishra, 2009); the Instrumental Orchestration framework (Trouche, 2005); and the Structuring Features of Classroom Practice framework (Ruthven, 2009). To concretise the discussion, the use of digital technologies for algebraic graphing, a now well established form of technology use in secondary school mathematics, will serve as an exemplary reference situation. Each of the frameworks will be illustrated through its application in a study of teacher expertise relating to this topic.