Dispositions and changing teacher practice in mathematics

We explore how different interpretations of learning can be integrated to form a theoretical framework for exploring teachers' perceptions of professional learning about mathematics teaching. Although it is possible to identify the separate, contributing factors that operate in mathematics classrooms, little is known about how teachers perceive factors interacting together to affect student learning outcomes. What is known is that large-scale professional development programmes can lead to increases, rather than decreases, in differences in achievement between student groups based on ethnicity, socio-economic status and gender (Young-Loveridge, 2000, 2003). From their point of view immersed in the complexity of everyday practice, teachers may perceive a different set of factors interacting in other ways than those imagined by the professional development designers making the learning experiences of limited value to them.

Work done in mathematics education by Skovsmose and Valero combined with Kemmis and Grootenboer's work on academic architectures provide a theoretical framework that enables this complexity to be unpacked. Skovsmose considered learning to involve ascribing meaning to different activities that learners are engaged in. He wrote"[m]eaning in learning comes to refer to a relationship between the dispositions of the learner, the intentions of the learner, the intended and unintended effects of learning activities, and the learner's reflections on these effects"(2005, p. 93). The complexity of factors that influence the actions of learners is described as a learning landscape (Alrø, Skovsmose & Valero, 2009). Different interrelated dimensions constitute this complex network of social practices (Valero, 2007).

Kemmis and Grootenboer (2008), using a scheme from Aristotle and adopted by Habermas, also discussed dispositions but within the context of how these dispositions were formed. Although there are many similarities in how Skovsmose (2005) and Kemmis and Grootenboer (2008) described the influence of socio-political/socio-cultural influence on dispositions, Kemmis and Grootenboer (2008) provided more details about how dispositions are shaped by factors external to the individual. They described three extra-individual structures and processes - culturally-discursive, material-economic and social-political - that"shape dispositions and actions, both in the educator's general response to a particular situation or setting, and in relation to their particular responses at particular moments"(p. 50). These processes were described as 'practice architectures'.

We explore in this paper the combination of these two approaches and how they can be used in devising powerful theoretical lenses for unpacking the complexity of why professional development may not lead to teachers adopting new practices.