We suggest that comments such as these are an example of participants speaking reflectively about aspects of practice, and it is to this aspect of the study that we now turn.
Participants as Reflective Practitioners Contemporary writers on reflective teaching (e.g., Loughran, 1996; Farrell, 2004; Pollard, 2005) acknowledge the distinction made by Dewey (1916; 1933) between “routine action”, which is relatively static, and “reflective action”, which “involves a willingness to engage in constant self-appraisal and development” and which “implies flexibility, rigorous analysis and social awareness” (Pollard, 2005, p. 13). To the distinctions between reflection-in-action and reflection-on-action first developed by Schön (1983), Farrell (1998) adds reflection-for-action, which he describes as proactive in nature: teachers (in our case study, mathematics teacher educators) can use ideas from their reflections in and on action, to plan for future teaching or other professional activities. For Pollard, the process of evidence-based reflection “feeds a constructive spiral of professional development and capability” (2005, p. 5). He suggests that the value of reflective activity is likely to be enhanced through collaboration and dialogue with colleagues because “collaborative, reflective discussion capitalizes on the social nature of learning” (2005, p. 21). We argue that such collaboration and dialogue is not restricted to teacher educators but is possible in any discipline in higher education, so long as there is a common interest in improving the quality of what is offered to students. Reflective activity, facilitated by the mathematics and materials design experts, was a key element of each of the workshops, of the tasks undertaken between the workshops and of the piloting of the collaboratively designed module. At the first “think-tank” workshop, participants reflected on their own teaching programmes and the materials they used. Between the first and second workshops, participants were required to reflect in more detail on their institutional materials and to send to Saide selected parts of these which they thought could be used in the ACEMaths module. At the second workshop, the reflective discussion led to decisions about what to include in the module and to plans for the adaptation of the selected material. At the third workshop, the initial group discussion established that to address issues of diversity in a mathematics classroom, the material contributed by the participant with expertise in learners with special educational needs (LSEN) would need further work of two kinds: (i) adaptation of the theoretical component, to be undertaken by the materials design and mathematics teacher education experts and (ii) inclusion of carefully scaffolded activities which would assist teachers in applying theory to the practice of teaching mathematics to learners with diverse learning styles and needs. These activities were collaboratively designed at the workshop. With the permission of the participants, the materials design and mathematics education experts visited each of the pilot sites to observe classes in which the materials were used and to interview the teacher educators who used them. Analysis of audiotape recorded data from the interviews indicates that most of the teacher educators’ reflections could be assigned to one of four categories: • Reasons for selecting parts of the module (e.g., “I looked at last year’s course book and this one was miles ahead of that one, I think because it is so much
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