A cascade model of professional development presents a particular risk that 'knowledge' promoted in a programme will be diluted or distorted as it passes from originators of the programme to local trainers and then to the target teachers (Soloman and Tresman 1999; Kennedy 2005). Careful monitoring of trainers' and teachers' knowledge as it is transferred through the system is therefore imperative. This paper focuses on the transfer of content knowledge through an in-service teacher professional development programme and offers an innovative methodology for investigating knowledge transfer, i.e. through insights gained during a mentoring process. The findings suggest that this methodology facilitated assessment of knowledge transfer because it involved the identification of knowledge in practice. The focus on knowledge in practice appeared to avoid a deficit model of trainers'/ teachers' knowledge and revealed that content knowledge was generally being successfully transferred throughout the system. A detailed analysis of different aspects of content knowledge transfer suggested various foci for additional training.
In this paper I report findings from a four year study of beginning elementary school teachers which investigated development in their mathematical knowledge for teaching (MKT). The study took a developmental research approach, in that the teachers and the researcher collaborated to develop the mathematics teaching of the teachers, while also trying to understand how such development occurred and might be facilitated. The Knowledge Quartet (KQ) framework was used as a tool to support focused reflection on the mathematical content of teaching, with the aim of promoting development in mathematical content knowledge. Although I focused primarily on whether and how focused reflection using the KQ would promote development, it was impossible to separate this from other influences, and in this paper I discuss the ways in which reflection was found to interrelate with other areas of influence. I suggest that by helping the teachers to focus on the content of their mathematics teaching, within the context of their experience in classrooms and of working with others, the KQ framework supported development in the MKT of teachers in the study.
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