Bretscher, N. (2015). Mathematical knowledge for teaching using technology (Doctoral dissertation). Available from ProQuest Dissertations and Theses Global database. (UMI No. 10094362)

Abstract: 

each”The focus of this PhD study is teachers’ knowledge and how it is involved in interacting with technology to produce the mathematical knowledge made available in the classroom. Contrasting connectionist and transmissionist teachers’ use of technology provides a means of making such knowledge visible, allowing an exploration of the nature and content of mathematical knowledge for teaching using technology. In addition, this study examines how and to what extent the mathematical knowledge made available through a teacher’s interaction with technology is distributed across the teacher and technology. The first, quantitative phase of the project surveyed English secondary mathematics teachers’ use of technology (n=183). Using Rasch analysis to construct a transmissionist measure of self-reported pedagogic practice, a surprising association is found between frequent use of teacher-centred software and a more connectionist orientation. The survey data also suggests that ‘teacher-centred’ practices involving ICT may instead be construed as ‘dominant’ practices, since they are most frequently occurring across all teachers. In the second, qualitative phase of the project, two connectionist and two transmissionist teachers were selected as case studies on the basis of their responses to the survey instrument. Data collection involved a semi-structured interview based around a GeoGebra file on circle theorems, two classroom observations and postobservation interviews. Data analysis using the TPACK framework suggests the nature of mathematical knowledge for teaching using technology as abstract, mathematical knowledge and yet simultaneously as mathematical knowledge situated in the context of teaching using technology. Using the Knowledge Quartet, a conceptualisation of the content of mathematical knowledge for teaching using technology in relation to the topic of circle theorems is developed, demonstrating the highly complex nature of such knowledge. Ameliorating this complexity, this study provides indications of how a distributed view of cognition might offer potential strategies for facilitating teacher interaction with technology.”