This study aims to examine how teachers’ mathematical and pedagogical knowledge develop as they learn to use a multi-representational technological tool, the TI-Nspire handheld device and computer software. It is conducted as an enquiry into the learning trajectories of a group of secondary mathematics teachers as they begin to use the device with a focus on their interpretations of mathematical variance and invariance. The research is situated within an English secondary school setting and it seeks to reveal how teachers’ ideas shape, and are shaped by, their use of the technology through a scrutiny of the lesson artefacts, semi-structured interviews and lesson observations. Analysis of the data reveals the importance of the idea of the ‘hiccup’; that is the perturbation experienced by teachers during lessons stimulated by their use of the technology, which illuminates discontinuities within teachers’ knowledge. The study concludes that the use of such a multi-representational tool can substantially change the way in which both the teachers and their students perceive the notions of variance and invariance within dynamic mathematical environments. Furthermore, the study classifies the types of perturbations that underpin this conclusion. The study also contributes to the discourse on the design of mathematical problems and their associated instrumentation schemes in which linked multiple representations offer a new environment for developing mathematical meanings. This thesis makes an original contribution to understanding what and how teachers learn about the concept of mathematical variance and invariance within a technological environment.

A growing consensus of researchers and practitioners has found that systemic, ongoing teacher professional development is more effective than traditional one-time workshops.

As seen in the descriptions of the two PD models, one of the primary differences between the models is the order and emphasis on formative assessment and on the use of TI-Navigator for formative assessment in the delivery. This design was generated due to the difficulties identified with implementing formative assessment in classroom. To use
technology to implement formative assessment adds another level of complexity. Project FANC is trying to determine if there is a difference, based on student outcomes, between
these two designs. After two years of PD, to check if there is a difference in student outcomes, pre and post student data is being collected. In addition, data is continually being collected on how teachers are implementing each of the PD models and the effects of these models on student learning. For a more in-depth analysis of teacher implementation, case studies of ten teachers are being conducted to give a picture of various degrees of implementation of formative assessment strategies using the TINavigator. Full results on the project will become available starting in December 2010.

This paper reports on two different models of professional development that were created to investigate the use of formative assessment in a networked classroom. Participants were divided into two groups with one group receiving formative assessment without networked technology in the first year while the second group received formative assessment along with technology. Data was gathered on
participants’ knowledge of formative assessment and their attitudes toward the use of technology.