@phdthesis{discovery10019941,
          school = {Institute of Education, University of London},
            note = {Thesis: (PhD) University of London Institute of Education, 2010.},
           title = {How does a multi-representational mathematical ICT tool mediate teachers' mathematical and pedagogical knowledge concerning variance and invariance},
            year = {2010},
        abstract = {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.},
             url = {http://ethos.bl.uk/OrderDetails.do?did=1&uin=uk.bl.ethos.534784},
          author = {Clark-Wilson, Alison},
        keywords = {Hiccup, instrumental genesis, mathematics education, mathematical generalisation,
multiple representational technology, teacher development, variance and
invariance.}
}