In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual
conference of the Mathematics Education Research Group of Australasia (Vol. 1). Palmerston
North, NZ: MERGA. © MERGA Inc. 2009
The Master, Servant, Partner, Extension-of-self Framework in
Individual, Small Group and Whole Class Contexts
Vince Geiger
Australian Catholic University
<vincent.geiger@acu.edu.au>
This paper reports on an aspect of a three year longitudinal study which investigated students’ use of
technology in individual and collaborative classroom settings. A socio-cultural perspective was
adopted to develop the MSPE framework which identifies modes of student technology use and
describes the student-student-technology relationships that developed as students worked in
individual, small group and whole class settings. Implications are discussed for how the framework
might lead to more sophisticated technology rich pedagogies in mathematics classrooms.
Introduction
While there have been attempts to theorise students’ usage of technology in the process
of mathematical learning (e.g., Doerr & Zangor, 2000; Guin, Ruthven & Trouche, 2005),
these appear to be founded on individualistic notions of knowledge development and so
fail to incorporate the role of collaboration between classroom participants, in concert with
technology, during learning, reasoning and understanding. This paper reports on aspects of
a study that takes a socio-cultural perspective on the use of technology to learn and teach
mathematics within both individual and collaborative contexts. Because socio-cultural
theory places interaction and activity at the centre of theory development, the relationships
that develop between both human and non-human agents are seen as central to an attempt
to theorise the nature of the practices of both individual students and of collectives of
learners when they work on mathematical ideas and tasks within collaborative, technology
rich classroom environments. Specifically, this paper aims to examine the role of
technology in mediating both individual and collaborative student learning. This will be
done by proposing a framework for students’ use of technology in individual contexts and
illustrating the categories within the framework with representative student comments
drawn from five Technology Questionnaires administered during the study. The remainder
of the paper will then extend the framework to small group and whole class settings.
Theoretical Framework
The perspective offered by socio-cultural theory was chosen to frame the study as it
emphasizes both the role of students’ own activity and interaction in intellectual
development, and the importance of tools in mediating learning. How tools, such as the
digital technologies, mediate learning, particularly in collaborative contexts, is an area of
limited attention in current research literature. Some studies have concluded that while the
formation of technology as a tool for learning requires interaction and negotiation between
students and teachers, the use of technology after this formation can inhibit productive,
collaborative interaction in the mathematics classroom (e.g., Doerr & Zangor, 2000). Other
investigations have attempted to incorporate a social dimension to how students learn in
concert with technology by theorising the role of the teacher as an “orchestrator” of social
interaction (e.g., Guin, Ruthven & Trouche, 2005). Neither of these positions, however,
place social interaction at the centre of the process of thinking, reasoning and learning, nor
do they support theory that suggests technology can be seamlessly integrated into ongoing
collaborative processes.