Developmental semiotics : the evolution of a theoretical framework for the description of meaning-making in mathematics education and in mathematics.
It is the purpose of this work to evaluate the possible contribution that
a semiotic perspective could make to mathematics education and mathematics.
This emphasis of this work is on the development of a semiotic perspective,
emerging from the work of C. S Peirce and L. Vygotsky, that embodies both
the philosophical and psychological notions of the role of the sign. This
perspective, termed Developmental Semiotics, evolves through the interplay of
the theoretical and empirical aspects of this work. Developmental semiotics is
applied in the form of a prototype as an empirical tool to two case studies, one
concerning algebra and one concerning co-ordinate representations. The results
of these studies serve to inform the evolution of the perspective and provide
some conclusions specific to the case studies arising from this way of viewing
learning in these contexts. The perspective is refined in the light of the studies
and a further case study is carried out, this time in the area of the history of
mathematics (the development of Boolean algebra), with the purpose of
evaluating the final form of the framework and informing on mathematical
development, creativity and motivation.
Developmental semiotics has implications at two levels, on the
macro semiotic level it brings forward the emphasis on the role of the sign in mathematical meaning-making, it rejects the traditional subject-object
dichotomy and through semiotic action accounts for the relativity in
mathematical meanings. At the micro semiotic level it describes mathematical
development in terms of progressive meaning making instances for increasingly
opaque signs and gives specific information about the meanings made by
mathematics learners in specific contexts. In some instances it has enabled the
identification of meanings that may be useful for mathematical progression.
This work hopes to contribute to mathematics education by bringing to
the fore the discipline of semiotics through emphasis on the role of the sign as a
meaning giving entity, and through provision of a framework and empirical
toolkit for the semiotic analysis of specific learning contexts. Furthermore it
may also contribute to both mathematics, by exposing the history of
mathematics to a semiotic analysis, and to semiotics itself by providing a
further context for the application of this cross disciplinary point of view.