Unifying complexity in mathematics teaching-learning development: a theory-practice dialectic.

This chapter addresses theory in relation to mathematics teaching and learning development, drawing on a research study to exemplify theoretical perspectives. In particular it addresses difficulties and issues which arise in a developmental process, from both theoretical and practice-based points of view. The areas of theory are those of inquiry, community, and critical alignment, which address developmental processes in mathematics learning and teaching; documentational genesis and instrumentation theory, which address the development of knowledge in teaching; and finally the use of a framework from activity theory, which addresses issues and tensions that emerge from observation and analysis in the research. The illustrative research study addresses perceptions of learning and its outcomes between a teaching team and a cohort of engineering students learning mathematics in a university system. Overall the chapter seeks to address complexity in the developmental process and important synergies between theory, practice and research.