Using multiple representation systems to deepen understanding of functional relationships in mathematics

This thesis describes an experiment using technology to develop conceptual understanding of functions through graphical representations. It examines the effects of including dynamic representations in a conceptual approach to the teaching of functions. The study was implemented over a 5-day period in a Grade 9 class in a small, generally working class, rural school in Eastern Massachusetts. Participating students were observed during class discussions and video analysis, and their written responses and created functions were analyzed. The procedure used in the experiment was based on the Theory of Didactic Situations and used the Didactic Engineering methodology. The structure and sequencing of the thesis is also based on these concepts. Conclusions are drawn regarding the effects of using multiple representations systems to deepen understanding of functional relationships and suggested improvements to the introduction of the function concept in high school instructional programs are given