Motion in Mathematics: Creating a “Dynamic Space” for Playful Reasoning
Although ‘Representation’ is one of the five process standards of the National Council of Teachers of Mathematics, and educational support documents advocate for the use of multiple and varied representations to facilitate conceptual understanding, it is only recently that the educational research community has begun to analyze teacher and student assumptions about representation (diSessa, 2004). Curriculum documents derived from the NCTM standards tend to under-theorize representation by reducing it to a finite list of recommended alternative ways of visualizing an abstract concept. Advocates of computer enhanced instruction, argue that student agency in mathematics comes through dynamic computer geometry environments whereby students are able to play and manipulate representations (Finzer, Erickson & Binker, 2000). This approach is meant to mirror the work of mathematicians who frequently employ visual representations and treat them as dynamic objects to be manipulated and analyzed qualitatively, thereby employing the various representations as flexible and changeable objects for enacting problem-solving strategies (Stylianou & Silver, 2004). Conceiving of representations as dynamic and changeable, and not simply as fixed and ‘equivalent’ translatable forms, is a learning strategy that often distinguishes those students who are successful in school mathematics from those who fail to succeed (Gagatsis & Shiakalli, 2004). This research project studies student beliefs about representations as they negotiate a dynamic computer environment. This action research project was implemented in a mathematics methods course for pre-service teachers. Course sessions were recorded and transcripts were analyzed using a discourse analysis framework for evidence of operative theories of representation.
Keywords: Dynamic Geometry, Space, Reasoning, Representation
Elizabeth de Freitas
Associate Professor, Curriculum and Instruction, Adelphi University