Geometry, subjectivity and the seduction of language: the regulation of spatial perception

Abstract

Following Husserl's speculations on how geometry originated, we suggest that spatial perception is seduced by language as a result of human attempts to capture, signify and share its concepts. And this language traps geometry and humans themselves in to the forms that have guided and regulated past practices, thereby obscuring possibilities for cultural growth and adjustments to new conditions. Some body movement exercises reveal student teachers' spatial orientations. The paper proposes that the very evolution of geometry, and the ontological status of its objects, relate to their representation in cultural forms referenced to human self-image. It is further argued that learning crucially relates to evolving mathematical or pedagogical understandings of spatial phenomena.

The Strategy the Use of False Assumption and Word Problem Solving

“…We have proceeded from the generally accepted assumption that ontogenetic development is not independent of phylogenetic development (Brown and Heywood, 2010;Dubinsky et al, 2005).…”

Experiencing the space we share: rethinking subjectivity and objectivity

“…In this sense, all school mathematics is embodied. Brown and Clarke (2012) have shown how school mathematics is a function of institutional contexts and regulated as such. Barad (2007) has shown how scientific phenomena more generally are functions of the inspection apparatus through which they are viewed.…”

“…Calder (2012) meanwhile indicates how perceptions of mathematical spaces as approached within mathematical classrooms might be managed in new ways through the facility of computer packages. Meanwhile, initiatives such as curriculum implementation in education and associated assessment impact on how a particular community builds its wider public understanding of mathematics and of associated technology/apparatus in ever-changing circumstances (Brown & Clarke, 2012). Those pedagogical practices ultimately come to define that community's conceptions of mathematics, and how that community expresses its demands on educational processes, and hence on teachers, in those areas.…”

Four conceptions of infinity

“…Throughout the history of mathematics, the development of pieces of knowledge surrounding infinity has resulted in fundamental turning points necessary for its further development. We have proceeded from the generally accepted assumption that the ontogenetic development is not independent of the phylogenetic development (Brown & Heywood, 2011;Juter, 2006) but the individual's development may pass through analogous successive stages and epistemological obstacles (Radford, 2006). During the development of our understanding of infinity, one can follow the same principle occurring within diverse languages or different curricula, namely the conflict between the unlimited continuation and the completed actualized infinity.…”