Constructing geometric knowledge: A narrative on circle tangencies in a generalised arbelos

Christer Bergsten

doi:10.31129/LUMAT.14.2.3139

Authors

Christer Bergsten Linköping University, Sweden https://orcid.org/0000-0002-3681-3535

DOI:

https://doi.org/10.31129/LUMAT.14.2.3139

Keywords:

arbelos, discovery learning, dynamic geometry environment, geometry, figural concepts

Abstract

In the context of explorative mathematical work within a Dynamic Geometry Environment (DGE), this article tries to communicate the author´s construction of (established and new) geometric knowledge linked to a generalisation of the classical configuration of an arbelos. With the aim to trace the genesis of knowledge construction, the story of a discovery learning process is presented as a mathematical narrative with an educational gaze, which brings personal meaning making and institutionalised mathematical knowledge together. The story is theoretically framed by reflections on educational research on DGEs, discovery learning, and mathematical narratives. Some historical remarks on a generalised arbelos, relevant for the discussion, are also presented. Finally, some critical issues related to the narrated experience of knowledge construction and their relevance to mathematics education are discussed.

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