Inquiry of the Past and Reflection on the Present
Inquiry of the Past and Reflection on the Present:
Teaching Rigour and Reasoning in Area Determination through Authentic Historical Sources
IND’s studenterserie nr. 119, 2024, speciale - matematik og didaktik.
Nynne Milthers & Amanda Wedderkopp
Vejledere: Britta Jessen & Tinne Kjeldsen
Abstract
In this thesis we explore how the implementation of authentic mathematical sources in a teaching sequence can be used to teach students in upper secondary school about rigour and reasoning within the subject of area determination. We are utilising works from two past mathematicians, Archimedes and Newton. In order to create an inquiry-reflective learning environment within the framework of The Anthropological Theory of Didactics, Epistemic configurations and the Multiple Perspective Approach, we propose a research methodology. Our proposal is based on Didactical Engineering within the frame of The Anthropological Theory of Didactics and further developed taking inspiration from a methodology by Kjeldsen andWillumsen of how original sources can be implemented in a teaching sequence.
We design an implement a teaching sequence which aims at encouraging students to an inquiry of rigour and reasoning within the chosen historical episodes in order to reflect upon rigour an reasoning in their contemporary context. Our study demonstrates that engaging with historical texts enables some students to identify the evolution of mathematical rigour and reasoning, but discrepancies in the students’ expected and actual knowledge made it difficult to implement the intended teaching sequence. Furthermore is sheds light on the students misconceptions of rigour and reasoning. The findings suggest that mathematical historical sources are valuable tools in identifying misconceptions and encouraging students in discussion within mathematics, which is not usual.