Unit:
Κατεύθυνση Διδακτική και Μεθοδολογία των ΜαθηματικώνLibrary of the School of Science
Author:
Petropoulou Kyriaki
Supervisors info:
Πόταρη Δέσποινα, Καθηγήτρια, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Η σύζευξη συντακτικής και σημασιολογικής αιτιολόγησης στη διδασκαλία της αναλυτικής γεωμετρίας της Β' Λυκείου
Translated title:
Linking syntactic and semantic proof in the teaching of analytic geometry in grade 11
Summary:
During the teaching of specialized mathematics in grade 11 of General high school, students seem to have a significant difficulty in solving exercises of Analytical geometry. This difficulty is mostly attributed to the lack of students’ familiarization with geometrical shapes on the basis of which they could express their solutions algebraically. In Analytical Geometry there are two Representation Systems of Proof: Geometry and Algebra and each one has its own structure and characters. In a syntactic proof, reasoning works entirely within the representation system of algebra while in a semantic proof the individual works, at least in part, within a different representation system (e.g. the geometrical). The use of a semantic strategy through the variety of its expressions can support the proving process. In this study, we designed and carried out a teaching intervention in a classroom during which, conjectures were used as a starting point for justification. Students were encouraged to use both representation systems (Geometry and Algebra) and to link them in their justifications. Findings and conclusions focus on if and how the students combined the methods of syntactic and semantic reasoning during this particular teaching intervention.
Main subject category:
Science
Keywords:
Representation system proof, syntactic strategy reasoning, semantic strategy reasoning
