How argumentation relates to formal proof process in geometry

Author:

Demiray Esra1ORCID,Işıksal-Bostan Mine2ORCID,Saygı Elif1ORCID

Affiliation:

1. Faculty of Education, Mathematics and Science Education, Hacettepe University, Ankara, TÜRKİYE

2. Faculty of Education, Mathematics and Science Education, Middle East Technical University, Ankara, TÜRKİYE

Abstract

This study aims to examine how being involved in an argumentation process relates to the formal proof process in geometry. Prospective mathematics teachers were involved in an argumentation process while producing conjectures before engaging in formal proof of the recently produced conjectures. To collect data, four geometry-proof tasks that involve two sections were employed. The first section of the tasks demands the production of conjectures, which stands for the term argumentation. The second section asks for the formal proof of one of the recently produced conjectures. Based on the data analysis, the affordances of being involved in argumentation before engaging in the formal proof process were listed as positive affective occasions, arrangement of knowledge related to the content of the task, visual aspect, and the veracity of the statement. Negative affective occasions and confusion related to the difference between conjecturing and proving were coded as constraints of being involved in argumentation before formal proof.

Publisher

Modestum Ltd

Subject

Education,General Mathematics

Reference45 articles.

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4. Boero, P. (2017). Cognitive unity of theorems, theories and related rationalities. In T. Dooley, & G. Gueudet (Eds.), Proceedings of the 10th Congress of the European Society for Research in Mathematics Education (pp. 99-106). DCU Institute of Education and ERME.

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