Norms That Regulate the Theorem Construction Process in an Inquiry Classroom of 3D Geometry: Teacher’s Management to Promote Them

Oscar Molina, Vicenç Font and Luis Pino-Fan
Additional contact information
Oscar Molina: Departamento de Matemáticas, Facultad de Ciencia y Tecnología, Universidad Pedagógica Nacional, Bogotá 110221, Colombia
Vicenç Font: Departament d’Educació Lingüística i Literària i de Didàctica de les Ciències Experimentals i de la Matemàtica, Facultat d’Educació, Campus Mundet, Universitat de Barcelona, 08035 Barcelona, Spain
Luis Pino-Fan: Departamento de Ciencias Exactas, Universidad de Los Lagos, Osorno 5312574, Chile

Mathematics, 2021, vol. 9, issue 18, 1-21

Abstract: This paper aims to illustrate how a teacher instilled norms that regulate the theorem construction process in a three-dimensional geometry course. The course was part of a preservice mathematics teacher program, and it was characterized by promoting inquiry and argumentation. We analyze class excerpts in which students address tasks that require formulating conjectures, that emerge as a solution to a problem and proving such conjectures, and the teacher leads whole-class activities where students’ productions are exposed. For this, we used elements of the didactical analysis proposed by the onto-semiotic approach and Toulmin’s model for argumentation. The teacher’s professional actions that promoted reiterative actions in students’ mathematical practices were identified; we illustrate how these professional actions impelled students’ actions to become norms concerning issues about the legitimacy of different types of arguments (e.g., analogical and abductive) in the theorem construction process.

Keywords: norms; professional actions; theorem construction process; three-dimensional geometry; abductive and analogical arguments (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/18/2296/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/18/2296/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:18:p:2296-:d:637626

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().