Abstract

(Objective)  This paper presents the results of a qualitative, descriptive research study characterizing the knowledge of prospective mathematics teachers at the National University of Costa Rica (UNA) concerning the concept of mathematical proof, using the Mathematics Teacher’s Specialized Knowledge (MTSK) model.

(Methodology)  This research employed an interpretive paradigm and a qualitative approach. A questionnaire was administered to 42 mathematics teachers in initial training during the first semester of 2021, in the fourth and fifth years of the Bachelor’s Degree program in Mathematics Teaching at the National University of Costa Rica. Content analysis was utilized to study the answers provided by participants. Groupings of answers were created to generate central ideas about the concept of proof.

(Results)  Based on the results, four central ideas were found about the nature of mathematical proof for the survey participants. These ideas are similar to the formal logical-syntactic and mathematical aspects (LSMA) or informal semantic aspects (ISA). Evidence for the five De Villiers (1993) functions of a proof was found. Moreover, new functions related to them were discovered in mathematics and in school mathematics.

(Conclusions)  The results provide input to trainers of mathematics teachers and researchers for the review and analysis of teacher training programs. Additionally, they contribute to the search for new research areas related to this subject.

Keywords: Mathematics teacher’s knowledge; mathematical proof; concept of proof; prospective mathematics teachers