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Thesis: Kol Murat
Middle East Technical University, Ankara, Turkey, 2022.
This study aims to investigate the nature of pre-service mathematics teachers’ collective mathematical argumentation processes in a technology-enriched learning environment. This design-based study designed a course to improve pre-service mathematics teachers’ technology competencies. In this context, pre-service teachers’ mathematical argumentation processes were evaluated with data obtained during a semester.
The data presented in this study were obtained from 10 pre-service teachers who enrolled in the course in the fall semester of 2018 and continued to the primary school mathematics teaching program at a state university in Ankara. The activities using argumentation in the lesson lasted for seven weeks. Multiple data collection methods were used in the study, and qualitative analysis methods were used in data analysis.
The data obtained from the study revealed that technology, instructor, and preservice teachers, who are the actors of the collective argumentation processes in a technology-enriched learning environment, played different roles and functions during the interactions. During the activities, it was observed that the teacher’s instrumental orchestration functioned in argumentation to varying degrees.
In addition, the technological behavior styles of teacher candidates in the collective argumentation process also varied according to the components of Toulmin’s argumentation model. The analysis of the study’s data also allowed the researcher to observe how the pre-service teachers use technology in inductive and deductive reasoning types that emerge integrated into the argumentation process.
Thesis: Sordi Mônica Marina
Chapecò, Brazil (2022)
The present work consists of a qualitative and bibliographic research whose objective is to analyze the validations of the Pythagorean Theorem in textbooks for the 9th grade of middle school, articulating the types of mathematical reasoning according to Balacheff and the semiotic representations of Duval. For this, Bardin's Content Analysis is used as a technique of data analysis.
Three collections of Mathematics textbooks for the 9th grade of Elementary School are selected, in the teacher's version, distributed in the last National Program of the Textbook, which occurred in 2020. The condition for choosing the collections is that they contain at least some validations of the Pythagorean Theorem. The following collections were selected: Essential Mathematics, Teláris Mathematics and Mathematics Trails. The validations of the theorem are studied based on two major categories of analysis, the types of mathematical reasoning described by Balacheff and the different registers and semiotic operations described by Duval. Subcategories are also established for the analysis, aiming to enable the articulation between the two authors.
The results of the research show that the textbooks of the three collections present different ways to validate the Pythagorean theorem, being the intellectual proofs of the demonstration type, which mobilize simultaneously the figurative register and the geometric register, the most used, followed by the pragmatic proofs that resort only to the figures or the action on them.