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Thesis: Liana Krakecker
Curso de Doutorado em Educação Matemática da Universidade Federal do Mato Grosso do Sul
Campo Grande – MS 2022
In this research, we had the general objective of investigating mathematical validation processes developed by students from a 9th grade class of Elementary School of a state public school in Mato Grosso, during the academic year of 2020. Specifically, we sought to identify how the students analyzed formulated and presented mathematical validations for their statements and/or conjectures, classifying mathematical proofs that were produced by them, as well as to identify elements related to the activities developed by the students that could favor the production of validations.
We analyzed the interaction we had with two students, considering our dialogues, speeches, writings and the resolutions presented by them for each activity, seeking to meet our research objectives. For the elaboration, application and analysis of situations, we rely mainly on Balacheff's Proof Typology Model, on Brousseau's Theory of Didactic Situations, possible functions of the mathematical proof signaled by De Villiers and other authors, as well as on research that dealt with the theme. At the end of this process, it was possible to identify that the students started to consider performing several tests and generalization elements in their tests.
Thesis: Mara P. Markinson
Graduate School of Arts and Sciences, Columbia University
Geometric proof-writing is a widely known cause of stress for secondary school students and teachers alike. As the textbook is the primary curricular tool utilized by novice teachers, a two- part qualitative study was conducted to determine (a) the types of proofs presented in a typical high school geometry textbook and (b) teachers’ preparedness and confidence to teach proof and proving.
I conducted a qualitative analysis of the selected textbook based on its presentation of proofs and proof tasks, and then used said analysis to inform the creation of a five-question content assessment on proof, which was administered to 29 preservice and in-service secondary mathematics teacher participants.