Supervisors info:
Ανδρέας Μούτσιος - Ρέντζος, Επίκουρος Καθηγητής, Παιδαγωγικό Τμήμα Δημοτικής Εκπαίδευσης (ΠΤΔΕ), Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)
Summary:
This dissertation examines the form of proving arguments in the 5th grade mathematics class depending on the type of problem (one solution, finite number of solutions, infinite solutions). The form of proving arguments is studied in terms of the mode of representation chosen (symbolic, visual, verbal), as well as in terms of the type of reasoning (empirical/inductive, analytical/generative). For the study of this specific subject, a systemic approach is followed. During the research, questionnaires were given to students of four classes of the 5th grade. These questionnaires study which arguments are more persuasive according to each type of problem for the students themselves, their classmates, as well as for their teacher. All the problems concern the thematic unit of fractions, as it is a particularly important part of the greek curriculum. Also, in the second part of the questionnaire, the opinions of the students on the proofs are studied. Afterwards, individual interviews were conducted with the teacher of each class, in order to see their views on the proof, on the various proving arguments that they consider acceptable in the classroom, as well as the preferences of their students, the teaching practices they follow, as well as their views on the institutional framework. Then, the first three sections of the school textbook were also studied, in order to see which mode of representation the school textbook chooses most often, as well as which type of reasoning. Finally, the four systems were studied separately. It was observed that students, teachers and the textbook tend to choose proving arguments that use symbolic representations and empirical/inductive reasoning. However, differences were observed between certain preferences in some systems, which highlights the necessity of a systemic approach to such multifaceted and complex issues.
Keywords:
proofs, proving arguments, mode of representation, type of reasoning
