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Teaching for the objectification of the Pythagorean TheoremSpyrou, Panagiotis, Moutsios-Rentzos, Andreas, Triantafyllou, Dimos 09 May 2012 (has links) (PDF)
This study concerns a teaching design with the purpose to facilitate the students’ objectification of the Pythagorean Theorem. Twelve 14-year old students (N=12) participated in the study before the theorem was introduced to them at school. The design incorporated
ideas from the ‘embodied mind’ framework, history and realistic mathematics, linking ‘embodied verticality’ with ‘perpendicularity’. The qualitative analyses suggested that the participants were led to the conquest of the ‘first level of objectification’ (through numbers)
of the Pythagorean Theorem, showing also evidence of appropriate ‘fore-conceptions’ of the ‘second level of objectification’ (through proof) of the theorem. The triangle the sides of which are associated with the Basic Triple (3,4,5) served as a primary instrument for the
students’ objectification, mainly, by facilitating their ‘generic abstraction’ of the Pythagorean Triples.
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Teaching for the objectification of the Pythagorean TheoremSpyrou, Panagiotis, Moutsios-Rentzos, Andreas, Triantafyllou, Dimos 09 May 2012 (has links)
This study concerns a teaching design with the purpose to facilitate the students’ objectification of the Pythagorean Theorem. Twelve 14-year old students (N=12) participated in the study before the theorem was introduced to them at school. The design incorporated
ideas from the ‘embodied mind’ framework, history and realistic mathematics, linking ‘embodied verticality’ with ‘perpendicularity’. The qualitative analyses suggested that the participants were led to the conquest of the ‘first level of objectification’ (through numbers)
of the Pythagorean Theorem, showing also evidence of appropriate ‘fore-conceptions’ of the ‘second level of objectification’ (through proof) of the theorem. The triangle the sides of which are associated with the Basic Triple (3,4,5) served as a primary instrument for the
students’ objectification, mainly, by facilitating their ‘generic abstraction’ of the Pythagorean Triples.
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Beziehungshaltigkeit und Vernetzungen im Mathematikunterricht der Sekundarstufe INordheimer, Swetlana 05 March 2014 (has links)
Die Notwendigkeit einer Untersuchung über Beziehungshaltigkeit und Vernetzungen im Mathematikunterricht ergibt sich einerseits aus den aktuellen bildungspolitischen Forderungen, andererseits aus den reichhaltigen bildungsphilosophischen Traditionen im deutschsprachigem Raum(KMK 2012, 11). Das Ziel der vorliegenden Arbeit besteht vor allem in der Reflexion von Beziehungshaltigkeit und Vernetzungen im Mathematikunterricht. Diese Reflexion ist durch drei Fragen bestimmt: Was kann man als Lehrer über Beziehungshaltigkeit wissen? Wie kann man als Lehrer handeln, so dass die Schüler Beziehungen zwischen mathematischen Inhalten erkennen bzw. selbständig herstellen? Um handeln zu können, muss man die Wirklichkeit oder die Praxis (bzw. Empirie) kennen, in der man handelt. In diesem Sinne ist die vorliegende Arbeit aufgebaut. Dabei wird ein Versuch unternommen, die klassische Aufteilung zwischen Theorie und Empirie bzw. Praxis des Mathematikunterrichts aufzubrechen, um eine Verzahnung zwischen diesen zu verstärken. Das Herzstück der Arbeit bilden zwei ausgearbeitete und in der schulischen Arbeit erprobte Aufgabennetze (Pythagorasbaum und Rund ums Sechseck), die den Rahmen zur Reflexion bieten. / The need for a study on relations sustainability and networks in mathematics stems, on the one hand, from current education policy requirements, and, on the other, from the rich philosophical traditions of education in the German-speaking countries (KMK 2012, 11). The goal of the present work consists, above all, in reflecting on relations sustainability and networks in mathematics lessons. This reflection is guided by three questions: What can one know, as a teacher, about relations sustainability? How can one act a teacher to ensure that students recognise relationships between mathematical content, or independently produce such relations? In order to act, one must know the reality or practice (e.g. empiricism) in which one acts. The project is focused on the development and testing of worked examples of concrete task networks ("Pythagoras’ tree" and "Around the hexagon").
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