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An investigation of prospective middle school mathematics teachers' argumentation, proof, and geometric construction processes in the context of cognitive unity

Demiray, Esr
The first purpose of this study is to investigate how prospective middle school mathematics teachers’ argumentation process while producing conjectures in the cognitive unity based activities relates to the proving process of conjectures they produced. The second purpose is to examine the global argumentation structures emerged while producing conjectures, the components of argumentation, and the functions of the rebuttal component. The third purpose is to investigate the approaches offered to perform geometric constructions asked in the cognitive unity based activities and to what extent they could perform geometric constructions correctly while using compass-straightedge and GeoGebra. The last purpose is to scrutinize the conjectures produced during argumentation and whether they could present valid proofs for the recently produced conjectures. To that end, the data were collected from junior prospective middle school mathematics teachers in the 2016-2017 academic year. The data sources are video recordings and audio recordings of the cognitive unity based activities, documents, GeoGebra files, field notes, and focus group interviews. The findings presented that conjecture production process relates to proving in both positive and negative aspects. Regarding argumentation, the mono structures and the hybrid structures emerged, new components of argumentation were offered, and the eight functions of the rebuttal component were reported. Both compass-straightedge group and GeoGebra group presented at least one valid approach for geometric constructions embedded in the activities. Lastly, it was seen that groups could not conduct valid proof for all statements asked in the activities.