Secondary students' proof schemes during the first encounters with formal mathematical reasoning: appreciation, fluency and readiness.

The topic of the thesis is proof. At Year 9 Greek students encounter proof for the first time in Algebra and Geometry. Thus the principal research question of the thesis is: How do students’ perceive proof when they first encounter it? The analysis tool in order to obtain an image of students’ perception of proof, the Harel and Sowder’s taxonomy, is itself a research question in what concerns its applicability under Greek conditions. Its applicability, of which there is strong evidence, provides the space to shape an image of students’ proof fluency, proof appreciation, proof readiness etc. In order to collect data with regard to answering the research questions in collaboration principally with the class teacher I constructed the two tests on proof that are presented in this thesis. The first test was administered to the students of Year 9 at the beginning of the school year 2010-2011 before the teaching of proof. The second was administered after the teaching of proof of the same school year. Students’ answers were analyzed and provided strong evidence that the Harel and Sowder’s taxonomy is applicable on them. Thus every answer was characterized in terms of the taxonomy. As a result every individual student but also the whole sample is depicted by proof schemes. The major findings of the analysis are the two following: • Students’ proof fluency is higher in simple proof issues. Although they face difficulties when the issues are more demanding, they show high proof appreciation. • There is strong evidence of the applicability of the Harel and Sowder’s taxonomy in a completely different socio-cultural and educational environment in comparison to that of its original invention and application. In the same vein the research proposes the mixture of proof schemes within one proof as theoretical and methodological contribution. Finally from the findings emerge new research questions as e.g. • How teaching and curriculum affect students’ proof schemes? • What is the origin of mixed proof schemes?

Name dc:type.qualificationname

other

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

University of East Anglia

Year dc:date.issued

2014

Author dc:creator

• Kanellos, Ioannis

Language dc:language

en