Sánchez, E. & Sacristán, A.I. (2003). Influential Aspects of Dynamic Geometry Activities In the Construction of Proofs (original) (raw)
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Influential Aspects of Dynamic Geometry Activities in the Construction of Proofs
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As a key objective, secondary school mathematics teachers seek to improve the proof skills of students. In this paper we present an analytic framework to describe and analyze students' answers to proof problems. We employ this framework to investigate ways in which dynamic geometry software can be used to improve students' understanding of the nature of mathematical proof and to improve their proof skills. We present the results of two case studies where secondary school students worked with Cabri-Géomètre to solve geometry problems structured in a teaching unit. The teaching unit had the aims of: i) Teaching geometric concepts and properties, and ii) helping students to improve their conception of the nature of mathematical proof and to improve their proof skills. By applying the framework defined here, we analyze students' answers to proof problems, observe the types of justifications produced, and verify the usefulness of learning in dynamic geometry computer environments to improve students' proof skills.
TO PRODUCE CONJECTURES AND TO PROVE THEM WITHIN A DYNAMIC GEOMETRY ENVIRONMENT: A CASE STUDY
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This work is a part of a larger study aimed at investigating the effectiveness of a suggested approach, which presents geometric problems through a daily-life story using dynamic geometry software for both school pupils and undergraduate students. The present paper aimed in particular to enable undergraduate students to feel the importance of geometry in daily life, to share in the process of formulating geometric statements and conjectures, to experience the geometric proof more than validating the correctness of geometric statements, and to start with a real-life situation going through seven steps to geometric proof. The content of the suggested approach was organized so that every activity is a prerequisite for entering the next one, either in the structure of geometric concepts or in the geometric-story context. Twelve undergraduate students from the Faculty of Education in Suez Canal University, Egypt participated in the study experiments and responded to three Likert-type que...
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