RAMÓN MARRADES and ÁNGEL GUTIÉRREZ PROOFS PRODUCED BY SECONDARY SCHOOL STUDENTS LEARNING GEOMETRY IN A DYNAMIC COMPUTER ENVIRONMENT

ABSTRACT. 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 con-ception 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