HIGH SCHOOL TEACHERS ’ COGNITIVE SCHEMES SHOWN IN PROBLEM SOLVING APPROACHES BASED ON THE USE OF TECHNOLOGY

This study documents the type of proof schemes that high school teachers developed and used in problem solving scenarios that involve the use of dynamic software (Cabri-Geometry). Research questions that helped organize and structure the development of the study include: (i) To what extent does the high school teachers ’ process shown to pose questions or formulate problems influence their ways to validate mathematical relations or conjectures? (ii) What types of problem solving strategies do the participants use to identify and support conjectures that emerge as a result of constructing and examining dynamic problem representations? Results indicate that the subjects ’ use of dynamic software to represent mathematical objects and situations dynamically not only favors their ways to formulate conjectures; but also the schemes ’ construction to support and validate those conjectures. How does a mathematical relation emerge? What does it mean to prove or demonstrate a particular mathematical relation? What types of arguments are important to validate a mathematical conjecture? How visual, empirical, geometric, and analytic arguments are used to validate mathematical relations? To what extent do the systematic use of dynamic software favor or enhance a particular ways of reasoning and thinking about proofs ’ construction? Th