||Square Root of 2 and the Idea of Convergence: A Socratic Experience
||María Ángeles NAVARRO and Pedro Pérez CARRERAS
Our purpose is to reveal the details of the complex logical structure underlying the concept definition of convergence. Our strategy is to facilitate the building of a suitable concept image of convergence by taking v2 as idée fixe and guiding hand in the process of design of a Socratic dialog which is the basis for an interview performed on students of first year college studies. Besides paper and pencil and verbal exchanges, interviewer and interviewee make profuse use of a computer generated tool to cover, on one hand, the arithmetic and visual components of the idea of convergence and, on the other, to recreate the dynamic character of this concept. Success is attained if the interviewee is able to translate the constructed concept image into algebraic and logic terms, for which purpose our experience starts with a fine tuning in quantifiers in common and mathematical language. This educative experience wants to highlight the importance of linking the process of discovery, understanding and conceptualization in theory building and the role played by the computer in attaining this goal in the form of a battery of actions that could be implemented prior to formal mathematical instruction in the classroom.