Teresa Rojano

This article reports the outcomes of a study that seeks to investigate the role of feedback, by way of an intelligent support system in natural language, in parametrized modelling activities carried out by a group of tertiary education students. With such a system, it is possible to simultaneously display on a computer screen a dialogue window and a window with a microworld that are dynamically hot-linked to each other. While users work in the microworld, they can enter into dialogue with the system in natural language. The article discusses the case of one pair of participating students. In their case, the feedback provided by the intelligent support and by the microworld at key moments of the modelling activities, such as understanding the phenomenon, building the model or predicting, was crucial to their ability to build a spreadsheet model and, consequently, to their understanding of the long-term behaviour of the phenomenon being modelled.

This article centers on studying the progress of algebraic syntax once students have surmounted initial obstacles found in the transition toward symbolic algebra. It specifically analyzes students' progress concerning the operation on the unknown, when the latter is represented by an expression that involves a 2nd unknown. In curricular terms, students face such a situation when they learn the classic methods to solve systems involving 2 linear equations with 2 unknowns. Results from this empirical study show that extending previous algebraic syntax to the 2nd tier of representation of the unknown requires fundamental reconceptualizations such as that of algebraic equalization and that of mathematical unknown.