TITLE:
Means of Choice for Interactive Management of Dynamic Geometry Problems Based on Instrumented Behaviour
AUTHORS:
Philippe R. Richard, Michel Gagnon, Josep Maria Fortuny, Nicolas Leduc, Michèle Tessier-Baillargeon
KEYWORDS:
Didactics of Mathematics; Competencies; Geometric Thinking; Tutorial System; Related Problems; Dynamic Geometry; Instrumented Behavior; Cognitive Interactions; Conceptions; Mathematical Work Space; Means of Choice; Didactic Contract
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.3 No.3B,
October
25,
2013
ABSTRACT:
Our paper presents a
project that involves two research questions: does the choice of a related
problem by the tutorial system allow the problem solving process which is blocked
for the student to be restarted? What information about learning do related
problems returned by the system provide us? We answer the first question
according to the didactic engineering, whose mode of validation is internal and
based on the confrontation between an a
priori analysis and an a posteriori analysis
that relies on data from experiments in schools. We consider the student as a
subject whose adaptation processes are conditioned by the problem and the
possible interactions with the computer environment, and also by his knowledge,
usually implicit, of the institutional norms that condition his relationship
with geometry. Choosing a set of good problems within the system is therefore
an essential element of the learning model. Since the source of a problem
depends on the student’s actions with the computer tool, it is necessary to
wait and see what are the related to problems that are returned to him before being able to identify
patterns and assess the learning. With the simultaneity of collecting and
analysing interactions in each class, we answer the second question according
to a grounded theory analysis. By approaching the problems posed by the system
and the designs in play at learning blockages, our analysis links the
characteristics of problems to the design components in order to theorize on
the decisional, epistemological, representational, didactic and instrumental
aspects of the subject-milieu system in interaction.