Dominique Guin

The Complex Process of Converting Tools into Mathematical Instruments: The Case of Calculators

Transforming any tool into a mathematical instrument for students involves a complex ‘instrumentation’ process and does not necessarily lead to better mathematical understanding. Analysis of the constraints and potential of the artefact are necessary in order to point out the mathematical knowledge involved in using a calculator. Results of this analysis have an influence on the design of problem situations. Observations of students using graphic and symbolic calculators were analysed and categorised into profiles, illustrating that transforming the calculator into an efficient mathematical instrument varies from student to student, a factor which has to be included in the teaching process.

Towards Models of Interaction Between an Artificial Agent and a Human One

We present a transposition of a model of interaction in machine learning which may show the way to describe a wider range of interactions in learning environments. It takes into account the basic role of interaction and collaboration and the necessity of various teaching styles which occur at different moments in different domains. Our model provides a possible way to describe didactic interactions between two agents: the teacher is an artificial agent (agent A) whereas the learner is a human one (agent H). Flexibility and adaptibility of this model come from the distinction between an agent and the various roles successively played by him during the different phases of learning.