Abstract: Function is a key concept in school mathematics. In Vietnamese mathematics textbook, the concept of function is constructed through many classes, but the analytic expression always prevails. Can we teach the concept of a function that integrates multiple representations and creates conditions for students to build their own knowledge? The process of teaching and learning always requires interaction, especially in an environment that integrates information technology such as mathematical software, Internet. By the didactic approach, students learn by an adaptation process (assimilation and accommodation) to the environment, which creates contradictions, difficulties and imbalances. According to Brousseau (1998) “In didactic situations, the environment is a system of resistance to students, that is, to alter the state of knowledge in a way that the student does not control”. Casyopée software is a functional teaching software designed and developed by Lagrange (2002) and colleagues. This is the only software that studies functional relations with the integration of two algebraic and geometric modules. This study will focus on the following questions: +) How is the concept of function expressed in the general mathematics program of Vietnam? +) How does the presentation of the textbook affect the concept of the student about the concept of function? +) What is the role of Casyopée software in teaching and learning function concepts in an integrated environment of multiple function expressions?
Keywords: Casyopée, functional expression, environment, learning.