The aim of this paper is to present the results of an experiment carried out in the Mexican Autonomous Metropolitan University (UAM) based on recent theories of educational research on building up knowledge. The research group was studying "Calculus 1" following the Programme of Intervention, "SAM" (Mediated Learning System), an innovative teaching project in mathematics. The Programme of Intervention, "SAM", is based on the theories of the cognitive paradigm, and an important element of such Programme is concept mapping. The Programme considers that through the use of concept mapping in the study of mathematics, cognitive abilities can be acquired leading to an improvement in the intelligence coefficient of the students. Through the Programme the teacher is the agent between the curriculum contents and the students. He designs the classroom presentation and the concept mapping according to how the student learns. The teacher considers that concept mapping is an important element to develop skills.
In the education context, the cognitive paradigm considers that education must be oriented towards the achievement of meaningful learning (it must make sense) and towards the development of general and specific strategic abilities of learning. Teaching, concretely in the classroom, from the point of view of this paradigm, must allow for the learning of the contents of the curriculum in the most meaningful way. This has the implication that planning and organization of the didactic processes are vital for the creation of the minimum conditions for meaningful learning.
In addition, with regard to teaching within the framework of the cognitive paradigm, the teacher must start from the idea that the student is active and can learn meaningfully, that he can learn to learn and to think. The teacher must concentrate on the task of the combination and organization of didactic experiences in order to achieve learning.
In order to bring information that will contribute in some way to aspects related to the teaching and learning of mathematics, the initiative arose of undertaking research concentrating on a Programme of Intervention designed "SAM" (Mediated Learning System). Such a programme-a special way of acting in the classroom-would consider mathematic contents as a vehicle to develop awareness in the student, understanding cognitive development as the development of a collection of cognitive skills. One of the important elements of the Programme "SAM" is concept mapping.
The Programme "SAM" takes into consideration the thought processes both of the teacher and the student; processes proper to the analysis of the cognitive paradigm. The program is based on Ausubel's theory of meaningful learning (Ausubel, Novak & Hanesian, 1988). It is a Programme that follows the model Learning-Teaching (how the one who is learning learns, based on which, it is possible to design the teaching) and serves as a tool to achieve student learning where the teacher acts as a mediator for the learning.
The Programme, on one hand, considers the abilities and cognitive skills as objectives, and on the other, mathematical contents and method are considered as a means to achieving these objectives. From this point of view, the Programme orients the teaching towards cognitive development, which is why it is considered as a Programme of cognitive intervention. The Programme has objectives by skills: Develop skills of induction and deduction considered as a part of a capacity for logical reasoning and develop the skills of situating, locating and expressing graphically as part of the capacity for spatial orientation.
The Programme "SAM" achieves its objectives when the teacher uses concept mapping as a support material during action in the classroom. The teacher has to arrange and organize the contents of the subject in order to facilitate learning. …