Continuidad entre la formacion matematica basica y la formacion matematica universitaria: una propuesta didactica.

The high failure rates in the first mathematical courses at the college level reveal a problem in the secondary - college education transition. Despite efforts made by universities elsewhere, and in particular, at the Pontificia Universidad Javeriana, Seccional Cali, they has been promoting changes in the curricula and teaching strategies for improving the mathematical outcomes by the end of the first mathematical course, failure rates have remained virtually the same even with a slight upward trend. This fact shows a discontinuity between the two educational levels, there are differences between the "basic mathematics formation" acquired for a student in its secondary education and the “minimal mathematical performance" required for a student at the university level. This project proposes a methodological approach to the teaching and learning of mathematics that aims to remove such a discontinuity. This proposal initiates before students enter to the "normal" university academic life and continues thought monitoring and support during its first mathematical course. It is based upon the Didactic Engineering Methodology and theoretically has three core elements: Different semiotic representation systems that interlock to create didactic multi-register, different levels of reasoning in the learning of mathematics and a social-constructivist approach that guides classroom interactions among students and between teacher and students. With these theoretical elements in mind is propose a mathematics organization and didactics that guides the design, testing and validation of this proposal.