This text shows the initial findings of an investigation that sought to implement an alternative model for the teaching of mathematics at a public university in Norte de Santander, Colombia, using virtual platforms to support teaching. The research paradigm focuses on the mixed method to identify the positive elements and aspects to improve of this didactic proposal. Among the findings, it is highlighted that one of the difficulties in implementing this tool refers to the limitations of space in the material attached to the platform, which meant proposing only the links of the material created. Implications for teacher training and suggestions for future implementations are discussed.

This research included a sample of students aged between 8 and 16 years, residents of San José de Cúcuta city, Colombia, belonging to socio-economic strata 1 and 2. Multiple intelligences (musical, logical-mathematical, interpersonal, naturalistic, intrapersonal, kinesthetic, linguistic and spatial) were measured according to the proposal by Gardner and school performance as an average of each subject taken during the first two cuts of the school year. The authors applied a principal components analysis with the purpose of characterizing and analyzing these students according to multiple intelligences, academic performance and their relationships. The sample consisted of 60 girls and 61 boys whose average age was 12 years (95% CI: 11.7 – 12.4 years). In the logical-mathematical intelligence was where the students obtained the highest average score, while in musical intelligence the lowest. In the rest of the cognitive capacities they reached similar averages. In relation to the subjects that this group of students studied, the best average grades were in behaviour, religion and physical education and the lowest in English. Through the principal components analysis it was observed that there is no evident association between the types of intelligences and the grades in the school subjects. Girls, in general, achieved better average scores in all subjects compared to their male counterparts (p < 0.05). Except for naturalistic intelligence, males show a greater development in the rest of the intelligences, in contrast to the girls who have higher scores in naturalistic intelligence.

Attached to the differential calculus concepts, particularly the of limit and continuity usually difficult environment to its conceptual construction, since it is usually oriented to the domain of algebraic processes, restricting the understanding and thus limiting learning and appropriation of the same. This research was developed by students of the hotbed of research in mathematics education, aiming to promote the correct conceptual apprehension of the themes of the differential calculus, through the design and implementation of various didactic sequences, based on didactic engineering as research methodology. Sequences used different registers of semiotic representation such as graphical, algebraic, natural and tabular. The activities were implemented in students belonging to the “Facultad de Ingeniería, Universidad Francisco de Paula Santander”, Colombia. Through the raised situation a better apprehension on the understanding of the infinitesimal of the meaning of the boundary (related to the continuity of this) and a better insight on the graphic understanding of limit and continuity, has strengthened since they had the opportunity to visualize the object of study in a direct way.