A mathematical model was defined to characterize the association between reading comprehension and mathematical competence in high school students aspiring to engineering careers at the University of the Guajira. The sample consisted of five hundred (500) students from grades six to eleven in the year 2017. The BECOMA and the Reading Comprehension Assessment Model were the instruments used to collect the information and its reliability was made through Cronbach's Alpha. The mathematical model was developed by linear regression between the variables of reading comprehension and mathematical competence for high school students with aged between 14 and 22 years. The mathematical model that best fitted the sample data was the reciprocal of natural y-logarithm of x with high statistical significance (p = 0.000), confidence level of 95%, correlation coefficient R =-0.993899 and determination of R 2 = 98.7834%. The Homocedasticity of the data was verified by the F-Fisher test (p = 0.4032241), the normality by Shapiro-Wilk (p = 0.777541) and the independence of the residues by Durbin-Watson (p = 0.3149).

The association between metacognition, self-efficacy and school of origin was analyzed in 950 students of the engineering programs of the University of Cartagena between 2014 and 2016. The instrument for measuring metacognition was the "Learning Self-Regulation Inventory" designed by Lindner, Harris and Gordon (1993), which was modified for the requirements of the research Selfefficacy was measured with the Self-Efficacy Inventory for Learning (SELF) and the school of origin was identified by survey. The values of 0.90 and 0.94 for the Cronbach's Alpha enabled the validation of the Learning Self-Regulation Inventory and the self-efficacy inventory for learning respectively. For the relationship analysis, the variables were crossed and the bar diagrams and the 2x2 contingency tables were constructed by applying the Chi-Square independence test, which showed statistical significance between the metacognition and self-efficacy variables. The results indicate that there is a significant degree of statistical significance (p <0.05) between metacognition and self-efficacy (p = 0.047) at a confidence level of 95%. This allowed us to identify that the engineering student at the University of Cartagena understands his own cognition process and is able to select learning strategies that allow him to achieve his academic achievements.