Background: In order to provide skills that enable people to realize their potential, education should not only develop knowledge and aptitudes, but also contribute to the formation of attitudes and positive values. Education systems should be judged in terms of this multidimensional character of education, and the available information indicates that countries differ in the degree to which their students are able to acquire cognitive and non-cognitive competences. Therefore, it should be of interest to improve our comprehension of the development of both types of outcomes, a complex process that depends on personal, family, school and contextual factors. While most empirical studies that try to explain educational quality have only considered cognitive results, this study focuses on the non-cognitive ones. Methods: We estimate a multivariate multilevel regression model that simultaneously analyzes the determinants of two outcomes attained by Argentine students in the Program for International Student Assessment (PIsA) 2012 study: a cognitive result the achievement level in Mathematics and a non-cognitive one the openness to problem-solving-. Results: Both types of outcomes seem to differ in their explanatory factors: schools appear to play a greater role in the determination of cognitive achievements than non-cognitive competencies. However, attributes such as gender or home socioeconomic status have a significant influence in both cases. Furthermore, although school characteristics seem to be less relevant than individual ones in the determination of both types of results, there is also room to improve their development at school. Conclusions: The heterogeneity regarding the variables which explain both types of school outcomes suggests that the policies designed to improve each one of them should be different. Nonetheless, the development of these competencies mainly requires an improvement in socioeconomic and educational conditions at home.