The constructivist approach is based on the idea that knowledge can never be passed from one person to another. The only way to acquire knowledge is to create or construct them. The constructivist approach changes also the role of the teacher in the educational process, the task of them is to organize the environment so that the student himself can construct the cognitive forms that teacher wants to give him. In the paper, the nature of the constructivist approach is identified, different aspects regarding mathematics education are analysed as well as the potential impact on the development of mathematical competences in the context of sustainable development is discussed. The study process and learning methods appropriate to constructivist approach also were studied. In order to illustrate the need for a constructivist approach in mathematics education, the survey of students from Latvia University of Life Science and Technologies (LLU) and Riga Technical University (RTU) were carried out, the results of which proved that mathematics learning at universities has to be changed. The current study proved that the constructivist approach radically changes the process of teaching and learning mathematics, connecting it with daily life, rather than teaching only abstract formulas and using a creative approach to mathematical tasks solving. This study shows that using constructivist approach to the teaching of mathematics, the competences needed for sustainable development are boosted.