Traditionally, cognitive skills in mathematics and language have been described as key indicators for success. However, the social, technological, and economic changes that have occurred in the 21st century have made critical thinking, creativity, communication, and collaboration, key competences to face the challenges of a rapidly changing world. In this study, we developed a Computational Thinking (CT) curriculum based on student-centred pedagogical strategies to enhance these four competences. This curriculum was designed under the socio-cultural vision of learning, in which individuals interact in communities to build significant knowledge. An embedded mixed-method approach was implemented to evaluate improvements in competence development both in quantitative and qualitative ways in a sample of 42 students. The results indicate an encouraging increase in skills related to the competences of interest thanks to the implementation of a student-centred pedagogical curriculum based on CT. Additionally, by designing the curriculum under socio-cultural ideas of education the results show that the students and the teacher were able to form a community to facilitate teaching and learning.