Competence-based education should encourage critical thinking in students. However, an appropriate pedagogical method should be selected to guarantee results. The aim of this research was to identify the potential of the Problem-Based Learning approach to develop critical thinking skills in high school students in the area of technology and computing. Two instruments were used: Olivares and Wong’s critical thinking section of the Individual Generic Skills Test, and Charles’ rubric for written essays. The former measured the levels of critical thinking, while the latter examined the written argumentation that participants used to evaluate, interpret and explain everyday problematic situations. The results obtained from both instruments suggest a positive improvement in critical thinking disposition and written argumentation, specifically in relation to the sub-competence of explanation. The students also displayed a self-regulated attitude and adequate performance during the intervention.