Abstract:

In mathematics education, critical thinking is a key competence characterized by analyzing and evaluating information. Learning environments that require students to justify choices and question results are particularly relevant for such competence. Different types of tasks, such as open-ended and exploratory tasks, are especially powerful in fostering critical thinking, as they place students in situations that are cognitively demanding and non-routine.

This study intends to characterize the critical thinking developed by lower secondary students during the exploration of a set of tasks, discussing also the impact of the specificities of the tasks in the students’ critical thinking development. It adopts a qualitative approach based on case studies. The analysis of critical thinking was done through indicators such as students’ justifications of their choices, decision-making processes and validation strategies.

The findings show that students demonstrate critical thinking essentially when confronted with contradictory results or some type of inconsistency (e.g., by the real-world context). In such situations, students were able to reflect on their strategies, justify their choices and reconsider assumptions. When encouraged to question and review their solutions, students engaged in error analysis and correction, evidencing the development of critical thinking. Nevertheless, this reflective behavior was often reactive rather than spontaneous and self-initiated, with students frequently seeking confirmation from the researcher before accepting or rejecting results.

Overall, these findings suggest that the development of critical thinking depends on explicit pedagogical support that encourages autonomy and critical evaluation. The conclusion of the study also includes a discussion about the characteristics of the tasks and their potential for fostering critical thinking in mathematics education.

Keywords:

Mathematics, critical thinking, basic education.