Developing the critical thinking skills of future citizens has become a major educational challenge for schools in the 21st century. However, defining critical thinking is no easy task. As a result, different approaches to educating it in the school context coexist. One approach is transversal, based on a better understanding of certain cognitive processes at play in the exercise of critical thinking. Through experimental research, we studied the ability of fifth-grade elementary school students to counter three common cognitive biases. To this end, we designed an explicit teaching sequence aimed at making students aware of correlation-causation bias, confirmation bias and appeal-to-authority bias, and identifying these in themselves and in others, so that students know how to counter them when necessary. In the sessions on appeal-to-authority bias, we also worked on validating sources. We additionally studied the evolution of certain characteristics of cognitive flexibility and creativity active in the exercise of critical thinking through activities involving changes of point of view, multiple categorization and analogies. Using a cross-control approach, we analyzed the data collected before and after the teaching sequences across four experimental designs. The overall results show that a brief intervention aimed at improving understanding of cognitive biases enabled students to go against these and overcome them to some extent. At the end of the experiment, it also appeared that the students seemed to be more flexible and creative in the proposed activities. Our results are promising and encourage us to explore cross-disciplinary approaches to develop students' critical thinking skills and help them become enlightened, responsible citizens.