Problem-posing as a didactic resource in formal mathematics courses to train future secondary school mathematics teachers

Beginning university training programs must focus on different competencies for mathematics teachers, i.e., not only on solving problems, but also on posing them and analyzing the mathematical activity. This paper reports the results of an exploratory study conducted with future secondary school mathematics teachers on the introduction of problem-posing tasks in formal mathematics courses, specifically in abstract algebra and real analysis courses. Evidence was found that training which includes problem-posing tasks has a positive impact on the students’ understanding of definitions, theorems and exercises within formal mathematics, as well as on their competency in reflecting on the mathematical activity.