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

Abstract

Beginning university training programs must focus on diferent competencies for mathematcs teachers, i.e., not only on solving problems, but also on posing them and analyzing the mathematcal actvity. This paper reports the results of an exploratory study conducted with future secondary school mathematcs teachers on the introducton of problem-posing tasks in formal mathematcs courses, specifcally in abstract algebra and real analysis courses. Evidence was found that training which includes problem-posing tasks has a positve impact on the students' understanding of defnitons, theorems and exercises within formal mathematcs, as well as on their competency in refectng on the mathematcal actvity.