How are motivation and self-efficacy interacting in problem-solving and problem-posing?

Affects are intuitively accepted as having a role in the key stages that determine success in problem-solving (PS) and problem-posing (PP). Two disjoint groups of prospective mathematics teachers with similar background and competences have been exposed to PS and PP activities, respectively, and they had to describe their affective states during these activities. The students’ reports have been analyzed from the perspective of epistemic affects, motivation, and self-efficacy. While in the PS context, several students expressed reluctance to report emotional feelings or frustrations over failing to find a solution for the given problems, in the PP context, a phenomenon of adaptation to one’s own cognitive possibilities appeared and the posed problems created a state of comfort/ enjoyment in students. PP conveyed a sense of autonomy and control to a greater extent than PS. It seems that intrinsic motivation is influenced by factors that are different in PP vs PS tasks, with an effect on perceived self-efficacy. The PP activity instilled a robust sense of coping efficacy, which made the students perceive their work as successful, to a large extent. In PS, the initially perceived self-efficacy triggered motivation to persevere with the solving, while in PP, the initial motivation generated by a novel task evolved into students’ perceptions of self-efficacy and confidence in one’s own capabilities. The conclusions of this study can help prospective teachers to use emotions in teaching for understanding, anticipating, and dealing with students’ ideas about mathematics and mathematical thinking and, finally, for improving students’ self-esteem and self-confidence, with an effect in more successful results.