The importance of problem posing in mathematics and mathematics education has been acknowledged by many schools. However, one of the frequently reported findings in the studies on students’ and teachers’ problem-posing performance is the poor quality of the created problems. Thus, there is an added value in exploring the mental constructs that are involved in posing a problem. This paper is concerned with the construct of considerations of aptness and its impact on the problem-posing processes and eventually posed problems. The data come from three problem-posing studies: with high-school students, prospective teachers and an expert in creating problems for mathematics competition. In all the three studies, the participants worked on the same billiard problem-posing task. The findings revealed that the students employed a limited scope of considerations of aptness; the teachers manipulated their considerations and posed multiple problems to meet a broader scope of considerations; and the expert chose the considerations that he wants to meet and persisted in posing a singular problem that will answer to these considerations. Methodological and pedagogical perspectives of considerations of aptness are discussed.

billiard task, considerations of aptness, expert-novice paradigm, mathematical problem, problem posing.