Problem posing in the context of teaching for advanced problem solving

Three teams of pre-service mathematics teachers were engaged in an assignment of designing teaching sequences aimed at empowering high-school students to understand solutions to International Mathematics Olympiad problems. The assignment was rich with problem-posing opportunities. The data - the sequences, posed problems and reflections - were analyzed in order to reveal the underlying structure of the participants' problem-posing experiences. The findings support two conclusions. First, problem posing in mathematics teacher education can be promoted a-didactically, as an implicit objective of an activity having teaching for problem solving as an explicit goal. Second, problem posing that requires pre-service teachers to cope with mathematics that is challenging for them, provides rich learning opportunities and can result in worthwhile posed problems.