The aim of this article was twofold. First, to propose a model for assessing mathematical challenging problems and second, to investigate the abilities of a group of in-service teachers to propose mathematically challenging problems based on the model suggested. The results indicated that mathematical challenging tasks may be characterised as those that are cognitively demanding and also require from students to develop other key competences: digital, social, communication in mother tongue, learning to learn and sense of initiative. About half of the participants of this study were able to provide mathematically cognitively demanding tasks which encompassed at least three of the other key com-petences. Participants appeared to find most difficult to incorporate in their mathematical tasks the " digital competence " and " learning to learn " .