This study analyses school mathematics teachers’ attitudes towards using provocative mathematics questions in teaching and assessment as a potential pedagogic innovation. By a provocative mathematics question, we mean here a question designed to deliberately mislead the solver. It normally calls for an impossible task. For example, the question might ask for a proof of something that is not provable or show the existence of a solution of an equation that does not have a solution. Often a catch is based on a restricted domain or indirectly prompts the use of a rule, formula, or theorem that is inapplicable due to their conditions/constraints. Five groups of school mathematics teachers did a mini-test consisting of provocative questions. A post-test questionnaire was given to the teachers to obtain their feedback on the possible use of provocative questions in their teaching practice to enhance students’ critical thinking skills. Teachers’ responses are discussed and analysed in the paper.