Abstract:

Fake news and so-called deep fakes are getting more common in our society. Therefore, abilities to recognise mistakes and think critically are very important nowadays. To enhance students' critical thinking skills we propose including so-called provocative or ‘impossible’ questions in teaching and assessment in mathematics. Such questions look like typical routine questions but in fact that have a catch – they are deliberately designed to mislead the solver. The intention is to prepare students for real life better. As a pedagogical strategy, provocative mathematics questions demonstrate the importance of being alert and ready to analyse everything. They enhance a habit of questioning the question and not to take anything for granted which is an essential part of a mathematical way of thinking. This study analyses school mathematics teachers’ attitudes towards using provocative mathematics questions in teaching and assessment as a potential pedagogical innovation. 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. Teachers’ responses are discussed and analysed in the paper. We suggest that practice in solving and posing provocative questions should be an integral part of training of prospective mathematics teachers, and be included into professional development of in-service mathematics teachers. Taking into account a solid professional background of mathematics teachers, the investment in training them in using provocative questions in a classroom and assessment might be very small – attending just 1-2 workshops. However, the benefits for their students and society are enormous. These benefits include but not limited to recognising mistakes and fake news, identifying contradictory information, eliminating impossible cases, using sceptical and unbiased analysis, making rational judgement and decisions based on factual evidence, and other traits of critical thinking.

Keywords:

Critical thinking, mathematics, assessment, innovation.