Asking mathematical questions mathematically

Abstract

It is proposed that the style and format of the questions used by lecturers and tutors profoundly influence students' conceptions of what mathematics is about and how it is conducted. By looking at reasons for asking questions, and becoming aware of different types of questions which mathematicians typically ask themselves, we can enrich students' experience of mathematics. Drawing on recent work by Watson and Mason stimulated by the ideas of Zygfryd Dyrszlag, the paper proposes that mathematical themes, powers, heuristics and activities generate a mathematical discourse which is not always represented in the questions students are asked, and that the real purpose of questions is to provoke students into construal, into constructing their own stories which constitute meaning and understanding, and which equip them for the future. The use of questions of whatever type depends on both scaffolding and fading their use with and in front of students, so that students internalize the questions into their own learning and doing of mathematics. The framework directed—prompted—spontaneous is proposed as an alternative to scaffolding—fading for informing interactions with students.