Inquiry without students' questions is not inquiry
My attention was recently drawn to an Ark Academy document. Ark is a UK academy chain that uses the Singapore method to teach maths. So I was intrigued to read that one of their maths departments follows an inquiry approach. Each half term the department uses two 'Fertile Questions' to focus learning in years 7 and 8, although what inquiry takes place in the classroom is not specified. What is clear, however, is that the head of department has generated the questions. Indeed, the 17-page document is all about the generation of those questions.
Inquiry that develops from a teacher's question is a feeble form of inquiry at best. At worst, it is no sort of inquiry at all - just a reproduction of the conventional maths classroom where the teacher asks the question and the students find the required answer. 
Inquiry is built on inquisitiveness and curiosity. And for those to be articulated, students need to learn how to ask questions. When students inquire into their own questions, levels of motivation, engagement and confidence rise. Students become self-starters who take responsibility for their own learning. Importantly, they lose the fear of giving the wrong answer because they control the question under consideration.  
These consequences of student questioning are evident in inquiry classrooms. They are also emphasised in 
two important books. The first one, Make Just One Change, introduces the Question Formulation Technique, through which students produce, improve, prioritise and reflect upon their own questions in a structured process. For teachers who doubt whether their students can formulate questions - and it is a skill that most, if not all, of them will never have encountered in formal education - this technique is highly recommended. The second book, The Art of Problem Posing, relates specifically to maths education. It proposes four levels in the process of developing questions: listing attributes (of the starting point), modifying the attributes by asking "What-If-Not?", posing problems and then analysing them.
For the authors of both books, the stimulus is fundamental for encouraging students to generate questions. It must not be a teacher's question because that reinforces traditional practices and obstructs the process of students asking their own questions. Instead it has to be a provocative statement, an intriguing diagram, or a curious equation or theorem. Inquiry Maths lessons start with exactly these styles of prompts. (Click here to read the Inquiry Maths guidelines for creating a prompt.)

Andrew Blair
April 2013