10 Frequently asked questions

Yes. All students deserve the opportunity to experience the excitement of inquiry. Often students are in bottom sets because they do not have the higher order skills required to regulate learning. Inquiry Maths gives all students the opportunity to develop those skills. Moreover, it is not the case that attainment in mathematics can be used to predict an inquiry disposition. Students with higher prior attainment in the subject can be more anxious about inquiry because they are likely to have achieved their 'success' in traditional classrooms by answering repetitive exercises.

Inquiries might seem to start slowly, but the construction of a shared understanding in the first phase leads to a deeper understanding of procedures and concepts later in the inquiry. Indeed, it is essential that inquiries start slowly to ensure the involvement of everybody in the inquiry. Students are often more motivated to learn when answering their own questions and, consequently, their learning is faster and more memorable than in normal lessons.

The frequency of inquiries depends on your national or state curriculum. In England, for example, inquiry encompasses one of the three aims of the National Curriculum. So a third of lessons, it could be argued, should be based on the processes of mathematical inquiry. Furthermore, students will become fluent in applying procedures (another aim of the curriculum) during inquiry, so the fraction could justifiably be more than a third. It is our contention that the whole curriculum could be taught through inquiry, but that might not be possible because of departmental, school or curricular restrictions.

Sometimes it is hard to go it alone in a department that promotes teacher transmission and student performance. However, when you try inquiry, you might find unexpected interest from colleagues who themselves are looking for ways out of the sterile traditional model of teaching. Students who are used to repetitive practice are likely to find the thinking processes associated with inquiry challenging at first. Use a structured approach in your first attempts.

This question comes from Alex Zisfein, a secondary teacher of mathematics in New York City, who felt the prompts are more suitable for advanced classrooms, rather than for general education groups. There are two ways to make the prompts more accessible  Firstly, the teacher can take more responsibility for structuring the inquiry by, for example, preparing a pathway for students to follow in the first lesson and then planning subsequent lessons that respond to the students’ questions and observations. Secondly, prompts can be adapted to ensure they are both familiar and unfamiliar. Familiarity gives students confidence to analyse and transform the prompt; unfamiliarity generates curiosity to understand the prompt more deeply.