Seven objections to teaching mathematics through inquiry

A recent survey found that UK secondary maths teachers use inquiry less than their EU neighbours. Why is that so? When I run workshops about inquiry learning, teachers experience the creativity and higher levels of motivation that inquiry can produce. Audiences comment on the energy, excitement and sense of novelty in the sessions. Yet, in discussion, seven objections to inquiry arise regularly.

(1) Inquiry learning is so different from the normal teaching in my school that it will be too difficult to implement.

This is not an argument against inquiry learning, but a comment on the traditional forms of teaching that dominate school mathematics. It is hard to go it alone. However, when you do try inquiries, you will find unexpected interest from staff who themselves are looking for ways out of the standard transmission models. Admittedly, students often find the freedom offered by open inquiry too difficult to use constructively. Go for a lower level of inquiry - structured or guided - at first.

(2) The openness of inquiry is too unpredictable for inexperienced teachers to prepare confidently for the lesson.

This is a genuine concern and not only for newly qualified teachers. In challenging schools, I have seen inquiry lessons descend into chaos very quickly. Students need to be trained to be inquirers. Take small steps, building up to an open inquiry over months, rather than weeks. Inexperienced teachers can open up the start of the lesson to students’ questions and observations, then close the inquiry down by imposing a rigid structure. Longer phases of succeeding lessons can be given over to student-driven inquiry.

(3) You cannot expect ‘bottom sets’ to inquire because they don’t have the skills.

One of the main reasons that students are in bottom sets is because they lack precisely the metacognitive skills that inquiry can develop. This is a question of social equity. All students deserve the opportunity to experience the excitement of inquiry.

(4) Inquiry takes too long; we haven’t got the time to cover the curriculum as it is.

Inquiries might 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. Students are often more motivated to learn when answering their own questions, and so their learning is faster and more memorable as the inquiry develops.

(5) You cannot be certain that the lesson objectives will be met in inquiry lessons.

With the teacher monitoring the mathematical validity of students’ aims and activities during inquiry, curriculum objectives will be met even if they are not in a prescribed order. Often, students will challenge themselves to meet objectives at a higher level than expected. Furthermore, inquiries integrate concepts from different areas of maths, making the subject more connected and meaningful.

(6) My students won’t ask any questions at the start of an inquiry.

Try them and they will surprise you. If you can engage students’ natural curiosity (whatever their age), then you have the basis for a successful inquiry lesson. That is why setting the prompt just above the understanding of the class is so important.  

(7) Maths is a deductive, logical subject and inquiry is an inductive, exploratory method of learning – they don’t match.

Although new mathematical ideas end with a rigorous deductive proof, they start through an inductive process of noticing and conjecturing. This integrated process can be experienced in inquiry with the teacher acting as the representative of mathematically deductive language.

Andrew Blair, March 2013