# Right and wrong in the inquiry classroom

Last week, I was giving table-top presentations on Inquiry Maths at a cross-phase conference at the University of Brighton (UK). During one of the presentations, a primary teacher exclaimed that she wished she had had the opportunity to learn mathematics through inquiry as her lessons would have been less threatening than they were. “It’s an excellent way to learn because there’s no right and wrong in inquiry,” she asserted.

I knew what she meant. The inquiry classroom is not like a traditional mathematics lesson in which the teacher’s closed question has one right answer; nor is it a classroom in which a handful of students always know the right answer and everybody else defers to them. In the worst cases of traditional education, students are so fearful of being exposed as ignorant for giving a wrong answer that they try to hide.

Instead, inquiry encourages students to pose questions and direct and monitor the learning process. There are no right or wrong answers in this. Although some questions might be more sophisticated and some decisions on how to develop the inquiry might lead to more productive pathways, all questions and decisions can provide opportunities to learn.

Nevertheless, it is incorrect to say there is no right and wrong in inquiry lessons. The inquiry classroom is not the relativistic, knowledge-free zone often portrayed by traditionalists. Such a caricature serves a simplistic idea of education that says if the teacher is developing ‘skills’, then she cannot also be imparting ‘knowledge’. Indeed, in the inquiry classroom there is more right and wrong than in traditional classrooms.

Let’s look at the level of knowledge. In inquiry lessons, students have a greater interest in developing the right understanding of concepts and procedures because they are using them in their own inquiries. I have observed many traditional mathematics lessons in which students, who are practising some procedure as an end in itself, only care if the authority in the classroom – be it the teacher or textbook – decrees their answer to be right. In inquiry, right and wrong are not simply ordained from above; rather, they are applied and tested in contexts that students have helped construct, with the teacher acting as the final arbiter. In this role, the teacher represents a wider mathematical culture that safeguards (and occasionally revises) right and wrong meanings.

However, there is an even deeper level to the meaning of right and wrong in inquiry classrooms – and that is at the level of methodology. Classroom inquiry should mirror the domain-specific process through which new knowledge is constructed.

Take the example of mathematics. As Polya and Lakatos have convincingly shown, the discipline of mathematics synthesises inductive thinking (exploring, conjecturing, generalising) with deductive reasoning (conceptualising, analysing, proving). It is through this combined process that mathematical knowledge has advanced historically. For mathematics inquiry to be ‘right’, it should allow students to experience the relationship between the two forms of reasoning unique to the subject.

In the traditional classroom, right and wrong are shallow concepts that amount to no more than a teacher’s tick or cross; inquiry addresses the concepts of right and wrong both culturally and methodologically. In this way, inquiry holds itself to account at a far more profound level than traditional teaching.

Andrew Blair, June 2014