Chelsea Young, an MYP teacher at the Canadian International School in Singapore, has set up a website on inquiry in mathematics as part of her Masters in Education course. Chelsea's goal is to "dispel some of the misconceptions regarding inquiry." She contacted the Inquiry Maths website with some questions for her website. Dr Andrew Blair replied.
1. What three pieces of advice would you give a new teacher looking to incorporate inquiry maths into their primary mathematics class/department?
Firstly, open inquiry in which students direct their own learning is the end of a long process, not the beginning of the process. Students have to be taught how to take responsibility for learning through inquiry and how to identify legitimate lines of mathematical inquiry.
Secondly, preparation for classroom inquiry involves the teacher in planning resources and interactions that serve to structure and guide learning.
Thirdly, structure and guidance during the inquiry are contingent on the levels of independence and initiative shown by the class or individual students in a situated and unique context. Adapting your response to ensure each student remains hooked into the inquiry at an appropriate level of challenge is the essence of effective inquiry teaching.
2. Everyone seems to have a different take on inquiry learning and some research has been taken out of context over the years. What is your overall stance on inquiry mathematics, what makes you so passionate about it, and what evidence do you rely on?
Yes, the definition of inquiry is broad, particularly in mathematics. Some refer to ‘enquiry’, which might mean students drawing on different areas of maths to create a solution for quite a closed problem. Or ‘enquiry’ might be interpreted as teacher-led discovery in which students are set a task that is designed to lead them into noticing a general pattern or rule. My own definition links to the classic conception of inquiry first developed by Dewey in which the acquisition of knowledge occurs through the process of inquiry. However, Dewey’s method of collecting ‘data’ and testing hypotheses is not the method of mathematics (although Dewey argued otherwise). Mathematical inquiry is underpinned by a dual process involving induction and deduction, which requires students to conjecture and generalise, and then reason and prove – although rarely in a linear way with each one following neatly in turn.
I am passionate about inquiry because I want students to experience the creative way mathematicians develop the subject. I want them to ‘do’ mathematics, not, as often happens in mathematics classrooms, practice lots of meaningless procedures. When students use procedural knowledge during an inquiry, they do so in a context that is meaningful and relevant to answer questions or test conjectures.
The evidence I rely on is wide-ranging and comes from different sorts of studies, both quantitative and qualitative and small- and large-scale. There is a reading list on the website that includes research into the outcomes of inquiry. For example, inquiry can make the subject seem far more inclusive and supportive than the experience students get in traditional classrooms.
3. Duckworth (1991) states that when students think their role is not to reproduce a method but to come up with an idea, everything changes. How can mathematics teachers change traditional questions into inquiry questions which evokes mathematical thinking?
I don’t think that teachers should be devising the inquiry questions. A key feature of inquiry, for me, is that learners are answering their own questions. In my experience, students are more motivated, more engaged and learn more deeply when answering their own questions.
They can generate good questions on two conditions: firstly, they are taught what constitutes a good mathematical question; and, secondly, they are presented with an intriguing stimulus, which I call a prompt, that arouses their curiosity. It is the role of the teacher to devise a prompt just above the students’ current level of learning in order to promote the processes of noticing, questioning, and wondering. For most teachers, it is also the case that the prompt has to lead students into a conceptual field that is linked to the curriculum.
4. What is your favourite inquiry maths resource (outside your amazing website).
My favourite resources are those that stimulate students to question, speculate and generalise. They must also be open enough for students to generate different lines of inquiry at both concrete and abstract levels. Many of the resources on Don Steward's Median website contain rich mathematical ideas that can form the basis of inquiry.