www.inquirymaths.com © 2013 Andrew Blair

Caitriona Martin talks with Andrew Blair (both teachers of inquiry maths) about the enlargement prompt. Their conversation raises some important issues about inquiry maths in relation to the curriculum. CM: I tried out the enlargement inquiry with my year 9s recently as we were doing transformations. It helped some of them to think about scale factor and combinations of transformations – a couple even worked out the centre of enlargement once I had shown them what that was. AB: I used the prompt with two year 10 classes last week and I found that the students talked about an enlargement without defining one properly. They needed - and requested - a lot of instruction about enlargements with all types of scale factors. CM: Interestingly, at the start of the inquiry, lots of students asked questions about the area of the shapes (but not comparing the area of the two) and other things that were not really anything to do with enlargement. I encouraged them to carry on investigating whatever they were interested in as I didn’t want to stifle their inquiry – often pupils find out things that I hadn’t thought of so I didn’t want to try to steer them in a particular direction. AB: You were much braver than me! I asked the classes to describe a transformation or transformations at the start, thereby directing them towards enlargement because enlargement was in the scheme of work. I knew in four weeks time they’ll be assessed on the topic. CM: The inquiry made me realise that I can’t assume what pupils are going to

investigate and what they are going to get out of it – and therefore can’t plan to cover a topic by doing an inquiry … at least not the way I was doing it! It’s the first time I had actually planned to use an inquiry lesson to cover content. Interesting! AB: I felt I was not running a full and open inquiry by directing so clearly, but the pressure of the syllabus outweighed my dissatisfaction on this occasion. I suppose there are different levels of openness. My lessons were more like ‘guided’ or ‘structured’ inquiries. CM: For me, the students’ mathematical creativity is paramount. AB: Yes, and handing over the running of the inquiry to students. I suppose what I’d say is that you cannot hand over control all the time, but you should aim to get as close as possible to student independence even with the pressures we have on us to cover the content. CM: It's a real dilemma but it's helpful to see that a version of inquiry can be used to enhance what would be a standard lesson. I think I previously saw standard lessons and inquiry lessons as two separate entities which couldn't really gel but I would love to be able to introduce elements of inquiry more often, in addition to open inquiry lessons. AB: I think some elements of inquiry maths would be features of good teaching in any classroom. However, ultimately our aim is for students to assume responsibility for their learning. And for that to happen, they need to experience full inquiry lessons as often as possible, with the independence and opportunity to structure learning that inquiry brings.