It’s a really important question Elizabeth, and one we also struggle with. Responses from my maths department colleagues generally fall into two categories – “inquiry doesn’t work in maths” and “we already do a lot of inquiry – we call it ‘investigation'” (and it is true that, when done well, maths ‘investigations’ can also be inquiries and can be enhanced by viewing them through the lens of the FOSIL cycle). As a maths graduate myself, who also taught Year 9 maths briefly, I have been trying to work out how to address this. I don’t believe that inquiry is inherently unsuitable for any subject, but I do appreciate that it seems harder to apply in some subjects than others and have been trying to work out why.
Ever since we started the IB MYP here last year, my colleague Lucy has been working hard on how to ‘do’ inquiry in MFL with Year 7 and 8 (11 and 12 year olds). Lucy has an MFL background and is an outstanding librarian with considerable background in inquiry. The stumbling block here was that the students did not yet know enough French (in this case) to conduct a meaningful inquiry using resources entirely written in French, but it was not productive for them to spend too much time using resources in English when the goal was for them to learn French. With Year 6, the French department was happy for them to spend some time learning about French culture using English resources, but by Year 7 they really wanted them to be focussing on the language. Lucy and the French department have done an excellent job of designing an inquiry which meets all these needs for Year 8 (which we will write about separately), but it got me thinking that the problem with maths is actually a language problem too.
As a maths graduate, I often describe my experience to non-mathematicians by telling them that school maths is like learning a language. When you get to university you then use that ‘language’ to essentially study the mathematical equivalent of literature and poetry. If you are that way inclined, school maths is fun but university maths is beautiful and exciting. The problem is that we cannot ask students (and particularly younger students) to “do research on” a particular topic (e.g. inequalities) because the likelihood of them finding something useful that they actually understand is slim. The advantage of this is that maths hasn’t traditionally suffered from the rash of lazy, poorly designed, copy-and-paste-masquerading-as-research tasks that plague other subjects (“go away and find five facts about…”). The disadvantage is that many maths teachers think inquiry doesn’t work in maths.
So why bother? I think this image of maths as a language is important in thinking about students’ perceptions of maths. I have a six-year-old son who loves stories and books, but has only recently started to enjoy reading for himself. Why? Because until his reading reached a certain level, he found the kinds of stories he could read for himself really tedious. Maths can be like that for some students, who might otherwise become excellent mathematicians. At the necessary basic ‘language learning’ level, it can seem tedious and pointless – but what if we could give them a glimpse of where it was going and why it mattered? Effectively ‘read aloud’ some of those novels that they might be able to access later. Also, one of the biggest stumbling blocks I found for a certain group of students in maths was when they could follow a pattern and get a right answer, but didn’t understand why it worked. This created two problems – they couldn’t deal with questions that were essentially along the same lines but were very slightly different so their ‘pattern recognition’ approach didn’t work, and they had to learn so many patterns and rules that they inevitably made mistakes and ran out of ‘brain space’. The students who succeed in maths are the ones who want to understand why a rule works – and inquiry is ideal for this.
I realise that this doesn’t really answer your question, Elizabeth, and I don’t entirely have an answer (- yet, as Carol Dweck would say) but I think at this stage the why is more important than the how. Changing practice is hard work and in order to get colleagues to ‘buy in’ enough to want to collaborate on this, you have to first convince them why it is going to be worth the effort. I have, however, found a few interesting resources that might be worth a look in terms of demonstrating what inquiry looks like in maths and giving some concrete examples, and I will try to post these tomorrow.