This post was going to be part of the Virtual Conference of Mathematical Flavours, which you can see all the keynote speakers and presentations here: https://samjshah.com/mathematical-flavors-convention-center/. The prompt for all the blog posts that are part of this conference is this: “How does your class move the needle on what your kids think about the doing of math, or what counts as math, or what math feels like, or who can do math?” In the end, it didn’t end up being there, because my computer started dying painfully at the critical time, but I still want to highlight the Virtual Conference anyway because it was a great idea.
There are many things I could have written about this, but I think I will choose one thing that is about my approach in the MLC to student questions. In the MLC everyone is worthy to ask both stupid and smart questions.
My Maths Learning Centre is a place where any student doing coursework at the Uni of Adelaide can visit to talk about their maths learning with a tutor (often me). People come to talk about all aspects of their maths learning in all sorts of places where maths appears, from dividing whole numbers by hand to understanding proofs about continuity of functions between abstract metric spaces. My point here today is that people from both ends of that spectrum and everywhere in between are allowed to ask questions that are about basics and questions that are about deep connections.
Imagine a student who has always been good at maths, who finds things easy and quickly grasps abstract definitions. It is natural for such a student to fold their goodness at maths into their identity, which often means they become extremely embarrassed to show any sign of struggling. They’re supposed to be the smart student and this simple stuff is supposed to be obvious for them. So if they have a question about the basics, they hide it and hope it will come clear eventually.
The thing is, having a question about something simple doesn’t make you stupid, and it doesn’t even make you not smart. Having a question about how to get from line 3 to line 4 is at the very least a sign that you’re paying close enough attention to wonder about that step; having a question about the definition is a sign that you know definitions are important; and having a question about some random bit of algebra or notation you happen to have never seen just shows you want to learn. In my Maths Learning Centre, I try to make it a place where everyone can ask a “stupid” question. Where stupid questions are treated with respect and answered clearly, with encouragement to make sense of what is happening.
Now imagine a student who has always struggled with maths, who just never seems to understand the explanation the teacher is giving the first time, and who struggles to get through the first few of the exercises. It is natural for such a student to fold their badness at maths into their identity, which often means they don’t even try to understand things and just look for some step-by-step instructions they can follow so it will be over with as quickly as possible.
The irony is, they never finish their exercises, so they never get to be part of that part of a maths class where the early finishers ask the deep and involved questions about theory and beyond-curriculum interesting stuff — the very stuff that can make maths a lot more fun. I know for a fact that students who feel they are bad at maths are intelligent people capable of logical and creative thought, and they deserve to ask their deep questions. So in my Maths Learning Centre, I try to make it a place where everyone can ask a “smart” question. If a student who is struggling asks about infinity or quaternions or what my PhD was about, I will damn well discuss it with them. If they look at the work they’re doing and ask how it is connected to some other bit of maths, we’ll explore that together. That curiosity is a treasure to be prized and I will not squash it by saying we have to get on with the assignment now.
And you know what, it turns out that many a basic question is actually a deep and clever question after all. Recently a student who was struggling asked why it was ok to add two equations together. Not one student in my ten years of working at the MLC has ever asked that question! There must be something really special about the person who asks this question, right? And it’s a really deep question about the nature of equality. I want my Maths Learning Centre to be a place were it is okay for everyone to ask a question that is simultaneously stupid and clever.
That’s all I have to say. I believe everyone deserves the chance to ask stupid questions and to ask clever questions and to ask questions that are simultaneously both. They are worthy to have their questions taken seriously and the answers discussed with respect for the humanity and intelligence of the asker. I have to always remind myself to give students the chance to ask these questions when I’m with them, especially students who are struggling to articulate the questions for whatever reason. And maybe if they’re not asking, I’ll sometimes ask the questions for them and we’ll answer them together.
How will you welcome all people in your learning spaces to ask all kinds of questions?