So I’m sure most math educators have heard of Marian Small in some way, but for me, she’s been simply transformational. She has deeply impacted the way that I not only teach, but interact with my students.
There are so many things that I’ve learned from her, but here are a few that come to mind during my work on a daily basis:
Making sure that students can choose an appropriate entry point into a question. Things like, instead of saying “Find the equation of the line through the points (2,3) and (5,7)” saying “An increasing line goes through (2,3)…what other point might it go through? What could it’s equation be?”
This question doesn’t only have multiple entry points, but it actually forces students to THINK about so much more than the slope equation and the equation of a line. It also gets students to engage with all of the terminology that we want them to engage with.
When I say the words “What might it be…” instead of “What is…” in my classes, I definitely see students become more relaxed, more at ease, and in turn, more engaged and more willing to take risks.
We often talk about being ready to give feedback to answers we want, or answers we anticipate. Dr. Small has also talked a lot about being ready and prepared to offer feedback to thinking that you had no idea was coming…generic questions like “Oh…why do you think that is?” or “Oh…why did you think of doing it that way?”. The other thing that Small does so well is model curiosity for students. There is a huge importance in the tone in which we ask the question “Why would you do it that way?” It could be either a shut down question, or a feedback opening question…
This is something I haven’t actually heard her talk about, but I just see the way she models it, and having applied it in my class, it does wonders. Instead of applying complex math terminology from the start, she uses very simple language to start, and then builds up the math vocab. So when asking a Which One Doesn’t Belong question involving algebraic terms, she won’t say “Which expression doesn’t belong?” but she’ll say “So…like…which one of these guys doesn’t fit?”
My students have commented on the fact that this encourages them to participate, and they feel at ease. The worries of math class doesn’t creep up on them, and they don’t feel anxious at all. This allows me to make sure that many more of my students get the chance to be successful and to be heard.
Anyway, I’m sure I’m not doing justice to everything Dr. Small has taught me, but I want to keep my blogs short. I’ll probably do another post on her impact in the future. I was very happy to see Dr. Small speak again, and I got to tell her a very important truth: I use a lot of her ideas when I teach the OISE Math AQ, and the reason is that without her ideas, I don’t think I’d even be the type of teacher that gets the opportunity to teach an AQ. So thanks again, Dr. Small 🙂