On Friday, I invited a first year teacher from my school to sit in on one of my Maths lessons. When I mentioned it to her, she leapt at the opportunity to see how someone else taught. I didn’t really have much of an idea about whether the lesson was going to be overly exciting, but what I really wanted her to observe was the sense of community I had developed with the students in the class. This also gave me an excuse to not plan anything out of the ordinary and, through giving her a more authentic experience of a “normal” lesson, it meant less work for me.

The class I was teaching was an All-Boys Year 10/11 Maths class. We were in our 2nd or 3rd lesson of the Trigonometry and Vectors unit (not that it is all that relevant for this blog post). Quite quickly, I realised that the way I was teaching was extremely different to how I taught when I was a first year teacher. What I also realised was that 30-40 minutes into the lesson, I hadn’t taught any curriculum what so ever.

I had just been to an awesome workshop in the holidays by Amie Albrecht (@nomad_penguin) that featured Mary Bourassa‘s Which One Doesn’t Belong problems (http://wodb.ca/). These are the kind of resources that don’t need any prep time and are fun to make yourself. More importantly, the discussions with students about their thoughts and hearing them share opinions with each other has developed an incredibly open and safe learning environment for my students.

I have been creating and using images like these:

And asking questions like:

• What do you notice?
• What do you wonder?
• Which one doesn’t belong?
• If there’s a question mark, what should it look like?
• Why do you think that?
• Do you think any of your classmates thought the same?
• What else might someone think?
• What are we assuming?
• What type of language do you notice that we use when we make assumptions?
• Do you notice the passive words that we use when we don’t have measurements?
• Do any of them belong at all?

Through this, I found that we had spent nearly an hour talking about our thoughts, how we learn, and how we feel when we learn and find out information for ourselves. At no point did any of my students ask about the purpose of the activity or discussion. This wasn’t something I was surprised about either. My students knew what to expect in the lesson – that they would have think, discuss their thoughts, and challenge their own perceptions.

This is something that I have been doing more and more of in my lessons; talking about learning. It takes time too. Had I rushed through the slides, shortened discussion or time to think, I don’t believe that my students would have benefited nearly as much as they did. As well as this, the teacher has to feel comfortable with giving time to rich discussions about students’ intuition, reasoning, and questioning.

It’s something that is so important for mathematicians to be good at, yet we scarcely give time to ensure that they have the opportunity to explore, inquire, and learn more about.

I’m learning more and more from each reflection I write, conversation I have, and lesson I teach in maths. I don’t know whether or not I’ll stop learning, but what I do know is that while I am, my teaching is improving and my students are benefiting… Well I hope they are anyway!

More WODB pictures I used below: