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Yesterday, I had one of those experiences in the MLC that makes me love my job.

The Maths 1B students were working on a linear algebra proof today, and as I came up to one of the tables, Fred (name changed) was explaining the beginning of his proof to the rest of the table. When I arrived at the table, he was leaning over two of the other students to point at a section of the lecture notes. He noticed I was standing there and said, "But David can probably do this better than me." I responded, "Not necessarily. You keep going," and I sat down in his chair.

Fred continued to explain, and I think he did a very good job. I was very pleased that he kept flicking through the lecture notes to point out different theorems, though I thought it was interesting that at no point did he write anything down.

Then one of the other students said, "so is that the end?" And Fred said that no, this was just the beginning, there was still more after that, and I could see in his eyes he was having a sinking feeling as he tried to think of how to move on to the next bit.

So I asked him if he could pass me a whiteboard marker. I stood up to the wall and said, "I just want to write down where we're up to." I asked the students he had been talking with to tell me what they'd done so far, and I transcribed it to the wall, asking them to explain why each line worked. And then we got up to the end of what they had already done.

"So what now?" I asked. There was a short silence, and then Fred piped up with a comment about what we needed to know next. I asked why that was important to know, and this started a discussion of what goal we were heading for.

And here is where the really great stuff happened. The students at the table offered suggestions of things to try, looked up definitions and theorems in their notes, helped each other refine their maths language, asked each other questions when they weren't sure of things, welcomed new students into the discussion when they wandered over to listen, discussed how to make the proof their own when they wrote it to hand in, and basically really worked together to construct the proof. It was a pleasure to be a part of it.

It's this sort of thing that makes my job such a joy – seeing students learning and supporting each other to succeed.  On a day containing many other parts of my job that are much less joyful, it was something I really needed to see.

This comment was left on the original blog post:

Steven 8 February 2016:

Indeed, I also did enjoy reading your post regarding on how crucial and effective to have a group discussion i.e. working together. I’ll be sitting UMAT this year and I hope i can find someone/group as well to discuss on some UMAT questions and produce interesting results like the above.