Some lessons work best when you do (almost) nothing

Returning to my blog after many years absence, I found this Feb 2017 post in my "drafts" folder, waiting for posting.  I think it's still worth posting now in March 2019 (!).

It's a new school year, for me the start of the seventh year teaching. And this week I think I taught my best lesson ever. The surprising thing is that I barely taught anything. In the words of one of my mentors, a teacher with 35 years experience, "you know it's a great lesson when you do almost nothing. You sit back*, close your eyes, and you hear the student conversation taking place - they are talking about mathematics - and you'll hear how they think - and then you know what you need to teach, specific to each student."

For this lesson, I handed out "A/B quizzes" to the students which looked liked this:

They are designed to test skills in way that encourages students to help each other. In the A/B quiz lesson design, different students get different papers (see the letter in the bottom right hand corner of the paper). They can help each other if they like, but since the questions are slightly different, they have to actually teach each other rather than just share answers. Half way through the period, the students form into groups with those who did the same paper and compare their work, teaching each other anything they need to. Then they repeat the process for a second round, using a different version of the "A/B" quiz.

It was amazing to watch this group of students work together. I saw them struggle through the harder integrals with negative fractional powers, debating with each other what the correct answers were. Every single student was involved, no-one was left out.  I mistakenly had some indefinite integrals on the quiz, which I hadn't taught yet, but the students who had worked ahead taught the others how to do them. And they loved the lesson, "Integration is so much fun, Sir!" I think they packed a week of learning into forty minutes. I only taught for the last ten minutes, reinforcing some of their findings and explaining a few finer points of the setting out and reasoning required to provide the highest quality solutions.  It felt like one of the best lessons I had ever taught - but strangely I had barely done any teaching.

OK - I'm exaggerating when I said I did nothing. The lesson happened as a result of many months working with this group of students, building trust, confidence and openness.  It does take a fair bit of training to get students working effectively in groups for this process - to ensure they actually help each other and look carefully at each other's work, rather than just "looking for an answer". I did design a very specific learning sequence for the topic, selecting items in the diagnostic quiz designed to elicit discussion and to expose any difficulty students had executing the required skills. And it does take many years of experience teaching a topic such as Integration to anticipate what difficulties students will have, how to diagnose them and how to provide the necessary support.

And that's the joy of the Art and Science of Teaching - sometimes the very best lessons have very little 'visible' teaching. But if you look closely, you'll see a lot of visible learning - and it will take many years of experience to feel like you got the best out of a particular lesson plan.

Would this work for every lesson? Absolutely not! It's my view, after trying many different approaches, that when teaching mathematics, four out of every five lessons should follow more traditional, explicit instruction supported with ongoing and regular formative assessment. And for the fourth or fifth lesson - try lots of different things - the more student-centred the better. "A/B" quizzes are a lesson design that works really well - the gift that keeps on giving, year after year.

* Update for 2019: I've found an even better way to run a lesson like this! Coming soon...