In this post, I outline a model for observing and talking about lessons.
In this model, the observer* records an account of something significant. The account is brief-but-vivid, purely descriptive and non-evaluative, following Mason’s Discipline of Noticing. The key is to be brief but detailed, to be challenging but not critical, to not try and explain why.
The accounts may be connected to something the teacher is working on, but not necessarily. The account may be of something a teacher does, but having done it a number of times, many accounts seem to focus on what the students are doing (see below).
Following the lesson the teachers talk about the account. This should be a conversation about teaching, a dialogue.
This week, me and a colleague (Christian) used this approach to observe another colleague's (Katy's) lesson. We made separate accounts, which Katy then agreed we could talk about in this week's department meeting, in order to explore the process.
Here is the account I made: Katy was working through the following example on the board: Evaluate 10^(1/3) x 25^(2/3) / 2^(5/3). At the end of a lengthy calculation, she stopped and asked: "What are the key ideas we are using here?"
Perhaps remarkably, Christian had chosen to record the same event, focussing on Katy's question: "What are the key ideas...?"
In the meeting, we read the account, and then discussed it. Katy was pleased we had singled out this sentence; she has been working on encouraging students to be more reflective. The question had come from reading Mason, Burton & Stacey's Thinking Mathematically. She had noticed that students were not sufficiently generalising from the specific examples they worked on. Katy gave an account of how her Yoga teacher teaches in such a way as to enable her to practise outside of lessons, and that she would like to bring this into her teaching.
I wondered why Katy had chosen this (rather complex) example. It turned out that the example was offered by a student, and that at this moment, she valued the opening created by accepting the student's offer.
The question 'What are the key ideas here?' is also an opening, although Katy described an urge to seek answers matching a (closed) list in her mind; this resonated with a number of other teachers in the room. Katy formed a question: "When is it appropriate to open and close?'' Perhaps knowing when to open and contract, when to attend to the part or whole, to isolate or connect, is one of the key skills of teaching.
The question 'What are the key ideas here?' was also intended as a slowing down; Katy recalled a question that she had noticed written on my board: 'If we go quickly, we learn less?'
This brought to mind an account I recorded in Christian's lesson that too involved a slowing down: The student had asked "Is this the right answer?". He then checked through the work slowly and deliberately, pointing at and commenting on the student's work line by line, corroborating and reassuring, then saying: 'The key thing there was the patience... You went through it step by step, well done!'
We discussed the importance of slowing down, patience, attention to detail, Dorothy Heathcote's struggle for quality. [Both Christian and Katy also noted how the detailed recording of their speech had made them realise the need for clarity of expression.]
The word patience brought to mind an account I had made of another of Katy's lessons: I watched closely as one student explained a solution to a problem to another. It lasted for around 5 minutes. The student explained his answer with such patience, slowness, pausing, quietly, making eye contact - he studied her face, with gentleness.
This is an important account as the teacher is not included. I wonder what we could learn by watching students more closely; this model provides a framework for this. [Here are some more accounts and further notes]
This model for observing lessons is not based on a list of what makes good teaching (I'm not sure such a list exists). There is no pro forma. It is based on attending closely to what is happening in the lesson, and then talking about it.
The conversation about the account is dialogic, upon which both parties might reflect. I avoid the use of the term feedback as this implies something (advice? opinion? judgement?) given to another in order to effect change, and years of unhelpful feedback has lent the word negative connotations for me.
The conversation around this single account (a single question, really) lasted around an hour, included around 10 teachers of whom 3 were non-mathematicians and one was from another school (who described it as 'intense'!).
At the end of the meeting, Katy read something she had written during the meeting: 'Investigating a moment... a window into widening.' I think this summarises the approach beautifully.
*I think this model might be expanded to include accounts from the observed, as well as the observer, to explore events of significance to the one teaching, whilst developing self-noticing (thanks to @TFrancombe for this insight).