The discipline of noticing
I have been reading The Discipline of Noticing by John Mason. Not only has it had a huge impact on my own practice, but it has also changed the way I view and feedback on others’ teaching. In this post, I will focus on the effect on my teaching.
The book outlines the benefits of systematically noticing and recording significant events that occur in our teaching. By reflecting on these accounts (with oneself and with others), we can start to identify common themes and ways to act should these events occur in the future. In this way we will become more sensitive to what is happening during teaching, and build a repertoire of approaches that enables us to act on what we notice, thus improving student learning.
Mason gives the example of the time he realised he was repeating students’ words back to the class. He recognised that he did it all the time, that it had become a habit, and that he wanted the freedom not to repeat back (p. 11):
The point is that ’repeating back’ is not necessarily good or bad in itself, but rather whether I am choosing to do it, or whether it chooses me…
The Discipline of Noticing is this process of noticing that a habit has formed, reflecting on it, and then considering whether to choose to act in this way, or to act differently, rather than re-act through force of habit.
The first crucial step in this process is intentional noticing. As Mason describes (p. 29):
Since what we fail to notice is unlikely to have much influence on our actions, it follows that in order to alter our actions it makes sense to work at broadening and deepening our sensitivities to notice different aspects of our professional practice.
The next step is to move from noticing to marking, in which you become able to recall what you noticed (p. 38):
It is precisely because we mostly only notice but do not mark that so much of our experience passes us by and fails to be called upon for further development.
We must then try to move from marking to systematically recording. Mason suggests recording significant events through writing brief-but-vivid accounts; these accounts should be clear, concise and impartial (p. 39):
If we want to be in a position to analyse some event, some situation, then we must first be clear on what that event or situation consists of, as impartially as possible.
Mason describes this as accounting-of, not accounting-for. An account-of describes events as objectively as possible, without evaluation, judgment or explanation. This brings to mind Bryan Meyer’s comments on his view of his role of teacher-observer as data-collector; I talk more about my thoughts on the implications of this on teacher observation and feedback in my next post.
Of course, there will always be interpretation in any description, but we must aim to be as descriptive as possible, perhaps focusing on particular incidents rather than general feelings. By smoothing out disturbances, or implying explanation or justification, we lose some of the potential ‘energy’ of the account. As Mason describes (p. 62):
The extent to which a collection of accounts leaves open possibilities, does not theorise or account-for, is the extent to which there is potential for influencing and informing the future.
But how do busy teachers find the time to record these events? Mason suggests taking only 5 minutes at the end of the day to record around two or three brief-but-vivid accounts, ones that spontaneously come to mind.
There are a couple of issues for me here, such as: how can we (as teachers) maintain an accurate picture of an event in our mind when there is so much going on during a lesson? And by the time we come to record what we notice, how accurate are the reports?
I have found that merely remembering is not quite enough to capture the essence of an event. I have found it more evocative to take photographs and record audio (no video as yet, but I might consider it in the future). I find audio particularly useful as I am interested in classroom dialogue; it is easy to just record a voice memo on my iPhone, and the quality is generally good enough. Also, if I don’t have a lesson straight afterwards, I make a very brief note at the end of a lesson rather than wait until the end of the day. Then I collate these ideas together every couple of days (sometimes in the form of a blog).
Once we have started noticing and recording events, the next step is to collect accounts together, both of your own and of others, analyse them, and look for common themes. Why did we notice and record these particular events? Do we want to change something about these events? If so, how might we act differently next time? What will trigger us to act differently next time? Mason summarises this process perfectly (p. 72):
Finding yourself doing something is easy; catching yourself about to do something and choosing to act differently in a more informed manner, is much harder. It requires effort and technique. Choosing in the moment to act in a certain way requires two things: noticing a possibility to choose (i.e. recognizing some typical situation about to unfold, and having alternatives from which to choose...”
We notice events, record them, and analyse them retrospectively. However, the real aim of the Discipline of Noticing is to (p. 75):
…draw the moment of awakening from the retrospective into the present, closer and closer to the point at which a choice can be made.
This sentence has stuck with me. My aim for teaching this year is to build my repertoire of approaches, and then apply them in the right situation. This is exactly what the Discipline of Noticing is designed to help you achieve; it provides a framework that guides you towards the repertoire of approaches that might be required, and raises awareness of when these approaches might be suitable. Of course, it does not tell you how to perform these various approaches – this requires a great deal more research, reflection and practice.
Here are two simple illustrative examples from my practice which I have been using to achieve my aims of opening-not-closing dialogue.
When I receive a student response, or am checking their work, I often feel the urge to correct students or provide answers before students have had the time to think for themselves. I now notice the urge, remind myself to open-not-close, and use one of a number of key phrases such as:
- "What do we think about this?"
- "Do we agree or disagree with this?"
- "Would anyone like to add anything to this?"
- "That's interesting; why do you think that?"
- "Would you like to revise your conjecture?"
- "Why does this make sense to you?"
These connectives are all designed to continue dialogue, to value students' as sense-makers, to create a culture where conjectures and partial solutions are seen as valuable contributions to more complete solutions, to allow students the time and space to think more deeply about Mathematics.
I am working on a range of strategies to foster whole-class dialogue. I would like students to be able to discuss and revise conjectures in public, and decide as a group what makes sense.
These strategies range from a full inquiry approach, to more simple tactics; I call two of these simple tactics 'one question, many solutions' and 'many questions, one solution'.
In 'one question, many solutions', all student responses to a single question are written on the board, and we work as a class to decide which solution makes the most sense. This idea came from Magdalene Lampert's excellent book Teaching Problems and the Problems of Teaching.
Here is an example of 'many questions, one solution' I used this week. I wanted students to work on writing a variety of algebraic expressions in the form a.x^b, and I know that students find working with algebraic fractions particularly difficult. So I wrote the following expressions on the board and asked students to work in pairs to express them in the required form.
After monitoring students working in pairs, I selected pairs to make a conjecture about any unanswered question on the board. I wrote each response on the board without evaluation. After this process, the board looked like this:
I asked the students to discuss in their pairs which conjectures make the most sense to them. As expected, most students were confident explaining the bottom two questions; these were explained relatively simply, and I deleted them from the board, leaving the following:
At this point, students were very unsure about the responses left on the board. There was a lot of discussion, especially around the fact that three of the expressions have the same answer! We decided to focus on these three expressions:
I then asked: "Are all the expressions different? How do you know? Which conjectures make the most sense to you? Why?"
Students worked in groups to discuss each response. One group noticed that C was just half of x, so the expression was not correct. Another group arrived at the conclusion that none of the expressions are equivalent (by substituting a value for x).
After some time, one group identified that 2/x is double 1/x, so B makes the most sense. I opened this to the rest of the class with the question, "What do we think about this?" This reasoning was accepted by the class, so we decided it was correct.
Following this, I decided to clarify the correct response to expression A, and compare it with expression B. This left the final two responses:
However, before we could start our analysis, the pair that gave the bottom response asked if they could revise their conjecture. They gave the correct response, and the rest of the class were in agreement about both responses.
These two examples illustrate my desire to open-not-close dialogue, and encourage students to make sense of their responses. The Discipline of Noticing has allowed me to recognise when I want to open-not-close, and I am developing a repertoire of approaches that I can call to mind when I notice this desire.
As a teacher, this is hugely liberating; I have found myself choosing to act in new ways, rather than re-acting or opting for habitual (and perhaps safer) approaches. It sounds like a contradiction, but I find myself making ‘prepared in-the-moment choices’, which are clearly having an impact on the quality of learning for my students. I find myself teaching in the ways I have always wanted to teach, and students are learning mathematics they way I want them to learn.
You can read more from John Mason on in-the-moment pedagogy here. In the next post I will talk about how the Discipline of Noticing is having an important impact on the practice of my department as a whole.