11.2. Classroom Culture
What I used to think
I never really gave that much attention to the culture of my classroom. As long as my students were working hard, not misbehaving too much and ideally laughing at my jokes, I was more than happy. Surely I did not need anything else to ensure that my teaching was effective?
Sources of inspiration
My takeaway
It sounds ridiculously obvious to say, but for any assessment strategy – formative or summative – to work, students must actively and honestly participate. There are three factors that could prevent this, all of which we can change.
1. A fear of mistakes
If students are afraid of making mistakes, how can we learn from their misunderstandings?
We have probably all taught students who leave questions out in tests and homeworks for fear of being wrong, and we all know that such actions make it incredibly difficult to help them, as we have no indication of how much or in what areas their understanding is lacking. However, in my experience, far more common is a fear of making mistakes away from the written page. Many formative assessment strategies – and indeed the one I am going to focus on in this chapter – require students to be public about their answers, displaying their thoughts in front of me and their peers in the moment. If students fear making mistakes, and the consequences of those mistakes, then it is highly likely that they will fail to provide us with any useful information at all. After all, for the child who fears failure, not giving a response is far less daunting than having a go.
Lemov (2015) encapsulates this in the concept of creating a Culture of Error. He explains:
This shift from defensiveness or denial to openness is critical. If your goal is to find and address the mistakes your students make, your task is far more difficult if your students seek to hide their errors from you. If, in contrast, they willingly share their struggles, mistakes, and errors, you can spend less time and energy hunting for them and more time fixing and learning from them.
So how do we create this culture of error, and hence overcome this potentially fatal problem?
I have discussed the crucial role the teacher plays in this process back in Chapter 2. Specifically, I discussed the need to ensure that students respect each other’s answers, whether they are right or wrong, and that any deviation away from these high expectations is tackled head-on.
But such teacher actions can only take us so far. More than this, the questions we ask students need to be seen not as tools of assessment, but as tools of learning. This will be equally important when we look at the power of testing in Chapter 12. We can only hope to achieve this if there are no negative consequences for being wrong. We can do this by not grading or recording students’ responses to the formative assessment questions we ask in class, for the presence of a grade or record puts a premium upon success, and they are not needed to inform our decisions in the moment.
There also needs to be positive consequences for honest participation. As I explained in Chapter 2, mistakes need to be embraced as learning opportunities. I know that sounds ridiculously clichéd, but it is true. When I interviewed Doug Lemov for my podcast, he shared some excellent advice for doing exactly this. If a student makes a mistake, we need to thank them. We need to explain that such a mistake is likely to be shared by lots of other students, and hence by making it, sharing it, and giving me a chance to fix it, they have genuinely improved the understanding of many of their peers.
The beauty of the strategy I am going to describe in this chapter is that built into to every multiple-choice diagnostic question are three mistakes. Even if students do not choose one of these options, I will often discuss them. This serves a dual purpose – it allows us to dig deeper into the skill or concept (more on this later) and it also makes mistakes and the discussion of them a regular and important part of the lesson.
2. Students opting out
The second factor that can render any assessment strategy – but in particular classroom-based formative assessment – limp and ineffective is the classic opt-out. Some students may choose not to give an answer, not for fear of being wrong but, to put it bluntly, because they cannot be arsed to think. A shrug, an utterance of ‘I don’t know’, or a wall of silence tells us absolutely nothing about a student’s understanding of a given concept, and thus leaves us powerless to help.
Allowing such a response also conveys the message that non-participation is absolutely fine. Wiliam (2011) argues that engaging in classroom discussion really does make students smarter. So, when teachers allow students to choose whether to participate or not – for example, by allowing them to raise their hands to show they have an answer, or settling for a lack of response – we are actually making the achievement gap worse, because those who are participating are getting smarter, while those avoiding engagement are forgoing the opportunities to increase their ability.
Doug Lemov to the rescue once again. During our podcast conversation I asked Doug how to deal with a response of ‘I don’t know’. Doug explained that he would ask another student to help get them started and then return to the original student to see if they could carry on. If they still could not (or would not), then we can get another student to complete the answer, before returning to the original student, asking them to repeat the answer, and then giving them a follow-up question. The key point is that students need to see that a response of ‘I don’t know’ is going to lead to just as much work, so they might as well actively and honestly participate from the start.
3. Finding comfort in one correct answer
Directly related to students themselves opting out is a common practice amongst teachers (myself very much included) that essentially does the student’s job of opting out for them. See if this scenario rings any bells:
Me: So, does anyone know what -5 – -2 is?
(3 hands go up, one of which is Josie. Josie always gets everything right)
Me: Josie, go for it
Josie: -3, sir
Me: And why is that, Josie?
Josie: Because subtracting a minus is the same as adding a positive, and negative 5 plus 2 gives you negative 3
Me: Loving your work as ever, Josie. Okay, let’s move on.
Writing this makes me feel ashamed, as that is exactly how many of my early attempts to assess the understanding of my students proceeded. In Black et al (2004), a teacher is quoted as describing such a scenario as ‘a small discussion group surrounded by many sleepy onlookers’. Likewise, when I interviewed Dylan Wiliam for my podcast and asked him to describe an approach in the classroom that he doesn’t think is effective, he replied ‘teachers making decisions about the learning needs of 30 students based on the responses of confident volunteers’. Rarely have truer words been spoken. I find solace in the fact that I am not alone. Dylan Wiliam (2016) himself describes a similar experience:
When I was teaching full-time, the question that I put to myself most often was: ‘Do I need to go over this point one more time or can I move on the next thing?’ I made the decision the same way that most teachers do. I came up with a question there and then, and asked the class. Typically, about six students raised their hands, and I would select one of them to respond. If they gave a correct response, I would say ‘good’ and move on.
One of Coe’s (2013) ‘poor proxies for learning’ is ‘(at least some) students have supplied correct answers’, and it is easy to see why. I am seeking comfort in one correct answer. When Josie once again produces a perfect answer and a lovely explanation, I make two implicit assumptions: first, that this is down to my wonderful teaching; and second, that every other child in the class has understood the concept to a similar level. But, of course, I have no way of knowing that. By essentially opting out the rest of the class, the only information I am left with concerns Josie.
There are ways around this. We can use lollipop sticks, or random name generators to ensure each student has an equal chance of being selected. We can use Lemov’s (2015) concept of ‘cold-call’, which, as we discussed during our podcast interview, Doug feels ascribes more meaning to each student’s answer as we have chosen them for a reason. We cannot tell Josie if she was right or wrong, but instead ask the rest of the class to indicate by raising their hand if they thought Josie was correct, or challenge another student to explain Josie’s reasoning.
All these adaptations certainly improve my initial process, but they all suffer from the same fatal flaw. All students are not required to participate to the same degree, and so the only student’s understanding I have anything resembling reliable evidence about is the student answering the question. Rosenshine’s (2012) third principle of instruction is: ‘Ask a large number of questions and check the responses of all students’. I am failing to do that.Lemov (2015) has a series of useful techniques under the umbrella of ‘No Opt-Out’ that can help counteract students opting out themselves as well as via the actions of the teacher. However, the strategy involving diagnostic questions that I am going to outline later in this chapter has the full participation of each and every student built in to its very core.
What I do now
I am always conscious of the need to ensure all my students actively and honestly participate when I ask questions. In Chapters 2 and 9 I argued that too much struggle and failure can be detrimental to both motivation and learning. However, that is not to say that mistakes should not be embraced. Mistakes – specifically how students cope with them and learn from them – are a key part of mathematical development. Likewise, without honest and active participation from students – all students – we are left to blindly guess at what they do and do not understand, and hence the help and support we offer may prove to be ineffective.
Fortunately, the use of diagnostic questions brings mistakes (and misconceptions) into the open, treating them as the learning opportunity that they are, whilst at the same time encouraging full class participation. Hence, I use them every single lesson, with every single class, every single day.