How prescriptive should a Head of Department be?

More than most are… in my opinion!

Jul 04, 2023

Hello!

I hope you are well.

I am a bit nervous about this week’s newsletter, as I suspect many people will think I am talking rubbish (again). So, I am going to send it, and then hide somewhere.

It is aimed primarily at Heads of Department (HODs), or those with responsibility within a department. But I hope it will also be of interest to any teacher to reflect upon how things are done within their department, and if there is a need for change.

Oh, and it’s another long one, so make sure you are sitting comfortably.

Three things I have seen during recent school visits

School 1
Year 11 are revising algebra in preparation for their upcoming GCSE exams. I pop into three lessons and find students using a variety of resources plucked from the internet of varying quality. Then I visit the HOD’s lesson and see students working on this task:

Students are conjecturing, reasoning and thinking hard. After the lesson, I ask the HOD why everyone isn’t using a version of her task. The HOD replies that she wants her colleagues to have the freedom to choose their own resources when planning their lessons.

School 2
Year 8 are learning about speed, distance and time. In one lesson, students are rearranging equations using the balancing method to make different variables the subject. In the next room, another Year 8 class are using formula triangles. I ask the HOD afterwards whether it is okay that students are taught different methods. They reply that it is fine and that colleagues choose the method they are most comfortable with.

School 3
Year 9 are doing their Do Now. There are four questions projected on the board which students answer in their books. Students have around five minutes to do this, then the teacher goes through the answers. In four lessons, this is done by asking for volunteers and Cold Calling students to contribute. Students are instructed to correct anything they got wrong in green pen. Several students are Busy Tricking, and when I ask a selection of students to explain how they got the answer to Question 2, none can. In the fifth lesson, the teacher asks students to copy their answers to Question 1 onto their mini-whiteboards and show her when instructed. She then does the same for Question 2. Because she has evidence of the effort and understanding of all students, she can respond accordingly, confirming the correct answer to Question 1 as everyone has it right, but spending more time on Question 2 because there is a spread of answers. When I quiz students about Question 2, they are much better at explaining how to do it. After the lesson, I ask the HOD why everyone doesn’t do their Do Nows like the fifth teacher as it is clearly more effective. The response was that he did not want to tell teachers how to teach, and anyway, lots of his staff don’t like mini-whiteboards.

Before we go on, a few questions for you:

Could any of these scenarios happen in your department?
If you were the HODs in each of these three scenarios, would your responses have been the same?
Which – if any – scenario feels the most problematic in terms of the possible impact on student learning?

Three types of prescription

The three scenarios above are examples of teachers being given freedom of choice, first over the resources they use, second over the methods they teach, and third over the pedagogy they employ. The more I see scenarios like this play out, the more I am convinced that a greater level of prescription could benefit most maths departments.

Let’s look at each in turn…

1. Consistency of resources
Resources are where the discussion around prescription often starts and ends. Here are different approaches I have seen, roughly ordered from most prescribed to least prescribed:

All colleagues must follow the prescribed PowerPoint/booklet for their class
All colleagues must start with the prescribed PowerPoint/booklet, but should adapt for the needs of their class
There are key elements of a lesson that all colleagues must use (such as a centrally planned Do Now, task, example, or sequence of questions), but colleagues can use whatever else they like in their lessons
There is a prescribed end point to each lesson or unit of work (such as an Exit Ticket or Low-Stakes Quiz), but it is up to each colleague how they plot a route to it
So long as they are following the order of the scheme of work, colleagues can use any resources they like

Where does your department fit in this list? Does that feel like the right level of prescription to keep standards in all lessons high?

2. Consistency of methods
I don’t think a consistency of methods is discussed enough, or in sufficient depth. On the surface, it may seem okay that students get taught different ways to do things. But as soon as you consider the impact of students changing class mid-year, or getting a new teacher at the start of next year, the problems become apparent. There is also the issue of a teacher showing students a method that works a treat in Year 7, but then completely falls apart when the concept gets more complex in Key Stage 4.

Here are some topics that I regularly see being taught using different methods in the same school:

Written multiplication
Multiplying decimals
Dividing fractions
Finding the highest common factor
Solving ratio problems
Finding the nth term of sequences
Solving equations
Rearranging formula (aka formula triangles)
Expanding brackets
Factorising quadratic expressions

Which of these do you have common methods for that all teachers follow? Are some topics more important than others to have a common method?

3. Consistency of pedagogy
This is the one that is hardly discussed at all, but I think it is the most important. You could have a fantastic resource, or a brilliant method, but if the underlying pedagogy of how both are delivered is not sound, then it will significantly reduce the chances of students learning. If colleagues are using pedagogy that lesson drop-ins, conversations with students, or data suggest are ineffective (this is why collecting critical evidence is so important when trying to improve practice), then why not insist they use more effective ways?

I gave one example of this in the first section – the way the Do Now is presented. Another is worked examples. I very rarely see a consistent approach to worked examples across a department. Whilst it may be a step too far to insist everyone does their worked examples in exactly the same way (using Silent Teacher for the initial example, for example), it feels sensible to insist that everybody follows these principles:

No student should be writing anything down whilst the teacher is modelling so their full attention is on the teacher
The initial worked example should be presented alongside a related example for students to try so they can draw comparisons
Before moving on to independent practice, teachers should do a whole class check for understanding

And yet I very rarely see such direction in place in a department.

Think about the following:

How the Do Now is delivered
How the prerequisite knowledge check is carried out
How worked examples are modelled
How teachers go through the answers to practice questions
How lessons end
How Low-Stakes Quizzes are run
How teachers question students
How teachers respond to a check for understanding

Which of these does your department currently have a common approach for? Are some more important than others to have a common approach?

Why are HODs not more prescriptive?

Every HOD wants consistent high standards of teaching and learning across their team. But in most of the schools I visit, there is a reluctance from the HOD to be too prescriptive. When I push them as to why, three responses dominate:

1. I wouldn’t like to be told how to teach, so it is not right for me to tell others

I think there are a few issues here. First, the HOD is likely to be more experienced than their colleagues, and hence probably in a stronger position to make good choices concerning resources, methods and pedagogy. I am not sure that is true of all members of their department, especially when there are non-specialists and inexperienced teachers. Second, I suspect more teachers than the HOD might think would welcome more guidance and prescription, especially if it would reduce search costs and mean they could collaborate and reflect with members of the department who are trying the same thing. Finally, we need to remember that what teachers prefer to do is not the most important thing – it is all about what is best for the students.

2. If I prescribe everything, my colleagues will become lazy, doing no thinking for themselves and not adapting to the needs of their students

This can and does happen, especially with prescribed resources. I have seen teachers click through a PowerPoint with genuine surprise at what is appearing on the board, suggesting this might in fact be the first time they have ever looked at it. But there are ways to mitigate against this that we will discuss below. And I would argue this is the lesser of two evils: decent resources, methods and pedagogy delivered poorly at least give the kids a fighting chance to learn, whereas poor quality resources, methods and pedagogy, no matter how invested the teacher is in them, leave little chance for learning to take place.

3. Good practice will emerge naturally

I hear this a lot from HODs. They hope that by doing things like putting good resources in the departmental folder, discussing methods in departmental meetings, or even running CPD on pedagogy in departmental meetings, colleagues will make changes to their practice under their own steam. I am not convened this happens as much as HODs might hope, and when it does happen it is usually not with the colleagues who most need to change. I have both sat through and delivered enough CPD sessions where colleagues were shown good ideas, everyone nods along and promises they are going to try them out, and then a week later it is all but forgotten. And if colleagues do eventually decide to make a change, then how long is it going to take? And what is the impact on students learning in the meantime?

Can you relate to these responses HODs give? What do you make of my responses?

How can HODs be more prescriptive and ensure that translates to better classroom practice?

Let’s start with something that does not work: simply telling colleagues that everyone must do the same thing. I made this mistake when I first introduced Low Stakes Quizzes to our department. There was no staff buy-in, and so there was no student buy-in, and so after a few weeks the idea was dead in the water.

Colleagues need to be shown the rationale for the decision, and then given time to question, collaborate, plan and rehearse. And then, when they have tried the idea out, given the opportunity to reflect. Departmental meetings are ideal for this.

Let’s look at how we could introduce a greater level of prescription for each of the three categories.

1. Resources

Choose a quality task for an upcoming topic that you want everyone to do in their lessons. For example, let’s say fraction arithmetic is coming up for Year 8s, so you choose this task from the late, great Don Steward:

Give everyone 10 minutes to work through the task as mathematicians. This time to simply do some maths, separate from any concerns about differentiation, is so important and something that is not done enough in departmental meetings. Colleagues can work independently or collaboratively, and the environment needs to be safe and supportive, especially for colleagues who lack confidence in their subject knowledge.

Then, when colleagues have had the opportunity to engage in the task, pose two questions:

How would you support students who are struggling with the task?
How would you challenge students who have completed the task?

Give colleagues an opportunity to consider these questions independently first, before they share their thoughts with a partner, and then finally share ideas with the department.

By the end of this process, you should have lots of ideas for how to adapt the task itself, or how the task is introduced, or the support materials students are provided with. Most importantly of all, you should have a group of colleagues who are both prepared and excited to use the task with their students. And then in the next departmental meeting, you can spend time reflecting on what went well and what didn’t, before choosing another task for another year group.

In my experience, no one complains about being prescribed a task to use if this process is followed.

2. Methods

Here, Jo Morgan’s wonderful book, A Compendium Of Mathematical Methods, is a Godsend. Pick a topic from the book that everyone is teaching soon, choose a question, and then model how to solve it using the many different methods presented in Jo’s book, challenging colleagues to try each method with a related problem. Once colleagues have tried out each method, ask the following two questions:

Which method are your students most likely to succeed with?
Which method most allows us to build more complex ideas upon?

Think, Pair, Share again works well to generate ideas. But at the end of the day, a decision needs to made, and so long as colleagues have had the chance to consider alternatives, air their views, and understand the justification for the final choice, most come on board. The final piece of the puzzle is to then give colleagues who are not familiar with the method time to practice it alongside the support of colleagues who are more secure with that approach.

3. Pedagogy

As I argued above, this might be the most important one of the three. Unfortunately, it is also the most difficult to get right. The key point is the focus cannot be on the tool. Saying to a group of colleagues: “Right, we are all going to use mini-whiteboards in our Do Now” simply does not work. Instead, we need to enable colleagues to reflect on their practice by asking the right question.

Let’s take the Do Now example from the start of this newsletter. As a reminder, most colleagues were going through the answers, involving one or two students, and asking everyone to make corrections in green pen. As a result, teachers had very little evidence of student effort or understanding.

First, ask colleagues to describe to their partners how they currently run their Do Now. Then ask a question: “How easy would it be for a child to get away with not thinking and not understanding during the Do Now, and you not pick up on it?”.

This should lead to an honest reflection where colleagues identify that their pedagogy could be improved. This then opens the door for an alternative. Don’t present it like it is the be-all and end-all, present it more like this:

The Do Now is so tricky to get right. I have been experimenting (and failing!) for a while. This is how I currently do my Do Nows.

(then model what you do)

It is not perfect, but it helps me find out what my students really understand, and not what they tell me they understand, which can be quite scary! There may be other ways to get all students to share their answer, but I think mini-whiteboards is the most appropriate. I know there are issues with the logistics of giving them out and collecting them in, as well as concerns about kids messing about with them, but I would like us to have a discussion now about how we can overcome those challenges, and then I would like everyone to experiment - just for a week and just with one of your classes - at doing the Do Now this way. Then next week, we can reflect on what is worked and what hasn’t, and go from there.

Again, when presented like that, I find most colleagues come on board.

What do you think?

So, there you go. There is my argument for why many maths departments would benefit from a greater level of prescription, and some suggestions about how you could go about this for three areas: resources, methods and pedagogy.

But all of this is very easy for me to say. You know the barriers you face. They may be time constraints, or they may be to do with the personalities, status or past experiences of your colleagues. Bringing about change is rarely easy. So I am really interested in:

1. Which of the three areas do you think your department could most benefit from a move to greater prescription?
2. How would you go about making this change?

Please let me know in the comments

Three final things from Craig

If you want more thoughts and ideas about leading a maths department, check out my recent podcast episode: How to lead a maths department
Have you subscribed to my other newsletter, the Tips for Teachers newsletter, where you will receive a tip in your inbox every Monday morning to try out in your classroom that week?
Have you checked out my Tips for Teachers book, with over 400 ideas to try out the very next time you step into a classroom?

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