I’ve observed a lot of lessons this year. Inside science, outside science, novice teachers, expert teachers. Lots and lots of other people’s lessons. I’ve also been observed lots. As much as I’ve been in others’ classrooms, others have been in mine. In general at TTA we take the philosophy that “feedback is a gift” and that if someone else has been gracious enough to let you into their room to learn from them, the very least you can do is provide them with some feedback that will help them be even better.

Within my department, the stakes are high in terms of the feedback I give. I don’t want to give feedback that’s so general and generic it can’t be acted upon. But I also don’t want to give feedback that’s so specific it won’t be actionable until this time next year when the lesson I observed is repeated. What I really want to do is find something that allows us to think in a general sense about what goes on in our lessons, but come away with specific techniques that can be used in those lessons.

In a lot of the lessons I have seen, and in my own lessons which have been seen, there has been an issue with ratio. This is a concept I first read about in Lemov’s Teach Like a Champion 2.0, and below is the training which I led in my department on it. I hope you find it useful and, if you have any, please remember that feedback is a gift.


Ratio is an incredibly powerful concept that allows for sophisticated discussion of classroom practice and its eventual improvement through dedicated strategies. That’s a mouthful of a sentence, but I can’t think of a better way to put it. Before we look at what Ratio is, we need to start with the work of Professor Coe in his landmark work A Triumph of Hope Over Experience. In that paper, he famously argued that we have become distracted when discussing and judging learning. He decried the fact that we had become preoccupied with observable proxies for learning like busy or engaged students and had patted ourselves on the back when such proxies were achieved or observed in a lesson. But if all that is a distraction, then what should we become focussed on?


I think that line is crucial: learning happens when people have to think hard. Without hard thought, no learning. However many jazzy activities you do in the classroom: no hard thought, no learning.

It’s at this point that ratio comes into the picture, as it is a way of describing and delimiting hard thought. There are two types of ratio:


So it is about both individual students and the collective, how much thought is happening both within and across the group. We could set up a neat little axes:


Obviously the golden zone is the top right, where all your students are thinking and they are thinking hard. Let’s illustrate with some examples:


Before I give you “the answer” where do you think this sits, but just on the horizontal line (participation ratio)? I don’t want to confuse things too much by using both axes at the moment, so just to start with, does asking a question like this get lots of students thinking, or not a lot of students thinking?


You guessed it: calling a student’s name and then asking a question is a surefire way to lower your participation ratio, as the other students – whose names haven’t been called – are almost guaranteed to not be thinking about the answer. This is why Lemov is so insistent about the use of Cold Call. Ask the question first, then call a student’s name. Sounds easy peasy, sounds obvious; yet it’s very easy to forget.

Ok so let’s go for another scenario. In this case, the teacher uses Cold Call, and the third bulletpoint below is the transcript of what happened in the lesson:


Where do you think that should go? Think about it first…

I reckon it goes right here in green:


A bit better than our last one, but not a lot better. Why? Because the Wait Time wasn’t long enough. They posed the question, then asked a student, who then had to pause and think for quite a while before answering. Let me ask you this: while that student was waiting and thinking, what were all the others doing? You betcha: confident that they wouldn’t need to answer the question, they switched off and waited for the other student to answer the question. The whole point in doing the Cold Call flies out the window.

So in what ways can we increase participation ratio:


Some of those are obvious, but I’ll elaborate on a couple that might not be/

Accountability measures are where you hold a student accountable for their engagement. For example, if I ask a student a question and they don’t know the answer and they should, I’ll “have a go” at them and tell them how annoyed and disappointed it makes me that they don’t know the answer to this. I will warn them that I am going to ask somebody else the same question, and will then come back to them later on with the exact same question (I jot their name down and the question on my mini-whiteboard on my desk so that I can follow through on this later). This lights a bit of a fire under them to be extra attentive, and it builds a culture in your classroom of students paying attention to you and to one another.

The next three bulletpoints are very similar and were promoted at the recent Michaela Science conference, if a student answers a question, I’ll jump to a different student and say “what did she say?” or do that with something I’ve just said. As above, this builds – over the long term – a culture of engagement and thought.

Check for mistakes is also a useful but under-used one. If a student is going to give a long answer, or is asking a long question, there’s a danger that the rest of the class will stop listening. A script like “hand on a second Daniel this is really interesting I’d like everyone to listen carefully to what Daniel is saying and put their hand up immediately if they spot something that they think they can answer/say better/use a keyword. Ok, Daniel please start again.”

Independent practice here is of course the only surefire way to guarantee that everyone is participating. Students need that nice long period of just sitting quietly and working individually in order to consolidate new information, and it’s a great opportunity for you to get your participation ratio high.

Alright, let’s start looking at the other axis: think ratio – how hard are your students thinking?


Now you should be able to think about where it goes both on the x axis (how many students are participating) and on the y axis (how hard are they thinking). Where do you reckon?


The mini-whiteboard routine is good, and it puts the participation ratio up. But – and I’m hoping this isn’t lost on you if you’re not a scientist – they aren’t thinking very hard. They do the first one correctly, but all the subsequent ones are exactly the same, just with different numbers. There’s nothing that makes them more challenging, so students aren’t thinking all that hard.


Regular readers of this blog may recognise the above – it’s my attempt to describe what makes some work challenging and other work not challenging. I’m not going to go into that too much now, but suffice to say there are loads of ways to increase the challenge of a task, and if they are getting every question right, you should probably change something to make sure the challenge is kept at a good level. In this particular case you could increase the challenge by any of:

  • Unit conversion
  • Rearrangement
  • Giving values in standard form
  • Using an eyepiece and objective magnification
  • Throwing in a question which uses another formula…

So there you have two case studies of times where the ratio isn’t optimal, and some ideas as to how to fix that.

Below, I’ve got a little activity which has 7 further scenarios involving sub-optimal ratio. For each one you write if you think the participation and think ratios are high or low, and based on that what could be done to improve the ratio.

Coming to an agreement about the “right” thing to do in each scenario is an extremely powerful tool as it means you can walk into anyone’s lesson and rapidly identify if the essential ingredients are there for a high ratio, and if they’re not, have a shared language around what can be done about it. Which brings me right back to my definition at the start:

Ratio is an incredibly powerful concept that allows for sophisticated discussion of classroom practice and its eventual improvement through dedicated strategies.

Further scenarios for activity are below. If you want to know my thoughts on them, click here.

A teacher is questioning students and walking around the classroom, moving towards students who are answering questions. Their movement goes into the classroom as opposed to around the edges and their body and head are facing the student who is answering the question.
Students are working quietly but one of the questions in the practice set relates to material they covered a very long time ago and haven’t revisited since. The teacher is moving around the classroom supporting students with that question. The support they are providing is very similar from student to student
Students are learning about organ systems in groups. Each group has been given a fact sheet about a particular organ system, told that they need to learn it and that any member of the group will be asked to explain what is on their sheet to the rest of the class
The teacher is going over an assessment going question by question. The students have their test papers out in front of them. At each question the teacher carefully describes how they would approach the question and models how they would answer it.
A student answers a question and the teacher uses a series of Stretch It follow-ups to test the reliability of that student’s responses.
During whole class questioning, a student demonstrates poor behaviour. The teacher tells them to leave the classroom which results in a short conversation. Once the student has left, the questioning continues as before.
The teacher expertly models a difficult concept and does a check for understanding via questioning. Seeing that the students understand the concept, the teacher moves on to the next concept to be taught.

Ratio activity

Update 12/7/20: it turns out a version of the graph I used above was displayed at the Michaela Science Conference in January ’20 so it could be that the idea for the graph came from there. It’s also plausible that we all plagiarised Lemov so hey.