Boosting the participation ratio during our explanations
How can we ensure more students listen, think and understand during our explanations and worked examples?
A couple of newsletters ago, I shared an exercise I often do with the maths departments I support to encourage them to reflect upon the participation ratio at various stages in their lessons. As a reminder, a good way to reflect on the participation ratio is to ask yourself:
How easy would it be for a student in this phase of the lesson to be either not listening, not thinking, or not understanding, and you not pick up on it?
I asked teachers who read the post to choose the phase of their lesson where they felt they needed to boost the participation ratio the most. The results suggest we have a clear winner: the explanation and worked example phase.
This is also the phase of the lesson where I need to boost the participation ratio, so I have been thinking about it a lot. So, in this post, I am going to share five ideas for boosting the participation ratio during explanations and worked examples.
What not to do
An obvious way to boost the participation ratio is to ask students lots of questions during an explanation or worked example. But we need to be careful what we ask them questions about. If we question students about a new idea that they know little about (What do you think we do first? Why can't we do this?) there is a danger that our explanation or worked example descends into a game of Guess what is in my head. I have both seen and delivered explanations like this. They take ages and are inherently confusing to students as wrong answers fly around the room until someone - usually by a process of elimination - stumbles upon the correct answer.
Idea 1: Check for listening
So, if we don't ask our students questions about new knowledge, then what could we ask them questions about? Well, first we could simply check if they are listening. If our students are not paying attention, then it does not matter how clear our explanation is as they will not understand it. The simplest check for listening is to ask students to repeat something you have just said. This could be done using Cold Call (What did I just say the subject of this formula is... Holly?) or Call and Respond (The first thing we do to both sides of the equation is... 3, 2, 1... MULTIPLY BY 3!).
Once students realise you will be regularly checking for listening, they have an added incentive to be paying attention.
I discuss the importance of high-frequency checking for listening during explanations with Science teacher Pritesh Raichura on an upcoming episode of my Mr Barton Maths Podcast (due for release 28th June). As a sneak preview of our discussion, check out these graphs of two different classrooms from Pritesh’s wonderful blog post:
Idea 2: Ask questions about the prerequisite knowledge you have just assessed
Another thing we could question our students about during an explanation or worked example is skills they have met before which are key to this new idea - in other words, the prerequisite knowledge. Now, we only want to do this if we have recently assessed that prerequisite knowledge and have evidence that it is secure. If we don't, then we run the risk that we ask students a question that we assume they know the answer to, but it turns out they don't, and then we are forced to pause our explanation or worked example and intervene.
Again, assessing prerequisite knowledge during an explanation or worked example works well via Cold Call or Call and Respond. But you can also use mini-whiteboards:
So, we have seen we need to multiply both sides by 3. On your mini-whiteboards, please write down what the left-hand side of the equation will look like after we multiply by 3.
Idea 3: Use Silent Teacher
Whilst I like to check for listening and ask questions about prerequisite knowledge during an explanation, when it comes to modelling a worked example I like to start with my Silent Teacher approach. For those not familiar, this is where I model the worked example in silence, pausing at key points to challenge my students to consider: What has he just done? What do I think he will do next?
Now, of course, whilst I am creating the optimal conditions for students to focus and think hard by removing any distractions, it would be very easy for a student to not participate at all during Silent Teacher. They could simply stare at the board whilst their mind wanders elsewhere. That is why it is important I have two whole-class checks for understanding coming up next. It is also important that my students are aware of this so they have the incentive to engage.
Idea 4: Check for understanding using Step by Step
The first of these whole-class checks for understanding following the worked example is called Step by Step. Here, I give my students a problem to solve that is of a similar difficulty to the worked example, but first I ask them to just write the first step on their mini-whiteboards. For example, if the problem I wanted them to solve is:
I would say:
On your mini-whiteboards, write down the first operation we are going to do to both sides of the equation.
Students would hover their boards face-down to indicate they are ready, and then when I say would hold their boards up so I could see in 3, 2, 1...
If all students have got this correct, I would move on to the next step:
Good. So, we subtract b-squared from both sides of the equation. On your mini-whiteboards, write down what the left-hand side of the equation would look like after we subtract b-squared.
And so on.
Step by Step may also be suited to assessment via Call and Respond. For example, I could ask the following to ensure students have read the question correctly:
We are going to do a Call and Respond. What letter do we want to make the subject of the formula… (wait)… 3, 2, 1…
There are two things I like about this stage of the worked example process:
All students are involved, so the participation ratio is high
If something goes wrong, then I know the exact part of the process where it happens, and I can pause and intervene accordingly
Idea 5: Check for understanding using the Tick Trick
Following Step by Step, I want to see if students can solve a similar problem on their own from start to finish. I ask them to do this on their mini-whiteboards and show me when I ask. There is likely to be too much information on each student's board for this to be a thorough check for understanding, but I certainly get a sense of whether all my students are participating. I can also be tactical and pay particular attention to the boards of the weaker students in my class.
The way I assess this second example is to use Adam Boxer's Tick Trick. I ask students to put their boards down and watch me. I then write the first step of the solution on my board, and say to the students:
If you have written exactly what I have written, then give yourself a tick.
I ask students to hold their boards up again to show me their tick so I can see if everyone is participating and pick up on any students who have done something different.
Then I do the next step of the solution, and again ask students to tick if their step matches mine.
Here is what I love about the Tick Trick:
Again, everyone is involved, so the participation ratio is high
Again, I can pick up the exact stage of the process where students are struggling
It forces students to look carefully at their working out, and not just the final answer
If there is a particular way I want students to set out a solution, then this is a great way of making sure they are doing it
Reflection
So, here are five ways we could boost the participation ratio during explanations and worked examples:
Check for listening
Ask questions about prerequisite knowledge you have just assessed
Use Silent Teacher
Check for understanding using Step by Step
Check for understanding using the Tick Trick
Here are some questions to consider:
Which of these do you already do?
Which of these could you try?
What would you need to change to make them work for you?
What other things do you do that help boost the participation ratio during the explanation or worked example?
Please let me know in the comments.
Three final things from Craig
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Thanks so much for taking the time to read this, and have a great week!
Craig