Once we have obtained a large sample of reliable data from our check for understanding, it is time to respond. If we don’t respond, then there is no point in doing the check for understanding in the first place.
Diagnosis
You ask a question and see the responses from all your students. How do you respond in each of these scenarios:
- Nearly everyone gets it correct?
- Some get it correct?
- Few get it correct?
Evidence
In his excellent book, Responsive Coaching, Josh Goodrich presents 6 Big Teaching Challenges:
Responding appropriately to data we gather on our students’ learning is challenge #5, and is where many of the lessons I see fall apart. There are several reasons for this:
- The teacher has not obtained enough reliable data and so does not respond appropriately to the needs of the class
- The teacher responds the same way – either moves on or goes over the answer – regardless of what the data tells them
- The teacher spends too long going over things that students do understand and not enough time on things students struggle with
Solution steps
I like a system. For the rest of this section, I will show you my system for determining how I respond to three common scenarios when I ask students a question:
- Nearly everyone gets it correct
- Some get it correct
- Few get it correct
It is far from perfect. But I hope it gives you a basis for determining appropriate responses.
Preliminary steps
Gather data
In order to determine how best to respond, we first need some data from our students. This data needs to be representative of our students’ level of understanding. Therefore, relying on the answer of one confident, high-achieving volunteer is not good enough. Cold Call a student is better, but it still gives us just one data point.
Here are more effective ways of gathering this data:
- Multiple Cold Calls – Cold Call several students. We can be strategic in our choices, maybe choosing a high, middle and low-attaining student
- ABCD cards – We can ask a multiple-choice, diagnostic question and get all students to indicate their answer
- Mini-whiteboards – For me, this is the go-to. I get to see every single student’s response, and I am not restricted to questions with a finite number of answers as I am with ABCD cards.
Don’t reveal the answer
I watched a lesson where the teacher checked students understanding of Question 2 (0.81 divided by 0.9) by asking them to put their answers on mini-whiteboards.
Roughly half the students got the answer correct.
I transcribed what the teacher said next:
Teacher: Well done to those of you who got an answer of 0.9. We need to be really careful with questions like this because…
She then proceeded to explain a common mistake students make, and how to avoid it.
A few minutes later, I chose three students who had written the answer of 0.9 and asked them why the teacher had said they needed to be careful with questions like these and how to set out their work so they didn’t make that mistake. Here are their responses:
- Not sure
- Something about the decimal
- I moved on to the next question
These students were not listening because they didn’t feel they had to. They knew they had the answer correct.
A few minutes later, two of these students got Question 7 wrong because they had not followed the teacher’s method:
The teacher made the mistake of revealing the correct answer before her explanation. As soon as you confirm the correct answer, students stop thinking and paying attention:
- Anyone with that answer will conclude that they understand, and so do not need to pay attention to your next move. They may even choose to go off-task and distract others
- Anyone who does not have that answer may lose confidence and feel this is yet another thing that they do not understand
To maximise the amount of time students spend paying attention and thinking, hold off revealing the correct answer until you have finished your explanation.
Three scenarios
There are an infinite number of combinations of student responses. But to keep things simple, I want to distinguish between three scenarios. This will help develop some general principles that you can apply and adjust to the variations you see in your classroom.
The three scenarios are:
- Nearly everyone gets the correct answer. By nearly everyone, I mean above 80%. 80% is a good threshold to aim for. It is the figure Rosenshine uses in his Principles of Instruction and is often quoted in discussions of mastery, such as in Mark McCourt’s book, Teaching for Mastery. 80% means that in a class of 30, no more than 6 students have the wrong answer. This is a small enough number to check in with them later in the lesson.
- Some get the answer correct. Here, I mean anywhere from 80% correct to 40% correct. The key point here is that there is not enough knowledge in the room for me to move on quickly, but there is enough knowledge in the room to involve the students in the next step.
- Few get the answer correct. Once we fall below the 40% figure, there is widespread confusion. Involving the students directly in the next step is likely to exacerbate the confusion, so our response will be different.
My choice of percentages should not be seen as gospel. For some questions, such as those assessing prerequisite knowledge, you might want to raise the threshold to 90%. If a question is part of an extension activity to stretch your highest-achieving students, then the threshold might be lower.
Scenario #1: > 80%
Write the answer
Even if all students are showing the correct answer, it is always worth writing it down instead of just verbally confirming it. Verbal information is transient. If a student mishears or is not paying attention, they have no way of accessing that information again.
If you want to draw students’ attention to a particular way of setting out the answer, you may choose to quickly model the solution. But, as we shall see, time is of the essence here.
Check-in with students later
Because we have a high threshold, the number of students who did not know the answer is small enough that we can check in with them individually later in the lesson.
I recommend writing down the names of these students. Often, I hear teachers say things like, “I will come and check in with you later,” only to forget when a million other things fly into their working memory in the intervening period. Writing down the names of these students at this stage of the process means you don’t have to rely on remembering who they are.
Option 1: Move on
The default next step in this scenario is to move on. It may be tempting to probe students further to get a truer sense of the depth of their understanding, but doing so has an opportunity cost – it will leave you less time to support students on questions where their understanding is not so secure.
I observed a lesson where a teacher fell into this trap. Students had all nailed Question 1 of his Do Now:
But he continued to push them to explain their reasons and comment on each other’s explanations. This was all great stuff, but the clock was ticking.
Most students had got Question 3 wrong:
But we were now 12 minutes into the Do Now, so the teacher gave a super-quick explanation and told the confused roomful of students he would come back to it another lesson.
That is why I advise moving on when we have evidence that understanding is secure – you are likely to need those minutes later in the lesson.
Option 2: Ask a What if question?
If you have time to spare, or the concept is a particularly important one that you want to delve deeper into, then asking a What if question is a good idea. What if questions are based on the question you just asked students. Tw good prompts are:
- What if I changed the question to _?
- What if someone wrote an answer of _?
So, if this is te original question:
You might ask:
- What if someone wrote 15 + 3x? Are they correct?
- What if I change the 5 to a 4?
- What if I change the plus to a minus?
- What if I change the 𝑥 to a 2𝑥?
- What if change the 3 to a 3𝑥?
What if questions work especially well if students have responded to the original question on mini-whiteboards because they can be challenged to make a minimal change to their working out and answer to respond to the change in the question.
But, to return to my previous point, the default response if students have answered a question correctly is to move on!
Scenario #2: 40% to 80%
Make student responses visible
When we have a range of responses, our first step is to make those responses visible to the rest of the class. There are several reasons for doing this:
- Verbal information is transient. If we have Cold Called, some students may not have heard or been paying attention to the response of their classmates. If we have asked for responses via ABCD cards or mini-whiteboards, students do not have the advantage of our position at the front of the class. Making student responses visible alleviates these issues.
- The written responses provide a frame of reference. Students can refer to, compare and contrast the responses during the next steps in the process without needing to remember what was said.
- Sharing the responses gives students more thinking time. Research suggests teachers give students sufficient time between hearing an answer and asking them to do something with that answer. Making those answers visible slows things down and provides those all-important few seconds.
- Sharing the responses gives us more thinking time. The same research suggests that we use student responses better if we allow a few seconds between hearing a response and instigating the next step.
There are several options for making student responses visible.
1. We could write them on the board
2. We could hold them up
3. We could put them on display
4. We could use a visualiser
Option 1: Warm Call
We now have two options, the first of which is to Warm Call. A Warm Call differs from a Cold Call because you have collected data on students’ understanding first, so you can be strategic about which student you call upon.
Referring to the answers you have made visible, choose students that have given different answers:
- Tommy, I can see you think the answer is _, please could you tell us why?
- Heena, I can see you think the answer is _, please could you tell us why?
There are two things to be aware of here.
First, you need a culture in your classroom where students are not afraid to share their answers and reasoning, even if they might be wrong. This takes time to build.
Second, you must hide your tell. Giving away the correct answer at this stage robs students of the opportunity to think.
We all have verbal tells. Perhaps a sigh, a shake of the head, an “Are you sure???” when we hear a wrong answer. Adopting a neutral “Thank you” response, regardless of whether the answer is wrong or right, is a good way to combat this.
However, the most common way teachers give away the answer at this stage of the process is the order in which they call upon students to share their answers, either always starting with the correct answer or leaving it until the end. Students pick up on this. So:
- If using ABCD cards, go in alphabetical order – start with a student who chose answer A, then B and so on
- If using mini-whiteboards, start from the left of the room and sweep to the right
Option 2: Turn and Talk
Our second option when student responses are mixed is to instigate a Turn and Talk. Here, it is important to provide a clear structure to the discussion, and ensure students have something to talk about if they both agree on the same answer.
I like this format:
- The person closest to the door goes first
- Tell your partner what you think the answer is and why
- Listen to their answer
- If you disagree, can you convince them?
- If you agree, why might someone think a different answer is correct?
Following the Turn and Talk, you can jump straight to the next stage. Or you can sample some discussions. Here are three good questions to ask tob find the best pairs to call upon:
- Put your hand up if you disagree with the answer of your partner
- Put your hand up if you changed your mind during your discussion
- Put your hand up if your partner said something you found interesting
Which option is best: Warm Call or Turn and Talk?
Both have their place. Warm Call is easier to manage, but only a few students get to share their answers. Turn and Talk is tricker to manage, but everyone has an opportunity to contribute.
The choice is yours!
Why don’t you just explain the answer?
I am a big fan of telling students how to do things. But in this scenario, I would like to do either a warm call or a Turn and Talk first. There are three reasons for this:
- There is sufficient knowledge in the room
- I want to confront misconceptions directly
- I want students to have an opportunity to talk maths
If I am short of time, or this is the Do Now, then I will cut out the Warm Call or Turn and Talk and jump straight to the model. But, I will ensure I refer to the answers I have written on the board in my explanation.
Revote
Now students have the opportunity to revote. Here are the instructions I give students:
- You have now heard a few different answers
- You can choose to stick with your original answer, or you can change
- But if you change, be ready to explain why
The revote provides evidence of whether understanding is moving in the right direction.
During this phase, it is important to watch out for students who haved changed their minds.
- If using ABCD cards, look for students reaching for a different card.
- If using mini-whiteboards, look for students picking up their pens.
Question some switchers
Now we need to question those students who have changed their mind. This again provides evidence of whether understanding is moving in the right direction.
If we assume they understand the answer without probing them further, we risk this happening:
Here is the prompt I use:
Sam, I see previously you thought the answer was___, but now you are going for___. Please tell us why
At the risk of sounding like a broken record, the fact that we have made student responses visible makes this stage of the process so much more effective as we have a frame of reference:
If you did not manage to spot the switchers, you can always ask students to put their hands up if they changed their minds, or if you did a Turn and Talk ask who managed to change their partner’s minds.
Model
We now need to step in and clarify what the correct answer is. The usual protocol for explanations applies here:
- Ensure students have empty hands and eyes on you
- Make the explanation clear and concise
It is also a good idea to refer to the wrong answers in your explanation to ensure you confront those mistakes and misconceptions:
Finally, ensure you highlight the correct answer or cross out the wrong answer. Verbal information is transient, and we don’t want to risk students remembering the wrong answer.
Ask a follow-up question
The temptation for many teachers at this stage of the process is to say something like:
- Does that make sense?
- Is everybody happy?
- Any questions?
None of these are reliable evidence of student understanding.
Instead, we need to ask a follow-up question to see if our explanation has made sense, and we need to see the responses from as many students as possible.
Many teachers don’t appreciate how hard it is to think of a good follow-up question on the spot. It needs to test the same skill at the same difficulty level but still requires some thinking. I have lots of examples of teachers failing to think of a good follow-up question in the noise of a lesson, such as this pair:
Or here where students got the original factorising question wrong because they did not factorise fully:
And yet the follow-up question that way made up on the spot did not address this error:
If possible, plan follow-up questions in advance.
Here is a nice example of a teaching sequence following the model of responsive teaching we have built so far during a Do Now:
Students nailed Question 1, so the teacher moved on quickly. However, the mini-whiteboards showed a range of answers for Question 2. So she wrote these on the board:
She then asked students to do a Turn and Talk, followed by a revote and a teacher explanation. Finally, she gave students a follow-up question that she had planned in advance:
Respond in the moment
To keep things as simple as possible, here are three things we could do after the follow-up question:
- If more than 80% of students are correct, move on. We have evidence in the moment that their knowledge is where it needs to be.
- If fewer than 80% of students have the correct answer and it is prerequisite knowledge for the upcoming lesson, or a hinge-point in the lesson, then you are obliged to explain and recheck for understanding again.
- If fewer than 80% of students have the correct answer and it is spaced retrieval practice disconnected from the lesson, move on and come back to the topic at a later date.
In the second scenario here, you may choose to do this intervention with a smaller group, instead of with the whole class. If appropriate, the students who have displayed understanding can continue with the next task. Or you may give them an extension activity based on the current question, such as:
- Explain why someone might choose one of the incorrect answers
- Change the question as little as possible to make one of the wrong answers correct
- Create your own diagnostic question on this topic
- What if I changed the question to this?
Scenario #3: < 40%
Model
Finally, we turn our attention to the third scenario, where most students have got the answer wrong.
The temptation here may be to ask a student who has the correct answer to explain. I think that is a risky strategy. I have seen too many lessons go to pot when a teacher asks a student who has the right answer, and their explanation is either wrong or convoluted.
In this scenario, most students are not secure in their knowledge, and I believe they need a clear and concise explanation from the teacher.
So, it’s back to:
- Empty hands, and eyes on me.
- Clear and concise explanation
- Refer to the wrong answers in your explanation
- Highlight the correct answer or cross out the wrong answers
I include checks for listening when modelling in this scenario as I want to ensure I have my students’ full attention. I use my Explain, Frame, Reframe, Rehearse framework to draw students’ attention to the critical parts of the explanation:
- Explain: The proper name for the C-shape is co-interior angles
- Frame: What is the proper name for a C-shape?… Emma
- Reframe: What shape are co-interior angles?… Mo
- {checks for listening continue}
- Rehearse: Turn to your partner and talk through the steps of the solution
Checks for listening are the only types of questions I will ask students during this phase.
Of course, you can check for listening during the modelling in the other two paths – it is never a bad idea. However, checks for listening are especially important in the scenarios where there is widespread confusion.
Ask a follow-up question and Respond in the moment
Then, just like in Scenario 2, we need a well-chosen follow-up question, and then we need to respond appropriately.
Check again soon
In Scenarios 2 and 3, we found evidence of a lack of understanding. Sure, in the moment, that lack of understanding seems to be resolved, but we could be observing performance rather than learning.
The way to avoid this is to make a note to check students’ understanding at points in the future. This could be:
- In the next lesson’s Do Now
- In this week’s homework
- In next week’s Low-Stakes Quiz
How students answer the question in the future will give you much more reliable evidence of their learning.
Implementation planning
Here are the ideas we have discussed:
Use these to complete the prioritisation exercise here.
