The perils of Rounding Up students' answers 💬

Do you recognise this type of classroom dialogue? Is it a problem?

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Rounding Up - example 1

Here is an interaction between a student and a teacher I saw recently:

• Teacher: What is the first step to solve 6𝑥 + 5 = 29?

• Molly: You move the add 5 to the other side, and it becomes a takeaway 5

• Teacher: Exactly, you subtract 5 from both sides of the equation because subtraction is the inverse of addition

What is going on here?

This is known as Rounding Up. This type of teacher response was a common feature of my teaching for many years, and it prevails in many of the lessons I am lucky enough to see in the schools I now visit.

In Teach like a Champion, Doug Lemov explains:

Rounding Up involves a teacher responding to a partially or nearly correct answer by affirming it, and in so doing, adding critical detail (perhaps the most insightful or challenging detail) to make the answer fully correct.

Can you recognise this in your own teaching?

Is Rounding Up a problem?

I think so. For these three reasons:

1. The student thinks they have understood, when really they haven’t

2. The standards in the class fall, because students realise they can get away with half-baked answers

3. The message is that, in this classroom, the teacher does the hard work

Do you agree Rounding Up is a problem?

What is the solution?

The solution, I think, is to push for excellence. So, something like this:

• Teacher: What is a good first step when trying to solve 6𝑥 + 5 = 29… Molly?

• Molly: You move the add 5 to the other side, and it becomes a takeaway 5

• Teacher: Let’s improve this answer together. The add 5 does not move, but it does seem to disappear from the left-hand side of the equation. What happens to it?

• Molly: I’m not sure

• Teacher: How did you know that taking away 5 would be involved, because that is correct?

• Molly: Because taking away 5 is the opposite of adding 5?

• Teacher: Yes. Can you remember the proper words we use for taking away and opposite?

• Molly: Subtracting and inverse?

• Teacher: Love it. So, what do we do to make the add 5 look like it disappears?

• Molly: Subtract 5?

• Teacher: Yep, and if we do something to one side of the equation…

• Molly: We do the same to the other side

• Teacher: Exactly. Right, Molly, let’s put this all together. What is a good first step when trying to solve 6𝑥 + 5 = 29?

• Molly: Subtract 5 from both sides of the equation

• Teacher: Because…

• Molly: Because subtracting 5 is the opp… I mean the inverse of adding 5

• Teacher: Superstar

Sure, this takes longer, but it is more genuine, and addresses each of the three problems outlined above.

Following this interaction, I would check other students have been listening, either by Cold Calling some students and asking them to repeat what Mollie had said, or instigating a Turn and Talk.

What do you think? How closely does this mirror your approach in your classroom?

Rounding Up - example 2

Recently, I have noticed another type of Rounding Up in the maths lessons I have been watching. Here is an example from a Year 8 lesson I saw last week:

• Teacher: I want to share £20 in the ratio 3 : 2. How do I start… Flynn?

• Flynn: No idea

• Teacher: Well, first, I need to know the number of parts. How many are there?

• Flynn: No idea

• Teacher: There are 3 parts here, and 2 parts here. What is 3 plus 2?

• Flynn: Five

• Teacher: Exactly! Okay, so what do I do next?

• Flynn: No idea

• Teacher: Okay, so I am going to share £20 equally between these 5 parts, so 20 divided by 5 is…

• Flynn: 4

And so on…

Take a moment to consider what is happening here?

The student is clearly contributing to the solution, and what they are saying is correct, but it is the teacher who is once again providing the critical insight. Just like in the solving equation example, there is a real danger that the student (and maybe the teacher) concludes the interaction thinking they understand how to share in a ratio.

This one is more difficult to solve. Responding to the initial No idea with some of these responses might help:

1. What question did I ask? (to check the student has actually been listening)

2. What do you know? (to get things moving)

3. I am going to ask three students what they think, and then come back to you to see which answer you think is the best (to provide support, but not let them off the hook)

4. Okay, listen to me explain, then repeat it back to me, and then I am going to ask you a related question (again, this provides support, but does not let them off the hook)

Once again, this takes more time. But I think it is time well spent in creating a classroom environment where thinking hard is the norm.

Do you recognise this in your own teaching?

How could you combat it?

Let me know in the comments below!

🏃🏻‍♂️ Before you go, have you…🏃🏻‍♂️

1. … secured your place on our Marvellous Maths 3 CPD day?

2. … checked out our incredible, brand-new, free resources from Eedi?

3. … read my latest Tips for Teachers newsletter about the dangers of saying: "If you got the question wrong, make sure you have corrected it"

4. … listened to my most recent podcast with Tom Sherrington, Emma Turner and Ollie Lovell?

5. … considered booking some CPD, coaching, or maths departmental support?

6. … read my Tips for Teachers book?

Thanks so much for reading and have a great week!

Craig