The fog clears and here we are.

Nobody in this class is right bothered about maths, and that has been made very clear. We’re in a key stage 3 classroom in the pupil referral unit. I am side by side with the teacher and the support teacher.

This is true 100 per cent continuing professional development on steroids. Professional learning, researching and reflecting, in the moment, with the kids in the room. The adults are all noticing, while the yoof are settling.

There’s a bit of gentle banter and the reading books are out. A few Bear Grylls mixed in with some Dahl, and a dash of the Wayne Rooney Annual 2006.

I draw a rectangle on the whiteboard and give it some dimensions: 5m x 8m.

“What’s that, Sir?” asks Lennon, mildly.

Using my best when I’m saying it, it’s like I’m thinking it on the spot but actually it’s in my plan approach, I respond to Lennon with, “Well, let’s say it’s the plan of a piece of waste ground next to an old people’s home.”

“My nan’s in one of them!” pipes up Dylan, and I nod.

I know what you’re thinking, dear reader.

This is the class with Lennon and Dylan in it. Orbison is away today.

I go on to attempt to hook them into a narrative; a fictional case study regarding this piece of waste land that is adjacent to an old people’s home. The good news, I say to the children, is that the old people’s home has discovered that this patch of land - measuring 5m x 8m - actually belongs to them!

And now, I offer, the home wants us to put forward some designs for a brand new “Garden of Reflection”, which the old people will be able to enjoy. This is definitely something we can do, I enthuse, and, to be fair, they all seem up for it. Even Kimberley smiles and, at this point, that’s enough for me.

We get some sheets of paper and map out the potential Garden of Reflection. We think about how large a space 5m x 8m would cover. Some of us realise it’s quite big; others think it’s too small for their initial plans.

“If we are going to have a Garden of Reflection for the old people to enjoy, what shouldn’t we put in it?” My sideways question echoes around for a bit, and I realise that they’re all thinking about it. Like, you know, properly thinking.

Then a hand goes up. Then another. I take the responses in turn and we note them on the map.

• Cobbles
• Steps
• Dangerous animals
• Loud music

So, I ask, what should we have in a Garden of Reflection?

Lennon cries out before anyone has time to think: “Sir! Don’t be putting in one of those seats with a brass plaque on it saying, ‘He loved it here’.”

Brian, the support teacher who looks a little like Noddy Holder, raises his eyebrows and chortles, as if asking Lennon for more information.

Lennon looks at him, declaring, “Listen, Bri, when there’s a granny darn, tha dunt want to remind ’em they’re nearly forrit.”

(Reader, I’ve really done my best on the transcription here. I love hearing the beautiful Barnsley twang, but will have to go back to Barry Hines’ A Kestrel for a Knave for a masterclass on writing it darn. I mean, down.)

And so we think of what we should have in the garden and take the time to consider our budget, which, after lunch, will be reduced by 20 per cent, owing to cutbacks. It’ll wind them up a bit but only in the sense that they want to get the job done. There’s healthy learning tension right there - it’s inside the story, so it’s safe.

The laptops are getting some hammer in the name of research and Kimberley is checking out what she calls “flat escalators”. I don’t know what they are, but she explains: “Flat escalators, Mr Roberts. Not going up, not going darn. Just flat.”

“A travellator,” offers Brian, and I nod.

“Whatever you just said,” smiles Kimberley, pointing at Bri. “Just flat. We can put the grannies on at one end o’ the garden, press a button and then Bob’s yer uncle: off they go.”

As she mimes one of her grannies being taken around the garden, pointing and waving, we all crease up.

“How long will the circuit take, you know, on a patch of land 5m x 8m, Kim?” I ask, trying to do the bringing-it-back-to-content-delivery thing.

She stops her mime and looks at me.

“We can work that out, Mr Roberts. Don’t panic yersen.”

I smile. “I won’t.”

And the fog descends.

I don’t remember how we got back to the maths in the end but we did. Sometimes the journey is more exciting than the destination.

Hywel Roberts is a travelling teacher and curriculum imaginer. He tweets as @hywel_roberts. Read his back catalogue and follow him on Facebook.