##### By Mark Dawes, May 2024

I was fortunate to be able to see an extremely experienced teacher use an NRICH task with a group today. The task was one that was new to me (*Add to 200*) and you can find it here (https://nrich.maths.org/11110), although this post will make sense without needing to read/do the task.

I was struck by many things, but in particular by the number of self-deprecating or anxious comments. For example, I heard all of the following:

“I am not as good at problem-solving as <name>.”

“I only did this …” (before explaining something that was a brilliant way to start).

“I probably shouldn’t say this, but I want to use my calculator” (when calculations weren’t the focus of the task).

“Our ideas aren’t as good as the smarty-pants table’s.”

“I’m on that table, but I’m not a smarty-pant.”

“I’m happy to stop there.”

“I’m near the bottom of the set.”

What year group might these comments have come from? You might want to read the comments again: Are you picturing a primary or secondary class? Mixed-attainment or setted? KS2, KS3, or KS4? Pupils working together or individually?

(Spoiler follows)

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It was a group of secondary maths teachers from four schools, who worked together on the problem as part of a session on an INSET day. The experienced teacher was Charlie Gilderdale, from NRICH.

I worry about *pupils* who use language like this to describe their own mathematical ideas, because I hope their experience in my classroom will encourage them to become confident mathematicians who do not feel anxious about doing mathematics, or about their place in the class. I therefore found it interesting that many maths *teachers* responded in this way.

**Is it that experienced teachers are within their comfort zone regarding the content they teach, so a problem like this is something we aren’t usually faced with?**

We are all very comfortable factorising quadratics, or solving difficult GCSE probability questions, because we know the content well, and have seen similar questions before. Perhaps it’s just that we aren’t used to solving problems like ‘Add to 200’, so it’s like a different subject (it’s not the same maths that we teach every day). Are the negative comments a defensive act?

**Were many members of this group just naturally self-deprecating?**

I have PE teacher colleagues who are extremely competitive and who would never be negative about their own ability. For example, a few years ago I lined up on the Cambridge Half Marathon start line alongside one such colleague. “I didn’t know you’re a runner” I said. “I’m not”, he replied, “but I’ve got a bet I can beat the runners in the PE department.” “How far have you run in training?” “About 8 miles.” Wow – what self-confidence! (He crashed and burned between miles 11 and 12!)

While my history-teaching colleagues will talk about their areas of specialism (“I’m a medievalist”, “I’m an ancient historian”), they don’t disparage their knowledge of the second world war or the Russian revolution. Why should this be different for maths teachers?

**Is it the unfamiliarity of being in this environment?**

While we usually work together with our colleagues in many different ways (planning, sharing resources, observing each other, supporting, dealing with challenges, etc), we aren’t usually doing maths together in this way. Given we were working on a problem aimed at KS3 pupils, should this have been an issue?

**Is***everyone***(except the occasional deluded PE teacher) anxious in this sort of scenario?**

A slight frisson of concern can be helpful, because it keeps us on our toes, and encourages us to stay focused and think harder about the problem, but if it spills over into anxiety, it can have a negative effect on our thinking and performance. *See ‘How Children Fail’ *by John Holt, in particular, the "July 27, 1958" section (pages 22-24 in 1990 edition) - pdf available here.

**Is it that it’s an unfamiliar social environment that we need to navigate?**

While some colleagues might have found the task a challenge, it was also potentially difficult knowing how to behave If you have an idea. If you get a solution (or a partial one), what should you do?

o Tell everyone in your group?

o Ask others to check your work?

o Guide them towards your idea without giving it away?

I don’t think there is a right answer to this.

**What have I taken from this experience?**

Even very strong mathematicians find problem-solving difficult. I know I frequently talk to a class about not being afraid to make mistakes, not being worried about having a go, etc, but I don’t think I had appreciated quite how much negative language would crop up amongst a group of teachers. It may be worth sharing with our classes that even maths teachers can sometimes find working in a group on unusual maths a little intimidating.

**Final thoughts**

I wouldn’t want to leave the impression that this was a negative experience: far from it! Everyone seemed to me to be enjoying working on some maths together and there were lots of lovely positive noises “ooh – that’s nice”, “surely that can’t be true?”, “wow – that’s brilliant”. Some colleagues made their own conjectures (sometimes after answering Charlie’s original question and sometimes before), while two separate groups created their own new notation for certain ideas that cropped up. Some of these things came from colleagues who also made self-deprecating comments.

This perhaps makes it all the more important that we pay attention to the negative statements that are sometimes made about doing mathematics. And that we start with ourselves!

**Recommended viewing/reading:**

__How Children Fail____ __- by John Holt

__Mindset: How you can fulfil your potential____ __*-** by Carol S Dweck*

*Getting into and staying in the Growth Zone** - **article by Sue Johnston-Wilder and Clare Lee*

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Is there something else in play here? Is it that there isn't enough time spent during ITE (or, if preferred, ITT) engaging in being mathematical by future teachers of maths? In England particularly, we seem to have too narrow a focus on the mathematical content (in our national curriculum, in our assessments, in post-graduate ITE) and not enough focus on the disciplinary skills and attitudes that are just as important for success. Being a good teacher of mathematics surely requires one to be a good learner of mathematics...and to be a good learner, one needs to experience struggle, take risks, try ideas out, collaborate with others, build on others' thinking etc...how many qualified teachers of mathematics had strong experiences of…