Research School Network: “Read the question carefully- What does this mean?” – Using metacognitive modelling to support children’s thinking in Maths “Read the question carefully-What does this mean?” Using metacognitive modelling to support children’s thinking in Maths

I am sure many maths teachers are familiar with the phenomenon of a number of children arriving in their classrooms each year very proficient in arithmetic, mathematically fluent in terms of calculation, and able to apply this thinking to numerical problems with confidence. However, these same children’s scores on reasoning papers and their confidence with reasoning problems is disproportionately low compared to their aptitude with number problems, even when they are more complex.

How many times, as teachers, have we reminded these students to ​“read the question carefully?” Be honest – I’m sure I have done it hundreds of times!

Our recent work within the Research Schools network has led to me learning much more about cognitive science – and in particular how memory, attention, and explicit instruction can impact on teaching. I have also really strived to put myself in my pupils’ shoes as much as possible and really try and understand where they are coming from in terms of their learning. This, coupled with evidence around *metacognition and self-regulated learning, as well as some lessons from the evidence base around *teaching reading comprehension strategies, led me to somewhat of an epiphany when considering why each year a significant chunk of our cohorts appear to have this high arithmetic/​lower reasoning score pattern each year.

If they knew what ​“read the question carefully” meant – surely, they would already be doing so?

This led me to another, jarring question: what do I mean when I say, ​“read the question carefully?”

It turns out that what I mean is- read the question initially just with the intention of understanding it. This is different from reading it for an immediate solution. In the case of reasoning problems in maths, this often means several important things:

1. Read the question in small steps and check your understanding – can you visualise the problem?
2. Don’t try to take it all in and solve it in one gulp – this leads to cognitive ​“choking” and panic.
3. NOTICE the mathematical language, patterns or key information to help you know what to focus on first and what do next.
4. Make sure you have fully understood the problem before choosing an appropriate first step.

I have also come to realise that many teachers, myself included, can tend to leave all of this implicit. The danger in this is that children continue to expect to be able to solve problems that require a different type of mathematical thinking in the same way as more straightforward, apply-a-method questions, and then feel failure or stress when the same thinking fails in a different context. Most jarringly of all, I began to see things in a different way- they were struggling to reason because I wasn’t explicitly teaching them HOW TO THINK.

So, what did I change?

I began to think about teaching reasoning using similar techniques as I use to teach reading. I was already solving questions by annotating under a visualiser, but changed the stress of my input to be on how I was thinking as opposed to emphasising the modelling of the steps I took to find an answer. We then solved the problems together as normal.

What does this look like?

In my maths classroom, it depends on the topic, but often begins as a series of metacognitive observations:

​“Wow- this looks quite busy. I’m going to read it first in stages and make sure I can understand the question fully.”

​“Okay, I can see straight away that this is a missing angle question. I am going to read the information first and then check I understand what I’m looking for.”

​“I’m not going to worry about an answer straight away- I just really want to understand what’s going on.”

​“Okay, I can see a triangle, I can see it’s an isosceles because of the indicated sides. So I know 2 sides and angles will be the same…..”

​“I can see I need to find this missing angle out, but I can’t until I have this information here. So I’m going to ignore that for a second and see what else I can notice to help me…”

​“You know, when I first looked at this it seemed complicated, but now I understand what I need to find it’s much easier…”

I also use a structure for approaching a question to understand it fully:

​“What do I notice? What information is provided? What is missing?”

What else do I explicitly teach now?

As we began to frame our problem solving around the thoughts we are thinking in real time, and discussing these as a group, more things became apparent:

Pupils benefit from being explicitly told that problems are designed and defined by being problematic- the emotional and physical sensations produced by having to think hard, though initially uncomfortable sometimes, are both normal and welcome. It’s not meant to be easy and it’s okay to feel challenged.

They also need teaching that reasoning problems are not designed to always be solvable immediately in one chunk. I often use the analogy of a large pizza here- would you try and eat one in one go? Of course not – same principle applies here – take bites of understanding, chew them carefully before taking the next one.

So What?

Unsurprisingly, our reasoning scores appear to be improving encouragingly, and at the same time children’s levels of stress are reducing. The key takeaway for me as a teacher, constantly getting feedback from my children, is that we often assume too much. Explicitly teaching children metacognitive strategies is a strategy with a large and growing evidence base* and has really changed the way I teach mathematical reasoning. It has been delightful to see children embracing different ways of ​“being a mathematician” and beginning to enjoy complex reasoning problems.

*EEF Guidance Report – Metacognition and Self-Regulated Learning

**EEF Guidance report – Improving Literacy in Key Stage 2