Research School Network: What do you notice? What do you wonder? Tom Manners reflects on the power of prompts to support the development of conceptual understanding.

What do you notice? What do you wonder?

I have been very fortunate to work in maths education across all key stages. My work in primary schools has taught me so much that I can apply to secondary, and vice-versa, but if I was asked to share one idea that I have seen in primary schools that could have impact across all key stages, it’s the use of the prompts.

Recommendation 3 of the EEF’s report (2017) into Improving Mathematics in Key Stages 2 and 3 focuses on teaching strategies for solving problems and one of its key ideas is to ​“show pupils how to interrogate and use their existing knowledge to solve problems”. The word ​“knowledge” here could mean anything, subject-specific or not, but it is always advantageous for teachers to know more about their pupils’ knowledge. After all, recommendation 1 of the report reminds us that ​“assessment should be used not only to track pupils’ learning but also to provide teachers with information about what pupils do and do not know.”

So, imagine a classroom where children can speak freely and share everything and anything they know without fear of recrimination. A classroom where there is no fear of getting the answer wrong… because there is no wrong answer! Recommendation 5 of the EEF report addresses maths anxiety and that many pupils hold negative attitudes towards maths. National Numeracy (2022) suggests that pupils may experience maths anxiety when feeling humiliated for getting something wrong, or from the fear of being judged on how quickly they can produce an answer. So… now imagine a classroom where children don’t have that fear when presented with a task, where children are free to share their knowledge openly so that the teacher can assess them more effectively.

I recently saw the power of noticing and wondering in a Year 4 class that were being introduced to equivalent fractions. Preparing for the lesson beforehand, the class teacher and I considered the guidance from recommendation 2 of the report that says ​“Representations can be powerful tools for supporting pupils to engage with mathematical ideas. However, manipulatives and representations are just tools: how they are used is important.” We knew that a fraction wall could be used to demonstrate equivalent fractions, alongside explicit instruction, but we wanted to see if pupils could interrogate the fraction wall themselves through noticing and wondering. After each pair of pupils had been given a copy to discuss, they were asked to turn and talk and asked ​“What do you notice? What do you wonder?”

One pupil told the teacher that they saw steps and that the length of each step was changing. Another child said they saw a rainbow. Whilst these were not the intended focus of the lesson, these pupils felt that they had been heard and, given the climate created by the teacher, they were not afraid to share these ideas.

However, one pair of pupils opened the door to the intended learning. The image above, shows what they noticed. They saw a line going right through the middle of the fraction wall. They described it as a pattern. There was a line, then not a line, then a line and then not a line.

This was the hook the teacher needed. The teacher began to explore with the pupils what created this pattern and through looking at different rows, started to compare the sizes of different fractions. The children quickly identified that one half was the same size as two quarters, as the line that created the pattern matched up in the middle of the fraction wall. But it didn’t end there – other pupils then said that the row of sixths also had a line through the middle of the wall, as did the eighths. Through skilled questioning, the teacher drew out the idea that one half, two quarters, three sixths, four eighths etc were called equivalent fractions as they were the same size… and the intended journey for the lesson was underway.

This idea can be used in all key stages to allow the pupils to openly say what they see which gives more information for the teacher to respond to. Imagine a lesson introducing cumulative frequency in key stage 3. Why not present the image of a cumulative frequency graph and ask pupils what they notice when looking at three examples and one non-example (as per recommendation 6 of the report) and see what they notice and wonder. Would they notice that only the non-example goes ​“downhill” and wonder why… and the journey to conceptual understanding would have begun!

I wonder what would happen if teachers gave these prompts a try in their maths lessons. What would they notice?