I work in a larger than average primary school in a diverse but economically deprived area of north London. After joining the school in 2012 as a teaching assistant, I did a placement with Teach First and went on to complete Ambition School Leadership’s Future Leaders programme in 2016, as a member of the school’s senior leadership team with whole-school responsibility for maths.
More than half of the 950 pupils on our school roll are eligible for free school meals, compared to the borough average of 29 per cent, and the number of pupils with English as an additional language is well above the national average.
Like many schools we need to ensure that our curriculum is robust and challenges pupils, as well as being accessible for our diverse cohort.
In 2015, I had the opportunity to spend 10 days observing maths lessons in a number of schools across Changsha in China. What struck me most was that the lessons were very similar to our own, with one key difference: all of the children were confident, articulate mathematicians. In classes of 60-plus pupils, all children were vocal and could clearly rationalise their learning. While the content and curriculum coverage was similar, there was a marked difference in the level and depth of understanding.
As part of the Future Leaders programme, I had to design and implement a school impact initiative. After my trip to China, I decided to develop a reasoning-rich maths curriculum – a whole-school approach that would improve our pupils’ mathematical literacy and raise end-of-year standards in maths.
Although our school’s end-of-key stage maths assessment scores were in line with the national average – an achievement we were proud of – I did not want us to become complacent and aim for the same next year. The purpose of my initiative was also wider than simply raising attainment in maths. The ability to reason has a fundamental impact on a person’s ability to learn from new information and experiences, and these are transferable skills that pupils can apply in other subjects and beyond the school gates.
Proving the need for change
I analysed the end-of-year data for maths across the school and the findings confirmed the lack of reasoning progress – all year groups were scoring significantly higher in the arithmetic than the reasoning papers, despite the fact that reasoning is more heavily weighted. Where, on average, reasoning is worth around 60 per cent of the overall score, we were scoring an average 36 per cent across all year groups.
Sample question analysis of the assessment papers across the year groups found that the marks achieved on the reasoning papers were mostly obtained from calculation-heavy questions that did not require any explanation of understanding.
So my priorities were two-fold: to develop the confidence of teachers to deliver a reasoning-rich curriculum, and to increase pupils’ access to reasoning opportunities.
I didn’t want to introduce anything that could be perceived as a “bolt-on”. It can be overwhelming for staff to feel like there are many changes happening at once – particularly if they can be seen as a threat to teacher workload – so I made sure that the initiative concentrated on refining and improving planning and delivery.
I focused on the year team leaders and the teaching and learning teams, as they were in the best position to drive these changes and to monitor the outcomes. I needed to persuade staff that reasoning should be more than a mastery or stretch activity for children so I set up some initial meetings to share my data observations, get their feedback and ask them to suggest strategies for increasing reasoning opportunities in maths.
To develop teacher confidence, I used five hours of allocated twilight INSET sessions, spread across the autumn and spring terms, to challenge staff understanding of reasoning. I used some of the more difficult SATs questions from the previous papers and encouraged staff to explore a variety of methods using manipulatives and language to explain these. I challenged staff ideas of what reasoning looks like in the classroom using games that were focused around the development of language.
Bringing reasoning into the classroom
I agreed with year team leaders on how to incorporate reasoning opportunities into lesson planning and delivery. Discrete reasoning lessons that focused on the development of language and a reasoning success criteria were introduced to each unit of maths. Children at all stages of their learning were taught to structure their answers and given opportunities to orally rehearse and to challenge their own ideas and the ideas of those around them.
I encouraged teachers to create a maths vocabulary display with their classes that focused on reasoning language. To introduce pupils to the reasoning success criteria and speaking frame we used the A.P.E model (answer it, prove it, explain it). I adapted A.P.E stickers that I had used previously so that pupils would have a visible and familiar reference point for their reasoning. Alongside the explicit reasoning lessons, the A.P.E stickers in their books indicate to pupils when they need to use their success criteria and shared language and reasoning skills to further explain and justify their answers.
To support staff, I provided numerous examples and a bank of resources, including the NRICH activities, so staff would be confident delivering these in class. Games such as “odd one out” presented children with three different numbers, images and shapes then asked them to use mathematical vocabulary to decide which should be the odd one out and provide justification as to why.
We used variations on language-based games such as 21 questions, true or false and a place value game where children write a number on their whiteboard and play the yes or no game (in which their partner can only answer yes or no) to work out the number. Staff engaged with that activity in particular as they noted real improvements in the acquisition of place value understanding as children began to work out specific questions to shorten the number of yes and no questions asked.
Teacher and pupil impact
Teacher confidence in delivering a reasoning rich curriculum is starting to emerge and there were clear improvements in our spring and summer term assessments. Across years 3 to 5 the average score of 36 per cent on the reasoning papers increased to 39 per cent. It is still early days and as teacher confidence continues to increase I expect scores to rise steadily across the academic year.
The year 4 team was particularly successful at implementing the reasoning curriculum, and the team reported a noticeable difference in the ability of children to speak using the language of reasoning and to challenge and explain their ideas and the ideas of others.
Book monitoring showed that there were clear opportunities for children to wonder, communicate and explore particular concepts and children were clearly being encouraged to discuss and write their ideas more frequently.
The most significant result we saw was the surge in confidence among the children. In the summer assessments and key stage 2 SATs papers, all teachers in all groups reported that pupils were attempting and completing the harder questions compared to previous years and the autumn term assessments.
While our key stage 2 SATs results remained the same as previous years, this kept us in line with national average and the number of children obtaining “working at greater depth” doubled.
I was extremely pleased with how well staff bought into the initiative and, most importantly, pupils are now far more vocal and confident at justifying responses in maths lessons. It will be great to see this develop further across this academic year as we have more INSETs planned and staff will continue to share their expertise with each other.
- Kirsty Munns is a trainee school leader at Wilbury Primary School in north London and a graduate of the Future Leaders programme run by Ambition School Leadership.
Further information
- Ambition School Leadership is a charity that runs middle and senior leadership development programmes in England to help school leaders create more impact in schools that serve disadvantaged children and their communities. Visit www.ambitionschoolleadership.org.uk
- NRICH maths materials: https://nrich.maths.org