The HfL primary maths team are privileged to be able to work with teachers across hundreds of schools. It has been a joy to be back in the classroom after periods of remoteness – teaching real live children and having face to face conversations with teachers and leaders.
Teachers have been reflective and proactive in their response to the children they teach. Their feedback has been that our conversations have supported clarity around what is happening in their schools and enabled precise identification of the assistance needed to address issues noticed.
As a team of primary maths advisers, we have been able to consider these individual conversations and identify wider themes. This blog aims to share one element that we are noticing with teachers and leaders so that you can consider whether this is relevant to your school too.
One reflection that we have had with many schools is around phonics. We have been asking - Is there a phonics focus in mathematics?
Ridiculous, you might cry! Of course, there is no phonics focus in mathematics. Phonics are a primary element of teaching reading. Why would I even mention phonics as a primary mathematics specialist?
I’ll tell you why….
Many of the schools that I work with are currently heavily focused on developing their teaching around early reading. This is not a focus I disagree with. As my colleague, Kerry Godsman, put it in her recent blog, supporting leaders to review reading and pupils “developing the appropriate skills is crucial to accessing all other subjects and establishing a love of books [which] is something we all aspire to”.
It would seem right that because of this reading focus, there has been a heavy emphasis on developing the teaching of phonics. However, there seems to be much less emphasis on the foundations for mathematical success - what you might consider ‘the phonics focus’.
I suppose as mathematics advisers, we have been trying to unpick with schools, what has been helpful and effective in their focus on early reading, to be able to apply this to developing security in mathematical foundations. Some things that we have considered together include:
- to what extent do all teachers know what mathematical foundations are?
- how and when do teachers identify missing foundations?
- how are all staff enabled to address identified foundational gaps?
- to what extent are subject leaders working strategically to secure mathematical foundations across the school?
Do all teachers know what mathematical foundations are?
I would suggest that in many schools I work with, understanding key mathematical foundations is an area that is currently being developed within Early Years and KS1. Whether this is because many schools I work with are currently developing their use of Essential Foundations for Counting and / or Reception ESSENTIALmaths and are focused on how connections build into the primary curriculum or because there seems to be a keener external eye on how learning builds from Early Years foundations, I am not sure.
What I am sure about is that, currently, there seems to be much less clarity around mathematic foundations than around phonics foundations and this is particularly obvious across KS2 teachers. As I say this, I recall as a Year 6 teacher, that phonics training was a revelation to me in terms of identifying not only why some of my children were struggling so much (in both reading and spelling) but also how I might take action to support gap closure. It is essential that all teachers are similarly aware of key mathematical foundations.
For schools, this brings leaders to the reflection: what can be done to ensure that that all teachers know what the mathematical foundations are and how they build?
The intention is to strengthen teacher subject knowledge to enable gaps to be spotted early so that these can be addressed and to ensure that foundations are secured effectively enough to build on. Schools are approaching this in a variety of ways, with most agreeing that whole-school training in some form or other has effectively started the conversation, enabling year groups to see their part in the learning progression and crucially, to see how learning builds from its earliest foundations.
Until teachers are aware of the nature and importance of learning around pattern, classification, comparison and subitising (group recognition), number conservation and counting skills in securing a strong grounding in number (and therefore supporting longer term mathematical learning), they will be unable to know what gaps to look for or know that it is key to look for them.
It is interesting to reflect at this point on the number of times that EY staff have meetings separate to their primary colleagues. Whilst I understand that sometimes there are phase specific foci, I have often reflected that all children need the foundations and therefore, surely our most crucial resources are our EY colleagues. As an example, I recall an interesting conversation which developed in a recent INSET around developing reasoning which started when we reflected as a staff on what reasoning was and when we felt that we developed these skills within school. Reception staff quickly made links to the characteristics of effective learning and were able to share examples and this enabled focus on how skills in working mathematically might be developed.
How and when do teachers identify missing mathematical foundations?
A phonics screening check can give indications as to foundational gaps in understanding that can limit progress in reading but there is no phonics screening check in mathematics!
Before I run for cover as you throw things at your digital device, I am not suggesting that we need a phonics screening check in maths or even that the phonics screening check is the only time that we look for gaps in phonics foundations or indeed that phonics are the only foundations necessary to develop readers. However, the phonics screening check is one moment when a very precise assessment is used to observe what a child can decode and can support identification of specific gaps in understanding. What might a similar moment look like in maths?
We know that children without firm foundations will be limited in their progress later, but a particular problem in maths is that children can find workarounds which enable them to get the right answers without having secure foundations. Unfortunately, over time these ways of working lead to inefficiency, reduced flexibility and as complexity increases, more opportunities for mistakes and therefore inaccuracy. In fact, the opposite of the mathematical fluency that we are aiming for. Looking for missing foundations will require more than looking for incorrect answers.
When discussing this with schools, we often consider foundations in additive calculation progression and identify what a chid would do and say as they are at different points along the journey to fluency.
When asking, “How many?”, it is not the answer 9 that will tell us how fluent a child is in the foundations of mathematics; it is the route by which they move towards 9. So, when considering the question, we identify clues and elicit how these can be spotted or pupils prompted to explain further to establish how they are working. Essentially, we draw out the progression of responses that indicate different points along the journey to fluency:
- does the child “count all” incorrectly, either missing a dot from the count or double counting?
- does the child “count all” correctly using 1:1 correspondence?
- does the child recognise patterns within the total and use this to “count on”? For example, recognising the 5 and counting on 4 more.
- does the child recognise the numbers within numbers and so see 5 and 4 and identify this as a known fact totalling 9?
These are all steps in the progression towards developing mathematical fluency in mental calculation. The key will be identifying where pupils are on this journey.
How are all staff enabled to address foundational gaps?
Knowing what the key foundations are is one step; knowing how a child will behave at different points along the learning progression is another. But perhaps the most crucial step is that staff know what they need to do to address identified gaps and are enabled to do this.
This may seem like the simplest part of the puzzle – surely if the gap is known then teachers will know what to do to close it.
In my experience, this is not always the case. I have worked with many teachers recently, who can see that children have gaps and may even be able to identify what the gap is but are not sure how to deal with it. I think that this is because, in maths, we often see the symptoms and don’t necessarily return to the cause to address the issue.
For example, teachers I worked with recently identified that pupils in LKS2 were struggling to calculate mentally. They were able to identify that children didn’t have recall of number facts within 20 to enable them to develop efficient calculation strategies and that this was limiting success, but what they found challenging was knowing what this required them to do.
Weak recall of number facts is the symptom, and the root cause is weak number sense – children don’t know how numbers are related to each other. This becomes about the teacher knowing the progression in learning towards developing secure number sense. In addition, teachers are often challenged in terms of how they make time and space to take the actions needed.
Where teachers feel challenged to teach age-related content, there is bound to be pressure in finding this time and I find myself trying to convince staff that it is truly worthwhile and helping them to identify where to make this time and how to make appropriate connections to their age-related curriculum. It is helpful to support teachers to recognise that they are part of the wider team in the child’s development – taking time to address foundational gaps now will enable much greater chance for success and reaching age-related ‘standards’ across their mathematical journey. Not to mention the impact on pupil success and perceptions of themselves as mathematicians.
Thinking back to my initial phonics focus, I have recently seen real drive within schools to close phonics gaps, and highly focused teaching sessions being delivered with real skill by teachers and support staff. Many leaders share with me whole staff training that has supported both teachers and support staff to deliver high quality phonics teaching within lessons and interventions. For maths subject leaders, it becomes about considering how to enable similar focus and teaching for children with mathematical gaps, particularly as we have already mentioned that some children seem to be “coping” with their gaps and so they may be harder to notice.
To what extent are subject leaders working strategically to secure mathematical foundations across the school?
Examples of the actions that I am identifying with schools are:
- identify the extent of the problem: is this about isolated pupils, cohorts or systemic?
- provide subject knowledge training to staff so that they know key mathematical foundations and how learning progressions build
- provide training to enable staff to precisely identify foundational gaps
- provide support and challenge to ensure that teachers are securing mathematical foundations for all children
- provide whole school training to support effective enactment of new developments and to ensure fidelity to what is intended as an outcome and its implementation
As a class teacher, it is well worth making the most of opportunities to have conversations with children about ‘how’ they arrive at their answers. Listening to children articulating their thoughts provides valuable insight into their understanding and potential gaps they may currently be expertly ‘covering’.
As a subject leader, it would be worth considering the extent to which all teachers in the school understand the progressions in learning through the Early Years and primary mathematics curriculums. Strong subject knowledge and understanding of effective pedagogy is key in enabling any gaps to be closed, leading to more confident learners.
If this is something that you would like support with, see here for further details and to enquire about face to face or remote consultancy and training:
References and further reading:
 “Reviewing reading: guidance for English leaders” Published: 28 September 2021