ResearchEd National Conference 2025

The first Saturday in September has become a somewhat annual tradition for me to take down to Parliament Hill School in London for the ResearchEd National Conference. This year I was joined by two of my fellow National Education Leads; Ash Morris, who leads secondary science; and Sarah Hutson-Dean, who leads primary science, who I am delighted have contributed their experience to this blog as well.

Me, Ash and Sarah meet in London

Like many others, we started the day in the session with Professor Becky Francis CBE, hoping to maybe get a few advance insights into what might be reported when the Curriculum and Assessment review lands at some point before Christmas. I don’t think there was anything that isn’t already in the public domain, but there were some interesting points made, including the results of the 2024 parents survey indicating that the majority of parents think that the attention given to both core and “non-traditional” subjects is about right in schools, and that academic subjects featured in the top five list of things that parents and pupils at KS4 would like to spend more time on (alongside employment and interview skills, creative thinking and problem solving projects, digital skills, and finance and budgeting). Professor Francis did confirm that the review will examine GCSE volume and time spent in examinations, look at how to facilitate greater choice of subjects whilst maintaining the breadth of curriculum offer that is a key strength of our curriculum. Another key issue the review is looking at is disadvantage, where gaps are still significant, with a commitment to ensuring that “every young person can see themselves in the curriculum, and that it challenges discrimination and extends horizons”. Climate science, digital literacy and financial education were also mentioned as being needed to help young people navigate the opportunities and challenges they would face in the future. Professor Francis echoed the detail of the interim report when she highlighted there was a lot to celebrate about our education system, and many things that we do very well, and so “evolution not revolution” was what the review was looking to achieve.

After this it was my time for my own session on front-loaded feedback in maths, which I gave to a surprisingly large audience (given the other speakers on at the same time). The session seemed to go down well (I got top ratings from everyone that filled in the feedback form) and people coming to see me later to say that they had enjoyed it. 

Me in presenter mode!

Of course, the test for any session is whether people make use of it afterwards, so if you were there and you do incorporate the ideas then please let me know!

Oracy and literacy have been big on the agenda in recent months, so I decided to go and listen to Sarah Davies’ talk on using oracy to support literacy fluency in the next session. Hearing about Sarah’s journey after taking responsibility for literacy in her deputy head role was fascinating, and her commitment to ensuring that each child was treated as an individual and received the right pathway of intervention for them was inspiring. She rightly pointed out that if kids are not able to access exam papers, then all the content knowledge in the world won’t help them – and I was surprised to see maths exams being quite high up in the literacy demands (third only to English and Geography). One thing that Sarah shared that really resonated with me was a conversation she had with one of her staff members about why their top performing pupils were not able to secure places in top universities despite their excellent academic record, because they did not possess the oracy skills necessary to do well at the interview stage – something that would clearly hamper them well beyond applying for universities.

From Sarah Davies’ presentation

During this session, Sarah and Ash were back in the sports hall for the session by Peps McCrea and Dr Jen Barker. Here are Sarah’s thoughts on the session:

Peps McCrea and Dr. Jen Barker shared a powerful message: inclusive teaching is effective teaching. With educational outcomes declining and many teachers feeling underprepared to support children with SEND, they unpacked five drivers of system failure. Yet their talk was full of hope. They reminded us that how we learn is far more similar than different. Our shared cognitive architecture means we all benefit from strategies that secure attention, provide high-quality feedback, and establish strong routines. By designing lessons to be as accessible as possible for the widest range of pupils, and keeping adaptations minimal so every child engages with the same learning, we can lift outcomes without sidelining teachers. Practical strategies like highlighting key sections of text, chunking information with guiding questions, using choral responses, encouraging pair talk, and making the most of mini-whiteboards showed how small, thoughtful choices can have a big impact!

Sarah (with Ash) followed this up by listening to Professor Rob Coe talking about teacher expertise, and said:

Dr. Rob Coe’s session was a brilliant reminder of just how much teachers matter. He showed us that the impact of great teaching goes way beyond test scores, shaping students’ chances in life and even their wellbeing. So what sets great teachers apart? It’s a mix of deep subject knowledge, clear explanations, strong routines, supportive relationships, and lessons that really make students think. Rob shared the ‘Great Teaching Toolkit,’ which breaks this down into four areas: knowing your content, creating a positive and motivating environment, managing the classroom so learning time is maximised, and designing tasks that stretch thinking. One point that really stuck was that just clocking up years in the classroom does not guarantee expertise. Without the right feedback and focus, we can plateau. His challenge to schools was clear: if we want teachers and pupils to keep thriving, professional growth has to be a priority.

After a gorgeous lunch in the speakers lounge and a trip round to the farmer’s market, it was time for the afternoon sessions. The buzz recently with my fellow Twinkl National Education Leads has been around the recently released writing framework so I was very interested to go along to Clare Sealey’s session talking about it. Clare shared some great advice from her work on the sector panel and what the writing framework does and does not mean schools need to consider or do.

 

Whilst I was hearing all about the writing framework, Sarah and Ash were delving into the world of adaptive teaching and its links to cognitive science. Here is what Ash had to say about the session:

The standout session of the day for me was delivered by Jade Pearce, Trust Head of Education for Affinity Learning Partnership, on ‘Adaptive Teaching x Cognitive Science.’ Having always been passionate about the science of learning and committed to teaching in an evidence-informed way, I expected to leave with reassurance that my practice was on the right track. Instead, I came away with fresh ideas and practical adaptations, particularly around the ‘I do, we do, you do’ model for introducing new content, as well as approaches to questioning. Rather than relying solely on questions to check for listening or recall, the session highlighted different styles of questioning and their purposes, which added real depth to my thinking.

The final session I attended was led by Adam Robbins, unpacking the overly simplistic ideas that seem to exist in areas of the profession about motivation, particularly the idea that extrinsic motivation is a “bad thing”, and autonomy being absolutely necessary for motivation. Adam pointed out that there are plenty of times that people are motivated by extrinsic factors over which they have no control, but that these don’t necessarily lead to lack of intrinsic motivation, before unpacking the research that shows that there are levels of extrinsic motivation that tend to come with maturity as well as how extrinsic factors such as competence and relatedness can “fill the gaps” when intrinsic motivation might be lacking. A simple example is marking pupil, which has to be done (low autonomy) but that teachers might be motivated to do because they think it will make them more able to support pupils (competence) or because it feeds into a wider department plan that they are committed to (relatedness).

Outside of the sessions, it was great to catch up with old friends and colleagues like Kat Howard, Kris Boulton, Mark Lehain and David Faram. This is part of what keeps me coming back to ResearchEd; the combination of hearing about things that are really working for people in schools, insight into the latest thinking that might impact education, and the chance to touch base and interact with people who care about education as much as I do just cannot be beaten!

Ash agreed that it was a great day, saying:

Aside from the sessions themselves, it was inspiring to be surrounded by so many dedicated and passionate people, all giving up their Saturday in the name of research! A personal highlight was spending time with my colleagues, Pete and Sarah, and enjoying some excellent Greek food from the nearby farmers’ market at lunchtime, with Pete leading the way.

Is anyone else tired of GCSE maths bashing?

With the latest GCSE maths results showing a slight decrease in the percentage of pupils achieving 4+ the calls are coming again across social media for the GCSE maths to be “revamped”. In the main, this is about making sure the content is more “relevant” to everyday life or the world of work, with people saying that GCSE maths is no longer “fit for purpose” or that the content is a “waste of time”. Frankly, this is just wearing a bit thin for me now.

I am sure I have written this before, but one of my favourite interview questions to ask prospective maths teacher candidates was always, “A child asks you “why do I have to learn trigonometry, I want to be a hairdresser?”, how do you respond?”. Typically, responses to this fell into two categories:

1. Candidates would attempt to find some tangential link between knowledge of trigonometry and the ability to cut people’s hair to a style that they have asked for.
2. Candidates would move the discussion away from the particular content, talking about skills problem-solving and logical thinking that are developed through the study of all types of mathematics.

I have some affinity with the second of these responses but I also know that (a) transfer of these skills across domains is not something that generally happens (i.e. learning to solve mathematical problems doesn’t necessarily transfer to being able to solve non-mathematical problems) and (b) the skills-based argument is not a great one for justifying the study of particular content or a particular subject – is there no other way that pupils could develop these skills? The answer I hope for, which I rarely received, is the truth – that you won’t use trigonometry as a hairdresser and, in fact, most of you won’t use much of what you learn in school (be it maths or otherwise) outside of school. This is not the point of schooling. The purpose of schooling is to highlight precisely that knowledge that humanity has accumulated that pupils wouldn’t encounter in their everyday lives; in other words, to become educated about the world and the scope of human thought. When it comes to maths, this means an age and stage appropriate insight into the world of abstract human thought, where we can reason and generalise beyond specific contexts or problems to probe the deeper uniting structure underneath.

Now, let me reassure you, this question was not a deal-breaker for me in any stretch – a poor answer to it has never cost someone a job in my departments. The question is asked so that I could get a sense of the candidate’s own values when it came to teaching mathematics, and how they could communicate those to pupils. Are they someone whose first thought is to try and make it relevant, make it useful, or simply celebrate that learning trigonometry is simply about becoming more learned. Want to be a hairdresser? Fine. Be a hairdresser that knows trigonometry, that can appreciate poetry, that understands the importance of the 5 pillars in Islam; simply because knowing is better than not knowing. Understand that being educated is a desirable state not because it is useful (although it certainly is), but because it is part of the human experience – we have large brains precisely because we are supposed to learn, and grow in the learning.

The study of mathematics is the study of a subject that has been at the forefront of human thought and innovation for over 4000 years. Advances in mathematical knowledge and understanding have shaped humanity’s transformation throughout that time. It is one of the great disciplines of human intellect and experience, and it is absolutely right that a core and foundational knowledge of this should be passed onto every child, whereas in previous generations it might have only the domain of the privileged few.

And the truth of the matter is that when it comes to 16-year-olds, this works for the majority. The pass rate at 4+ for maths is not outside of the norm. It is higher than that for English Language, Spanish, Computer Science, Geography and History (among others). Even at 5+, the government’s “strong pass” benchmark for comparing internationally, over half of 16-year-olds achieved it. Of course I would like this to be much higher, but that is not necessarily the fault of the qualification. The GCSE specification does what it is designed to do – state the knowledge that is deemed to be the core and foundational knowledge in the subject, and then assess the level at which pupils have acquired it. We can and should discuss whether the assessment does this in a way that has consequences, like driving certain practices that are not in the best interest of learning mathematics, and whether there are alternative approaches we can take that would lessen these consequences. We can also discuss, as with any qualification, what the core knowledge and skills should be that are included. But for mathematics the driving force in this discussion should not, in my opinion, be one of utility. Rather, it should be about whether the knowledge and skills provide the necessary insight into our discipline. Part of this will be about applications, sure, but this should be examining the applications of the knowledge deemed suitable, not looking at which knowledge is required to secure particular applications.

Don’t get me wrong, I have real sympathy for those that don’t secure the grade 4. More should absolutely be done to improve their experience of mathematics learning and assessment, and to support them with alternative ways to demonstrate and gain recognition of their knowledge. I would also support an analysis of the role that GCSE maths has in being a requirement for future pathways for study and employment to ensure that it is only used when absolutely necessary. It doesn’t make sense to me that certain job roles, apprenticeships, or further study options require a level 2 maths qualification, or that progression in those fields hinges on whether a person achieved this by the time they hit 18. I understand that part of the reason that maths comes under this increased scrutiny compared to the other subjects I listed is its status as a core subject and gatekeeper to many of the future opportunities that pupils might pursue. And whilst I think the status of core subject is justifiable based purely on the impact that mathematics has on the lives of human beings, everyday or otherwise (and even when it isn’t recognised), I think the gatekeeper status is one that could be re-examined for a lot of cases.

It is easy to say that GCSE maths isn’t fit for purpose, or that it needs to change in order to accommodate more students. What is harder, but in my view ultimately more beneficial, is to accept that GCSE maths should assess a breadth and depth of mathematical ideas, and that different pupils will secure these at many different levels, and yet to continuously and tirelessly work on improving curriculum coherence, pedagogy, approaches to assessment, and the wider societal issues so that more pupils are able to reach these benchmarks. For me, this is what the mathematics education sector, and wider educational sector, should be focusing their attention on, and what I hope the upcoming curriculum review will help to make a reality.

On Horizontalness and Verticalness

Over the last couple of days, I have been having a very interesting discussion with James Dixon, a numeracy learning specialist from Australia, about the use of vertical versus horizontal representations. It stemmed from James’ post on LinkedIn which included an article (that is definitely worth reading if you work with primary age mathematics learners, and that some secondary teachers may also find useful) about things to consider before introducing “vertical addition”; which we might call in the UK the “formal addition algorithm”.

It was question 2 that got me thinking about the role of horizontalness and verticalness in early addition and subtraction calculations – “Should addition number sentences be represented horizontally before vertically?”. The main thrust of the article here is that the rigidity brought in by teaching vertical addition limits pupils’ use of, and receptiveness to, alternative strategies (as well as some interesting research in point 3 about single-digit versus multi-digit conception). This made me wonder, “Would this still happen if all approaches to addition and subtraction were modelled vertically?” So instead of writing:

3 + 5 = 8

We would write:

   3

+ 5

    8

Even when first introducing learners to the concept of addition (and similarly for subtraction).

Of course, I don’t just mean writing vertically in the abstract, I also mean modelling vertically with our concrete and pictorial representations, so instead of this:

We would show this:

Instead of this:

We show this:

Instead of this:

We show this:

(I considered having the number line increase going downwards there, but I thought that would be a step too far for most people – although see my note on variation later on).

If we did this, right from the very beginning of pupils learning about addition and subtraction, would this stop some of the issues that James highlights in his article?

Now, of course, I don’t know the answer to this having (a) never worked with children that young in an educational setting, and (b) not being aware of any school or other educational setting that has been this intentional about the orientation of the representations they use rather than just their choice of representations themselves. However, I can see some potential benefits as well as at least one potential drawback (although I may not be seeing all of the drawbacks given my unfamiliarity with the age range where this is first taught).

The obvious benefit is that the writing of all sums then mirrors what happens when we start to use the addition/subtraction algorithm, meaning that (at least potentially) this transition is less marked than it perhaps currently is when pupils move from mental strategies for addition and subtraction to written calculations involving algorithms. If, for example, I have learnt that I can sum 9 and 5 using a strategy such as:

Then this at least could mean that when I come to move onto the algorithm, I am already familiar with writing sums this way and so it is only left to understand why I start with the ones column and progress up the powers of 10. Even if I am working with larger numbers but using a “decomposition” strategy rather than the algorithm, such as carrying out 342 + 251, I can model these vertically rather than horizontally:

Which has the potential added benefit that this mirrors how a number like 251 would be decomposed on a Gattegno or place value chart.

This, however, is also the source of the potential drawback that I can see – would setting out the symbolic record for every addition and subtraction strategy vertically rather than limiting verticalness to the algorithm risk confusing these approaches. My heart wants to say “no” provided that these strategies are fully secured and embedded using appropriate concrete and pictorial representations, but my head tells me that things are rarely so simple.

There is also the nagging bit of me that reminds me that I am writing the sums vertically from top to bottom, but using the number line vertically from bottom to top. I have a strong feeling that this disconnect might cause issues, although I also think that we should be varying the orientation of the number line regularly, as well as the direction of increasing value, lest pupils form the misconception that this is an essential rather than non-essential property of the number line. Variation theory tells us that deliberately varying the essential and non-essential features of a concept is part of what leads to a deeper understanding of the concept and so I can see how, at an appropriate point, it would actually be beneficial for learners to see and work with number lines that run both horizontally and vertically, and where the direction of increasing value is up, down, left and right. This could potentially be done after the number line is introduced, completely separately to its use in helping to model addition and subtraction strategies, so that by the time pupils see a number line paired with an addition or subtraction approach they are comfortable working with number lines in all configurations and so having a number line that increases in value in a downwards direction would not be a particular barrier to using it to make sense of the strategy.

Another possible benefit to this way of writing calculations would be the use of the equal sign. It is well documented that pupils often harbour misconceptions about the number line being an operator or instruction meaning “provide the result of”, which is due in part to them answering endless questions of the form “3 + 4 = 7”. Whilst recognition of this, and possible remedies for it (such as writing calculations leading with the equal sign, e.g. 7 = 3 + 4”) are becoming more prevalent, the above vertical representations have the benefit of using the equal sign in a way that shows the calculations are equal rather than simply the result. In fact, the use of the equal sign is actively avoided for the statement of the result of the calculation. This should then help to reinforce the meaning we want pupils to take about the equal sign, namely that it tells use about the relationship between different mathematical expressions.

Finally, it would potentially solve some issues when it comes to working with algebraic expressions. As a secondary teacher, I know that there is often confusion that arises when simplifying expressions such as 3x + 5 – 2x + 4, with pupils often subtracting incorrect terms in the expression. Of course, a good manipulative or representation helps enormously with this sort of thing, however if the first thing a pupil thought to do when faced with something like this was to re-write it vertically, like:

    3x

+ 5

  – 2x

+ 4

This might help pupils with identifying more clearly which terms are added and which terms are subtracted from the total.

Like I say, there might be drawbacks I haven’t spotted here, but absent someone pointing them out to me I think there is enough in this for teachers to at least consider changing their way of symbolic recording of calculation from a default horizontal to a default vertical, and would be very interested to hear about the experiences that people have if they do (or already have).

My morning routine and a nice maths prompt

I have a somewhat quirky morning routine. I think it started as a way to occupy my mind during my morning commute. I don’t drive a car and so for the last 11 years of my teaching career, all spent in the same school, I used to use a combination of roughly 40 minutes walking and an eight-minute train journey to get to school each day. I like to be up for quite some time before I have to be active – to ease myself into the morning – and so I used to get up at 6 am, leave the house around 7:15, and arrive at school shortly after 8 am. During that time before I left the house, and then during the journey to school, I run through a series of games on my phone with an almost religious regularity.

It starts with the daily Wordle, then the daily Quordle (both the Classic and the Sequence, as well as the Weekly when I solve my first Classic of the week). Then I move onto the maths games, starting with the Ooodle, the OoodleMax and the Time Square grid, followed by the Nerdle. Then it is onto geography, with the Worldle (and its different rounds), the Statele, and then the Globle. I finish off with the Daily Sudoku, and then have recently added the Countle at the end. Since leaving teaching I have continued to play these games as part of my morning routine before starting my work from home.

The reason I mention all of this is that my attempt at the OoodleMax today prompted me to consider a nice mathematical relationship, that would make an excellent prompt for learners that could be used at multiple levels.

This was today’s Ooodle Max:

The goal is to use the numbers from the keypad on the right-hand side, at most once each, to fill in the blanks and make the target. Like other Wordle type games, numbers go orange if they appear in the calculation, but are in the wrong place, green if they are in the correct place in the calculation, and grey if they are not used at all. This was my first guess:

Having used 12 and 15, and without really thinking about it, it occurred to me that to be close I should use 13 and 14 in the multiplication. I then knew the “2” would have to be the divisor of the division, so I then set about figuring about what the dividend would be. This was my second guess:

I was lucky in that I got the 13 and 14 the right way, but what struck me is the relationship between the value of 13 × 14 and 12 × 15. It reminded me of the result that I knew about, which is that the square of an integer is always one more than the product of its adjacent integers. This is, of course, easy to prove mathematically for learners that can expand binomials. Given three integers  then we have that . It got me thinking that there must be a wider pattern to this, which of course there is; given four numbers , the product  and  (so a difference of 2), and then given  we have  and  (a difference of 3) and so on. There is an obvious symmetry here, as we get further away from a central value the difference between the products increases by one and starting the list each time with  makes this relatively clear each time.

The algebraic exploration of this is clearly a nice activity for those that can access the algebra, particularly proving the overall general case. However, it also struck me that these sorts of related calculations, and the general structure underpinning the relationship, can be explored without the need for algebra, using concrete manipulatives:

These are representations of 2 × 3 and 1 × 4, and then 4 × 5 and 3 × 6 – following the same pattern as 13 × 14 and 12 × 15. The question then becomes how is the red array related to the yellow? It is a relatively simple matter to see that we can move counters from the bottom row of the yellow arrays and attach them to the side to create the red arrays, but we will always have two counters left over.

It should also be within the capabilities of many learners to reason why this must always be the case; the number of rows in the red array is two less than the number of columns in the (original) yellow array, and so when we move counters from the bottom row of the yellow array to the side to extend the size of each row, we will always leave two behind. This sort of argument can then be generalised further to any of the related calculations.

So, what would the task look like? I haven’t decided fully yet, but as an inquiry prompt it might be something like this:

Calculate the following:

        (a)   2 × 3 and 1 × 4   

        (b)   3 × 4 and 2 × 5

        (c)    4 × 5 and 3 × 6

        (d)   13 × 14 and 12 × 15

What do you notice about each pair of results?

Could you write down other pairs that would produce the same result?

Can you explain it?

Can you find other pairs of calculations that always follow a different rule that is like this rule?