The technical details of the 2023 progress model for KS2 have now been published by the DfE. The model is broadly similar to the 2022 model, which I blogged about here. Every year there are minor adjustments to the ‘expected outcome’ for each Prior Attainment Group – these adjustments are down to slight changes in the national average outcomes each year. 

The more significant change affecting the model this year relates to changes in the way children were assessed at KS1 in 2019, compared to 2018. (The 2019 KS1 cohort are of course the children who have just completed KS2.) The differences at KS1 relate to how children were assessed if they were working below the ‘Working Towards’ standard. 2019 saw the introduction of the 'Pre Key Stage Standards’ (PK1 to PK4 at KS1) and the removal of P-scales from P5 to P8. In constructing a model for calculating progress from KS1 to KS2 in 2023, scores needed to be assigned to each of these pre-key stage standards so that a measure of ‘prior attainment’ could be produced.

The range of scores used then for converting KS1 attainment into a prior attainment score for calculating KS2 progress now looks like this:

For children with SEND assessed using P-scales, the points range from 0.25 (P1i) to 1.75 (P4).
As per previous years’ models, the prior attainment score is found by converting a child’s teacher assessments in reading, writing and maths into scores, from the above table, and then combining those three scores into one score as follows:

• calculate the average of their reading and writing scores, to give a score for English
• calculate the average of this English score and their maths score

Based on this ‘weighted average’ score, children are then allocated into a Prior Attainment Group (PAG) and this forms the input measure of the KS2 progress model (in all subjects). 
The full details are available in the DfE’s technical guidance, but here are two simple examples:

Example 1 – a child who was assessed at EXS in all three subject areas at KS1

Their combined prior attainment score is 8 points.
In 2023, the national average scaled scores for children with a prior attainment score of 8 points were as follows:

This means that, to achieve a better than average progress score, children with this prior attainment need to score above those figures. If they achieved a scaled score of, say, 107 in reading, their progress score would be +1.62 (the difference between 107 and 105.38). If they achieved a scaled score of 103, their progress score would be -2.38.

These average outcome figures are only marginally different from those in the 2022 model (effectively the same, to the nearest whole number).

Example 2 – a child who was assessed at GDS in all three subject areas at KS1

Their combined prior attainment score is 10 points.

In 2023, the national average scaled scores for children with a prior attainment score of 8 points were as follows:

In this example, to achieve a positive progress score, the child would need to achieve a scaled score of at least 114 in reading or 113 in maths.  These are both 1 scaled score higher than was the case in the 2022 progress model.

Understanding the way this works for writing is a bit more complicated, as I discussed in the blog about the 2022 progress model. 

I have produced a free downloadable attainment & progress calculator tool (scroll to the bottom of this page to download it). Using this tool you can easily see for any pupil, by entering their KS1 attainment and either their raw scores from the KS2 tests or their scaled scores, what the ‘expectation’ (i.e. national average outcome) is in the 2023 model. The tool then calculates each pupil’s progress score and produces a cohort-level average progress score. It will also indicate whether this score would be deemed to be ‘statistically significant’ (more on this below).

A cautionary word about analysing this data

It is always best to start from the view that data can raise interesting questions and form the starting point of a discussion, rather than jump directly to conclusions from the data. Data tends to raise more questions than it answers. 

The methodology used to calculate a progress model inevitably carries a bit of ‘statistical noise’ or margins of error, as it is based on what has happened ‘on average’ for different groups of pupils, but no child actually behaves in an ‘average’ way. Every child is unique and complex, and there are bound to be day-to-day differences in how they perform in an assessment activity. So, there may be children whose progress scores come as a surprise – maybe they performed better than you might have expected on the day of the test, or maybe the opposite. At cohort-level though, these variations (some positive, some negative) would hopefully mainly cancel each other out. It is when you find that a large proportion of learners within a cohort appear to have underperformed that we might begin to notice this as a pattern and ask questions about what happened.

This is where statistical significance can help us. As the size of the cohort increases, variations from the norm become more meaningful and might become more worthy of exploration.

It is important to be clear about what is meant by ‘significant’ in this context.

‘Significantly’ does not mean the same as ‘very much’ and ‘significant’ does not necessarily mean ‘important’

In common parlance we might use ‘significantly’ to mean ‘very much’ or ‘noticeably’, e.g. “it is significantly hotter today than yesterday”. In the language of statistics, ‘significantly’ has a more precise meaning than that – it is better to think of it as expressing a degree of confidence in the data.  If a progress score is statistically significantly above or below the national average, what that means is that we can say with a high degree of confidence that progress in that school is above or below the average.  It doesn’t necessarily mean that the progress score is a lot better or a lot worse than average, just that it is better or worse and that we can be pretty confident in that assertion. (95% confident, to be precise – although even a 95% certainty does still mean we will be wrong 5% of the time.)

Likewise, significance is not the same as importance. If something in the data is deemed to be statistically significant, that might mean it is important but, as the song goes, ‘it ain’t necessarily so’. (And something could be important even without being statistically significant.) 

It is for the users of the data to interpret and decide (taking into account all their other contextual knowledge about a school and that particular cohort of children) whether something is important or meaningful. For example, we might observe a significant drop in results from 2022 to 2023 – but that drop might have been entirely expected based on the two cohorts being very different, so we wouldn’t necessarily be concluding that some radical action was required based on that one observation. 

So, what about next year and beyond?

This 2023 data will be the last time we see KS2 progress scores for a few years. Next year, the children completing Year 6 will be the children who finished Year 2 in Summer 2020, when statutory assessments were cancelled due to Covid. The same applies to those children who complete KS2 in 2025. So, in those years there will only by KS2 attainment data – no progress measures at all (as has been confirmed by the DfE).

2026 and 2027 will see a return to progress scores based on the sort of methodology that we currently have in place, i.e. based on children’s progress from KS1. But after that it all changes. The children currently in Year 2 will not be statutorily assessed at the end of KS1 and their KS1 attainment will not be collected by the DfE. This cohort of children all took part in the Reception Baseline in the academic year 2021/22, and that will be the input measure used to calculate their progress when they complete KS2 in 2028. (This is, of course, assuming there are no changes to national policy between now and then.)

It is perhaps worth taking this opportunity to remind readers that progress is always more than just a number. The published progress scores serve to give us an indication of how well pupils have made progress compared to the national picture, but these statistics are always a proxy for what really matters, which is the actual lived experience of children in that school: how well have they made progress through a well-thought-out curriculum, how securely have they acquired the knowledge and skills expected of them, to equip them for the next phase of education? Even in the years when we will have no published progress scores, these will still be crucial questions to explore. I wrote more on this in a previous blog, What do we mean by ‘progress’ and how can we reassure ourselves that pupils are making it?
 

Question: What do Albert Einstein, Chris Packham, Jazmin Scarlett, and Sarah Rankin all have in common?

Answer: All of them were pupils with SEND who have gone on to have outstanding careers in science. 

• Albert Einstein, Physicist, dyslexia
• Chris Packham, Naturalist & tv presenter, autistic spectrum disorder
• Jazmin Scarlett, volcanologist, juvenile arthritis
• Sarah Rankin, Stem cell biologist, dyslexia & coordination disorder
• For more information see: The Royal Society – Celebrating Scientists with disabilities

A classroom teacher looking over their new class registers for September may feel daunted by the prospect of meeting the individual needs of a large number of pupils with SEND in their lab. However, with the right challenge and support there might just be the next Einstein in the classroom!

The number of pupils identified with SEND has increased by 87,000 since 2022 in English schools. (ONS 22nd June 2023) In secondary schools alone this number has increased by almost 24,000. Numbers have increased for the 6th consecutive year and there are now over 1.5 million pupils identified with SEND ranging from the most significant and complex to comparatively minor in English schools. (Ofsted Research & Analysis: Supporting SEND). Most of these pupils attend mainstream schools and are entitled to a broad and balanced curriculum, which includes challenge, high expectations and builds aspirations. It is important to ensure that the curriculum is not made easier but that students receive the right adaptations to the curriculum and high-quality teaching so that they are able to access new learning.

How can we ensure that our delivery of the Science curriculum enables our pupils with SEND to be successful?

Helping students to break down science knowledge and tasks is a key step in supporting them to be successful scientists. Rob Butler (ASE) describes sensible strategies to manage cognitive load for pupils with SEND during practical work. Adam Boxer (RSC) talks about the benefits of the slow practical. Whilst recognising the need for individual risk assessment for pupils with SEND, (CLEAPSS guidance, G077) there are many similarities between the two approaches which suggests that strategies which improve outcomes for pupils with SEND will also improve outcomes for all pupils. Teachers should feel reassured that high quality teaching for students with SEND does not come at a cost to other students. 

The EEF (Education Endowment Foundation) has said “to a great extent, good teaching for pupils with SEND is good teaching for all.” They have identified five specific approaches, which are particularly well evidenced, as having a positive impact on pupils with SEND.

Here we focus briefly on one aspect and discuss the importance of metacognition as an example. The EEF states that the use of ‘metacognitive strategies,’ which involves pupils thinking about their own learning, can be worth the equivalent of an additional +7 months’ progress when used well. 

A good starting point for developing metacognition in secondary science teaching is to focus on using the cyclical 'plan, monitor, evaluate and regulate' as a structure. Adapted here by John Spencer: Five ways to boost metacognition in the classroom. 
 

This can be used in science lessons alongside complex calculations, practical activities, and evaluations, allowing students to be systematic and strategic in problem solving. This supports the learning of disciplinary knowledge and working scientifically, which is embedded throughout the secondary science curriculum. 
Supporting pupils with SEND to use the metacognition cycle in their approach to scientific tasks enables them to break down the process and reduce cognitive overload.

A very brief overview of questioning to support pupils in working through the cycle is shown here:
 

Teachers explicitly modelling this thinking for the pupils and walking them through the cycle supports them in embedding the process and applying this questioning to further scientific tasks. Alongside this cycle the other EEF recommended strategies such as scaffolding and explicit instruction should take place. Watch out for future updates on this. 

This is just an example of how one of the recommended ‘five-a-day’ approach can be used within your science lessons to ensure that high-quality inclusive teaching is delivered. 

If you would like more information about, SEND, Secondary Science or the Secondary Science conference please contact:
Joanna.Conn@HfLeducation.org Secondary Science adviser
Anna.Mapley@HfLeducation.org Secondary Science adviser
Becky.Rothwell@HfLeducation.org SEND adviser.

In the first of this mini-series, (Making fluent and flexible calculators: why counting is not enough), I reflected on the importance of taking a deep look at how children solve simple addition and subtraction calculations. I considered why it wasn’t enough just to let them solve simple calculations through counting and the need to stop children from being caught in the counting trap.

This time, I have turned my attention to understanding why gaps in developing additive reasoning lead to difficulties later in children’s longer maths journey. I return to my crucial statement - 'Why getting the calculation correct is not enough’. But this time, I consider why we must blatantly pay attention to additive reasoning. If children in your class struggle with multiplication, division, fractions and/or percentages, they may not have already secured the strong foundations in additive reasoning that they need.

Shortly after publishing the first blog in this mini-series, Ofsted released ‘Coordinating mathematical success: the mathematics subject report’ (July 2023). As one of the main findings for primary schools, they highlighted:

“Pupils’ gaps in knowledge tend to be centred around, but not limited to, addition facts in younger year groups. This was for some, but not all, pupils. These early gaps in knowledge may not become apparent until a significant amount of time has elapsed. This is because it is possible, in the medium term, for pupils to understand what is being taught and then keep up with extra classroom support and slower calculation. However, this is at the expense of the later ability to access the curriculum.”

Additive reasoning is foundational to multiplicative reasoning

I have long questioned why some children seem able to move into KS2 maths easily and others struggle, particularly with multiplication.

Why am I talking about multiplicative reasoning when Making Fluent and Flexible Calculators explores, develops, and enhances children’s ability to solve addition and subtraction calculations?

It is because additive reasoning forms the foundations for developing multiplicative reasoning (see Figure 1 below). During the course of the project, we have repeatedly seen large proportions of pupils using counting to solve simple addition/subtraction calculations. They have yet to develop trust in a range of strategies and haven't developed the habit of looking for ways to simplify the calculations. Instead, they revert to counting or, slightly better, depend on a single strategy (for a more detailed discussion on the strategies children spontaneously use in the project, see the first blog in this series)

Figure 1: Reasoning progression phases from EYFS to KS4 and beyond

Each phase is progressive, building understanding and knowledge vital for success in the next phase. To be blunt, if a child doesn't secure the required learning in the additive phase, they will struggle with the multiplicative.

Too many children are trying to solve multiplication calculations with understanding and knowledge only from the counting phase. This is why some struggle to understand and accurately answer multiplication questions and find proportional reasoning, such as fractions, percentages, and ratio, ‘a bridge too far’.

To illustrate this, consider what happens when children solve 9 x 6 when this fact is not fluently recalled:

Child A

Child A is in the counting phase, so they solve the calculation by drawing an array; nine rows with 6 dots in each. Then they count each dot, starting from 1 (count all) or, slightly better, from 6 (count on).

Child B

Child B is in the additive phase and solves the calculation through skip counting. They now recognise that there are 9 groups, and each group is equal to 6. They no longer see each item (dot), but rather 9 repeated equal units of 6. They solve through applying repeated addition, so even though they are solving a multiplication calculation, they are employing strategies from either the counting or additive phase.

Child C

Child C’s solution is representative of the multiplicative phase. They have developed an understanding of the two different dimensions of multiplication - the number of groups and the size of groups. They can flexibly manipulate both dimensions to break the multiplication into groups to which they fluently know the answers. They must employ skills from both the multiplicative and additive phases to succeed at this stage.

In addition to the macro-progression of counting to additive to multiplicative, each phase has a micro-progression

Children start with unitary counting; counting all the dots, one to one. This strategy is not time efficient and has massive potential for error. They do not see the array as representative of multiplication or the relationships between two differing dimensions (number of groups/size of group) but rather just a series of single dots. The child’s ability to estimate if their answer is correct is minimal.

Rhythmic counting is how many children first solve multiplication calculations when they start to recognise groups; they emphasise the number pattern but are still counting in ones. When counting in sixes, they would whisper 1, 2, 3, 4, 5, and shout 6, whisper 7, 8, 9, 10, 11, shout 12 and so on. They recognise the repeated addition structure but still employ skills from the counting phase.

As children get more confident with rhythmic counting, they can often skip count some of the patterns but then revert to rhythmic counting to complete the calculation. This is called ‘hybrid counting’. For example, 6, 12, 18, 24, 30…whispering 31, 32, 33, 34, 35, call out 36; whispering 37, 38, 39, 40, 41, call out 42, etc.

The cognitive load is huge when using this method as children must keep track of numerous pieces of information all at once, including:
      a)    the number of groups of 6 that they have counted
      b)    which number they are currently on
      c)    which number comes next in the number sequence (particularly challenging if it crosses a decade boundary)
      d)    how many more they must count on to complete the next group of 6.

However, if children are confident in additive reasoning, then they can start to simplify the repeated addition calculation and compact the amount of information they are processing, releasing cognitive space. A child’s thinking might be:
I know 5 x 6 is 30, so 30 + 6 = 36, 36 + 6 = 42, 42 + 6 = 48, 48 + 6 = 54.

During this intermediate stage, children use additive reasoning strategies to solve the sub-calculations required to multiply 9 and 6:
 

Ability to use base facts 

In the first blog in this series, I discussed the importance of children developing mental addition and subtraction strategies to prevent them from being stuck in the counting trap.

But the ‘Fluent and Flexible’ project has also highlighted another issue. Thompson (1994) highlighted that children must understand that mathematics is about “working with relationships”.

The entry data from the project shows that many of the children aren't spontaneously using their base facts to help with other calculations (the National Curriculum refers to them as ‘derived facts’). Children do not see relationships between calculations and are not using what they already know.

For example, suppose pupils know that 9 + 4 is 13. It is then anticipated that they would use this information flexibly to solve other related calculations, such as 90 + 40, 19 + 14 and 13 - 9, but we found that many children involved in the project weren’t. Instead, they see all calculations in isolation. They aren’t in the habit of anticipating and seeking ways to make the calculations easier using known facts.

Not seeing associations between calculations has implications for their longer journey in maths. Children need to build the habit of seeking patterns and seeking ways to simplify calculations in preparation, not just for more complex additive calculations, but also multiplication (if I know 3 x 4 is 12, then 30 x 40 is 120, 13 x 4 is 10 x 4 + 3 x 4). Children need explicit instruction, time, and practice to seek and trust relationships.

Moving beyond known multiplication facts

The ability to use additive strategies is much more than just being more efficient within the times tables facts. As they progress through the curriculum, children will have to use additive reasoning to solve calculations beyond their known multiplication fact range.

Additive reasoning impacts multiplication success

To summarise, additive reasoning develops this kind of understanding and knowledge:
      a)    numbers can be broken into smaller numbers (composite units/part-whole models)
      b)    how to use base facts to seek derived facts – going beyond memorised facts
      c)    to select, with reasons, from a range of strategies to simplify the calculation.

In the 2023 Key Stage 2 mathematics paper 1: arithmetic, there were 15 questions that explicitly involved multiplication or division (excluding those that contained fractions). Of these, at least 9 can be simplified and solved using additive thinking strategies.

Examples include:

That there are many ways to solve each calculation is critical here. It is up to the children to decide. They have the agency so select the option which exploits their strengths.

We need to explicitly help them establish the habit of seeking patterns, build their understanding and trust in additive reasoning so that they will continue to look for relationships within and between numbers. This will help them to learn to seek out ways to simplify calculations rather than mechanically applying the same strategy over and over again.

This foundational flexibility enables them to build more sophisticated ways of solving calculations, preparing them to be successful with more complex calculations.

It is vitally important that we aren’t satisfied with children getting simple addition and subtraction calculations correct, but that we overtly focus on the strategies and the understanding that the child is applying. We should constantly question ‘are they building foundations to enable success for the next stage of their maths journey?’

Is this a key focus in your school?  

The HFL Education Primary Maths team can work with you in school to develop mathematical fluency through The Fluency Package or the teaching and learning of multiplication facts through The Multiplication Package.

Find out more about the Making Fluent and Flexible Calculators

To keep up to date: Join our Primary Subject Leaders’ mailing list

To subscribe to our blogs: Get our blogs straight to your inbox

References

2023 Key Stage 2 mathematics paper 1: arithmetic
Contains material developed by the Standards and Testing Agency for 2023 national curriculum assessments and licensed under Open Government Licence v3.0

Ofsted (2023) Coordinating mathematical success: the mathematics subject report Available at: www.gov.uk/government/publications/subject-report-series-maths/coordinating-mathematical-success-the-mathematics-subject-report 
(Accessed: 31 August 2023)

The transition from Early Years to Year 1 can be a big step for pupils and staff members alike. When thinking about the knowledge and skills the children need to move into Key Stage 1, schools should be thinking about progression through the school as well as allowing children to experience as many different opportunities as possible. For example, topics such as ‘Plants’ are done in many year groups, however, if each year group completed an enquiry on how to best grow a bean from its seed into a mature plant their experiences would be limited.  

Therefore, it is important to think about the following:

• Progression from EYFS
• Any crossover between EYFS and Year 1
  • Ensuring this is for a key purpose, or
  • Ensuring this is to a different depth
• Ensuring the EYFS activities themselves have a clear focus.  

This blog endeavours to use the relevant information for EYFS from OFSTED’s Finding the Optimum: the science subject report and offer some suggestions as to how schools can ensure they show effective planning and progression from EYFS to KS1 in science. The report focused on the teaching and learning of science across primary and secondary schools.

The highlighted sections have been taken directly from OFSTED’s Finding the Optimum: the science subject report (2 February 2023).

It is important that children in Reception have a key focus when undertaking an activity. This could be to learn something substantive e.g. some objects float and some objects sink or simply to be able to observe and describe what they can see. They may wish to ask questions about what they experience but not all questions have to be answered (as many concepts they may encounter in EYFS may be too far beyond their ability to understand at this point). 

Recommendations 

Statutory Framework for the early year's foundation stage 

ELG: The Natural World 

Children at the expected level of development will: 

• explore the natural world around them, making observations and drawing pictures of animals and plants; 
• know some similarities and differences between the natural world around them and contrasting environments, drawing on their experiences and what has been read in class; 
• understand some important processes and changes in the natural world around them, including the seasons and changing states of matter

Topics from the Year 1 Programme of Study include the following: 

Plants 

• identify and name a variety of common wild and garden plants, including deciduous and evergreen trees
• identify and describe the basic structure of a variety of common flowering plants
• identify and name the roots, trunk, branches and leaves of trees

Animals, Including Humans 

• identify and name a variety of common animals including fish, amphibians, reptiles, birds and mammals
• identify and name a variety of common animals that are carnivores, herbivores and omnivores 

Seasonal Change 

• observe changes across the four seasons 
• observe and describe weather associated with the seasons and how day length varies. 

Materials 

• distinguish between and object and the material from which it is made
• identify and name a variety of everyday materials, including wood, metal, plastic, glass, water and rock, 
• describe the simple physical properties of a variety of everyday materials
• compare and group together a variety of everyday materials based on their simple properties 

You can see that there is a lot of crossover between EYFS and Year 1 in terms of topics and thus it is important for opportunities across the Key Stages to be varied to fully develop children’s understanding. New learning is fragile and is best embedded through many linked experiences. Allowing children the opportunities to grow many different types of plants, for example, will allow them to use similar skills in new contexts.

It can also allow them the opportunity to do the following:

• link their learning to literacy through many fantastic texts (Bloom, The Gigantic Turnip, Ten Seeds, From Seed to Sunflower, A Seed is Sleepy, Sunflower Shoots and Muddy Boots and many, many more)
• link their learning to maths in terms of measuring the height (using non-standard measures – how many cubes tall, how many cars tall?)
• link their learning to art in terms of sketching the different flowers they see

The more directed opportunities the children are given, the more transferrable their knowledge and understanding will be. 

However, this is not just knowledge-based. The children’s Working Scientifically Skills should also be developed in EYFS. A good visual representation can be found in HFL’s working scientifically wheel for EYFS: 

This tool can help EYFS teachers to focus their units/activities around the working scientifically skills and preparing these skills for use in Year 1. 

This can be a challenge across the curriculum, but particularly in science due to the overlap of subjects and very specific national curriculum requirements at each stage. It is important to ensure the mapping of EYFS enquiries and the specific focus of each in order to ensure children are ready to progress to Year 1 and that the same activities are not revisited without a clear purpose. 

Vocabulary 

It is equally important that when new units are introduced to children in reception, that the correct vocabulary is being used. Some units that may include magnets, forces, electricity, heating and cooling for example, are units that won’t be covered again until Key Stage 2. Therefore, when looking for correct vocabulary, it is important to look at the requirements for those units and plan accordingly. There was an example in a recent report that stated children in Year 3 who were studying magnets were using the word ‘sticking’ to describe ‘attraction’ and that this misconception was not acted upon. It is important that children are exposed to the correct terminology (as appropriate for primary) and that it is modelled correctly to ensure we are not perpetuating misconceptions. The focus here is not on early years children using this terminology at this point, but on exposing them to correct vocabulary that will support their learning throughout the curriculum.

Resources to help

• The EYFS Matrices from PLAN Assessment have a great range of activities to undertake in the Early Years and focus on building the knowledge and experience necessary to progress into the KS1 and KS2 curriculums. Used alongside the KS1 and KS2 knowledge matrices, it is a clear way to show progression from EYFS – Year 6. 
• Primary Science Education Consultancy also has a document that shows progression in Growing Plants from EYFS to Year 6 with a different focus in each year group (including experiencing growing different   
• Explorify has introduced a set of activities geared specifically towards EYFS  
• Primary Science Teaching Trust, play observe ask- provision maps with activities to support learning in EYFS
• HFL working scientifically wheels

Top Tips for EYFS to keep in mind 

1. Ensure a clear focus for each activity (why are the children doing this – what are you intending for them to get out of it?) 
2. Ensure exposure to age-appropriate scientific vocabulary (so we don’t perpetuate misconceptions later in the curriculum) 
3. Ensure progression between year groups (different experiences allow children to apply their knowledge and understanding to new situations) 

Introduce the working scientifically skills in Reception so children begin building an awareness of the skills they are using  

Voices from the Classroom

Our new blog series, Voices from the Classroom, allows primary science teachers to share particularly effective practical experiences they have had with their classes. It’s a great way to showcase what your school is doing and written guidance and examples are available for those of you wishing to participate.

If this is something you would be interested in participating in, please e-mail Charlotte Jackson charlotte.jackson@hfleducation.org