In recent years, schools have invested in high-quality phonics teaching, with many adopting validated Systematic Synthetic Phonics (SSP) programmes. Rightly so - we know that a phonics-first approach remains the most effective way to teach young readers the code of written language - enabling them to accurately decode the words on a page and develop their language comprehension. Children need both ‘good word reading’ and ‘good language comprehension’ to become ‘good readers’, as detailed in the simple view of reading:  

Why do Year One pupils need fluency instruction? 

It’s a valid question - and one we asked ourselves when we began the trial phase of our Year One Reading Fluency Project. Children in Year One are still developing their knowledge of Grapheme-Phoneme Correspondences (GPCs). Because of this, both their decoding accuracy and reading fluency are still emerging, and since fluency acts as a bridge between word recognition and comprehension, their overall understanding of texts is also still in development. 

However… 

Through our work with Year One teachers and pupils, we’ve observed a key pattern: while many children grow increasingly confident in recognising GPCs or words in isolation - such as on flashcards or during phonics assessments - they often struggle to apply this knowledge when reading connected text. Even with well-matched decodable books, some pupils fail to recognise familiar words or rely heavily on overt sounding out, which disrupts their fluency, hindering their comprehension and of course their enjoyment and attitudes toward reading and books in general. 

Many children also face challenges with foundational reading skills, such as tracking text with their eyes or fingers, and understanding basic print concepts like directionality, spacing, or how books ‘work’. 

We’ve also seen similar challenges in writing. Many pupils find it difficult to transfer their decoding skills into accurate spelling, highlighting a fragile link between decoding (reading) and encoding (spelling). 

This led to the launch of the Year One Reading Fluency Project: Foundational Fluency. 

Following a successful trial and pilot phase, the project is now in its first official round. It forms a key part of our wider Reading Fluency family, designed to strengthen the foundations of fluent reading from the very start. 

How does the project work? 

The Year One Reading Fluency Project is designed to develop children’s accuracy and automaticity, and later their prosody, thereby strengthening the fluency bridge to comprehension and enjoyment. 

Authentic assessment

Through high-quality, diagnostic assessments, teachers are supported in closely analysing their pupils' reading behaviours. This insight directly informs fluency instruction, making it more targeted and effective. Many teachers have described the assessment process as ‘eye-opening’, offering a clearer picture of what children can - and can’t yet - do as developing readers. 

Accessible reading

Many teachers involved in the Year One Reading Fluency Project have found that, although phonics assessments often place children within a specific book band, stage, or phonics phase, the texts at these levels are frequently pitched too high. While pupils may have been exposed to the relevant GPCs or vocabulary during phonics lessons, this knowledge is not always securely embedded or readily accessible when reading in context.

By lowering the pitch of independent reading texts - ensuring they are truly decodable and matched to pupils’ secure knowledge - teachers notice a significant improvement in both reading confidence and engagement. Children are more likely to access the text successfully, leading to a greater sense of achievement and willingness to re-engage with reading.

As Dr. Timothy Rasinski highlights in his research, reading fluency is not just about speed and accuracy, but about fostering a sense of competence and motivation. When children feel successful, they are far more likely to persevere and develop a positive relationship with reading. This echoes the findings of our own research into Reading Fluency, which emphasises the importance of explicit fluency instruction. 

Explicit fluency instruction  

At the heart of the Year One Reading Fluency Project is repeated reading - a powerful strategy that allows children to revisit a carefully selected text multiple times. Through guided, purposeful repetition and the use of targeted strategies, pupils are supported in developing automaticity, which in turn reduces cognitive load. With decoding becoming more effortless, children are freed to focus on other elements of fluency and of course, comprehension and enjoyment.

Alongside repeated reading, the project places strong emphasis on explicit vocabulary instruction, print awareness, and oral language development. These elements help pupils become active, reflective readers who can monitor and make sense of what they read. 

Each fluency session is intentionally designed to support not just accuracy and automaticity, but also prosody, confidence, and deeper text understanding. Together, these components lay a strong foundation for long-term reading success - and a lifelong love of reading.

The outcome: promising progress from trial to pilot

The results from our trial and pilot phases have been highly encouraging. Analysis of pre- and post-assessment data reveals clear progress across several core areas of early reading fluency:

Fluency

On average, children made a 3.5-point gain in their fluency scores, based on Dr. Tim Rasinski's fluency rubric, with an impressive 97% of pupils showing progress - demonstrating the project’s effectiveness in building confident, independent readers.

Accuracy

We observed a substantial 16 percentage point improvement in reading accuracy, with 82% of children achieving over 90% accuracy by the end of the project. Accurate word recognition is a vital foundation for fluent, meaningful reading. Significantly, teachers reported noticeable changes in their pupils’ application.

Automaticity

Children’s reading rate also showed significant gains, with an average increase of 10.5 words per minute, reaching an overall average of 24.7 words per minute. This increase in reading rate, combined with maintained or improved accuracy, reflects a freeing of pupils’ cognitive load with meaningful development in automaticity!

Reading Behaviours: Growing Confidence and Motivation

The data shows clear progress in key reading behaviours, particularly in motivation and engagement. A growing number of children now report that they enjoy reading – now, both at home and at school. Many describe themselves as ‘good readers’, reflecting a positive shift in their perception of themselves as readers.

Teachers have also observed noticeable improvements in oral and reading blending, the ability to combine individual sounds to form words - whether heard aloud or seen in print - with less overt sounding out and greater fluency in decoding. Children who were once reluctant readers are now showing increased enthusiasm and confidence, becoming more willing and motivated to engage with texts independently.

During the project’s final review, teachers voiced powerful reflections, including:

• “One girl, who used to sound out every word, now reads with automaticity!”
• “My children are now checking for errors and self-monitoring.”
• “My less confident readers are now so enthusiastic and can’t wait for the sessions.”
• “We have seen more engagement with home reading and an improvement in reading attitudes!”
• “Children have loved bringing the text to life!”
• “A previously less confident reader asked to read in assembly… and they did!”

…and that is the point of reading!

Join us! 

These outcomes underscore the value of focused fluency instruction and the importance of carefully matched, accessible texts. As we continue to refine the Year One Reading Fluency Project, these findings inspire confidence in the impact it can have on young readers’ success. 

To find out more about participating in the Year 1 Reading Fluency Project: Foundational Fluency, email us reading.fluency@hfleducation.org.

Wake up, check phone, shower, get dressed, wake up child, eat breakfast… Sound familiar? This is pretty much my morning routine during the week. It is not exciting and sometimes the timings alter (depending on how tired I am) but generally it remains the same and prepares me, and my family, for the day ahead. We all have different routines to help us navigate our day. We even have routines within routines! However, not all routines are effective, and this can impact on the success of completing a task, time keeping and controlling emotions. Does this sound familiar to what you see in provision? Routines play a crucial role in not only maintaining structure to the day but also in supporting child development. 

Firstly, it is important to remember that a routine is different to a timetable, although some parts of our routine are dictated by time, such as mealtimes, access to other rooms/spaces and collection times. Routines are more fluid in nature and can sometimes be referred to as the rhythm of the day. This involves creating a consistent yet flexible framework for your day, helping you manage tasks, transitions, and downtime effectively. 

What are the benefits of effective routines? 

Sense of security

Predictable routines help children feel safe and secure. Knowing what to expect reduces anxiety and stress, making them feel more in control of their environment.

Emotional regulation

Regular routines help children develop self-regulation skills, which are essential for managing their emotions and behaviours. This stability allows them to face daily challenges with resilience and confidence.

Independence and responsibility

Following a daily schedule teaches children to complete tasks on their own, such as choosing, using and returning resources or locating and collecting belongings. This builds confidence and prepares them for future responsibilities.

Time management skills

Understanding time and schedules helps children prioritise daily tasks, manage transitions smoothly, and balance play, learning, and rest. 

What makes an effective routine?

Consistency is key! All children like to know what is happening in their day, therefore establishing consistent routines through a carefully planned provision will be beneficial to everyone. 

Visual aids

The power of visual aids should never be underestimated. Sometimes, as adults we can appear to ‘go through the motions’ of using visual sequences, instructions or prompts but it is important that we continue to draw children’s attention to them frequently, especially when there is a change in routine. On many occasions, children have approached me, as an adult in the provision, to find out what is happening next and I always ask, “How can we find out?” Most of the time, I will be led to the visual timetable which has varying levels of success depending on how much value the practitioners have placed on implementing them. Some children will require extensive visual aids to enable them to access the curriculum but remember that all children will benefit from them - as long as they are used consistently and by all adults within the provision. 

Makes sense

Ensuring that that routines make sense is important. This requires careful consideration about the types of activities on offer. For example, if you have a timeslot to use a space for physical development followed by an adult led writing activity, you might find that this is very adult intensive and can be overwhelming for children in the early years. This can also be very onerous for the adults in the provision who are likely to be trying to set up activities whilst supporting children with transition points. Ensuring there is a balance and flow to routines will enable everyone within the provision an opportunity to process what is happening now and provides an awareness of what is coming next. 

Routines within routines

When you break down aspects of the day you will find that other little routines appear, usually out of necessity. These routines often appear naturally and are impacted by the layout of the environment. For example, you are unlikely to be able to fit ten or more children in cloakroom areas, so you manage this by filtering children off in smaller groups. Consider the expectations that you set throughout the day for completing tasks such as collecting belongings. You also cannot be everywhere at once and by providing simple, memorable instructions children will be able to develop their independence skills. Using short rhymes such as “Coat, Bag, Bottle” sung in a rhythmic way can be enough to remind children to collect these items. Mnemonics or visual aids to enhance these incidental routines can also be very helpful. 

Evolves

As the year progresses, just as with your learning environment, the routines will evolve to meet the changing needs of your cohorts. Reflecting on parts of your routine that no longer feel necessary and looking at where time is being maximised to support learning and development is crucial. “This is the way we always do it” is one of the most dangerous phrases that can be heard within schools and settings. We have to be openminded to change and reflective about all aspects of our practice. The children in front of you today will change so it should not be surprising that routines will need to change too. 

Overall, routines provide the structure and consistency that children need to thrive socially, emotionally, and academically. Do you have any specific routines in mind that you'd like to establish or improve for your cohort? If this is something you have identified as an area of development for your provision, please contact us for details about consultancy from our early year advisers and consultants earlyyearsteam@hfleducation.org. 

Why do children often find written division challenging and how can we best help them to overcome this?

In this blog my aim is to explore some of misconceptions within division that are evident to me, as pupils move towards formal written division in KS2.

Introduction

After the initial work on place value and mental strategies has taken place, children in Key Stage Two often move onto formal methods for calculation, including division.

This learning involves key concepts which are inextricably linked through the idea of ‘Multiplicative Fluency’, and I would like to share some insights from witnessing children carrying out calculations, the accompanying misconceptions linked to progression and the underlying links to both subject knowledge and my own associated research. In considering this process, I was led to the Julius Caeser quote as the title of this blog where the ’conquer’ reference relates to addressing those misconceptions.

The Mastery Readiness Programme

For several years, at HFL Education, myself and my colleagues, Nicola Adams, Laura Dell and Nicola Randall, have been Mastery Readiness Leads, supporting schools across Hertfordshire through the national Mastery Readiness Programme in association with the NCETM Maths Hubs. 

An integral part of the programme is to plan and deliver a series of workshops for Mastery Readiness Lead Teachers linked to the ‘Catalysts of Change’ that need to be considered before continuing the route through the overall Mastery Programme towards teaching for Mastery success:

One of the ‘Five Catalysts’ is Arithmetic Proficiency. Under this banner in the above graphic, you can see the key areas of development are focused on number facts linked to automaticity, number sense, accuracy, efficiency, flexibility and the importance of practice. To that end, it should be recognised that these aspects are all linked to mathematical fluency and as a result of considering this rationale a workshop that focused on multiplication and division was subsequently delivered to Mastery Readiness delegates from ten schools entitled ‘Multiplicative Fluency’.

Misconceptions within Multiplicative Fluency

In my extensive experience of observing primary school children in action closely and conducting a wide variety of Pupil Voice interviews, including carrying out the Lesson Study process that focuses predominantly on the children and not the teacher, I have found that the children do not automatically make specific links between division and multiplication. Often, when asking groups of children (including those who were deemed to be working at age-related expectations) what helps them to be able to carry out long (expanded) and short division effectively, few of them make any links to times tables or multiples and factors. I realise that this appears to be unfathomable, and I think that it is because division and multiplication are often taught separately, and so some children have not yet made the connections between multiplication and division, because they see them as being separate entities. The links needs to be represented effectively throughout children’s maths learning to allow networks of connections to be consolidated.

Multiplicative fluency relies on an understanding of multiplication as repeated addition. and division as repeated subtraction, supported by the concepts of equal grouping and inverse operations. Children need a deep understanding of sharing and grouping, which is developed throughout EYFS and Key Stage One.

In ESSENTIALMaths V2 multiplication and division are explicitly linked. For example, in Year Two this involves the correlation between arrays and fact families:

In my experience, the above representations can be problematic for some children, as they appear not to recognise the separate groups within the whole, even though they appear to be clearly demarcated by the red oval shaped lines. Again, this may seem to be unfathomable, but I have witnessed this misunderstanding on many occasions. I believe that this is because insufficient time is utilised in allowing children to explore the conceptual ideas through the manipulation of concrete materials i.e. the use of counters, before moving to pictorial depictions. I have found that one particular activity has the potential to address this situation.

It involves placing counters as an array on a sheet of A4 paper and asking children the following range of questions:

The children can then manipulate the counters if they need to and articulate and/or generate a range of statements that could include calculations.

The next step is key in facilitating opportunities for children to make specific links to multiplication and division including inverse operations:

Carrying out this process allows specific formative assessment to take place where children's understanding and any associated misconceptions or errors can be realised. I have witnessed such comments as ‘I can see groups of two’, ‘I can see four’, ‘There are two lots of six’.I believe that this eradicates any preconceived ideas of what a teacher might expect children to see, when in reality the outcomes might not meet the intended expectations. Children can then, of course, be directed towards understanding equal groups linked to multiplication and division. I have found that this process may require further ‘scaffolding’ to allow children to gain in-depth understanding and involves a representation, that I have adapted further, that was initially shared with me by Rachel Rayner, a former colleague and now headteacher.

It is also relevant to children moving towards using formal calculations, including remainders linked to fractions and decimals, and how this correlation, and the associated conceptual understanding, can be embedded to allow children to become fluent in their calculations. Through the utilisation of the Concrete – Pictorial – Abstract (CPA) rationale, an effective pedagogical approach could look like this:

Begin with a focus on the correct mathematical language.

(Please notice that the calculations are already complete - it is the mathematical process that is the focus.)

In this calculation, we want children to notice that we are taking equal groups of four.

Children place the counters in equal groups (of four, in this case) within the rectangles, which are being used as a scaffold.

Children can now see that you can make 5 equal groups of four counters. In this case there is nothing ‘left over’.

I have been utilising this for several years now as it provides a clear ‘picture’ of the process and involves representation of the calculation using the CPA approach. Linking the Concrete (the counters) to the dividend and then to the Pictorial in the associated scaffolded array, and to the Abstract (the written amounts) clearly shows the layout at the beginning of the process - I see it as being imperative that children also begin with the physical counters to manipulate, and that they write the associated calculation.

Potential misconception to be conquered: that we can only divide by sharing out one at a time.

We want the children to recognise that they can share the counters by grouping them equally into the rectangles rather than always deferring to a sharing (placing one at a time) method. If they can only carry out this process through sharing, the introduction of formal written calculation for division may need to be delayed, to avoid further misconceptions developing.

At this point it may be tempting to move the process forward into written division, but pupils may need time for further exploration first, to develop understanding and make connections. Key questions could include:

What else can you see?

What other calculations could you carry out?

How could this be represented as multiplication?

Can you manipulate the counters to show a different division calculation?

Potential misconception to be conquered: that multiplication and division are separate operations

We want children to recognise that division and multiplication are inextricably linked, part of the same bigger concept, rather than unconnected operations.

The next step introduces the idea of quotients:

This step is crucial where the link is explicitly made to remainders and what they ‘look like’. If we add one to the dividend of 20 to make 21 and still divide it by 4 then there will be one remaining or ‘left over’. The positioning of the counter is also crucial.

Potential misconception to be conquered: that the remainder is not really part of the quotient (or answer) and so doesn’t have a value of its own.

We want children to understand the value of any remainder rather than misinterpret its meaning.

This process can then be continued:

Before the main key misconception can be conquered:

If one more is added to the dividend to make 24, we want pupils to see that this creates another equal group as another multiple of four that can be added to the existing groups.

So here we can see that 5 remainder 4 equates to a quotient of 6. This scaffolding could be ‘faded’ and the children explain and show their understanding using the ‘Pictorial’ by drawing the rectangles and representing the counters, which could be circles or dots or anything else that represents the concept before moving completely to the ‘Abstract’ (written symbols).

The key understanding here is that if the dividend is increased by less than the amount of the divisor, then there will be a remainder which is included in the quotient. For me, this does not get explored in sufficient depth; too often, remainders and quotients are taught purely in the abstract and children are not able to make generalisations and recognise situations where this occurs. This, alongside the lack of correlation between multiplication and division, including repeated addition, repeated subtraction and multiples and factors does not ensure that the children have the necessary skills required to be able to calculate effectively.

In referring to Mastery Readiness Catalysts of Change, and the section entitled ‘Arithmetical Proficiency’, further recognition of different situations when performing calculations can be realised once deep understanding of the language of division and ‘what that actually looks like in practice’ has been understood. Flexibility and efficiency, linked directly to ‘securing number facts’ and ‘automaticity’ can be enhanced through effectiveness in Multiplicative Fluency.

If, for example, the calculation 96 ÷ 4 = is attempted by children, it is my experience that this will, more often than not, be attempted to be solved through the utilisation of a short formal division method:

As part of learning this process, I would always ask to children to articulate their understanding:

Within this scenario Dienes Apparatus is used to show that what is actually happening is 10, as the quotient from dividing 90 by 4 is regrouped with the 6 in the ‘ones’ column to result in 16 which is then divided by 4.

The national curriculum includes an expectation that year 3 pupils can ‘Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods.’ Within that scenario we also want the children to realise that flexible regrouping in this example is directly linked to division through the Distributive Law and in terms of efficiency, no formal method is required. The calculation can be written as (20 x 4) + (4 x 4) which is also linked to Multiplicative Fluency via understanding of multiples of four and can thus be calculated mentally.  On a few occasions, when I have been exploring this particular question in Pupil Voice sessions, children have asserted (once the mental strategy had been introduced to them) that it could also be calculated mentally via addition of 10 x 4 and 10 x 4 and 4 x 4, and on one occasion a child showed great delight in sharing that it could also be calculated as 24 + 24 + 24 + 24 = 96 via (6 x 4) + (6 x 4) + (6 x 4) + (6 x 4) because “I know that six times four is twenty four and I am really good at doubling”.

For me, this demonstrates deep understanding of Multiplicative Fluency within Arithmetical Fluency which can also be linked directly to a widely recognised rationale within the world of academic mathematics research. Richard Skemp explores the idea of ‘Intelligent learning’ which involves creating networks of ‘schemas’ or conceptual structures that ‘act as tools for future learning’ where longevity is achievable through deep, long-lasting and versatile understanding. He also links this rationale to the theoretical idea of the difference between ‘instrumental (or instructional)’ and ‘relational’ understanding where the former is defined as ‘rules without reasons’ and the latter involves ‘knowing what to do and why’. These can be recognised as the relational aspect allowing mastery of mathematics and instrumental understanding involving rote learning.

I believe that it is important to realise that children need to be immersed in both of these aspects as they make their mathematical journeys, including, as highlighted in this blog, their progression into formal division in key stage 2, where ‘Multiplicative Fluency’ is required and can be enhanced to allow children to ‘divide and conquer’ effectively.

Questions for maths subject leaders to consider:

• In key stage 1(KS1) and lower key stage 2 (KS2), how carefully do teachers explore both sharing and grouping, when introducing division?
• Throughout KS1 and KS2, do teachers explicitly link multiplication and division, for example, referring to children’s knowledge of multiplication tables and demonstrating how this supports their mental and written division work?
• Is time given to exploring the meaning of any ‘remainders’ when these begin to arise and what their value is, in relation to the calculation?

References:

Skemp, R. “The Idea of a Schema,” in The Psychology of Learning Mathematics: Expanded, 1st ed. (New York: Routledge, 1987), p.24.

Skemp, R. “Relational Understanding and Instrumental Understanding,” in Mathematics Teaching in the Middle School, vol. 12, no. 2. (National Council of Teachers of Mathematics, 2006), p.89.