When I searched ‘problem-solving skills’ online, a list appeared in which the top eight search results were articles about how to develop these skills written by career development companies and job advertising agencies. Why is this?

Clearly, problem-solving is a crucial life skill.

So how do we teach these skills to our young learners in primary school?

Often, when working with teachers and leaders to analyse outcomes from diagnostic or statutory tests, the outcomes show that children are more confident and accurate in solving arithmetical calculations (think SATs paper 1 questions) than they are at interpreting and solving reasoning problems (think SATs paper 2).

This blog will focus on some specific problem-solving skills that will enable pupils to access and solve reasoning questions (as in the KS1 SATs paper 2) by the end of Key Stage 1. But of course, they are more widely applicable.

I will use Question 13 from the 2022 KS1 SATs paper 2 (reasoning) to exemplify this teaching approach.

 

 

Step 1: Direct pupil focus

The purpose of this first step is to reduce anxiety and potential information overload. We want pupils to focus on the structure of the problem before rushing to find a solution.

To do this…

• remove ‘the maths’
• remove ‘the question’
• ask… What do you notice?

 

 

Children may discuss what they can see in pairs, in small groups or as a class. They may benefit from sentence starters such as…

• I can see…
• I have noticed…

These observations may be simple and that is fine. We want to get children engaged and talking.

They may say:

• I can see 3 pencils
• I have noticed a triangle

Step 2: Refine pupil thinking

To do this…

• provide a list of key vocabulary
• expect pupils to articulate their thoughts in full sentences
• ask pupils to listen to others to see if they can add more details or be even more precise

 

 

Now they may say:

• I can see that the shape has 3 sides. It’s a triangle
• I have noticed that there are 3 pencils laying end to end between two vertices

The reference to the 3 sides and 3 pencils is important as it should spark thinking for use later in the problem-solving process.

Step 3: Build on what they know

To do this…

• reveal information from the question bit by bit
• after each reveal, ask the pupils, ‘What do you know now?’
• ask pupils to suggest any additions to the vocabulary list

 

 

Children may discuss what they know now in pairs, in small groups or as a class. They may benefit from sentence starters such as…

• I think that…
• I know that…
• if… then…

They may say:

• I know that 3 pencils will fit along each side because all the sides are equal in length
• if there were 3 pencils along each side, then there would be 9 pencils altogether

Don’t worry at this point if children come up with suggestions that answer the question that will be revealed later. This is a positive thing!

It means the children are tuning in to information within the correct domain and making connections between shape and other areas of mathematics.

Step 4: Consider ‘the question’

To do this…

• BEFORE revealing the question, ask pupils, ‘What could the question be?’

This allows you as the teacher to assess whether the pupils are considering the structure of the problem.

 

 

In this example, are they coming up with questions that involve equal groups, for example?

If a child came up with a question such as, ‘How many pencils would we have if we took one away?’ this can of course still be valued (and answered) but it would indicate that the mathematical domain in which the child is thinking is not one that this picture would naturally allude to.

This information can be considered within class teaching or in rehearsal time going forward.

Step 5: Reveal ‘the question’

 

 

To do this…

• ask children to read the question aloud. Perhaps read it aloud as the teacher and then ask children to repeat it back.
• ensure children understand all of the words within the question and link this to the model and vocabulary list if needed.

Step 6: Represent the problem

To do this…

• ssk the children, ‘How could we draw the problem?’
• ssk the children to compare their drawings to a partner’s. Can they see where each part of the problem is shown? Can they explain their drawing or model to someone else?
• support children to make connections

 

 

As Gill Shearsby-Fox says in her blog about the importance of valuing pictorial recording,

‘We must make time and space for these opportunities and not over-scaffold children’s mathematical thinking with worksheets or prescribed representations, or else maths will become what ‘painting by numbers’ is to art. It might create a lovely picture but can be completed without thought or understanding and isn’t retained or remembered.’

Children may draw:

 

A picture based directly on the image provided showing a continuation of what has been drawn already.

 

A picture of the pencils, removed from the original image, in 3 equal groups of 3.

 

An iconic representation of the pencils. The circles have a 1:1 correspondence with the number of pencils and in this case, are laid out in an array.

 

A symbolic representation using conventional symbols (digits) to represent each quantity of pencils. This part whole model clearly shows the 3 groups of 3.

 

Step 7: Find the answer

To do this,

• ask children to identify on their drawing or model where the answer is shown
• ask, ‘Is there an operation needed?’

 

 

Children may use the operations:

• 3 + 3 + 3 = 9
• 3 x 3 = 9
  While the multiplication fact is not within the coverage of the KS1 curriculum, this may be a known fact for some children.

Ask children to check that they can see the 3 + 3 + 3 within their drawing. Can they see it on someone else’s drawing? Does it look the same? Does it matter?

Step 8: Check the answer makes sense

To do this…

• consider all the information the pupils used while problem-solving (the image, the vocabulary provided, the key words in the question, any models or drawings)
• ask the children to complete the sentence, ‘The answer is … because …’

 

 

They may say:

• the answer is 9 pencils because 3 pencils fit along each side and there are 3 sides. 3 plus 3 plus 3 equals 9
• the answer is 9 pencils because 3 equal groups of 3 make 9 altogether

Developing independence in solving problems

What we would like to see over time is pupils developing more and more independence in using skills and ideas from these steps to solve problems themselves.

When planning a sequence of teaching and learning, refer to the SATs papers for questions that it would be opportune to drop in, either in the way outlined above, as a teaching opportunity, or as an independent or paired discussion task to allow assessment of how pupils tackle them.

This will also provide crucial information about which of the steps the children tend to find the trickiest. Is it articulating what they notice in full sentences? Is it drawing a model to support with choosing an operation? Or is it something else?

Whatever the sticking point, this can form the focus of teaching going forward.

There are plenty of past papers from which to choose questions and these can be accessed here:

• Key stage 1 tests: 2022 mathematics test materials
• Key stage 1 tests: 2019 mathematics test materials
• Key stage 1 tests: 2018 mathematics test materials
• Key stage 1 tests: 2017 mathematics test materials

Further reading

What do we mean by ‘pictorial’ in the CPA approach?

 

End of Key Stage 1 - mathematics assessment toolkit

The HFL Education ‘End of Key Stage 1 - mathematics assessment toolkit’ provides Year 2 teachers and subject leaders with a suite of resources and tools to identify the strengths and areas of development through detailed question level analysis following the completion of a set of practice or statutory SATs papers.

 

 

Accompanying the analysis spreadsheets, documents and tracking tools is a digital guidance video that explains each of the resources and how to use them.

End of Key Stage 1 mathematics assessment toolkit

References

• Department for Education (2021) Development Matters: Non-statutory curriculum guidance for the early years foundation stage. Available at: https://www.gov.uk/government/publications/development-matters--2 (Accessed: 25 August 2022).
• 2022 Key Stage 1 mathematics paper 2: reasoning
  Contains material developed by the Standards and Testing Agency for 2022 national curriculum assessments and licenced under Open Government Licence v3.0

 

I don’t think that we can write a blog series about the 2022 KS2 SATs without firstly acknowledging the disruption to the last 3 years of education which has been vast and varied. However, no matter whether you agree or disagree that the assessments took place this year, the fact is that they did. So, what can we learn from them?

In our first blog in the series, we explored the similarities between the 2022 and previous arithmetic papers with particular comparisons to 2019. In this blog, we will switch our focus to the differences. Finally, in the third blog of the series we will consider the reasoning papers.

I also think that it is really important to remind ourselves that this blog is not just for Year 6 teachers – this is a KS2 assessment at the end of the children’s primary school journey and so all teachers are involved!

Quick domain and year group comparison

Before we dive into key differences we have noted as a maths team, let us just touch on some of the similarities between the 2019 and 2022 arithmetic papers in terms of the domain and year group coverage as shown in the mark schemes.

As detailed in the first blog, the domain coverage remains much the same with the majority of marks shared between calculations and fractions, decimals and percentages (although as detailed in the previous blog, we should note the ‘hidden’ importance of place value understanding). With regards to year group coverage, the picture looks roughly the same across the two years as shown in the tables below:

 

 

In these tables, the primary reference from the mark schemes has been used. The total of 40 refers to the number of marks in the paper with the four 2-mark questions being attributed to Year 6 calculations.

These are referenced in the mark scheme as 6C7a (multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication) and 6C7b (divide numbers up to 4 digits by a two digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context).  

It is useful to note these similarities as it may be assumed that the types of questions asked will be largely the same which is fair to say, and it could be argued that the paper follows a very similar procedure in terms of the writing but in this blog, we will explore some of the more subtle differences and consider their implications.

A tricky opener?

Let’s start at the beginning with the very first question. Historically, the first question, or perhaps the first few questions, have been relatively comfortable for many of the children to access with questions such as:

 

 

Here is this year’s (2022) question which could be argued is a fairly tricky opener:

 

 

How do you do yours?

How did your children tackle this? I wonder how many children may have relied on a formal written method here but made the following errors:

• lined up the place value columns incorrectly given that one number is 4-digit and the other two are 3-digit?
• lined the columns up correctly however when calculating, made errors when adding three 1-digit numbers?
• or made calculating errors when needing to deal with the regroups required in the ones, tens and hundreds columns?

 

 

It would be interesting to use similar questions with classes this year to explore the calculation strategies that the children are choosing to use.

When adding 5 ones, 1 one and 9 ones, do they recognise the complements to 10 and then add 5 more?

Or perhaps when adding 5 tens, 0 tens and 4 tens, do they notice that this could be calculated by doubling 4 tens and adding 1 more ten (and then the regrouped ten from the ones column of course)?

Or perhaps they recognise that if adding the two 3-digit numbers, this could be rebalanced from 501 + 649 to 500 + 650; subtracting 1 from 501 and adding 1 to 649 to keep the sum equal.

1,150 could then be added to 6,155 – perhaps with the children rebalancing again to 1,100 and 6,205 by adding and subtracting 5 tens.

Some questions to consider could be:

• are the children over reliant on formal written methods and if so, do they use these accurately?
• do children have a ‘toolkit’ of strategies and choose these appropriately depending on the numbers at hand?
• is this ‘toolkit’ of strategies built up across the primary phase and revisited often so that children are confident with strategies?
• how often are children given opportunities to use multiple strategies to solve a calculation and then assess efficient and inefficient methods?
• how fluently can children add and subtract 1-digit numbers? Might strategies such as complements to 10, think or make 10, rebalancing, and doubles and near doubles be worth revisiting?

Equal shmequal?

The next difference worth noting is around the concept of the equals sign. As we know from much of our work with teachers and children, when the equals sign is in a less familiar position – perhaps the start of the calculation rather than the end – that this can cause problems.

Why?

Because the children don’t have a secure understanding of the role of the equals sign and what it actually means.

 

 

Having said this, in 2019, the QLA (question level analysis) recorded that the questions above had an average correct response rate of 94% and 93% so not only did the children cope with the fact that the equals sign is at the start of the calculation, they had accurate methods to solve the calculations. It may well be worth comparing how this year’s cohort got on with the following 2 questions:

 

 

Arguably, the calculations needed here should be well within in the grasp of Year 6 children, using their place value knowledge and base facts to solve question 7 and then perhaps a formal method of short multiplication for question 15 (Year 4 content). The shift here is to understanding the role of the equals sign and tackling the division and multiplication calculations which may be operations that children feel less confident with.

If some children are unsure about the role of the equals sign, perhaps only seeing it as meaning ‘the answer’, it would be worth specific exploration of this using equipment such as pan balances and Cuisenaire rods.

For example, start with a fact that the children are confident with and a question such as …… = 2 + 5 and allow children to explore using the rods. Which rod is needed to balance the scales?

Recordings or descriptions could be in the form of:

• 7 = 2 + 5
• 7 is the same as 2 + 5 or
• 7 is equivalent to 2 + 5.

This could then be extended to ….. = 2 x 5 with the children placing 2 lots of the rod worth 5 in one side of the balance and then finding the rod or rods that will balance the scales. …… = 2 x 5 can then be recorded as: 10 = 2 x 5 and 10 is equal to 2 groups of 5 etc.

Once this understanding is secure, this could be extended to division; again using facts that the children are familiar with.

It is often very useful for the children to rehearse saying aloud the calculation and using the word ‘something’ in place of an ‘answer’ box or missing number. For example,

‘Something is equal to 240 divided by 8 so 240 divided by 8 is equal to something’.

Some questions to consider could be:

• how secure is the children’s understanding of the equals sign? Do they have the misconception that = means ‘the answer’ or can they articulate that = means equivalent, the same as or draw comparisons with a balance?  
• did most of the children attempt these questions or were they put off by the fact that they involve multiplication and division?
• would the children cope better with these questions had they involved addition and subtraction and if so, what does this mean about the rehearsal time provided for the children across Key Stage 2?  

Of zero importance

What do each of the following calculations have in common?

 

Those of you who know the papers well may have noticed that these are three of the 2-mark questions. But our focus here is that all of these questions involve 0 as a place holder - another subtle shift in difficulty.

0 is hard to deal with, especially when found within more complex multiplication and division calculations.

These questions aren’t the only ones that involve 0.

 

 

I wonder how many children had the age-old common misconception that 0 x 989 = 989.

If children made these same mistakes in questions 19 and 33, this would cause more than one calculation error and loss of both marks, even if using the formal method.

Throughout questions 19 and 33, the children need to deal with place holders, not only when they are multiplying by the ones and then tens, but also remembering that when multiplying by the 8 tens for example, that this is 8 tens and not 8 ones and so although 8 x 7 = 56 is a useful base fact, it is actually 80 x 7 = 420.

How many times do we see children omitting the 0 when multiplying by the tens digit and not truly thinking about the place value? Often it is the children who may remember the process – multiply by the 3 then multiply by the 8 – who do not have secure understanding when multiplying by the tens digit.  

The zero is perhaps less problematic in the dividend in question 29. However, when subtracting 292 (4 groups of 73) from 306, hopefully the children do not swap the digits around to 9 – 0 and instead see that it is 30 hundreds subtract 29 hundreds leaving 1 hundred.

What may be trickier is that children will need to consider the fact that they need to firstly regroup 3 thousands into 30 hundreds, and then 306 tens before then dividing this by 73. Do they record these place holders at the start of their quotient to help them to keep track that 306 tens divided by 73 is 4 with 14 tens remaining?

Some questions to consider could be:

• do children really understand the effect of multiplying by 0? Can they demonstrate with drawings or models how 0 multiplied by any number will always result in the product of 0 by comparing this to multiplying by 1. For example, do they say ‘1 group of 989 is 989 so 0 groups, or no groups of 989 is 0 or nothing!’
• are children secure when multiplying by tens and hundreds digits? Are they able to articulate that it is 8 tens multiplied by 7 ones and 8 tens multiplied by 6 hundreds for example.
• are children given opportunities to deal with place holders in different positions in complex multiplication and division calculations? For example, are they presented in divisors and dividends? Are they needed in different positions in the quotients? Are questions written carefully so that all of these opportunities arise?

The only way is long division…

Let’s turn our attention to long division as our final difference.

In the mark scheme, children are able to gain a mark if they use the formal methods of either short or long division to solve appropriate questions – in the case of 2022, this is for questions 17 and 29.

 

 

Children are often encouraged to use these methods for these types of calculations as the mark scheme states that, ‘If the answer is incorrect, award ONE mark for the formal method of division with no more than ONE arithmetic error’.

Those of you who have had a lot of experience with the KS2 assessments are likely to know that in the past, all divisors (the number that we are dividing by) used for the 2-mark division questions have been prime numbers.

For example, divisors in the past have been 23 and 97 (2018) and 37 and 83 (2019).

However, this year, the divisor of 21 was used in question 17 – a composite number.

This opens the potential to solve this calculation using knowledge of factors and so potentially making this a more manageable calculation.

• if dividing 672 by 3 first, both 6 hundreds and 72 tens are divisible by 3 perhaps using base facts or knowledge of the distributive law?

  For example, regrouping 72 into 60 and 12. 672 divided by 3 is 224 which could then be divided by 7 (3 x 7 = 21 – the divisor) to give 32.

 

 

• if dividing by 7 first, 67 tens divided by 7 is a manageable calculation using the knowledge that 63 divided by 7 is 9. This would then leave a remaining 42 ones which is a multiple of 7.

  672 divided by 7 is 96 which can then be divided by 3 to give 32.

 

 

In the examples above, you will see that formal methods of division have still been used as a step in solving the original calculation, but these have been simplified by working with the individual factors in turn as divisors instead of 21.

To caveat this, had the children used a method other than a formal method of division and made 1 calculation error, they would not have been awarded a mark for their working out.

It could also be argued that using long division for this calculation (21 is quite a friendly number to multiply after all) using the factors complicates the method.

However, this question nicely highlights that multiple strategies could be used to reach the answer and their efficiency may change from child to child.

It also highlights that when children are rehearsing division methods, all methods should be explored and celebrated. In fact, for those who are very fluent with methods for division, having a formal method banned in a lesson could be more challenging and encourage flexibility and creativity.

Of course, when time is pressured, such as in the actual sitting of SATs papers or using them as a formal practice in readiness, children should be encouraged to use their most efficient and accurate methods.

Some questions to consider could be:

• what does the progression of division methods look like across key stage 1 and key stage 2 in your school?
• are children given opportunities to solve calculations in multiple ways and are calculations written to allow multiple methods e.g., using a prime number as a divisor?
• are different calculation methods shared and celebrated?

As mentioned in the previous blog, this series of blogs has been written before the QLA (question level analysis) is available and so it will be interesting to compare how your children did against national data especially where there has been a change in the way questions have been presented and subtle shifts in complexity.

If you have a chance to have a look at your data, you may want to use the ‘questions to consider’ throughout both blogs to consider implications for teaching and rehearsal, such as:

• checking foundational understanding by tracking back to simpler examples and
• ensuring variation in the types and presentation of questions that children are exposed to and explore.

Year 6 SATs analysis toolkit

The ‘Year 6 SATs analysis toolkit’ provides teachers and subject leaders with a suite of resources and analysis tools to identify specific areas of learning strength and development for pupils and classes when using any past SATs papers as practice (2016-2022).

Accompanying the analysis spreadsheets, documents and progress tracker is a digital guidance video that explains each of the resources and how to use them.

Included with HfL PA Plus subscription and available to purchase from:

Mathematics - Year 6 SATs analysis toolkit

References

• Mathematics test framework: National curriculum tests from 2016 for test developers
• 2017 Key Stage 2 mathematics paper 1: arithmetic
• 2018 Key Stage 2 mathematics paper 1: arithmetic
• 2019 Key Stage 2 mathematics paper 1: arithmetic
• 2022 Key Stage 2 mathematics paper 1: arithmetic
• 2022 Key stage 2 mathematics test mark schemes

Contains material developed by the Standards and Testing Agency for 2016, 2017, 2018, 2019 and 2022 national curriculum assessments and licensed under Open Government Licence v3.0.

 

I don’t think that we can write a blog series about the 2022 KS2 SATs without firstly acknowledging the disruption to the last 3 years of education which has been vast and varied. However, no matter whether you agree or disagree that the assessments took place this year, the fact is that they did. So, what can we learn from them?

In our first blog in the series, we explored the similarities between the 2022 and previous arithmetic papers with particular comparisons to 2019. In this blog, we will switch our focus to the differences. Finally, in the third blog of the series we will consider the reasoning papers.

I also think that it is really important to remind ourselves that this blog is not just for Year 6 teachers – this is a KS2 assessment at the end of the children’s primary school journey and so all teachers are involved!

Quick domain and year group comparison

Before we dive into key differences we have noted as a maths team, let us just touch on some of the similarities between the 2019 and 2022 arithmetic papers in terms of the domain and year group coverage as shown in the mark schemes.

As detailed in the first blog, the domain coverage remains much the same with the majority of marks shared between calculations and fractions, decimals and percentages (although as detailed in the previous blog, we should note the ‘hidden’ importance of place value understanding). With regards to year group coverage, the picture looks roughly the same across the two years as shown in the tables below:

 

 

In these tables, the primary reference from the mark schemes has been used. The total of 40 refers to the number of marks in the paper with the four 2-mark questions being attributed to Year 6 calculations.

These are referenced in the mark scheme as 6C7a (multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication) and 6C7b (divide numbers up to 4 digits by a two digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context).  

It is useful to note these similarities as it may be assumed that the types of questions asked will be largely the same which is fair to say, and it could be argued that the paper follows a very similar procedure in terms of the writing but in this blog, we will explore some of the more subtle differences and consider their implications.

A tricky opener?

Let’s start at the beginning with the very first question. Historically, the first question, or perhaps the first few questions, have been relatively comfortable for many of the children to access with questions such as:

 

 

Here is this year’s (2022) question which could be argued is a fairly tricky opener:

 

 

How do you do yours?

How did your children tackle this? I wonder how many children may have relied on a formal written method here but made the following errors:

• lined up the place value columns incorrectly given that one number is 4-digit and the other two are 3-digit?
• lined the columns up correctly however when calculating, made errors when adding three 1-digit numbers?
• or made calculating errors when needing to deal with the regroups required in the ones, tens and hundreds columns?

 

 

It would be interesting to use similar questions with classes this year to explore the calculation strategies that the children are choosing to use.

When adding 5 ones, 1 one and 9 ones, do they recognise the complements to 10 and then add 5 more?

Or perhaps when adding 5 tens, 0 tens and 4 tens, do they notice that this could be calculated by doubling 4 tens and adding 1 more ten (and then the regrouped ten from the ones column of course)?

Or perhaps they recognise that if adding the two 3-digit numbers, this could be rebalanced from 501 + 649 to 500 + 650; subtracting 1 from 501 and adding 1 to 649 to keep the sum equal.

1,150 could then be added to 6,155 – perhaps with the children rebalancing again to 1,100 and 6,205 by adding and subtracting 5 tens.

Some questions to consider could be:

• are the children over reliant on formal written methods and if so, do they use these accurately?
• do children have a ‘toolkit’ of strategies and choose these appropriately depending on the numbers at hand?
• is this ‘toolkit’ of strategies built up across the primary phase and revisited often so that children are confident with strategies?
• how often are children given opportunities to use multiple strategies to solve a calculation and then assess efficient and inefficient methods?
• how fluently can children add and subtract 1-digit numbers? Might strategies such as complements to 10, think or make 10, rebalancing, and doubles and near doubles be worth revisiting?

Equal shmequal?

The next difference worth noting is around the concept of the equals sign. As we know from much of our work with teachers and children, when the equals sign is in a less familiar position – perhaps the start of the calculation rather than the end – that this can cause problems.

Why?

Because the children don’t have a secure understanding of the role of the equals sign and what it actually means.

 

 

Having said this, in 2019, the QLA (question level analysis) recorded that the questions above had an average correct response rate of 94% and 93% so not only did the children cope with the fact that the equals sign is at the start of the calculation, they had accurate methods to solve the calculations. It may well be worth comparing how this year’s cohort got on with the following 2 questions:

 

 

Arguably, the calculations needed here should be well within in the grasp of Year 6 children, using their place value knowledge and base facts to solve question 7 and then perhaps a formal method of short multiplication for question 15 (Year 4 content). The shift here is to understanding the role of the equals sign and tackling the division and multiplication calculations which may be operations that children feel less confident with.

If some children are unsure about the role of the equals sign, perhaps only seeing it as meaning ‘the answer’, it would be worth specific exploration of this using equipment such as pan balances and Cuisenaire rods.

For example, start with a fact that the children are confident with and a question such as …… = 2 + 5 and allow children to explore using the rods. Which rod is needed to balance the scales?

Recordings or descriptions could be in the form of:

• 7 = 2 + 5
• 7 is the same as 2 + 5 or
• 7 is equivalent to 2 + 5.

This could then be extended to ….. = 2 x 5 with the children placing 2 lots of the rod worth 5 in one side of the balance and then finding the rod or rods that will balance the scales. …… = 2 x 5 can then be recorded as: 10 = 2 x 5 and 10 is equal to 2 groups of 5 etc.

Once this understanding is secure, this could be extended to division; again using facts that the children are familiar with.

It is often very useful for the children to rehearse saying aloud the calculation and using the word ‘something’ in place of an ‘answer’ box or missing number. For example,

‘Something is equal to 240 divided by 8 so 240 divided by 8 is equal to something’.

Some questions to consider could be:

• how secure is the children’s understanding of the equals sign? Do they have the misconception that = means ‘the answer’ or can they articulate that = means equivalent, the same as or draw comparisons with a balance?  
• did most of the children attempt these questions or were they put off by the fact that they involve multiplication and division?
• would the children cope better with these questions had they involved addition and subtraction and if so, what does this mean about the rehearsal time provided for the children across Key Stage 2?  

Of zero importance

What do each of the following calculations have in common?

 

Those of you who know the papers well may have noticed that these are three of the 2-mark questions. But our focus here is that all of these questions involve 0 as a place holder - another subtle shift in difficulty.

0 is hard to deal with, especially when found within more complex multiplication and division calculations.

These questions aren’t the only ones that involve 0.

 

 

I wonder how many children had the age-old common misconception that 0 x 989 = 989.

If children made these same mistakes in questions 19 and 33, this would cause more than one calculation error and loss of both marks, even if using the formal method.

Throughout questions 19 and 33, the children need to deal with place holders, not only when they are multiplying by the ones and then tens, but also remembering that when multiplying by the 8 tens for example, that this is 8 tens and not 8 ones and so although 8 x 7 = 56 is a useful base fact, it is actually 80 x 7 = 420.

How many times do we see children omitting the 0 when multiplying by the tens digit and not truly thinking about the place value? Often it is the children who may remember the process – multiply by the 3 then multiply by the 8 – who do not have secure understanding when multiplying by the tens digit.  

The zero is perhaps less problematic in the dividend in question 29. However, when subtracting 292 (4 groups of 73) from 306, hopefully the children do not swap the digits around to 9 – 0 and instead see that it is 30 hundreds subtract 29 hundreds leaving 1 hundred.

What may be trickier is that children will need to consider the fact that they need to firstly regroup 3 thousands into 30 hundreds, and then 306 tens before then dividing this by 73. Do they record these place holders at the start of their quotient to help them to keep track that 306 tens divided by 73 is 4 with 14 tens remaining?

Some questions to consider could be:

• do children really understand the effect of multiplying by 0? Can they demonstrate with drawings or models how 0 multiplied by any number will always result in the product of 0 by comparing this to multiplying by 1. For example, do they say ‘1 group of 989 is 989 so 0 groups, or no groups of 989 is 0 or nothing!’
• are children secure when multiplying by tens and hundreds digits? Are they able to articulate that it is 8 tens multiplied by 7 ones and 8 tens multiplied by 6 hundreds for example.
• are children given opportunities to deal with place holders in different positions in complex multiplication and division calculations? For example, are they presented in divisors and dividends?
• are they needed in different positions in the quotients? Are questions written carefully so that all of these opportunities arise?

The only way is long division…

Let’s turn our attention to long division as our final difference.

In the mark scheme, children are able to gain a mark if they use the formal methods of either short or long division to solve appropriate questions – in the case of 2022, this is for questions 17 and 29.

 

 

Children are often encouraged to use these methods for these types of calculations as the mark scheme states that, ‘If the answer is incorrect, award ONE mark for the formal method of division with no more than ONE arithmetic error’.

Those of you who have had a lot of experience with the KS2 assessments are likely to know that in the past, all divisors (the number that we are dividing by) used for the 2-mark division questions have been prime numbers.

For example, divisors in the past have been 23 and 97 (2018) and 37 and 83 (2019).

However, this year, the divisor of 21 was used in question 17 – a composite number.

This opens the potential to solve this calculation using knowledge of factors and so potentially making this a more manageable calculation.

• if dividing 672 by 3 first, both 6 hundreds and 72 tens are divisible by 3 perhaps using base facts or knowledge of the distributive law?

  For example, regrouping 72 into 60 and 12. 672 divided by 3 is 224 which could then be divided by 7 (3 x 7 = 21 – the divisor) to give 32.

 

 

• if dividing by 7 first, 67 tens divided by 7 is a manageable calculation using the knowledge that 63 divided by 7 is 9. This would then leave a remaining 42 ones which is a multiple of 7.

  672 divided by 7 is 96 which can then be divided by 3 to give 32.

 

 

In the examples above, you will see that formal methods of division have still been used as a step in solving the original calculation, but these have been simplified by working with the individual factors in turn as divisors instead of 21.

To caveat this, had the children used a method other than a formal method of division and made 1 calculation error, they would not have been awarded a mark for their working out.

It could also be argued that using long division for this calculation (21 is quite a friendly number to multiply after all) using the factors complicates the method.

However, this question nicely highlights that multiple strategies could be used to reach the answer and their efficiency may change from child to child.

It also highlights that when children are rehearsing division methods, all methods should be explored and celebrated. In fact, for those who are very fluent with methods for division, having a formal method banned in a lesson could be more challenging and encourage flexibility and creativity.

Of course, when time is pressured, such as in the actual sitting of SATs papers or using them as a formal practice in readiness, children should be encouraged to use their most efficient and accurate methods.

Some questions to consider could be:

• what does the progression of division methods look like across key stage 1 and key stage 2 in your school?
• are children given opportunities to solve calculations in multiple ways and are calculations written to allow multiple methods e.g., using a prime number as a divisor?
• are different calculation methods shared and celebrated?

As mentioned in the previous blog, this series of blogs has been written before the QLA (question level analysis) is available and so it will be interesting to compare how your children did against national data especially where there has been a change in the way questions have been presented and subtle shifts in complexity.

If you have a chance to have a look at your data, you may want to use the ‘questions to consider’ throughout both blogs to consider implications for teaching and rehearsal, such as:

• checking foundational understanding by tracking back to simpler examples and
• ensuring variation in the types and presentation of questions that children are exposed to and explore.

Year 6 SATs analysis toolkit

The ‘Year 6 SATs analysis toolkit’ provides teachers and subject leaders with a suite of resources and analysis tools to identify specific areas of learning strength and development for pupils and classes when using any past SATs papers as practice (2016-2022).

Accompanying the analysis spreadsheets, documents and progress tracker is a digital guidance video that explains each of the resources and how to use them.

Included with HFL Education PA Plus subscription and available to purchase from:

Mathematics - Year 6 SATs analysis toolkit

References

• Mathematics test framework: National curriculum tests from 2016 for test developers
• 2017 Key Stage 2 mathematics paper 1: arithmetic
• 2018 Key Stage 2 mathematics paper 1: arithmetic
• 2019 Key Stage 2 mathematics paper 1: arithmetic
• 2022 Key Stage 2 mathematics paper 1: arithmetic
• 2022 Key stage 2 mathematics test mark schemes

Contains material developed by the Standards and Testing Agency for 2016, 2017, 2018, 2019 and 2022 national curriculum assessments and licensed under Open Government Licence v3.0.

 

In 2011, the pupil premium grant (PPG) was introduced to help close the attainment gap between disadvantaged children and their peers. The funding is available for children in Reception to Year 11 and there is a set criterion for the eligibility for this funding found in the Pupil Premium overview:

• children who are eligible for free school meals, or have been eligible in the past 6 years
• children who have been adopted from care or have left care
• children who are looked after by the local authority

Service pupil premium (SPP) is additional funding for schools, but it is not based on disadvantage. Children are eligible for this funding if they have parent/carer:

• serving in HM Forces
• retired on a pension from the Ministry of Defence

Whilst this funding is a positive step in supporting disadvantaged and vulnerable children, there are a few challenges to identifying exactly who is eligible when starting Reception. These challenges include families’ lack of knowledge about the funding, later applications made due to children receiving universal free school meals or declining to apply through personal embarrassment.  There are a few strategies that schools have implemented to help gather this information sensitively to ensure all eligible children are able to receive funding sooner.

Transition procedures

It is important to gather as much information about children and their families prior to staring school. The transition level of need tool (TLoNT) should help you to identify vulnerable children to help prioritise an enhanced transition process, however, all children need effective transition procedures in place to enable them to settle into school.

• contact with feeder settings – ensure that you make time to visit the new children at their feeder setting in the summer term (PVI/school nursery/childminder). If this is a challenge, make time to have a conversation with each child’s key person remotely (telephone/video call) to find out about the child’s interests and potential barriers to learning. Use these discussions to find out whether the child is in receipt of Early Years Pupil Premium (EYPP) funding as this may be an indicator of eligibility for PPG funding. Parents/carers will still need to apply for PPG funding even if the child is receiving EYPP funding.
• parents and carers – include the PPG application form in your admissions pack as many parents/carers like to ensure they have everything prepared for their child to start school. Alternatively, take the forms with you to home visits or when having 1:1 conversations prior to the children starting. This way, you can talk it through with parents/carers or even help fill them in with them if required. There are occasions, where through home visits, practitioners will identify a vulnerability for the family, however, this might not indicate that they are eligible for PPG funding. These families still need to be monitored to ensure that should they become disadvantaged, the school are able to provide them with appropriate support.
• school events – use induction meetings to provide families with information on how the school can support them with home learning and relevant support services if required. Make families feel welcome through informal meetings or workshops to help build positive relationships. This could also be an opportunity to provide them with time to complete relevant paperwork. If you have asked families to complete documents digitally, this might be a challenge. Consider providing laptops/computers/tablets for parents/carers to access in school.

The Supporting Smooth Transitions toolkit has a wealth of information on how to enhance transition processes for children and families including resources that can be sent directly to them during the summer holidays which is when many families are most vulnerable.

 

 

Communication

Review your communication procedures to ensure that they are accessible to all families. Consider conducting a survey to find out the most effect method of communication for your families.

• emails
• texts
• school digital platforms
• social media
• telephone/video calls

If there are challenges with families understanding the communication coming from the school, this may hinder information being gathered in a timely manner. Ensure that all communication is inclusive of the families in your school community. Do you use simple, concise sentences? Do you use images or icons to enhance your messages? Have you considered recording voice notes/messages for parents/carers to be able to listen to? Can your messages be easily translated into various languages spoken at home?

Take time to review how parents/carers can communicate with the school. It should be just as effective as how the school communicates with home.

 

 

Initiatives

It could be worth offering incentives to families in return for the information required to identify eligibility such as a free…

• book bag
• school jumper
• P.E. kit

This also enables all children, including those identified as disadvantaged, to have appropriate school clothing/equipment. Whilst this type of incentive requires an initial outlay it is worth considering the long term gains. Once a child has been identified as eligible for PPG funding they will be eligible for the rest of their time in the Primary phase, irrespective of changing circumstances.

NB A child in Reception will attract £1, 385 for the Reception year and a further possible £8,310 by the end of KS2. This is a considerable amount of money to improve outcomes for that individual.

 

 

Roles and responsibilities

Whilst it is everyone’s responsibility to ensure positive outcomes for every child, it is best practice to ensure that a member of staff’s role is to monitor and evaluate the impact of funding on outcomes for disadvantaged children. One part of this role should be co-ordinating the identification of eligible families. PPG funding can be used to fund this member of staff to spend an allocated amount of time per week/term to oversee this. It would be beneficial if this person’s role included…

• attending welcome meetings and parent consultations
• contacting parents/carers either face-to-face or by telephone
• liaising with external professionals

By implementing a range of robust strategies, you will be able to identify children eligible for funding. It is then that you can consider how to allocate the funding to improve outcomes for individuals and begin to address social inequality.

For further guidance on a supporting vulnerable and disadvantaged children look at:

Resource: Making the difference - Early Years Toolkit 2021 edition - Supporting disadvantaged and vulnerable children

 

This blog has been lurking, unwritten, at the back of my mind for a while.

The danger with writing about ‘back to basics’ is that it becomes patronising, and this is not my aim. As teachers, we are a highly skilled and dedicated profession; my aim is certainly not to tell anyone what they already know.

The aim is to confirm, support and reflect on what we believe and know has impact on learning in the classroom. So that as you read, you nod along to yourself, safe in the knowledge that you already balance these suggestions appropriately, for the learning happening in your classroom or school. Like when you listen to a great speaker at an event, and they resonate with you in a way that both affirms your beliefs and strengthens your sense of purpose.

My focus is primary mathematics.

The role I play involves working with a range of schools, supporting subject leaders and teachers, modelling teaching, helping with planning, supporting learning walks, and leading staff meetings, among many other things. As a class teacher at heart, my driver is making both teaching and leadership manageable and effective, helping deep learning to happen in schools.  

After the first partial school closures in the spring/summer of 2020, what struck me was the incredible way teachers and schools so quickly adapted; to manage risk, to allow teaching and learning to happen, to create safe environments. Some choices felt like necessary measures to reduce the risk of transmission, such as children in rows where they might normally sit around tables in groups. Or giving children their own sets of stationary equipment to avoid the need to share. We were all anxious: we were worried about the risks, the impact on learning and the impact on children’s well-being.

However you feel about where we are now, 2 years on, there is definitely a feeling that things are gradually relaxing where possible and appropriate. You might be more likely to see children sat in groups again or sharing glue sticks. There might be a shared pot of pens and pencils rather than individual equipment packs. Some children in the youngest year groups may have now had their first experience of assemblies in the hall. We are finding ways to bring back our routines and systems (and holding onto some of the ones we like and have worked well for us more recently).

There has been a huge impact on children’s collective learning and well-being from the disruption of the last 2 years. We notice children have many gaps. Some of these are more social skills and self-regulation based; some more academic learning gaps.

We know we need to scaffold and track back, re-teach or pre-teach, to find and close those gaps.

So, how can we ensure our teaching is as effective as possible, particularly within this current scenario? How do we teach in a way that promotes learning opportunities, filling gaps but also aiming forwards?

Here are my thoughts, with a focus on primary maths and on the gaps within curriculum learning, but with many overlaps both across subjects and key stages.

1. identify the key learning. Where does this fit within the journey of the curriculum?
2. take a step back. What might need pre-teaching or reactivating, before children are ready to build towards the pitch you are aiming for?
3. consider your first example, model or question; make it accessible to all and then build on it.
4. model everything; the process, thinking, visuals and talk.
5. engage everyone; through the way you ask questions and call on responses.
6. allow sufficient practice and rehearsal time.
7. continually assess for learning. Does it look, feel, and sound like everyone is with you?

These thoughts in more detail:

1. identify the key learning. What is it you are trying to teach and what do you want the children to learn (to know or be able to do)? Where does this fit within the journey of the curriculum - what should have come before this and where is it going next?

2. take a step back. What might need pre-teaching or reactivating, before children are ready to build towards the pitch you are aiming for? Before launching into the learning, anticipate whether children will have the steps in place that should have come before this learning. There may be key points to re-cap or vocabulary to rehearse.

   We can sometimes be guilty of simply following our long-term plan. Whatever our long-term plan suggests, I would still ask myself; Why this? Why now? Pausing to consider what this learning builds from and builds onto. The ‘building from’ will also tell me what I need to pre-teach or reactivate, knowing that there may be gaps, insecure learning, or misconceptions.

   For example, in Year 5, I might be due to teach ‘reading timetables’ and ‘calculating with time’. Before I start, I will most likely need to check that children are secure with reading digital clocks in both 12 and 24-hour time. The learning about conversion between analogue and digital usually happens within Year 4. Reading time to the nearest minute on an analogue clock usually happens within Year 3. So, for the Year 5 learning to be successful, I need to check on this pathway, filling gaps as we go, to build solid foundations for the new learning. If I consider these aspects 2-3 weeks before the main input comes up, I could plot some of the pre-teaching and reactivation work into short maths fluency sessions, starters, or classroom routines, so that children rehearse reading an analogue clock, looking at digital 12 and 24-hour time and using the language of time (60 minutes in an hour, 24 hours in a day), before we embark on ‘reading timetables’ and ‘calculating with time’. Or I can plan in time for this at the start of the sequence of learning.

   Here is a set of matching cards to explore analogue and digital, am/pm, 12 and 24-hour time. This is from our ESSENTIALmaths planning and resources for Year 5. It’s from the first part of the sequence that focuses on reading timetables and calculating with time:
    

   

    

3. consider your first example, model or question; make it accessible to all and then build on it. Where do you need to start so that everyone understands and can follow what you are modelling?

   Using the same example as previous, ‘reading timetables’ and ‘calculating with time’, I need to select the right first example; something with a manageable amount of information. Is my focus reading timetable? How can I help the children focus on the reading and interpreting of the information?

   Again, this example comes from our ESSENTIALmaths planning and resources for Year 5.

    

   

4. model everything; the process, thinking, visuals and talk. Say and show what you are doing, how and why. Write it and draw it for pupils to see. Enable the children to ‘play along’ with the modelling. Mix modelling with questioning when the children are ready.

   This could be as simple as being really explicit about which part of the example you are explaining, pointing to and drawing everyone’s attention to the part you are thinking about. In maths, we talk about using the CPA approach (concrete, pictorial, abstract); ensuring that the physical manipulatives, pictures/diagrams and the abstract representations work together to build a deeper understanding.

5. engage everyone; through the way you ask questions and call on responses (talk partners, rough books, white boards, shared counting, choral responses and many other ways).

   For me, this one is a must. Even if the previous four points are in place, if children are just watching you, occasionally putting their hand up, they may not be truly engaged, and the understanding might not be as deep as you think. A way to allow children to process the learning and for you to assess their understanding is to use strategies such as small whiteboards and/or talk partners regularly. My personal preference is to use both. I want all children fully engaged and participating in the learning.

6. allow sufficient practice and rehearsal time. This enables children to process, develop fluency and confidence, develop understanding, and build memory. We know that when we say a child lacks confidence, we often mean they didn’t have long enough to practice and secure the learning. So, giving rehearsal time is often key for the confidence, fluency, and retention of learning.

7. continually assess for learning. Does it look, feel, and sound like everyone is with you?

   This might be during the input and can be easily done when scanning children’s whiteboards or asking questions. This might be when you are reviewing pupils’ work. The follow up to this would be:

   • what happens for the children who seem less secure?

   • what systems are in place?

Whether you are reading this as a class teacher or a subject leader (or from another school leadership role), you are probably already reflecting on whether this happens within your own classroom or school, the extent to which it happens and whether it is having the impact you want. Are learning gaps being filled gradually?

We started by saying that although this has a ‘back to basics’ heading, the aim is not to just tell you what you know, but to confirm the good practice already happening in classrooms, affirming what we do well but with a focus on ensuring that our efforts are put into the areas most likely to ensure learning happens.

The 7 points above may help to neatly summarise what we hope is happening in all primary maths classrooms, to allow all children to fully access the learning, after what has undoubtedly been a very disrupted time for them in education.

If you’re looking for support with primary maths teaching or subject leadership through in-school or remote consultancy, staff meeting or INSET sessions, please get in touch for further details.

 

As a TLA with HFL Education I have recently supported a Lower Key Stage Two teacher. She was particularly interested in the work of Derek Haylock, which she had studied at university as part of her Initial Teacher Training; and was keen to implement the ideas. As part of the Primary Mathematics Specialist Teacher Programme (MaST) that I attended at Brighton University I had significant experience of carrying out Action Research in classrooms through Case Studies based on the work of Haylock so I was also keen to be involved.

The support began with looking at maths theory linked to the teaching and learning of formal addition. Haylock (2010) asserts that the use of a variety of concrete and pictorial materials when teaching formal methods for addition and subtraction is vital if children are to understand the concepts. He advocates the use of a place value chart combined with a range of manipulatives and discusses the (often misused) terms of ‘carrying’ and ‘exchanging’ which is now more commonly referred to as ‘regrouping’.

This process is also linked to the rationale of allowing children to make connections in their learning. Haylock and Thangata (2007) assert that

‘Making connections in mathematics refers to the process in learning whereby the pupil constructs understanding of mathematical ideas through a growing awareness of relationships between concrete experiences, language, pictures, and mathematical symbols. Understanding and mastery of mathematical material develops through the learner’s organisation of these relationships into networks of connections.’

 

(Adapted from Haylock, D., and Thangata, F. (2007), Key Concepts in Teaching Primary Mathematics, London: Sage p.34.)

 

The teacher and I discussed how these networks can be effectively built through the children communicating their ideas across all situations in a variety of ways that allow them to demonstrate their clear understanding. Recognition of these relationships needs to be facilitated in cyclical ways to allow for both continued consistency of approach and subsequent impact. 

I was keen to implement these ideas in a Year Three class, where common misconceptions were not in the process of carrying out the formal method of addition but were concerned with the children’s explanations (and consequent understanding) of the mathematical processes. This was prevalent within a group of six children (I taught these children in two sessions with the Year Three teacher present).

My rationale for this, in terms of mathematical progression, was guided by the National Curriculum for Mathematics 2014 (NC) statement for Year Three:

‘Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction’

and the Related NC Statements of:

‘recognise the place value of each digit in a three-digit number (hundreds, tens, ones)’ – ‘identify, represent and estimate numbers using different representations’

and

‘add and subtract amounts of money to give change, using both £ and p in practical contexts’.

I also wanted the children to discuss their mathematical work and begin to explain their thinking, e.g., use appropriate mathematical vocabulary to talk about their findings by referring to their written work. My methodological approaches were to both engage in participant observation, interpret the verbal responses and to analyse written responses for conceptual understanding and correct use of the arithmetic operation of formal addition.

Assessment of their previous work saw the children having instrumental understanding (Skemp, 1989) where they have a mechanical, rote or 'learn the rule/method/algorithm' kind of learning but not relational understanding which is a more meaningful learning where the pupils are able to understand the links and relationships which gives mathematics its structure. My aspirations were to use the concrete materials to elicit the latter.

I discussed with the Year Three teacher how Haylock’s (2010) analysis of the terms ‘carrying’ and ‘exchanging’ and their associated confusion for children when carrying out formal methods for addition led to his recommendations for the use of resources where coins and number lines can be used in the exploration of the related place value.

 

 

 

(Haylock, D. (2010), Mathematics Explained for Primary Teachers, 4th edition, London: Sage p.14.)

 

Implementation and analysis

As a preliminary exercise the children used the Base 10 equipment and played the ‘Race to 100’ game from ESSENTIALMaths which is demonstrated by my colleague Gill Shearsby-Fox: Race to 100 (see link for details).

The overarching aim here was for the children to understand the term ‘regrouping’ where, for example, ten ones have the same value as one ten so ten ones can be regrouped as one ten and the ten ones can be exchanged for one ten. As a continuation of the preliminary exercise, I also related the coins to the Base 10 equipment and demonstrated how the ‘ones’ matched the pennies, the tens block matched the ten pence pieces and the hundred block matched the pound coins. I demonstrated that the coins could be exchanged between each other which had the same equivalent value. This involved exchanging ten pennies for a ten pence piece and ten, ten pence pieces for a pound coin. We also included, for example, 13p as 13 pennies exchanged for a ten pence piece and three pennies. The ‘Race to 100’ game was also played using coins.

All the coins were in a ‘bank’ which the children used to complete their regrouping and exchange transactions. The rationale for this was that they could then physically ‘carry’ the Base 10 equipment and the coins across to the next column in the Place Value chart.

The next step was to include the coins in an A3 sized place value chart alongside the Base 10 equipment (see below). 

 

 

Firstly, we placed coins and concrete materials and regrouped them and ‘carried’ them across without making formal calculations e.g. thirteen one pence pieces were placed in the ones column and ten were exchanged in the bank and then carried over to show one ten piece in the tens column and three pennies in the ones column. This was continued with the ten pence pieces and the pounds and with the Base 10 equipment. The children ‘played’ with this idea and constructed their own different amounts. They were then asked to show specific amounts and explain their reasoning. The next stage involved the use of the A3 place value grid to carry out formal addition calculations.  Digits were place in the columns with the coins as headings and the titles of ‘Hundred’, ‘Tens’ and ‘Ones’. The Base 10 equipment was also placed in each column. Another set of digits was placed underneath alongside concrete materials and the children added together the two, three-digit numbers. This was carried out initially without bridging tens or hundreds to show the initial concept. Bridging was then introduced in the ones and tens columns only, followed by another calculation with bridging to one hundred and beyond but not to one thousand (see below).

 

 

This is the result of 152 + 119. The one’s column had eleven ‘ones’ in it. Ten of these were regrouped for a ten pence piece which was carried and is underneath the tens column along with the ten block from the Dienes Apparatus. This was also shown as a written algorithm.

 

 

The children explored this idea before I demonstrated, using the concrete resources, how the number that was regrouped was carried over was put below the calculation line to be added in the next column. This was accompanied by the same formal calculation to show the connections between the formal methods with and without concrete materials. This realisation conforms with Haylock and Thangata’s (2007) ideas for children making networks of connections.

The thought process here was to allow the children to gain relational understanding from progressive steps. They then constructed and answered their own calculations and then they were asked to create calculations that would bridge ten and one hundred, and then answer them. This encompassed Bruner’s (1960) ‘Mode of Representational Thought’ where children need experience of mathematics at the three levels of ‘iconic’ (the Dienes apparatus and the coins), ‘symbolic’ (the calculation as numbers) and ‘enactive’ (manipulation of the concrete materials).

Findings

The impact was dramatic. All the children demonstrated and asserted that they understood the concepts. Their reactions were vociferous with typical 21st Century comments such as: ‘I get it, I SO get it!’, ‘That is sick!’ and ‘Wow, I understand completely!’ They were then asked to write calculations and explain their understanding verbally and in writing. The children took great delight in explaining that the small figure ‘one’ under the calculation was actually a ten or a hundred carried across after it had been exchanged (see below).

 

 

Conclusions and next steps

The specific and progressive implementation of resources based on analysis of maths theory compounded the children’s understanding by giving them a holistic overview. This was evidenced throughout the process and used and applied effectively. The children had clearly made a network of connections in their processes of learning where they constructed understanding of mathematical ideas through a growing awareness of relationships. 

 

(Adapted from Haylock, D., and Thangata, F. (2007), Key Concepts in Teaching Primary Mathematics, London: Sage p.34.)

 

As the graphic above shows, the children should also be able to make the connection between the coins and Place Value counters and reason mathematically to solve a calculation such as this:

 

 

This is planned to be continued with the teaching of zero as a place holder and subtraction for the children to make further connections especially with regard to decomposition and inverse operations. They should also be able to make connections with money and its equivalents and the concept of decimals should be made easily transferable through the children’s enhanced understanding of place value.

Haylock (2010) also asserts that although the National Curriculum for Mathematics (2014) outlines that ‘Calculators should not be used as a substitute for good written and mental arithmetic’, they could be used as an abstract resource especially with regard to the teaching of money. If the children are asked to put ‘one pound and five pence’ into a calculator, it will help to focus their thinking on the underlying mathematical structure of the situation and be able to enter £1.05 and not £1.5 with the latter being a common misconception.   Using the devices in this way as resources utilises them as companions to be included in a network of connections and not alternative methods.

The key point from the exercise is that the manipulation of the concrete resources, based on pedagogical theory related to the effective teaching of primary mathematics, demonstrated the connected understanding for the children who can then move confidently into the abstract and solve calculations with clear understanding.

The Year Three teacher asserted that she recognised the benefits of the both the rationale and the process and aspired to implement it further to continue to enhance her pedagogy.

Other recent related blogs from HFL Education include:

Back to basics in the maths classroom – 7 ways to make learning happen

What do we mean by ‘pictorial’ in the CPA approach?

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References

Bruner, J. (1964), Towards a Theory of Instruction, London: Belknap Press in Delaney, K. (1992), Teaching mathematics resourcefully, in Gates, P. (Ed), (2001) Issues in Mathematics Teaching. London: Routledge Falmer.

Haylock, D. (2010), Mathematics Explained for Primary Teachers, 4th edition, London: Sage.

Haylock, D., and Thangata, F. (2007), Key Concepts in Teaching Primary Mathematics, London: Sage.

National Curriculum for Mathematics (2014) https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study [Accessed 22 September 2022].

Skemp, R. R. (1989), Mathematics in the Primary School, London: Routledge.

UCL Libraries, (2014), http://libguides.usc.edu/content.php?pid=83009&sid=616083

[Accessed 22 September 2022].

 

 

What are your first thoughts when a colleague discloses a mental health issue to you? Is it ‘I don’t know how to respond to this’? If you’re a line manager, do you instantly worry that this disclosure will result in increased sickness absence? Maybe you’d worry about the employee’s ability to do their job? Or do you feel confident and comfortable enough to have an open discussion with them before making any preconceived judgements?  

If your first thought is ‘how best can I support this person?’ – amazing, the chances are you are part of an empathetic workplace that have succeeded in encouraging open discussions around mental illness; your setting is likely to have positive practices that help create an inclusive work climate - which is the goal.   

What can you do to get to that point? Unfortunately, not everyone understands mental health problems. Some people may have misconceptions about what certain diagnoses mean. I personally have struggled with Generalised Anxiety Disorder, Social Anxiety, SAD and PMDD for years. I don’t mind people knowing this now, but it took a long time for me to open up about it to my employers. I’m fortunate that I have a supporting senior leadership team and I hope they’d agree that this diagnosis hasn’t affected my ability to do my job. Them having the knowledge of my mental health issues, along with my Insights Discovery profile - which uses a model of 4 colour energies to help people understand themselves and others - they are fully equipped to understand my preferences and there is no stigma (I’m very ‘cool blue’/’earth green’ for those who are familiar with it!). Unfortunately, stigma and discrimination still exist in some workplaces, and that stigma can negatively affect relationships, work, education and the chance to live a normal life. Something that others often take for granted. Take a moment to think about whether there may be a feeling of prejudice at your setting around mental health disclosures. Recognising and accepting this is key to creating inclusivity. 

 

 

I appreciate that education settings are already doing a huge amount of work in terms of mental health and well-being – does your setting focus as much on staff well-being as it does its pupils well-being? Ideally, speaking about mental health problems should be an intrinsic part of the culture of your setting. Health is not always seen as a strategic enabler that drives performance. But it should be. If we feel well, we can perform better and of course this has a knock-on effect on the success and school experience of your pupils. If someone asked you the question ‘how do you encourage your staff to have open conversations about mental health?’, what would you say? One option for consideration might be the HFL Wellbeing Quality Mark which has a module on Staff Wellbeing.  

Talking about mental health can be difficult but it’s important to note that you don’t need to be an expert to talk about mental health, you are not expected to make a diagnosis or have all the answers. In many ways, it should be approached in the same way you would any other kind of health-related problem – seek specialist input. What you can do is ask questions and be willing to spend time listening to their answer. Imagine if that one question meant your colleague opened up about feeling overwhelmed and, for example, they disclosed to you that during their PPA time there’s a chatterbox who has PPA at the same time and they can’t concentrate so they’re getting further and further behind. Something so easy to resolve but not something they’ve been able to manage or had the confidence to address themselves. I appreciate issues are not always that straight forward but asking simple, open and non-judgmental questions and letting your employee explain in their own words how their mental health problem manifests, the triggers, how it impacts on their work and what support they think they might need, will help. Small changes you can make in your settings can go a long way in supporting someone’s mental health. Mind have some useful resources as a first step  

 

 

Earlier in the year I presented a ‘Managing staff well-being and mental health disclosures’ webinar to a school who wanted a bespoke session for their line managers at one of their inset days and ironically, for days I spent the lead up incredibly anxious and subdued, and after the session I spent days over-thinking perhaps what I should have said, or not said - but that doesn’t mean I can’t do it – I realised after this that I may just have to prepare differently to someone else and accept that any intrusive thoughts and the fatigue that follows will pass. The relationship between our performance and mental health is complex. Some people ask me how I can work in Human Resources when I have social anxiety, but for me it’s easy, there’s a purpose, a focus to the discussions and advice, it’s easy because it’s my job and it’s familiar; but send me to a school reunion with a room full of people I haven’t seen for over 20 years (how much over 20 I won’t disclose!) and I’ll be out of there quicker than you can say “small talk”!  

It is often wrongly assumed that all mental health problems lead to underperformance. It might be that it just helps for your colleagues to know, and it may explain some behaviours. It can feel scary but have, or encourage, that conversation.  

Another great tip is to be aware of what is happening in people’s personal lives as stress outside of work, for example due to illness, bereavement or financial worries might be contributing to them struggling to cope in the workplace. Again, have conversations, communication is key. It might be that you need to seek advice and support yourself. You’re not expected to have all the answers. It might be that you need to make an Occupational Health referral or if relationships have become strained or confrontational, mediation might help. Does your setting have an Employee Assistance Program you can direct employees to? If not, perhaps your setting could consider adopting one.   

 

 

I really like this Equality vs Equity illustration with the bikes, I thought it was a bit different to the one we’re all familiar with illustrating the stools. The supportive measures, the tools we use, look different for different people, there is no one size fits all when it comes to supporting a mental health issue. Traditionally employers have been aiming for equality to reach a more level playing field - what this doesn’t do though is take into account an employees’ physical, mental and emotional needs, which means in reality it continues to deliver an unbalanced end result. The concept of equity is to understand the individual needs of each person – and to offer a different level of support, so that each employee can reach the same outcomes as others. By striving for equity where possible, employers can create inclusive and diverse workplaces where everyone is given equal opportunity to succeed. I urge you to have a think about what this might look like in your setting, with your staffs’ different needs.  

If you notice someone who appears to be struggling, make the first move in encouraging the disclosure of a problem, it could be related to mental ill health. 

If you’re feeling overwhelmed, you have to reach out to somebody. You can’t do it alone. Whether it’s a friend, a colleague, a mental health first aider, a professional – reach out. 

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But – now that I’m actually doing it, I am recognising the same problem that is always there when I’m working with schools on designing a poetry curriculum. Namely: where to start?

It’s a problem that’s also a delight as there are so many possibilities, but it is important to clarify a few things at the beginning before we all disappear down the poetry rabbit hole. So, I tend to ask the subject leaders I’m working with to think first about two things:

• what do you want from your poetry curriculum?
• what do you want your children to get from it?

The answers have been many and varied. A few examples include: investigating a wide variety of poetic forms; linking poetry to other ongoing themes; exploring poetry and poets they are unlikely to meet anywhere else; building vocabulary; embedding an understanding of rhythm and metre in fun ways; engaging with image-rich language; developing spoken language through recital. I could go on and on! Most people want many things, but to keep the task manageable we’ve needed to pinpoint down to a few priorities for that subject leader and school – at that time. A curriculum can, and should, grow and change.

Once we’ve agreed the core intentions of this poetry curriculum, it’s at that point that we’d go to the national curriculum to see what actually, we have to incorporate.

There, we find the following. The box below contains the statements that include poetry as a part of the literature that children need to read, have read to them, immerse in, discuss and enjoy. (The bold is mine.)

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Y1

listening to and discussing a wide range of poems, stories and non-fiction at a level beyond that at which they can read independently

Y2

listening to, discussing and expressing views about a wide range of contemporary and classic poetry, stories and non-fiction at a level beyond that at which they can read independently

recognising simple recurring literary language in stories and poetry

participate in discussion about books, poems and other works that are read to them and those that they can read for themselves, taking turns and listening to what others say

explain and discuss their understanding of books, poems and other material, both those that they listen to and those that they read for themselves.

Y3/4

listening to and discussing a wide range of fiction, poetry, plays, non-fiction and reference books or textbooks

Y5/6

continuing to read and discuss an increasingly wide range of fiction, poetry, plays, non-fiction and reference books or textbooks

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I wouldn’t quarrel with any of it, although we do always end up pondering over why Y2 has so much more detail than the other years? And we normally decide that the last two statements in Y2 are equally applicable in years 3 to 6.

Then also, there are statements that are specific to the poetry element of an English curriculum.

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Y1

learning to appreciate rhymes and poems, and to recite some by heart

Y2

continuing to build up a repertoire of poems learnt by heart, appreciating these and reciting some, with appropriate intonation to make the meaning clear

writing poetry

Y3/4

preparing poems and play scripts to read aloud and to perform, showing understanding through intonation, tone, volume and action

recognising some different forms of poetry [for example, free verse, narrative poetry]

Y5/6

learning a wider range of poetry by heart

preparing poems and plays to read aloud and to perform, showing understanding through intonation, tone and volume so that the meaning is clear to an audience

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Once again, there are some peculiarities. Why are children expected to write poetry in Y2, but not in other year groups? Why are poetic forms a part of the Y3/4 expectations, but learning poetry, unlike in the other year groups, is not?

I think in all of the schools that I’ve done this with, (after we’ve finished enjoying exclaiming about inconsistency), we’ve agreed to iron those inconsistencies out. Here is an example of how we did this:

You will see that there were some generalisations common to all of the schools – keep them learning poetry in LKS2 as the prime example. The other important one was around poetic forms. By and large, we agreed that exposing KS1 children to some different poetic forms would support embedding the statutory expectation about recognising some different forms of poetry for the children in years 3 and 4. And also, that extending this to UKS2 would broaden and deepen that knowledge.

Beyond that though, the schools became brilliantly different in their approaches and desires. Most decided they wanted about six weeks of poetry, but for some that was one week every half term, for others, one two-week block every term, for others a mixture of those things. All will work; ‘which will work best for you?’ was always my question. (These were English lesson units. Some people wanted more, with additional poetry in some cases being read, discussed and enjoyed at other points in the day or as part of ‘guided reading’ lessons.)

Then, carving up the ways in which the expectations are delivered across the schools produced more variety. Some examples are below. My apologies for the different fonts; these are snipped from original documents.

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When doing this, we found it helpful to look at some different options as a way of expanding the discussion about what is possible. And at this point, I’ve tended to suggest going back to staff and sharing what we’ve agreed so far. Class teachers are the ones who have to deliver the curriculum and often people have favourite poems they want to include or poetic forms that they have tried and tested ways of teaching. We can add all of those preferences into the second stage of planning a poetry curriculum: that of choosing the content.

In most cases and apart from poem choices that teachers have requested, we’ve tended to populate the curriculum – usually at the class teachers’ requests for this first year. The hope has been that through teaching poetry, confidence will grow around choosing which poems to teach.

In the meantime though, we’ve chosen for them by:

• remembering old favourites
• leafing through anthologies – stopping to read aloud
• browsing websites – there are some fabulous ones, often with poets performing their own work.

And then we’ve needed to cross-check and question to ensure that:

• there is a mixture of contemporary and classic poems in each year group
• both male and female poets are present
• diversity has been taken into account
• any constraints from our original intentions (such as links across the curriculum for example), have been met

It’s never been easy! But it has always been fun and so satisfying. As a thought though, I’ve never done one, but actually, a ‘poetry choosing’ twilight CPD meeting, where staff could browse and compare and discuss might well be a pretty effective way of building some core content … If anyone decides to try that, do let us know.

I want to finish by coming back to a couple of sentences earlier in this blog,

A curriculum can and should, grow and change.

The hope has been that through teaching poetry, confidence will grow around choosing which poems to teach.

To design a poetry curriculum in the first place can be quite an orderly, systematic process. Managing a large and important task by breaking it down into small steps needn’t make it boring; it just makes it easier. But what is truly important is to then keep reflecting on whether it’s providing the impact and outcomes that you want it to. Review it. Ask the teachers and the children how they’ve enjoyed it. Are there particular poems they remember? What was it about those poems? Is there anything they’d like more of? Is confidence growing about choosing poems for themselves?

And be prepared for (in fact be joyful about) reinventing your poetry curriculum from year to year.

 

Many schools and academies are cautious about outsourcing their payroll provider. Payroll is a time-critical activity, so understandably this makes people nervous about making the change.   

However, with payroll software providers streamlining processes, offering comprehensive reports and easy to use tools at your fingertips, your team could claw back invaluable time to focus on other important tasks.   

In the current financial struggle, as education settings look to find efficiencies and cut spending in every direction possible, changing providers can save you time, energy and money.   

Here’s our five top tips to successfully move your payroll provider:   

1. Establish what you need from your payroll provider

Understand from your workforce what the full payroll requirements are and make an extensive list of service requirements. Are there any pain points that need to be addressed? Could you use this opportunity to expand your offer?   

2. Discover  

Research the market for payroll providers that are experts in the education sector, so that they can better suit your needs. Are they experienced in the different types of contracts you use? Ensure all suppliers are compliant with HMRC legislation, and they have a trusted security network to avoid any kind of data breach. Have they had the seal of approval, for example from the CIPP Payroll Assurance Scheme (PAS).  

3. Read the fine print  

Opt for a payroll provider with fixed costs. The last thing you need is to receive bills for hidden services during the year. Check that your above list of services are included in plan proposals. i.e Can statutory deductions and expense claims be calculated automatically.  

4. Migration   

Migration of your data is crucial. Check that your payroll provider offers support with this service, and that the costs have been included within your proposal. How are you going to switch from one provider to the next. Do they recommend a dummy phase or perhaps running two software providers in parallel. What effect will this have on your bottom line?  

5. Customer support and training  

Support: When you urgently need to speak to someone how can you make contact with them? Will you have a named member of staff that you can direct queries too or do you need to submit tickets via email? If so, what is their response time?  

Training: How are you going to make the most out of your new payroll software? What tools will be provided to train your staff? Are there demo videos, self-help documents or online webinars? How do your team prefer to learn?  

Above all do your research and work out what is best for your setting, you might be surprised by what you could get.  

 

I have the privilege of working with many schools across Hertfordshire and over the borders into other areas too. As you may or may not be aware, the HfL Education Primary maths team spend most of our time working in schools with children, teachers, and subject leaders to support the implementation of the maths curriculum.

Our work includes everything from working with individual children to develop their mathematical learning, to team teaching with teachers to look at pedagogy in maths lessons, action planning and monitoring with maths subject leaders and maths curriculum development. As you can see, everything to do with maths! We work with schools regularly over longer periods of time, so we get to know them well, so our support is bespoke.

This means, using Ofsted speak, we support schools with the ‘3 Is’ of their maths curriculum; their intent, implementation, and the impact.

In this blog, I would like to tell you about the journey I am currently on with two of my schools that offer special provision for pupils with special educational needs and disability (SEND).

Southfield is a primary school for approximately 80 pupils with Learning Difficulties, which include, Autism, Speech Language and Communication Needs, Global Developmental Delay and other conditions. 

The secondary school is an academy for 11–16-year-olds who all have Special Educational Needs. Traditionally a school for pupils with learning difficulties, they were recently designated as an LD, ASD and SLCN school by the local authority. Pupils have a range of needs including ASD, Global Developmental Delay, Downs Syndrome and rare specific diagnoses.

The secondary school, I have been working with since 2019 and Southfield since Easter 2022.

I should say at this point that my role in supporting these schools is focused on curriculum and pedagogy; not the pupil’s learning needs. I am fortunate to have worked with many children across my teaching career with a range of special educational needs and disabilities who have helped me to have some understanding of teaching for a range of learning needs. Both schools have the goal of developing their maths curriculum and it is for this that they want my advice.

If we refer to the ‘Quality of education’ section of the Education inspection framework, it says:

Inspectors will make a judgement on the quality of education by evaluating the extent to which:

Intent

• leaders take on or construct a curriculum that is ambitious and designed to give all learners, particularly the most disadvantaged and those with special educational needs and/or disabilities (SEND) or high needs, the knowledge and cultural capital they need to succeed in life
• the provider’s curriculum is coherently planned and sequenced towards cumulatively sufficient knowledge and skills for future learning and employment

Guidance, Education inspection framework

Updated 11 July 2022

With both schools, we started with thinking about developing a curriculum that is coherently planned and sequenced. Maths learning is hierarchical. I see it as an interconnected spiral, building upwards in small steps; new learning builds and is connected to what has come before.

For both schools, it was agreed that the ESSENTIALmaths resources, produced by the HfL Education maths team, would be a good place to start as these resources have been very carefully designed to build and connect the learning. However, I was very conscious, particularly for the secondary school, that to avoid it being like putting a square peg in a round hole, the resources would need adapting.

We knew that to meet the needs of lots of the learners, the small steps within the planning materials could be too big or could take too long. Ways to tighten the spiral were discussed.

Tightening the spiral

Here are the sequenced steps from the first two learning sequences from the Reception ESSENTIALmaths learning sequences:

Subitising (including equivalence, more and less)

 

 

Counting Skills (stable order and one to one correspondence)

 

The number range within the first learning sequence is between 1 and 6. In the second sequence, the range increases to counting within 10.

The steps in these sequences are already small and the number range is within the first decade but for some learners at these schools, without tightening the spiral, it could either mean that learning moved on too quickly and wasn’t secured or they would be learning the same thing for a very long time.

So, to tighten the spiral, these possible changes could be made:

Reduce the number range

• In the first sequence, initially secure subitising to 3
• In the second, keep the count to 5

Adapt the steps

• In the first sequence (in steps 3 and 4), the size of the objects within the groups of objects being subitised varies. Exploring this requires a secure understanding of conservation of number so initially comparing sets of the same sized objects would still enable the pupils to notice when values are the same or different without adding the extra challenge of size.
• In step 2 of the second sequence, mixing the objects in the set being counted could be built up in smaller steps. The sets could contain objects of the same type (for example, dinosaurs) with small changes being made to the sets being counted each time.

For example:

 

 

Postpone steps

• In both learning sequences, the final steps focus on subitising or counting when objects are moving or can’t be seen. Initially, these steps could be removed.

This doesn’t mean that the adapted learning would be not completed; these learning sequences would be revisited and then expanded to include all aspects of the learning within the original steps.

The next learning sequence in the progression focuses on comparing and developing the language of measure. Aspects of this could be taught and then the learning can loop back to the first learning sequence. The spiral is tightened and revisited without learning being missed or dragging on for too long.

Considering progression

The ESSENTIALmaths resources are written to match the Early Years Framework and National Curriculum expectations for Reception through to Year 6. This was another aspect of discussion as, in both schools, the pupils are not working at age-related expectations due to their special educational needs and/or disabilities. Also, in the secondary school, pupils are not within the primary age range.

In addition, in both schools, classes are organised considering pupil needs, rather than by age, meaning that pupils are not always with peers of the same age. Identifying starting points and then year-on-year transitions is an area that still needs to be ironed out.

Despite this, staff can now see the progression in maths more clearly using the steps within the sequences. The models provided, particularly of the talk, support their teaching and there is a greater consistency of mathematical models and language being used.

Developing subject knowledge

Another part of my support with both schools has been developing the staff’s subject knowledge.

In the ‘Quality of education’ section of the Education inspection framework, it says:

Inspectors will make a judgement on the quality of education by evaluating the extent to which:

Implementation

• teachers have good knowledge of the subject(s) and courses they teach. Leaders provide effective support, including for those teaching outside their main areas of expertise
• teachers present subject matter clearly, promoting appropriate discussion about the subject matter they are teaching. They check learners’ understanding systematically, identify misconceptions accurately and provide clear, direct feedback. In doing so, they respond and adapt their teaching as necessary, without unnecessarily elaborate or differentiated approaches
• over the course of study, teaching is designed to help learners to remember in the long term the content they have been taught and to integrate new knowledge into larger concepts

Guidance, Education inspection framework

Updated 11 July 2022

In both schools, the teaching of the curriculum is organised so that most subjects are taught by a single teacher. As a primary teacher myself, I see myself as a ‘Jack of all trades, and a master of none...’  I don’t see this as a negative, but I appreciate that I am not a specialist in a single area – I always have found I have greater aptitude for some subjects than others – I know I was never great at teaching PE or modern foreign languages, but I felt more confident with maths (unsurprisingly, due to the job I do now), science and art.

This meant that in both schools, like in most schools, there were varying degrees of subject knowledge and confidence in teaching maths across the school staff. Therefore, staff CPD has been, and continues to be, an important part of my role.

For both schools, training has been given to all staff on maths subject knowledge, particularly early maths concepts such as counting, subitising, ordering and comparing numbers, all of which support the teaching and learning of a sense of number. With all children, it is important that there is a deep understanding of these early number concepts because it is upon this all maths is built.

Memorisation and recall can sometimes mask whether this is understood or not. This can lead to some pupils being able to recall individual bits of information from long term memory but being unable to connect it to new learning or apply it.

The Deputy Headteacher of Southfield School reflected about the impact the training has had on staff:

“The CPD has definitely been impactful, with staff gaining the knowledge to teach early maths. I have never heard the word subitising used so often. It has made us think about the depth of knowledge as a building block rather accepting that if a child can count to 100, they understand about those numbers.”

Investing in professional development

Other ways in which the leaders at both schools have supported the staff to deliver the curriculum is to invest in specific training to implement and use the ESSENTIALmaths resources well. Teachers across both schools have had access to a mixture of online and face-to-face training. This has enabled them to understand how the resources can be best used to support understanding and delivery of the curriculum.

My work within the schools has included working directly with all class teachers to see how the resources can be adapted further to meet the needs of their learners. This is still very much a work in progress at the primary school as the resources are still very new, and time is needed to become familiar with them and to embed their understanding.

Developing independence and confidence

One thing we have recognised is that the curriculum is vast, and we must not lose sight of the overarching aims. At both schools, their goal is to develop the children into young people and adults who are independent, confident, and ready for their next steps.

Many of the pupils at these schools, like many pupils who attend special schools, will not leave school with same qualifications as their peers – GCSEs, A levels etc. At the secondary school, they have introduced assessments and qualifications that reflect the life skills that their pupils will need.

Together, we have started to map the knowledge and skills needed to complete the assessments and gain the qualifications, planning this into the ESSENTIALmaths progression. An outcome of this is that the progress through the curriculum as it stands will need reviewing; elements enhancing, and other aspects being removed or thinned out. Now that staff have been using the resources for a period of time and are more familiar with the progression as it stands, this is one of our next areas of development.

Purposeful assessment

Assessment across both schools is developing through teachers having a better understanding of the progression of the curriculum and having continued professional development. They are growing in confidence with formative assessment.

The secondary school have used multiple choice diagnostic assessments that have helped them identify starting points and quantify the security of the learning. In addition, due to the incorrect answer choices being carefully chosen, they have also exposed gaps and misconceptions. This means that future planning can be further adapted to address this.

In the Education inspection framework under Implementation, it says:

Inspectors will make a judgement on the quality of education by evaluating the extent to which:

• teachers and leaders use assessment well, for example to help learners embed and use knowledge fluently or to check understanding and inform teaching. Leaders understand the limitations of assessment and do not use it in a way that creates unnecessary burdens for staff or learners

Guidance, Education inspection framework

Updated 11 July 2022

The increased confidence in subject knowledge and having a clear progression in the curriculum, alongside assessments that inform planning and teaching, means that practice is developing to use assessment more effectively to inform teaching. Ways to track and monitor the small steps of progress at a whole school level is a challenge and still on the ‘to do list’.

Reflections

In writing this blog and reflecting on my work with both specialist provision schools, it has highlighted to me that when developing a maths curriculum, the principles are the same for all learners whether they have special educational needs and/or disabilities or not.

The intent of the curriculum needs to be clear, so pupils learn the mathematical skills and knowledge to achieve well. But in these special schools, the focus isn’t so much on data-based outcomes at the end of Key Stages; it is more focused on making sure that the pupils have the life skills and knowledge that ensure that they are ‘ready to take their place in 21st century Britain’, as David McGachen said in his Headteacher Welcome on the school website.

In my opinion, widening out our range of vision for what our maths curriculum is driving towards is a good thing (I am not naive enough to know it isn’t a huge challenge in our current system).

Broadening the horizons so it isn’t all about outcomes, percentages, and progress scores would help us see the purpose for maths in all aspects of life and more people might have a more positive view of the subject.

Nevertheless, tightening the focus on learners’ needs, would be a good thing, particularly those who have greater vulnerabilities or special educational needs and/or disabilities. Thinking carefully and deeply about how the teaching and learning can be broken down, scaffolded, and taught in those small steps so the skills and knowledge learnt is secure and can be applied is absolutely what is needed for the pupils at the schools I have talked about in this blog. But wouldn’t this be good for all pupils, whatever their needs?