If you look at your child’s maths homework or pop into their classroom, you may notice that the way maths is taught today looks nothing like it did when you were at school.

This can be unsettling for many parents because they don’t understand the new methods and don’t feel confident helping their child.  They may also question if their child is being appropriately challenged or if the new ways of doing things are any good.

Maths is taught so differently today because our knowledge and understanding of how children learn and understand maths has developed.  This is a good thing.  Just as you would want your doctor to be prescribing the most up-to-date treatments based on cutting-edge research (which might not be medication, but perhaps talking therapy or exercise), schools should be keeping up to date with the latest, cutting-edge research on how children learn and understand mathematics, and teaching in-line with this.

How is maths taught in primary schools today?

Let’s start with the word maths.  Maths is reasoning and problem-solving about problems in the world around us using logic.  What we were mostly taught at school under the name “maths” was actually closer to “arithmetic” in the form of memorising and solving number facts and calculation methods to be recalled at speed.  

Arithmetic is a branch of mathematics – it is not mathematics in and of itself.  And the speed thing is just something schools seem to have decided was important decades ago. 

Professional mathematicians are not always quick at solving arithmetic questions, and if they are, it is because they have excellent number sense – they can play around with and manipulate numbers.  They understand how numbers work.  When Rachel Riley works out the number round on Countdown in under 5 seconds, it’s because she has excellent number sense – she knows how to play around with the numbers to find the solution.  She isn’t just recalling facts, she’s applying her knowledge and understanding of number.  She is using logic to solve a problem.

What is “Mastery Maths”?

Most primary schools (and increasingly secondary schools) are now teaching a subject that fits the definition of “maths” much better – with arithmetic skills alongside –  and they are doing this using a method of teaching maths called “mastery maths”.

This teaching method originated in Singapore (one of the highest-ranking areas in the world for maths teaching) and began to be adopted in the UK about 8 years ago.  The school I was working in at the time was one of the first in Gloucestershire to implement this method of teaching.

The principles of mastery teaching are very different to how you would have been taught maths (and how I was taught to teach maths), and align with what maths actually is, and how children learn and develop an understanding of maths concepts. 

When my school introduced Mastery Maths, it really blew my mind and I didn’t think it would work after over ten years of teaching in ways that are perhaps more recognisable to parents. 

After just a few months teaching this way, I was totally converted and wished I’d been taught maths this way at school.  It is a much better way of developing maths skills that align with child development and ensures children understand what they are doing.  It teaches skills that are relatable to everyday life, and also the reasoning and problem-solving skills employers are, and most probably will be, looking for in the future.

Principles of Mastery Maths

Mastery Maths teaching is based on the principles that everyone can learn and enjoy maths.  It is about reasoning and making connections between concepts.  It is about developing a deep and secure understanding of key ideas that are needed to understand future learning.

It is about understanding how and why numbers work and connect, having mathematical dexterity, and being able to link concepts together.  For example understanding that multiplication and division are linked, and in turn, understanding that division is linked to fractions, and in turn, understanding that fractions, decimals and percentages are different ways of representing numbers less than 1. 

These skills set children up for success in any future mathematical study, and the use of maths in everyday life, far better than how maths used to be taught.  Most people disliked maths and find it hard to engage with because we were taught how to do something with no understanding of why it worked or why it was necessary or how it relates to other things, or that speed was a really important aspect (pressure of having to give an answer in a set time triggers our stress response and shuts the brain down into survival mode – not helpful!)

Mastery Maths teaching methods

In Mastery Maths – children are taught the same concept all together, broken down into small steps so that children build on previous learning and make connections.

This whole class approach makes people think that brighter children are not being challenged and children who are struggling are not supported.  This is not the case. Differentiation is still happening, but in much more subtle and effective ways.  Children who grasp the concept quickly are challenged by solving problems and reasoning about the concept, in more and more depth – they keep digging deeper and deeper into it so they have a solid understanding. Children requiring more help are supported with apparatus, different ways of presenting the concept to find a way that clicks for them, and repetition to practise and consolidate learning, alongside immediate, targeted teaching in small groups.

Research is very clear that putting children into ability groups and giving them tasks that create a ceiling on their ability holds children back and sends the message “this is all I think you will be capable of doing – don’t even try what that other table are doing”.  It impedes their learning, not develops it.  Expecting all children to be able to learn something (some will get there quicker than others) shows children they are capable and able to achieve.  And they do! You can read more about this research on my blog here.

The way concepts are presented is where most parents will come into contact with mastery maths.  You may see bar models, whole-part models, images of apparatus such as Numicon, place value counters or dienes apparatus.  These are all ways of representing a problem.  They are not methods like column addition or long division.  They help children visualise number problems and see them in different ways and how different connections can be made.  This helps learning not hinders it.  They will be taught the “traditional” methods, but, taking division as great example, diving straight into short or long division when children don’t understand that division is “sharing equally”, and firstly building a deep understanding of what this means through various representations, and then understanding we can divide through “repeated subtraction”, before moving onto the “traditional” methods– means that most children will struggle to understand what they are doing and therefore won’t remember the method.

By deeply understanding what dividing is and having done it in different (often less efficient, but more conceptually obvious ways) helps children take the step up to formal (“traditional”) methods because they understand why that method works.  The “ah ha” moments happen and they remember the formal method better, and if not, they have other methods to fall back on instead. They are able to access maths because they have a number toolkit.

Why not just teach them one method?

My Year 6 teacher always said “there is no right or wrong way to do maths” and she was spot on.  It doesn’t matter how a child gets to an answer if they have a method that works for them and they understand it.  There are a multitude of ways of reaching a solution – none is “better” than the other, although some are more efficient. It is important to develop an understanding of “efficient methods” but that is all part of the mastery process.

Why not keep things as they have always been? I’m OK at maths.

To return to my doctor’s analogy.  A few decades ago, if you had a bad back, doctors would have told you to lie down still.  Now, due to research and professional development of doctors, they will now tell you to move around as much as possible.  When this was a new idea it would have felt counter-intuitive and weird and “that can’t possibly work?!”

The way maths is taught is just the same.  The old ways are not necessarily the most helpful ways.  Just because something has been done a certain way for a long time, doesn’t mean it’s the right way going forward, in light of new research. 

Teaching methods are constantly being refined due to new research about how children learn. Teaching things the way they always have been is as unhelpful, and even as damaging as, prescribing treatments for medical issues which the research now shows impedes rather than helps.

How to help your child with maths:

If you feel unsure about helping your child using these methods you can:

• Ask your school for help in understanding the methods – many schools run parent information sessions to explain them.
• Ask your child to explain it to you.  If they can, it shows they have a really good understanding of the concept.
• Don’t beat yourself up.  You are not a qualified teacher and aren’t expected to understand these methods inside out.  Encourage your child to think back to their lessons and have a go.  Developing independence in learning this way actually helps learning, not hinders it, especially if they make mistakes (remember, mistakes are wonderful things and are needed for connections in the brain to be made).
• Read my other blog about how to help children with their learning here.

I use mastery maths methods in my tuition to develop a deep and secure understanding of maths concepts and to tie in with methods being used in schools so that children make links instead of being confused.

Contact me if I can help your child develop a love of maths.

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Throughout November I will be going live on my Facebook page to quickly explain some of the most common misconceptions, or stumbling blocks, that the children I work with often display, and provide advice on overcoming them.

I’ll take a look at each of them further in this blog.

The Maths Blocks:

Firstly, a couple of maths issues that crop up again and again: multiplying and dividing by powers of 10 and the commutativity of multiplication.

Multiplying and dividing by powers of 10.

A power of 10 is 10, 100, 1000 etc.  When I was at school, and I’m sure when you were too, we were taught to add zeros when we multiply by powers of 10 and to take zeros away when we divide by powers of 10. It was only when I was in teacher training college 20 years ago that I found out this is mathematically incorrect, and sets children up for problems further down the line (and probably helps explain one reason why I struggled with maths).  It is important to teach this correctly from the start so children don’t get stuck later on.  However, children are still being taught this “trick” and I’ve lost count of the times it has put a barrier in their way over the years.

So, if adding and taking away zeros is not correct, what is?

We need to understand that it is the digits moving and changing their place value.  When multiplying, numbers get bigger, so the digits move up the place values.  This leaves a space, or spaces, so we need to use a zero as a “place holder” to show there are no ones, for example. 

When we divide numbers, they get smaller, so here the numbers move down the place values.

So far, however, the trick of adding or taking away a zero works and gets the right answer, so what’s the issue?  Why does it matter whether we add or take off a zero or move the digits? 

Let’s start with looking at dividing.  When dividing, not all numbers have a zero on the end to “take away”.  If you have been taught to take off a zero and then you are presented with 32÷10, you are now well and truly stuck.  You have no idea how to solve this problem.  You get despondent and frustrated.  Maths becomes “difficult”.  If you have, however, been taught that the digits move, then this barrier never appears.  We just know what to do – move the digits.  No problem was created and we can continue to access maths and understand number. The digits might need to “jump” over the decimal point to become tenths or hundredths. When I was at school, I was told to move the decimal point.  Again, this is fundamentally incorrect.  The decimal point is fixed to the spot.  It doesn’t move.  It is glued down.  The digits move around it.

What about when we are multiplying?  We are adding a zero so why is it a problem?  The answer is because it leads to poor understanding of place value.  This is understanding what each digit represents – hundreds, tens and ones (sometimes called units).  If we just add a zero to 32 without moving any digits we still have 32.  We don’t write 32.0 because the zero tenths is not telling me anything useful, because I don’t need to know I don’t have any tenths.  Adding a zero on the end of 32 does not change the number in any way.  We need to move the digits, then place a zero in the empty place value columns to show clearly what the number is and avoid confusion.  A three in the tens column means 30, but 30 what?  31? 38?  The zero place holder is saying “there are no ones”.  This zero is vital.  And it’s vital it is in the ones column, not the tenths column.  Where it is means very different things.

Children enjoy practising these skills by moving numbers up and down a place value chart.  Imagine the numbers sprouting feet, or wheels, or being pushed in a trolley – whatever works to remember they are MOVING.

To know how many places on the chart to move, look at the power of 10 you are multiplying or dividing by.  10 moves one place because there is one zero, 100 two places because there are two zeros, 1000 three places etc.

Times tables are commutative:

Commutative means that the calculation can be written either way around.  3X4=12 is the same as 4X3 =12.  As I’ve explained in my blog “What Can I do to Help my Child with their Learning?”, it is best to learn all the related times table facts together as it creates less work in the long run.  If you know 3X4 = 12 you therefore know 4X3 = 12 and therefore 12÷4 = 3 and 12÷3=4.  That’s four facts for the price of one!  Lots of children, when presented with 12X5 for example, will say they don’t know their 12 times table.  When asked “do you know your 5 times table?” they say yes and know 5X12 = 60.  Understanding that you can swap the numbers around is liberating.  Children think the 12 times table is hard, or that they don’t know it.  They will know more 12 times questions than they think.  Turn the question around!

The English Blocks:

Over sounding phonemes and resistance to editing writing.

“Uh” Phonics:

Phonemes are the smallest unit of sound within a word.  Children are taught phonics from the early years and there is a huge focus on it in school.  Children will be familiar with the word “phonics” and “phoneme”.  We use phonics to sound out words to help us read and write (this is only helpful to a point in English as lots of English words are not phonetic).

The children I work with who struggle with reading and spelling often are not sounding phonemes correctly.  They say, for example, “c-hu – ah – t-hu”.  We don’t say cat “cuhahtuh”,  it’s “c-a-t”.  The sounds are very small and quiet, with no “uh” on the end.  The vowel sounds (a, e, i, o, u) are louder and may have a slight “uh” on the end, but the consonants are small, made by a little puff of air (b, p), or restricting the back of the throat (c, k, q) for example.  Encourage your child to say the sounds as small and quietly as possible (but still being able to hear them!)  This will help them hear the word they are sounding out – “c-a-t” sounds like “cat” -which helps with reading and spelling.

As a side note, I’ve noticed lots of children calling letters words – “how many words in the word?”  It’s also important to know the difference between the name of the letter (A – ay) and the sound it makes (“a” as in apple).

Proofreading and Editing:

Children are generally great at writing.  They have fantastic ideas which they write down eagerly.  However, many think that once they’ve written the last word (not necessarily with a full stop after it) they are done and it’s time to move on to the next thing.  When you explain that the next thing is to go over and edit the writing, they sometimes become frustrated and despondent, and issues around fear of mistakes and getting things wrong surface.

Children need to understand that writing is a process, and correcting their work is an integral part of that process.  Proofreading (finding spelling, grammar and punctuation errors) and editing (changing the word choice, word order, sentence structure etc) are essential parts of being a writer. Every writer goes through this process and every piece of text that has been professionally published goes through this process, multiple times.  Find your favourite book.  The author didn’t write those words first time, and then it was printed and you bought it.  Those words are there after a process of changing, correcting, adding in or taking out many, many times before it was printed and sent to the shop.  Being a proofreader and/or editor is a career.  People are paid to check writing and make it as good as it can be.  It is not a criticism or telling off.  It is an essential part of the writing process.

When children understand that the first draft of their writing is not the finished version and there is an expectation to proofread and edit, and that is done in an engaging, creative way, they are able to see this as part of the process and embrace the task of making their writing “as good as it can be”.

A first draft should be about getting ideas out of your head and on paper.  Children shouldn’t be worrying about how to spell words or where to put full stops at this stage.  What’s important is getting the ideas down.  The next stage is to check the spelling, punctuation etc.  Children should do this themselves first, before someone else checks it (it is good to have a fresh pair of eyes look at it which is why authors use professional proofreaders and editors.)  Instead of looking for all the things that need changing at once, focus on one thing at a time.  Are the capital letters correct?  Now the full stops and other punctuation?  Are there any words I know are spelt incorrectly, or I think might be?  Check them (put a wiggly line under them first).  Be a writing detective.  Put yourself in the shoes of your reader.  Have you made your writing as clear as possible for them?  Will they understand and enjoy it?

Drafts of writing should be messy.  There should be crossing out, insertion, asterisks to show where new sentences and paragraphs are that couldn’t be fitted in.  Use different coloured pens if it helps, but it’s not necessary.  This shows the child has gone back and thought about their writing, and corrected errors, embedding learning along the way.

Young children in Years 1 and 2 should be checking they have used capital letters and full stops correctly, and maybe checking 1 or 2 spelling words.  Build up the amount of proofreading and editing done as the children become older and more skilled in their writing abilities. 

Editing is often seen as a chore by children, but it is actually a really creative process.  Is there a better word or phrase to use to really get across what I want the reader to know or imagine?  What happens if I move the words around, take a word out, change a word, move a comma…?  Editing is being playful with language.  That is fun!

To see my short explanations of these misconceptions, please visit my Facebook page.  Coming in the new year will be my Learning Support Membership where there will be short, engaging video lessons and supporting activities to address these misconceptions. Do get in touch if you are interested in discussing how I can help support your child’s learning.

I’m now off to proofread and edit this blog before publishing!  What you are reading is not the first draft 😉.

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This was a common question at parent’s evening when I was teaching, and something I’m asked regularly by the parents I work with now as a tutor.

My suggestions are below.  Other than the first one which is the most important thing you can do to help your child with their learning, the rest are in no particular order.

Read

Reading is the most important thing children can do to help their learning along.  To find out more, have a read of my blog about the importance of reading here. It doesn’t matter what you read – books (fiction and/or non-fiction), comics, magazines, websites, computer games, instruction manuals, menus, shopping lists, cereal boxes…. just read!  It is the key to everything.

Your child listening to other people read is also fine.  It is important for children to listen to stories as much as reading them themselves.  Hearing someone else reading fluently helps them understand word pronunciation, rhythm, and expression.  It also helps them understand what is going on because they are not having to worry about “decoding” the words (turning the letters into sounds).  If you are confident reading yourself, then sharing a story at bedtime is an enjoyable experience for both of you.  If you don’t feel confident reading yourself, then audiobooks are also fantastic.  Don’t stop your child from listening to stories once they can read independently either.  Everyone loves listening to a story – even adults!

It’s OK for children to re-read stories they enjoy.  I’m an avid re-reader.  Familiarity develops confidence and enjoyment.  You also notice new things with each reading.  It’s also OK for them to sometimes read something “too easy”.  A variety of difficulty is important.  If they are always reading something that is a bit of a challenge, then reading becomes hard work and they no longer enjoy it.  After a “heavy” book about something serious, I usually choose a funny easy-read after it. 

Reading doesn’t have to be expensive either.  I’m a huge advocate of libraries.  They are free to join and are also now able to start running free events again.  You can also borrow audiobooks from them.  I used to love Saturday morning visits to the library as a child.  Books for free – what’s not to like?!

Times Tables

Recall of times tables is an important skill because it is so helpful across many areas of maths, such as fractions, percentages, and area.  It is a life skill. The children who struggle with maths invariably don’t have a solid recall of times tables.

There is a formal times tables test in Year 4 (which has been put on hold during Covid but will probably re-appear) and in Year 5 and 6 understanding of fractions, percentages, etc is made so much easier if children have good times table knowledge.

Don’t just learn them in order:

Eg 1X2, 2X2, 3X2, etc.

Do mix them up:

Eg 5X2, 8X2, 2X2, etc.

When we need to use times tables to access other areas of maths, it will be at random.  Eg a rectangle that is 5cmX12cm to find the area.  If we have to start at 1X12 and work though, it wastes a lot of time.  We need to just be able to recall 5X12 = 60.

Don’t just learn the answers:

Eg 2, 4, 6, 8…

Do say the question:

Eg 1X2=2.

Children who can only recite the answers in order have no access to what that number refers to and therefore really struggle to answer times table questions or apply them to other areas because they only know half of it.  They have to count up on their fingers to find out “how many 2s make 12” for example.  This is frustrating for them and wastes time. Say the whole times table out loud: “two times six is 12”.

Don’t learn the tables one at a time: 

Eg, the 2s, then the 3s, then the 4s etc.

Do learn the associated facts:

Multiplication is commutative (it doesn’t matter which way round the numbers are on either side of the X).  So, if you know 4X5 = 20, you automatically then know that 5X4 = 20.  This means that there is no need to learn the 12 times table because if you know the others, you automatically know the 12s.  There are only 21 times table questions you need to actually learn – the rest you know because you’ve learnt it the other way round! 

It’s also important to know that the opposite of multiplying is dividing, so learning the division facts alongside helps enormously when applying facts to other areas of maths.  So, if we are learning that 3X4 =12, we also learn that 4X3 = 12, and 12÷4 = 3 and 12÷3=4.  That’s 4 facts for the price of 1!

Do use what you know to help you with what you don’t:

If you know your 2 times table, then double it to find the 4s.  Double that to find the 8s.  Double the 3s to find the 6s, double that to find the 12s.  Alternatively, halve the 12s to find the 6s, etc. 

Also, your child may know up to 5X something but is stuck on 7X something.  Go back to 5X and count on 2 sets to find 7 times.  So many children start from the beginning and work up. Instead, start from what they know.  They probably know 10X but find 9X hard.  Start at 10X and take away one set and you have 9X. So much quicker than counting up from 1X.

Don’t worry too much about speed:

There has always been a big emphasis on recalling times tables facts at speed.  The Year 4 test does require questions to be answered at speed.  Whilst this can be helpful, especially when using the facts to help with other areas of maths so that you can carry on with the actual problem at hand and not end up bogged down in an extra task of working out 7X6 for example, it is not the bee-all-and-end-all.  There is a move in primary education now towards slower recall because speed can create anxiety.  Not everyone’s brain works quickly, and the time pressure causes many children’s brains to shut down (and adult’s – I’ve always suffered with “maths brain”.  I need time to think).  It’s OK to have to work it out, using a time-efficient strategy (such as the ones described above). 

There are so many fun ways to learn times tables.  Have posters up (children enjoy making their own), find songs and dances online, or download or have a CD to play in the car.  Use flashcards, or find games online (there are LOADS – Google “times table games”).

Praise effort not getting things right:

The children I work with who lack confidence in their learning all have one thing in common – fear of mistakes.  This is the biggest factor holding them back.  Before they can make progress academically, they need to reach the point where they are comfortable making mistakes.  Because making mistakes is how we learn.  Mistakes are fundamental and must be celebrated.  It’s OK to get something wrong, so long as we tried, and learn from the mistake so that we can iron it out in the future.  We need to practise things.  In our world of instant gratification and short attention spans children can find it difficult if they don’t understand something, or can’t do something, straight away. 

However, nobody ever achieved anything without trying.  Behind “successful” people there is a background of hard graft, failure, and perseverance.  It is effort, practise, and learning from our mistakes that needs to be recognised and praised, more than getting something right.  For example, a child may be struggling to work out a maths question. They have tried to solve it but got the wrong answer.  A great response would be something like: “Well done for trying that.  We have learnt that that isn’t the answer so let’s try another way.”  As the inventor of the light bulb, Thomas Edison said, “I have not failed. I’ve just found 10,000 ways that won’t work.”  Each way that didn’t work, was part of his path to learning what did work.

Have fun:

We learn best when things are enjoyable.  If your child is tired after school and needs some downtime, then this isn’t the best time to practise spellings, times tables, or reading.  Find a time when they are rested and ready to learn for homework tasks.  If it’s not happening that day, don’t force it.  There’s always tomorrow.

We learn all the time from life in general.  Get your child involved in the housework (pairing up socks is a great maths activity for younger children), cooking, shopping, etc.  They love it and it doesn’t feel like a chore to them!  There is maths and English to be practised all around us just from doing day-to-day things. 

Go to the library, museum, park, a walk in the woods…  Your child will be soaking up all sorts of information, such as: learning to cross the road safely; how to behave in public; finding out about cultures from the past and present; different plants and animals; how keeping fit helps us feel good, to name just a few.  I learnt where places are in the country by watching the football results on a Saturday afternoon (“Mum, where’s Bolton?”) and I also remember sounding out the word “fog” when watching the weather forecast.  Learning can happen anywhere, anytime.

If your child needs further help with their schoolwork, do get in touch to see how I can help.

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