Until now, the vast majority of our work at Complete Maths has been with teachers, supporting teaching and learning through CLASSROOM and CPD. The launch of TUTOR for Families means for the first time we will be able to work directly with parents and their children in supporting their maths learning. If you are a parent, and you’re interested in hearing more tips like the ones below, you can join our mailing list by clicking here
For all the thousands of hours children spend in school or college each year, what actually happens when they’re there can seem a mystery to those waiting at home. Parents and teachers have few opportunities within the year to speak, and when they do, it’s on the clock. Parents are often left to rely on their children for a full explanation of what they’re learning at school or college and how it’s going, but this is of course only part of the story.
Maths is one of the few subjects in which the core content of what’s being taught hardly varies — every generation will recall learning times tables, or converting fractions to percentages. But how it’s taught varies hugely, and if you’re a parent without a maths teaching background wanting to know how to support your child, it’s hard to know where to start. That’s why we asked our maths team, all of whom are experienced qualified maths teachers across a range of ages and contexts, for their advice.
We often associate using fingers as a negative sign that a child isn’t secure in counting, but in fact, it is thought to reduce what’s known as ‘cognitive load’. Cognitive load is comparable to tabs on a computer — the more tabs are open at any one time, the slower the computer is likely to run until eventually it crashes. Each new task or challenge is like opening a new tab on the computer. When introducing a new skill or a tougher problem, teachers will always aim to reduce pupils’ cognitive load as much as possible so that they can focus on just one thing. Counting on fingers means pupils’ brains have one less thing to think about, therefore freeing up precious space for the challenge in front of them.
Finger counting can also make it easier to perceive quantities without having to count them. This is known as subitising, and it’s something most of us do without thinking — recall the last time, for instance, you rolled a dice. If you knew the number you’d rolled without having to count each individual spot, you were subitising.
Of course, finger counting has its limitations and as children develop their understanding of mathematics, we want them to move to more efficient methods.
You can read more about the role of finger counting, and how to move children to other methods, here.
It might sometimes seem like the methods taught in maths class "nowadays" bear little or no resemblance to what you remember seeing as a child. Whilst it is true that mathematics teachers may decide to teach a variety of methods, often this is done to help with understanding or to provide a method that will work across a range of problems. It is also quite often the case that the methods will be superficially different but are really the same procedure.
If you are helping your child with a problem, ask them to explain the method their teacher has shown them. Having them explain the method to you is a great way to boost their own understanding. If they are unable to explain to you then their teacher needs to know that they haven't understood what is expected of them. Try to resist the urge to have your child do the question using "your" method. Most teachers would prefer a little note next to the homework saying "Jonny didn't understand what to do here" so they can address it next lesson.
As tempting as it can be to teach your child a trick that will get them 'the right answer', this can be damaging to their mathematical development, ignoring the need for a greater depth of understanding in favour of the correct answer. There is a false economy in teaching and using these tricks, as further down the line the prerequisite idea isn't understood fully and building on this knowledge isn't possible.
Nix the Tricks is an American book which looks at avoiding these shortcuts that limit mathematical development — it’s free to download, and offers alternative explanations to some of the tricks you might yourself have learned while in education.
As students become more mathematically able, the opportunities for finding the maths around you become more limited. Many of the ideas students work with as they approach end-of-school examinations don't scream 'real life', but it is important that children discuss ideas that they've been working with.
Very young children find great pleasure in counting the number of steps they're climbing, counting down from five before they 'blast off' and love to play 'shops', setting up a toy shop, taking money from you and giving you your change before bagging up the toy and wishing you a good day, As they become more mathematically literate, their focus might shift to the idea of time and knowing how long it is until dinner time, or how long they have left on their scooter, and they can be engaged here.
As they continue to grow, and their mathematical powers heighten, the opportunities might seem to dry up, but estimating the food bill whilst doing the weekly shop is an excellent way to engage a child with maths and you can sweeten the deal with incentives ("If you're within £2 of the total, I'll get you a sausage roll!"). The opportunities may not be there when students are mastering trickier concepts at GCSE and A-level, but just asking "What have you been looking at in maths today?" and "Tell me a little about it..." will go a long way to provide opportunities for retrieval of these ideas in a very casual manner.
Parents of young children might enjoy seeing below some of the maths Jonny Hall, one of our maths team, uses at home with his young son.
Whilst some children are able to understand school or college mathematics more easily and quickly than others, that doesn't mean that all children can't achieve the same level of understanding given sufficient time and support.
Many schools and colleges will set pupils based on prior attainment (how they have done in tests). This is often taken as a measure of a pupil's potential, but this should not be the case. Sets are a way of placing pupils in a class where they will get a level of support (and challenge) best suited to their current level of mathematical development. Being in a lower set should not mean that expectations are lower and that pupils can not still go on to achieve at the highest levels of school maths.
In most cases, success with school maths comes from hard work and from the belief that hard work will see pupils improve. Intelligence is not fixed. We are all capable of accruing knowledge and understanding complex ideas if we are determined and we work hard at it.
It is commonly assumed that being "good" at mathematics means being fast, solving problems before anyone else or finishing first on tests. This is not the case, and praising speed can have lasting negative effects.
Early in their mathematical development, many pupils experience short, single-step problems. Often, these problems can be answered quickly but we should try not to praise speed and instead praise effort, accuracy or clarity of explanation. As problems get more complicated, pupils who have received praise in the past for being fast will inevitably rush and make mistakes — often these are the pupils who show little or no working out in their answers. On the other hand, pupils who have been praised for accuracy, understanding and communication will often have more success.
Whilst it is true that quick recall of addition and multiplication facts can be helpful, it is far more beneficial in the long run for pupils to take an extra few seconds to think a little more deeply about strategy and communication.
‘Number’ refers to the quantity of something, whereas a ‘numeral’ is simply the symbol we use to write that number. Young children should always start with numbers — for instance, recognising who has rolled the highest number on a dice, matching numbers on dominoes, or (for a more seasonal example) spotting who has the most conkers.
In teaching terms, we talk about this as developing ‘number sense’, a key skill early on which involves pupils understanding numbers in a more concrete sense. A child might be able to count from one to ten, for instance, but without a strong number sense they are just repeating sounds by rote. Counting piles of conkers, or the spots on dice, or dividing socks into pairs of two can all help to relate an abstract sound — ‘three’ or ‘seven’ — to a concrete example.
Once children have an understanding of what a number means, they are then ready to learn the numeral by which it is represented on paper.
Subitising, the process referenced earlier through which a person perceives a quantity without counting it, isn’t possible once a child begins working with larger numbers. Imagine the difficulties in trying to subitise the spots after each roll of a 20-sided dice!
Instead, children can be introduced to larger numbers by breaking them down into tens and units. ‘Twenty three’ is an abstract concept — but ‘two tens and a three’ will make more sense to a younger child, and can be easily modelled using groups of physical objects. Cuisenaire rods are a great resource to help with this — a standard set consists of a range of rods in different colours, where each colour of rod can be used to represent a different quantity. The rods are all in proportion to one another, so children of different ages can benefit from using them: younger children might explore how ten ‘ones’ are the same as one ‘ten’, while slightly older children can use them to explore fractions and decimals, for instance.
Very, very large numbers can be even harder to visualise, but here the internet has stepped up. Last year, a viral video on TikTok showed the wealth of Jeff Bezos represented by grains of rice — a perfectly-modelled example of the difference between a million and a billion, and one which can be replicated at home!
We talk a lot at Complete Maths about helping children to be ‘more mathematical’. By this, we don’t mean being ‘better at maths’ in the sense of achieving higher test scores or exam grades (though of course these are both by-products of a child becoming ‘more mathematical’). Instead, we mean to help children think more like mathematicians, a skill that transcends the classroom and will help them in every area of their lives.
Thinking mathematically is ultimately about adopting a problem-solving approach to life. When you set out on a long journey and are given the choice of two routes, one over a shorter distance but navigating slower country roads, the other a longer distance but using only motorways, you are thinking mathematically when you make your decision. You are considering the relationship between speed, distance and time, as well as using probability to calculate the likelihood of heavy traffic at different times of the day. If you have a desired arrival time in mind, you are combining your knowledge of time with your knowledge of estimation and subtraction as you work backwards to determine when to leave.
Every time you go to the supermarket and must compare the cost of a branded pack of 10 to a Value pack of 15, you are thinking mathematically.
Every time you dismiss a takeaway restaurant with a single five-star review in favour of one with three hundred reviews and a four-point-five star average, you are thinking mathematically.
Every time you calculate how many points your team needs to take from its next three matches to win the league, or to qualify for a tournament, or to avoid relegation, you are thinking mathematically.
Your children, too, will be using their mathematical skills on a daily basis, but they may not have made the connection between this and what they are doing in their lessons at school. If children can learn to recognise when they are being mathematical, even at home, it can go someway to overcoming a belief that they are ‘bad at maths’ just because they find parts of it difficult. This very much feeds into our final point:
There is a social stigma attached to illiteracy, and often a sense of shame around an adult admitting they can’t read. Almost the opposite is true of maths — just think how many times a day you hear casual throwaway remarks like “I’m terrible at maths”, “I can’t do maths without a calculator” or “I was rubbish at maths too, you must get it from me”. What message does this send? Firstly, that being ‘bad at maths’ isn’t just common, it’s expected. Secondly, that being ‘bad at maths’ is both a fixed and an inherited trait. Neither of these mentalities helps children.
Just think: the greatest maths brains throughout history spent most of their time being stuck on a mathematical problem. When framed like this, it becomes easier to see being stuck as what is meant to happen as you improve. At its core, maths is about using what you know to try and find a solution to something you don’t. Think how dull a murder mystery would be if the very first episode told us who the killer was and how they did it, and then apply that same approach to learning maths. This is exactly the attitude we want to foster in children: the idea that if they can solve something immediately it’s too easy; the belief that getting stuck on or having to think hard about a problem isn’t just a positive, it’s the whole point; and above all the importance of the word ‘yet’.
“It doesn’t make sense — yet.”
“I don’t understand it — yet.”
“I can’t do it — yet.”
If children can adopt a ‘yet’ mindset, they won’t just be successful in maths, they’ll be successful in everything they put their minds to. As adults, we can model this mentality by never speaking about a subject in absolutes, and always looking beyond the immediate difficulty towards the future success.
As a parent, your child's school might have spoken to you about Dyscalculia. Dyscalculia is understood by many to be a specific learning difficulty related to maths in which children will struggle with basic skills like number bonds or counting backwards. It is far less widely known and researched compared to dyslexia, which refers to specific trouble with reading and letters, but pupils diagnosed with dyscalculia may need similar levels of intervention and support to be successful in maths. You can read more about some of the signs of dyscalculia here and, if you think they apply to your child, should make an appointment to speak to the SENCO at your child’s school as soon as possible.
All of the tips above will be just as helpful for a child with dyscalculia, and it should not be seen as a barrier to their success.
To access more advice for parents from our maths team, and to be kept updated on parent access for TUTOR, you can join our parent mailing list by clicking here
You can learn more about how to use Cuisenaire rods as a maths learning aid, and purchase your own set, by visiting their website: http://www.cuisenaire.co.uk
This Maths Fluency Set contains 100 Maths Fluency cubes in 10 colours, 15 double-sided activity cards, and a multilingual activity pack.
This article contains suggestions for maths games that can be played at home, and do not require any specific maths resources.