This week I will be joining Charlotte Watson of Wonderlearn English to record an interview which will be released the following week as part of Children’s Mental Health Week. This is a topic very close to my heart, so when Charlotte approached me to participate in this event, I jumped at the chance to spread the word!
What do Neurodiverse children often love and excel in? Art, creativity and science… Therefore the concept of offering small group lessons to children with similar learning differences but not necessarily exactly the same age was born. Topic-based lessons full of fun! Each session focusing on practical enrichment activities that inspire and encourage children to think, problem-solve and above all, understand the ‘hows? and whys?’
This week I took part as a panellist on a live Q & A session where we discussed What does a ‘Professional Tutor’ look like? I joined three other very experienced Tutors (Tracy Landsberg, Jay Shurley and Jo Broadey) who are also like me in The Tutors Learning Network where we support each other with networking and quality CPD each week.
We discussed four main points that came together to explain what we think makes a ‘Professional Tutor’. The tutoring industry is currently an unregulated one, and this means that there are no hard and fast rules that anyone setting up as a Tutor must follow.
Home learning during the pandemic can be a stressful experience for parents and children alike. If your child is struggling with a Specific Learning Difficulty, (SpLD), such as dyslexia, dyspraxia, ADHD or ASD, there are added difficulties to cope with and greater patience often required by parents.
Dyslexic children may need additional time to complete tasks, help with reading and recording, and may find live lessons move too fast.
To find out more, read Sarah Beard’s article https://www.dyslexiaservices.net/post/how-to-support-your-dyslexic-child-with-home-learning
Stepping out of your comfort zone and trying something new and challenging isn’t easy to do and creates anxiety. Last week I joined forces with Julia Silver founder of the Qualified Tutor organisation, and we recorded an episode for their podcast series. The podcast is now edited and available on all usual podcast sites.
You have to be fast to be good…’ ‘Some people just can’t do Maths, so there’s no point in trying…’
These are just two of the myths around Maths and Maths learning. These myths and others have been debunked in educational research many times over. I have been reading some of this research to keep myself abreast of educational theory.
There is an analogy in maths teaching which asks ‘are you an inchworm or a grasshopper?’
‘What is an inchworm?’
Now for us Brits, the first question is actually ‘what is an inchworm?’ So just to fill that in straight away for you they are one of those caterpillars that move forward by arching and straightening its body ‘an inch at a time.’
So what have these two insects got to do with maths? Well, they are analogies for two much more complex words and theories that are not in adult-friendly and certainly not child-friendly language — quantitative and qualitative learning styles. Put as simply as I can quantitative – means can be measured by quantity or is measurable. Qualitative – means measured by a looking at the whole and with a description.
How these two concepts words are difficult to understand or to apply to real situations but the inchworm and grasshopper are easier to understand and explain to children.
This graphic shows the way inchworms and grasshoppers think and react to learning. Which one do you think you are? What about your child?
So which insect is it best to be? Successful mathematicians are generally those who are skilled at applying and using both approaches as success in maths tends to require flexibility in thinking.
The most able children within a class will be the ones that can adapt and flip between both styles dependent on what the task is. For them, they are able to be a grasshopper jumping between concepts to notice that a question can be solved more efficiently and with less working out by linking the idea to another and then adjusting the answer. But equally, if a question is a harder or more complex one, they can work carefully and methodically using a set method.
Looking at this modelled example, the inchworm has learnt how to do long multiplication in columns or even by another pencil and paper method. They see that the question is multiplying so they use that standard method. The grasshopper, however, will look at the specific numbers given and notice how close to twenty 21 is and realise they can do this particular example in their head. Multiplying by 20 is same as doubling then times by 10. They would then add on the extra 32 to make 672.
Now look at the second example, this time isn’t so clear cut for our more able child. They could do the same double 43 is 86, times by 10 is 860. But this time when they go to add on the extra 43 the numbers are a bit more tricky and they might at this point chose to use a pencil method to add the 860 and 43 to make 903.
Our third example shows that the more flexible mathemetician will look at the specific numbers involved this time and because they have good number sense, they will realise that there are no easy, quick ways around this. They will have to do it by a standard written method for long multiplication.
Younger children might show their learning styles by linking number bonds to 10 with the specific numbers in the question. The inchworm will work from left to right each time, adding the next number on to their total. They will have to make five additions and cross the tens boundary, which also requires number bond to 10 knowledge. A grasshopper will have good number sense and can link between topics easily. For them, this question because of the specific numbers is very simple. They will notice straight away that there are three pairs of number bonds to ten. 8 + 2, 3 + 7 and 4 + 6. So quickly 3 x 10 = 30.
Another example is where the inchworm will do the whole standard layout, including the row of zeros. But the grasshopper will spot straight away that the numbers both end in zeros and they can use known facts and then adjust the place value all in their heads.
So you might be thinking from these examples I have given, why would you want any children to be aiming to be an inchworm rather than this seemingly very smart grasshopper?
Looking back at the original lists, there are negatives from being a grasshopper. They find it hard to be methodical; they prefer to calculate mentally not on paper and find learning set methods tricky. Lack of these three strategies can be the downfall of a child who only works like a grasshopper.
At certain stages in a child’s education, tests and exams require them to do their working out in a set way. These children will find it almost impossible to do this and will often come away with a low test score as they haven’t been able to conform to the standard methods expected. This is very frustrating for both child and teacher as they are more than capable and given different requirements they would probably excel. Equally, another reason for the downfall of a strict grasshopper is that they will go very fast and miss a crucial step or trip themselves up somehow.
It would seem that it is better to be a grasshopper, but sometimes grasshoppers just leap in, and there is no thought trail to the reasoning. They miss a crucial clue in the question or misread it and go down a blind alley. They are less logical, and sometimes this means they come unstuck in a way that the inchworm will not as they will be methodical even if this is slower. As the child becomes older and preparing for GCSE getting reliably to the correct final answer every time becomes critical.
So on things that we can quickly and efficiently do differently, it is good to be a grasshopper, but if something is really tricky, the inchworm is the best approach.
How can we encourage children to be both?
Questions like ‘is there another way to get to the answer?’ and ‘what other topic uses …?’ can help give prompts and scaffolding, so you encourage a child to think around a question and not just follow the same procedure each time. Also changing the numbers in the question in the way I did. Each time asking ‘let’s look at the numbers this time, is there a quicker way to do it this time?’
Is your child struggling with learning or remembering their times tables?
Do you want some tips of how to help them?
The age at which children are expected to be fluent and have instant recall of all their times tables up to 12×12 has in recent years gone down to Year 4, as compulsory timed tests have been introduced for Year 4. Now don’t get me started on timed tests! Needless to say, I do not think that timed tests are good for children, but unfortunately, the government in its wisdom have thought otherwise…
Anyway, Year 4 now have these times table speed tests in which they are expected to answer a huge number of questions in a pretty unrealistically short length of time. I know from scientific, academic research that putting children under this time pressure is massively counterproductive and in fact causes huge amounts of maths anxiety.
But, at least for the time being, these Year 4 tests are here to stay.
Why learn your times tables?
Why times tables are so important? Well there are so many parts and topics of maths that hang off the knowledge of times tables, the main ones are in this picture. So even without the government and the National Curriculum they are actually the cornerstone of number and algebra and your child will find the rest of maths and then taking a GCSE infinitely easier if they do know most and hopefully all of them with reasonable recall and can do their times tables without a calculator.
So how can we help your child get through them and the build-up towards it?
Firstly, there is the idea of just memorising these numbers, memorising them and repeating them parrot-fashion. Often this works for children, more often it doesn’t. Even if they can repeat it back almost like a poem or song, do they have any understanding about what this means?
Quite often, no, they actually don’t really know what this means.
I spend a great deal amount of time each week with my pupils dealing with the understanding behind learning times-tables, and it actually takes practice and hard work over a long period of weeks and months for these ideas and concepts to slot into place for the child. Therefore, in a blog post such as this, there is no quick fix. I need you to be realistic with your expectations. Your child won’t suddenly become amazingly good at remembering their times-tables within a few minutes using these ideas. Anything that I can explain here won’t suddenly make a huge amount of difference, that simply won’t happen as it takes time.
What I can do is try and give you some ideas and some of the things that I do over a long period of time as part of my lessons.
One of the first things is using objects such as counters and we lay them out in patterns, these patterns are called arrays. So for example, if I had 6 counters, I could lay them out in several ways. I could have one row of 6, 2 rows of 3, 3 rows of 2, or 6 rows of 1. All four of these ways of representing the number six are called arrays. Arrays are very visual, and this can be the turning point for children to see that number is represented visually.
If we were to now look at the 2 rows of 3 and the 3 rows of 2, which are two parts of the same thing really. These are two factors of six. So, we can write it as 2×3=6, or 3×2=6, or 6÷3=2, or 6÷2=3. I encourage children to write these four number facts out on a piece of paper or a mini whiteboard. They are matching what they see on the array with handwriting the number facts.
The pathways in the brain that are used to look at the visual array and as saying the number fact out loud, and to write the number facts on their whiteboard are all separate anchors into the facts. The more anchors we can have at the same time into a fact or a memory, the stronger the chance of the brain being able to remember that fact. If this process is repeated, it helps make the pathways stronger.
Playing with the arrays is worth doing every time they are supposed to be learning a new times table.
I always joke with my pupils from that advert for Safestyle double glazing that was on TV where the man says “you buy one, I say you buy one, you get one free” I tell them they ‘learn one and they get 3 free’. So knowing 2×4, they get all four of the number sums. They are getting the dividing sums for ‘free’ and also the numbers the other way round. They need to realise that 2×3 gives the same value as 3×2.
This means that actually if they were to look at the 12 by 12 grid of answers which looks like they’ve got to learn 144 facts they actually only need to learn 66 facts – so already psychologically that is less than half as many to learn as they initially think.
So which times tables to learn first? What order of times tables to learn?
The order in which tables should be learnt, and will have probably happened at school for them already, is generally we learn to double which is the 2x and multiply by 10 at about the same stage at school near the beginning of key stage one. The next times table that is introduced is the 5x as this has a clear, easy pattern and children can very easily learn to count up in fives 5, 10, 15, 20, 25, 30 etc.
So that means we have 2x 5x 10x that are learnt very early on and hopefully in a practical and multisensory way as they are still in KS1.
Then there becomes a very fast-paced sprint to learn the rest towards the end of KS1 and beginning of KS2. Sadly, this often doesn’t involve much hands on resources called manipulatives or even visual pictures, so often this is where a child will start to come unstuck.
They should come in the order of 4x which can be thought of as double and double again; and then 3x, although sometimes the 3x are taught first. After the 3x and 4x usually comes the 8x as this is double, double and double again. Sometimes at this stage, the 6x is also introduced. Then the 9x and the 11x as both the 9s and 11s have nice clear patterns to them. The 12x can be taught as a combination of the 10x + 2x value, they really aren’t actually that hard and are often talked about early on.
The last one is always the 7x, the 7x times table is, without a doubt, the most difficult one to learn. It has no patterns, it has no rhyme or reason to the answers they don’t link really to any other tables, and they just have to be learnt.
So this is the order in which they would usually be taught. So if your child is struggling to do them, and is being expected to do 6x or 7x, it is always worth going back and making sure that they are properly secure and have mastered the early ones – the 2x 5x 10x 4x 8x. Get them really strong on those ones, if they can feel that they are strong on something they will feel more confident to be able to move forward and tackle the trickier ones.
So what are some other tips and tricks that I use with my pupils?
We need multisensory anchors into the brain. Use different senses, so using techniques that suit visual learners, auditory learners, kinaesthetic learners. But actually one of the best things to do is use activities that use more than one sense at any time as this gives stronger anchors.
There are many commercially available times tables songs. A quick google or look on YouTube, and you can find some songs. There are many different ones out there, some better than others some in a style of tune that your child will like and engage with, but others not so. I suggest that if there is a particular times table that your child is finding hard to learn, you look for a song and you bookmark and play that song a lot. In the days of CD players in cars, it was easy to have a CD that had times-tables songs on it on, and as you drove to school, you could listen to the songs and both sing-along.
I know personally how well that worked with my child, and I know anecdotally how well it worked with so many of my pupils, my tutoring pupils and also my pupils in my classes when I was a class teacher. It is slightly more complicated to do nowadays, but you may be able to have it on a playlist on your phone that can then be played through your car radio through apple play or android. This dead time of being in the car on the way to school or on a journey is a great time to learn any kind of maths like this.
Listening to songs and particularly good is singing along to them too. So, this means that not only the brain is hearing the song, but the brain is replicating it to sing along, and this lays down good stronger anchors.
Times tables with pictures
So that is hearing things and singing along, or using counters to make it very visual.
The other type of way that can really help is another visual way.
There are some stories available in cartoon form or picture form that show each of the times table facts. I use one with my pupils, but it is now no longer available commercially for me to recommend it to you. But what I can recommend is that your child draws a picture for one of the times table facts like the one I’ve shown here.
The act of drawing, the 10 minutes or so that they spend with their colouring pens and pencils drawing a picture with the number facts in will again lay down powerful anchors in the brain. They can then make these pictures into their own little book. Because they have actually done the drawing and the thinking and then they have the picture afterwards to look at again all of these lay down multiple anchors to the fact because it has a story, and it the brain likes this.
Times tables interactive games?
There are many games available online to enable children to practice times-tables very quickly against the clock, do a search, and you will find many of them like ‘press the button’ from Twinkl and times table top marks https://www.topmarks.co.uk/maths-games/hit-the-button . Your child’s school may well have a subscription to Times Tables Rockstar https://ttrockstars.com/ or other similar websites. Now, these sites tend to be practising very much against the clock, which as I say, I from scientific reasons, really don’t like the timed element, but it’s here to stay so we have to work with it… Your child will probably have their own login for Times Tables Rockstar and can practice at home if they wish. Some children love the competitive element of these styles of website and games.
It needs to be stressed to them; they need to be competing against themselves. Comparing themselves to other people will only make them feel rubbish, and that will affect their anxiety, and that will then affect their working memory and their ability to do these types of tasks in a timed situation. So, ‘can I do something better than I did it yesterday?’
Yes, that is a healthy way of being competitive. ‘Josh’s on level 20, and I’m only on level 10.’ No, that’s not a healthy competitive idea because we don’t know why Josh is on level 20 and all that does is demoralise your child. Therefore, phrases to them should be about ‘getting better themselves’ in comparing themselves to themselves and their own self-improvement.
Activities that you can do together in real life
A set of activities that I use are with giant 12-sided dice. I have attached the pdf for you to print off the dice too. 12-sided-A4-sizeDownload
We print them off on to two different coloured cards, or they can be coloured in with pen afterwards. Print them off, cut them out carefully, fold on the lines and stick together carefully. You now have two dice with which to then play any times table games. Actually making the dice is a nice craft activity that your child can be part of. Although beware making the 12 sided dice is a little bit fiddly, and you just need to be careful with the folding so that all the sides match up neatly and then roll easily.
The first activity that you can do using the dice is just rolling one of the dice. Choose the times table that you want to focus on. For example, the 4x, have one of the dice sat showing the 4 and then roll the other dice. This now sets you up with a times table fact that will be ‘something times 4’. If needed, the child can use their counters in arrays to then count how many they got to give them an answer. Make sure they say out loud and get them to write the four associated number facts down. Keep repeating, rolling the dice to give another times table fact in the four times table, each time saying the number fact and writing down its four number facts.
The next activity is for when we are seeing the child getting better and quicker and knowing some of these without having to work them out. So, this time may be rather than using the counters for the arrays and getting them to write it down – it starts to be more of a quickfire game. So again, one dice is on one number, for example, the 4 and again just rolling a second dice. We roll it, we say what we see, and we say the answer out loud. 6×4=24.
Another dice game can be that we link it to the drawings that they have done for a particular times table. You lay them all out on the table and then roll the dice again and 6×4=24. Find the picture where you have got the 6 and the 4 of the 24 all drawn into a picture story, so again they are linking into the picture and are saying it out loud, and they are rolling a dice.
Yet another activity is a bingo-style activity. For this, if you are focusing still say on the 4x you would make some bingo cards together and using the numbers that are the answers that are in the 4x so you would have 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 made into a grid which would be the bingo card. Both you and your child could have a different grid with those 12 numbers put in different positions on the grid. Now you roll the dice, and it gives you 6×4 so your child has to work out what is 6×4 and then cover or cross out that number 24 on their grid. It’s a race to get ‘3 in a row’, and you take turns each time covering up whichever one it is.
To make this game harder you roll both dice and the answer may or may not be on your grid so, for example, to get 24, yes if we are dealing with the 4x we need 6×4, or we can also get there if the dice rolled 1×12, 2×6, 3×8. All those different combinations would still give you the possibility of covering up your 24 in your grid. This is a way of linking into other times tables and realising that other number facts can give the same answer and there is not just one way to get to the number. All of these are factors of 24; therefore, it means that 24 appears in all of these different times tables. This kind of understanding is actually crucial to long-term success in maths.
A harder version of times table grid bingo would be to use any of the times tables that they are now really getting more confident with and have those as the answers on their bingo grid and roll both dice each time.
These are just some of the ways that learning times-tables can be made more practical and involved. The more multisensory anchors that can be used at any one time, the more successful this will become. The more your child starts to succeed in remembering some of them the more the maths anxiety will not come to take brainpower away, and their anxiety will come down slightly, and they will then be able to work more under pressure.
You’ve heard me say many times in this blog now that I really don’t like timed tests. I just need to clarify that slightly. Once the child does know their times tables and has got recall, hopefully even instant recall the idea of doing something against the clock is not so bad. But, expecting a child who does not have recall to do something against the clock will absolutely not work. What will happen is the child will become anxious.
As a person becomes anxious, the body diverts brainpower away from what we call the working memory and also from the processing speed. This is to enable a person to run away and is part of the fight and flight system. Once there is less brainpower coming to the working memory and also slowing down processing speed, it becomes progressively harder to do anything under pressure or in a time situation. Because you then are not managing to do that task you become more anxious, because you’re more anxious you are getting less brainpower, and so on and so on becoming a horrible downward spiral that just means that you cannot possibly succeed on that task.
This is the issue I have with the times test situation, because I know the science behind it, I know that it will not work for children unless they are already really good at that task because that will not cause any maths anxiety to them; therefore, the brain will not divert brainpower. So asking a child who’s really confident to do it will not be a problem, but asking a child who was already struggling, it will be a massive problem.
Some of these ideas may help your child to start to succeed in remembering some of the early times table facts and then you can build on this just adding in an extra times table every few weeks using the same strategies.
I wish you luck!
If you want to know more about maths anxiety, please read my other blog posts regarding it where I give other tips and advice about helping your child to overcome maths anxiety.
If you would like to book a video call with me, please do get in contact at Judy@JMBtutoring.co.uk