Experts in cognitive psychology have shaped our understanding of how children learn mathematics. What their work tells us is fascinating - and it makes perfect sense to parents and teachers.
The Working Memory Bottleneck
Dr Abadzi, a cognitive scientist at University of Texas, argues that people are “basically prisoners to their working memory”, which contains everything in their minds at any given moment.
Working memory can only hold a small amount of information and it lasts only a few seconds, so the information must pass through it rapidly or it gets lost. Working memory can become a bottleneck in our brain function - making even simple thought processes feel complex as we go forwards and backwards get to the answer.
Speed is Critical
But there is a way round the working memory bottleneck. Research shows that when children practise tasks like mental arithmetic, it becomes automatic and unconscious, freeing up space in the working memory for more complex calculations.
This means it's not enough simply to be able to work out a calculation - what matters is getting it right and how fast you can recall the answer.
Working memory is also limited in capacity - studies show on average we can only hold 7 items in memory for 12 seconds.
Put simply - as soon as item no 8 pops into the working memory another item falls out to make way. However, rapid recall of maths facts allows learners to jump the queue - avoiding the working memory bottleneck.
It's also clear that focus and concentration go hand-in-hand with developing working memory. If a learner is distracted while doing a maths calculation, it easily overloads their working memory and disrupts their thinking.
Explicit and Implicit Memory
We have two types of long-term memory - psychologists call these explicit and implicit.
The explicit memory is the bit we're aware of - such as being able to recall a fact such as the name of a capital city. Explicit memory gets all our attention and yet its potential is dwarfed by its big sister, the implicit memory - the iceberg under the water.
Implicit memory is the unconscious memory of skills and how to do things, such as playing guitar or riding a bike. These memories are typically acquired through repetition and practice, and are composed of automatic skills so deeply embedded that we're no longer aware of them.
By helping children truly master the essential foundation skills in maths we shift the load from their conscious explicit memory to their unconscious implicit memory. With this comes a level of maths fluency needed to excel in higher order maths skills - such as analytic thinking and complex problem solving.
Teachers are in the construction business.
Memory networks are like bricks and mortar. If you want the second floor - it had better start after your put the first one in Dr. Abdazi
The Importance of Practice
It's interesting that after acquiring fluent skills we tend to forget the effort and practice that developed them - but this makes perfect sense because we've made them unconscious.
The danger is we also lose respect for the amount of effort and practice it takes for our children to acquire the same skills. Dr. Abdazi explains the science behind acquiring fluent skills in maths:
Memories are stored in neural connections;
Few neural connections are created at a time - because it involves building proteins which takes time;
We remember best the information we saw most recently and most often;
Practice and repetition over time works.
The cognitive science of learning mathematics, however compelling, isn't the same as real evidence. Fortunately, academic research into learning mathematics has tracked many learners over their entire school life looking for vital statistical connections between early learning and later success.
The conclusions are pretty clear - and they support the cognitive science:
What does that mean for us at Murrow Primary Academy?
Please please practise timestables and numberbonds with your children. We spend time in school doing this, we share songs, watch videos, chant and also carry out activities that encourage rapid recall of our work. There are games you can buy,
This is a list of resources that you could use at home.
Card Game of Timestables - £2 from the Book people
Timestables Rock stars – Why not say children have to do 15 minutes on that before they are allowed tablet time? Children have passwords as we provide this for them in school.
Percy Parker - Timestables– Search on You Tube – great way to sing along as a family
Recite them on the way into school.
Number bonds to 10 and 100 and Number bond pairing is another fluency skill that when sent to implicit memory will aid mathematical performance. (4 and 6 - 30 and 70, 200 and 800 etc)
Thankyou for your continued support. The earlier children learn their tables the quicker they are able to use them to attempt and succeed in solving challenges in maths.
Our children need to be exposed to more vocabularly. How many times do you feel that you use the same words and that there must be a word that would fit better? We have investigated many tools and research which other schools have used and it is clear that Mrs Wordsmith is the right resource for our school. Their ethos is based on research. Please see a summary of their journey below.
Quote from Mrs Wordsmith -
Our team of experts led by lexicographer Ian Brookes have used data science and corpus linguistic techniques to identify 10,000 words that make a real difference to children’s academic success – and which can rapidly accelerate your child’s literacy level.
So, how did Ian and the team arrive at 10,000? Let’s crunch the numbers.
1 million → 42,000:
The English language is mind-bogglingly vast. The Global Language Monitor claimed that English acquired its one-millionth word in 2009, and continues to acquire new words at the rate of one every 98 minutes.
However, this figure counts everything that could possibly be considered as a word, including lots of one-off inventions and obscure coinages that would not be understood by many people.
Most words, furthermore, are variations on a core of 42,000 ‘root words’. For example, the word ‘happy’ has numerous related forms: ‘happily’, ‘happiness’, ‘happier’, and so on. Learning just one variation of these root words provides a base for acquiring all the others.
42,000 → 37,000:
Not all root words are equal, however. Some, like ‘happy’, are so common that children don’t need to consciously study them – they’ll learn them anyway. We used data science to identify 5,000 of these ‘easy’ words, and removed them from our list.
37,000 → 10,000:
27,000 root words, though, are obscure words that most of us manage very well without unless we are scientists, academics, crossword enthusiasts, or Scrabble players. English is full of technical or old-fashioned words that children are unlikely to ever encounter, let alone be expected to use, by the age of 17. Words like ‘sphygmomanometer’, or ‘curglaff’, for example – discarded from our list,
The 10,000 words that matter:
That leaves us, then, with the 10,000 words that children really need to learn:
challenging words that develop children’s comprehension, writing, and analytical skills, and enhance their achievement across the curriculum. These are the words that children will encounter in the best literature, and which make up our 10,000 Word Journey.
About Ian Brookes
Ian Brookes is Mrs Wordsmith’s chief lexicographer. He is the former editor-inchief of The Chambers Dictionary and has led or contributed to the creation of over 50 dictionaries and reference books from Chambers, HarperCollins, and Oxford University Press.
With the research done we decided how this would have the most impact on the children, and it soon became clear that immersion was the way forward. We purchased dictionaries and picture books. If you want to see these then please go to www.uk.mrswordsmith.com
From the Spring term 2020 children in KS2 at Murrow Primary Academy will be learning new words every week. The words will be taught using the methods which have worked at another school in our trust. The words will be displayed in the classrooms. The words will be displayed around school and children will be encouraged to not only use these in their speech but also in their writing - that is how we will see the impact. The developers of Mrs Wordsmith have partnered with a team of award-winning Hollywood artists who transport these words into the progressive, culturally diverse, and technologically advanced world children now live in. Epic words, taught in an epic way, making smarter kids! All the words have associated actions that the children can personalise. This too helps memorising the words for future use.
As is the way at Murrow Primary Academy, we would ask that Parents and Carers support us with this. We acknowledge that the impact will be felt more if children are exposed to the words both at home and school.
Teachers will use some of the following techniques:-
Children will be rewarded when they use the words and they will soon be able to see how by using their newly acquired vocabulary their writing becomes more interesting.
How can parents help?
1) Ask children which words they covered in Monday's assembly. All children will learn the first word on Monday morning. KS2 children - Class 3 and 4 will then also get two other words during the week. Class 2 and Zebras will just have the one word a week. Ask them the action that goes with the word.
2) Have a competition at home of who can use the words the most.
3) Check the words on Twitter weekly.
4) Inform the class teacher or Head Teacher if children do use the words at home. Email firstname.lastname@example.org (impact)
The words that we will cover in Spring are:-
We are all looking forward to hearing how this helps children and the impact that this has on the children at Murrow.
Boys Boys Boys!!!!
I attended a Conference in July 2019 where we heard Gary Wilson speak. He has done research into the attainment of boys. Here in Murrow, traditionally boys do not achieve the scores of girls in the formalised assessments processes. Boys do achieve, boys do learn, but in different ways to girls. Having read around the subject, it became clear that boys tend to respond to positive role models and also to a more active way of learning - this is not to say girls don't!
Based on my reading, I decided to host our first FUDGE day - Friends, Uncles, Dads, Grandads and Everyone day. I invited Fenland Bushcraft to host a day for Fathers and children.
The day was planned - den building, whittling of sticks, fire building, marshmallow cooking and eating. The time was spent learning but also playing together. The children listened and played whilst their dads, grandads, uncles etc also enjoyed themselves.
The impact will be greater confidence of Dads to engage with learning, greater bonds with their children, children will also grow in confidence with what they achieved. Feedback forms are coming in and I cannot wait to hear some impact stories which the parents are getting good at providing.
Well thought it would be good to update you on where we are with reading.
Reading is happening - reading for pleasure - children choosing to read texts that interest them, comics and newspapers that have been bought are encouraging reading. Bunny the school dog has been in on numerous occasions - once a week - and she is hearing readers. She just lies there while the children read to her. Parent feedback has shown that children are loving this. It has also meant that Headteacher I have been able to hear every child read and this has enriched my understanding of where we are with our reading. Plans are afoot to role out Accelerated Reader as a way of assessing the children in KS2. We have also grown our sets of guided reading texts and the library now is a focussed resource for our teachers. Our little EYFS Zebras are taking part in their reading race and being rewarded with stickers. Parents - thank you for your encouragement of reading.
Never done a blog before - but wanted to add something more to what we offer parents.
Reading makes the world go round....
If you can read then you will be OK in life. Reading is a skill that is key to the future of our children. Parents and School need to be working very closely together to ensure that we help our children with this. From Zebras we start teaching phonics, but it is much more than just the semantics of phonics. We want children to love reading, we want children to love books. Stories add to life experiences, stories add dimensions to our imaginations and we need to be enabling this. Children should become hooked on reading, they should want to read, they should derive pleasure from reading.
The partnership needs to work with both partners focussed on ENTHUSING children with books.
At School we will be
Introducing our new library - Purchasing new and exciting books - Publishing book reviews - Having a book of the week - Teachers will read and share books with children - A focus text will support our topics.
At home please could you try
Sharing a book at least once a week - Bed time story - Telling stories on the way to school - Trips to the library - Buying a special book for birthdays and Christmas - Share the newspaper - Make books special. To try to help I attach some pictures which are the winners of the Teach Primary Book awards - some ideas for stocking fillers at Christmas.