5 General Election Maths Questions for the Kids

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Here are 5 general election maths questions to give your children a taste of the big event – and a little maths practice.

Question 1

There are 650 MPs in the House of Commons. How many MPs does one party need to win the election?

Hint – to win the election you need to have more MPs than all the other parties put together.  This is called a “having a majority”.

Question 2

Let’s say the Conservative party and Labour party  have 273 MPs each. How many MPs are they short of winning?

Hint – you’ll need to use the answer to question 1 to find this – see the answers below if you’re stuck

Question 3

Here’s an estimate for the election - it’s very roughly what the newspapers say is going to happen

Party MPs
Conservatives 273
Labour 273
Liberal Democrats 28
Scottish Nationalists 52
Green 1
Plaid Cymru 4
UKIP 2
SDLP 3
DUP 9
Sinn Fein 5
TOTAL 650

Who could the Conservative party join with to win the election?

Hint – of course it’s not as simple as this some parties don’t like each other and won’t ever club together.

Question 4

Who could the Labour party join with to win the election?

Question 5

Out of the 650 MPs 150 are women.  What fraction are women?

 


And the Answers . . .

Question 1

There are 650 MPs

The winning party needs half of them and an extra one. That’s 325 + 1 = 326

Question 2

If the Conservatives (or Labour ) have 273 they will need a further  326 – 273 MPs.

They will need 53 more  MPs.

Question 3

If the Conservatives have 273 votes they will need to join with other parties to get the 53 MPs they need to win and form a Government

This could be:

Conservatives ( 273 ) + Scottish Nationalists ( 52) + Lib  dems ( 28)  = 353 MPs

Question 4

Who could the Labour party join with in order to win a majority ?

If Labour have 273 MPs they will need to join with other MPs  to get the 53 MPs they need to win and form a Government.

This could be:

Labour (273) + Scottish Nationalists (52) + SDLP (3) =  328 MPs

Question 5

150 MP’s are Women.

As a fraction this is:

fractions

Which is not enough !

 

Our figures are very rough guesses and will certainly be wrong when the votes are counted, but it looks like this year’s election is going to involve a bit of maths to work out a winner.

I’ll update these numbers with the real numbers when we know more.

I’m Jane,

Co-founder of Komodo, & mum of two

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Reverse Engineering Success in Maths

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You can’t peer into a crystal ball to predict success in maths but there’s much to learn from the past. In this article I’m going to draw on academic research and Ofsted publications to “reverse engineer” the key factors that underpin success in maths. Academic research projects have tracked many learners over their entire school life looking for vital connections between early learning and later success.

The conclusions are pretty clear and very valuable to parents:

  • Early numeracy skills are critical. Lack of attainment at 16 tracks back to age 11 and even 7
  • Calculation Fluency – being able to work out arithmetic accurately and rapidly - is the strongest indicator of later success

The research highlights how important it is to ensure the maths learning foundations of are in place early.  Fluent calculation – mental maths –  is identified as particularly important as a platform for future achievement.

Here’s the research:

The Institute of Education, London:  “The development and importance of proficiency in basic calculation” ( July 2013 )

What we found

Basic calculation fluency (accurate and rapid solution of single digit addition problems and complementary subtractions) is the strongest correlate of success in mathematics in primary school and the most frequent symptom of difficulties in mathematics

Full paper

Ofsted: “Mathematics: made to measure” (2012 )

Key findings

Children’s varying pre-school experiences of mathematics mean they start school with different levels of knowledge of number and shape. For too many pupils, this gap is never overcome: their attainment at 16 years can largely be predicted by their attainment at age 11, and this can be tracked back to the knowledge and skills they have acquired by age 7

The disparity in children’s knowledge of mathematics grows so that by the time they leave compulsory education at 16 years, the gap between the mathematical outcomes of the highest and lowest attainers is vast. The 10% not reaching the expected level at age 7 becomes 20% by age 11 and, in 2011, 36% did not gain grade C at GCSE

 Full Paper

The Institute of Education, London & University of California “Early Predictors of High School Mathematics Achievement”

The present findings demonstrate

That elementary school students’ knowledge of fractions and division predicts their mathematics achievement in high school, above and beyond the contributions of whole number arithmetic knowledge, verbal and non-verbal IQ, working memory, and family education and income. The relations of fractions and division to mathematics achievement were stronger than for addition, subtraction, multiplication, verbal IQ, and parental education and income. These results were consistent across data sets from the U.K. and the U.S.

Full Paper

The good news for parents of young children is that success, or lack of it, isn’t a fait accompli – a little extra practice at home has a huge impact on learning outcomes. Komodo is designed to have the maximum benefit in the areas that really underpin future success – such as calculation fluency and mental maths. Furthermore Komodo doesn’t require heaps of time sitting in front of the screen – our approach is little & often learning which fits easiy

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Tips for Learning the 12 Times Tables – from a Rock Climber

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learning-12x-tables

 

The 12 times tables strike fear in children at first – but there’s no need. In this article we take a look at how to learn them in bite sized chunks. First of all put yourself into the shoes of a child who is new to the 12x tables. It’s daunting - like looking up a rock face you have to climb. You might already know that 12 x 12 is 144 but wow, this is a huge number and there’s a long way to climb to get there. The good news is you’ve been learning tables for a while now, you’re getting the hang of it -  and this is probably the last tables to climb!

Easy-learning-12x-tables

 

The Easy Part

Climbers look for easy ways up a rock face – perhaps a safe ledge to rest on or some great hand and footholds. The 12 times tables has two great safe ledges to climb onto and they’re  pretty easy to use – let’s take a look:

  • 1 x 12 = 12
  • 2 x 12 = 24
  • 3 x 12 = 36
  • 4 x 12 = 48
  • 5 x 12 = 60  this is a safe ledge to jump onto

There are a few ways to look at these multiplications:

  • Adding 12 each time is a common method:  12+12= 24,  24 + 12 = 36,  36+12 = 44
  • Also notice the pattern in the ones columns:  12    24    36    48    60    72    84   96  108   120    the 0,2,4,6,8,0 pattern repeats through all the 12x tables.
  • You can use the half and double method :   So  3 x 12   becomes  6 x 6 = 36
  • Or use partition – faced with 4 x 12 =  split it into 4 x 10  add   4 x 2  so 40+8 =  48

The Walk to the Summit

learning-12x-tables-summit

The last three 12 times tables are also relatively easy to remember once you’re at the 120 ledge:

  • From 10 x 12 = 120 we can add 12 to get 11 x 12 = 132  and another 12 takes us 12 x 12 = 144
  • We can also “climb down” from 10 x 12= 120 to  9 x 12 = 108

 learning-12x-tables-scary

The Scary Bit

Between our two safe ledges at 5 x 12=60 and 10 x 12=120 is the scary part:

  • 10 x 12 = 120   a safe ledge to jump onto
  • 9 x 12 = 108   you can climb down -12 from 120 to get here
  • 8 x 12 = 96   memorize this one an extra ledge
  • 7 x 12 = 84  climb up +24 from 60 to get here
  • 6 x 12 = 72  climb up +12 from 60 to get here
  • 5 x 12 = 60   (START HERE)

Round Up

They say mathematicians make good climbers because they’re always looking for the best route through a problem. When you’re faced with a problem in maths it also helps to think like a climber – break the problem down into chunks and see if there are any safe ledges to jump onto and hold on while you figure it out. When we do this for the 12 times tables we soon see they’re not so difficult after all.

Here’s a useful worksheet versions of the 12x tables rock face:

12x-tables-Worksheet

worksheet version fill in the safe ledges first!

I’m Ged, Co-founder of Komodo , maths teacher and dad. If you have any questions please get in touch.

I have a little confession to make here – I was more of a wanna be rock climber than the real thing. The times I took to the rock face it was with an instructor and a safety harness!

 

 

 

 

 

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Merry Christmas and a Happy New Year

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KomodoChristmas

Merry Christmas and a Happy New Year

Prizes Prizes Prizes to be Won:

KomodoSanta

  Here’s How to Build the Komodo Santa Claus and Win a Super Prize:

We’ve tried to make the paper-toy super easy to build, and our test builders, aged 9 and 7, managed okay – with a tiny bit of grown up help.

Here are the instructions:

  1. Print the paper-toy in colour onto A4 sized stiffish paper,  200g paper is ideal
  2. Cut out the body parts and accessories – making sure you also cut out the many glue flaps
  3. Starting with the bigger body parts, fold all flaps first then glue – we found Pritt stick to be ideal
  4. The arms and tail are double-sided – so need to be stuck together
  5. Post a Super-Santa Photo onto our Facebook Page or send it to hi@komodomath.com  and we’ll post for you - First names (only) will be mentioned
  6. Every Entry Wins a Prize!

Here’s the Komodo Santa Claus paper-toy:

Right Click & Save As to Download the PDF template

Right Click & Save As to Download the PDF template

Here’s the 2 page PDF printable template to get started. The end date is 1st January and it’s open to all subscribers.

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The Transforming Power of Education

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As we approach Komodo’s second anniversary we’re very proud to start supporting  Many Hopes – an amazing charity that transforms the lives of street children and orphans in Kenya through education. After a chance meeting with the founders Thomas and Anthony, we were completely inspired by their ambitious vision and amazing achievements. Our first contribution will educate one child for one year, but we see this as the start of a lasting partnership - as Komodo grows we aspire to do much much more.

Many Hopes is quite unique in its strategy and approach – in their own words:

“We believe that loving and educating a network of children who have endured the worst of poverty and exploitation is the best way to equip them to eliminate the causes of the injustice they and their neighbours have suffered. We believe in tackling the causes of injustice, not just housing the victims of it.”

manyHopesInvest

There are a few things we really like about Many Hopes:

  • They’re passionate about the transforming power of education – and we are too
  • 100% of donations go into the schools and educational projects
  • Their projects are designed to be sustainable within ten years
  • Their work is not faith based – children come from all religions, Christian, Muslim or none – they can pray and worship as they wish
  • Most importantly they aspire to break the cycle of injustice through education:

“Nobody cares more about justice than those who have suffered injustice. If we equip children who have suffered the worst of exploitation with the education in their heads, the confidence in their bellies and the network at their fingertips to match that desire already in their hearts, they will do work we could never do”

Our donation was match funded by a wealthy American family fund – so this means education for two children for one year! We’ll keep you posted with Many Hope’s amazing school project from time to time. Thanks for subscribing to Komodo – without your support this wouldn’t happen at all!

Ged, Jane & the Komodo team

To find out more about Many Hopes or to donate visit manyhopes.org

 

 

 

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Your Child’s Concentration – How to Improve it

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Concentrate

 

Even as I’m writing this my mind is drifting  – did I return that letter to Kate’s school, I need to buy flights for Christmas before they rocket in price, will I get soaked on the way home . . .   I swipe these distractions aside and try to maintain my focus – but it’s not easy. Concentration is the raw ingredient that gets stuff done, but being able to concentrate is far from straight forward – it’s an elusive quality that’s hard to conjure at will – even for adults who are more self-aware and have access to fresh coffee!    

Concentration is even harder for our children, but it’s important and there are some things we as parents can do to help.

What’s the Big Deal about Concentration?

The education system has its cycles of what’s in or out of fashion and there’s an endless debate about what skills are important and how to teach them. Surprisingly concentration rarely surfaces as a skill or quality that warrants developing alongside the likes of communication, imagination, confidence, creativity, group work  . . (all important too!) . .  This is surprising because although classroom teaching styles have evolved a lot over the past thirty years – less of the chalk and talk we suffered – the exam system hasn’t changed one bit – and here concentration is everything. And if, like us, you live in an area that has academic selection for grammar schools you will be more aware than most of the importance of concentration in preparing your child for a crucial hour long exam. It’s not just about exams – concentration is required for listening to the teacher, focusing on classroom tasks and most aspects of learning.

How Parents Can Help

We sometimes forget that our children spend all day in a class of thirty other kids where individual attention is in short supply. This means your child will probably get more one-to-one attention from you at home during homework time than all day at school. We can have a big impact at home on education and we can do much to ensure better concentration. Here are some aspects of your child’s life that influence their ability to concentrate:

Sleep

An obvious easy-win in the concentration battle is getting enough sleep. As this BBC article suggest we’re talking about 10 to 12 hours per night for a child of 5 for 11. Establishing a bed-time routine always helps and makes an early bedtime easier to implement.

Emotions

I mentioned earlier that as adults we’re more “self-aware”. Of course this is wishful thinking – adult or child, we’re all emotional beings and more often than not we’re completely unaware of being driven by our emotions. When it comes to concentration nothing gets in the way more than worry – so if your child is worried about something find time to talk it through with them. It may be pretty trivial and easy to resolve, but if it’s persistent and happening in school consider talking to the teacher.

a worried brain

Diet and Water

I think we all agree that a balanced diet helps maintain concentration – after all if your child is hungry or fizzing with sugar they’re unlikely to be thinking straight.  There are a few foods that are worthy of a special mention:

  • Oat Cereals, such as porridge, release their energy slowly – so breakfast keeps children going through to lunch.  The opposite is true for sugary cereals – so ditch the sugar puffs and coco pops!  Confession here – my kids recently rejected their porridge for weetabix but it worked while it lasted! 
  • Omega Fish Oils – If your child has issues concentrating or is coming up to an important exam I’d consider this supplement simply because it’s cheap, harmless and there’s growing evidence supporting the benefit to concentration and learning.

Water is very important to the brain and dehydration has a clear impact on concentration. This is something we often consider only in summer time but it’s really worth ensuring your child is hydrated in winter too. Most schools are on top of this, but if not a tap-filled water bottle is an easy answer – annoyingly my son’s new secondary school believes drinking water is best delivered via the caterer’s vending machines!

Exercise

Several research studies point to exercise being beneficial to school children’s concentration. This study from Denmark even suggests walking to school – as opposed to driving - improves concentration and the effect last all morning. Aside from the obvious health benefits of exercise it’s useful to know that it’s good for concentration too. Sending the children outside to play for 15 minutes during a long homework could be a win-win situation.

Relaxation

Rest and relaxation is of course important for concentration – so balance home learning with down-time. Personally I’m a little concerned that some forms of down-time such as console games are actually exhausting in terms of concentration. I’m thinking particularly of my son’s post-gaming lull in attention which usually takes thirty minutes or more  to shake off. I’ll come back to this in another article.

Distraction and Focus

For younger children the kitchen table is the ideal place to do homework - because you are are likely to be around to help - but it’s worth remembering that TV, radio and even telephone conversations can be distracting. As learners reach ten or older and become more independent consider a desk in their bedroom or another room and best not to allow devices during homework time. Also try asking them to set a target time to complete the work - this can help them focus.

Concentration as a Good Habit

By setting up the environment and conditions for learning at home and instilling the idea that learning is important we can improve concentration. If we do this consistently then it becomes a good habit - and perhaps even a lifelong one.  

By Ged McBreen co-founder of Komodo &  mathematics teacher

 

Komodo’s little-and-often approach to learning maths uses short regular practice sessions ( 10 minutes 3  to 5 times per week ) that fit into the busy home routine. It’s designed to develop fluency in maths in a way that’s effective and rewarding – without keeping children at the screen.

 

 

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Build a Paper-toy Komodo Competition

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paper-toy-komodo-ivy

A shy Komodo is photographed at night

At Komodo we love our paper-toys - they’re cool and kids love making them. There’s a maths angle too – in seeing how a 2D plan folds into a 3D shape. Now we’ve taken this to a new level, thanks to Niall our very own paper-toy master craftsman.  We’ve made a Komodo paper-toy and we’re asking you to build it and enter our competition.

Instructions

We’ve tried to make the paper-toy super easy to build, and our test builders, aged 9 and 7, managed okay – with a little grown up help. The amount of grown up help of course depends on age and how “crafty” your child is in cutting and sticking the model – a good look at the Komodo photos before making helps.

Here are the instructions:

  1. Print the paper-toy in colour onto A4 sized stiffish paper, 200g paper is ideal
  2. Cut out the body parts and accessories – making sure you also cut out the many glue flaps
  3. Starting with the bigger body parts, fold all flaps first then glue – we found Pritt stick to be ideal
  4. The arms and tail are double-sided – so need to be stuck together
  5. We’ve numbered where to stick the arms, tail and legs
  6. You can choose a tongue – hey you could even design your own!

Here’s the Komodo paper-toy:

Right click and "save link as" to download the 2 page PDF

Right click and “save link as” to download the 2 page PDF

Here’s the 2 page PDF and here are the JPEG versions Free paper-toy Komodo page 1,  Free paper-toy Komodo page 2

The Competition

Some Komodos are so shy they only come out at night under cover of thick ivy leaves – see the photo above.

Some have very particular tastes – this one only feasts on fresh passion fruit flowers:

papertoy-komodo-passion-fruit

Some are quite cheeky and are often caught raiding the fruit bowl:

komodo-in-fruit-bowl

 

The Competition is to build your Komodo paper-toy and photograph it in its natural habitat. Please tell us a little bit about it if you wish!

The Rules:

You can enter the competition by adding your Komodo paper-toy photo to our Facebook page.

  • Please add your child’s first name and age
  • A little story is most welcome
  • Or you can email it to us – hi [at] komodomath.com –  and we’ll add it to this blog post ( Note that we’ll only refer to your child’s first name and age )
  • The competition will be judged by Niall - our paper-toy master craftsman
  • The competition will end at midnight on Tuesday September 30th
  • It’s open to all children – whether you’re a current Komodo subscriber or not

 

The Prizes:

Papertoy-Monsters

A copy of the wonderful “Papertoy Monsters Book” will be sent to the best two entries in each age ranges:

  • Age 6 and below
  • Aged 7 & 8
  • Aged 9 to 11

If you have any questions please comment below or on our facebook page

Good Luck Everyone!

 

 

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Fractions come early in the new Primary Maths Curriculum

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This week sees the start of a new primary maths curriculum in England – here’s my previous article summarising the changes.

One change is that fractions are to be introduced earlier – in year 2. This makes sense since children have a pretty intuitive understanding of fractions by age 6. 

As our “Introduction to Fractions” video suggests, children become aware of fractions at the dinner table - so don’t miss this opportunity to discuss them. Of course if there are always four of you sharing the pizza it can get a bit predictable – so mix it up and ask some “what if” questions such as “what fraction would you get if there were five of us?”

Welcome back Roman Numerals

Another quirky addition to the curriculum is Roman Numerals up to “XII” in year 3 and “M” in year 6.  The rationale is to help preparation for algebra because we have letters representing numbers – however Roman numerals have a pretty unique pattern. Let’s see if you can remember or guess some of these:

IV

VII

IX

XI

MCXII

 

Answers at the bottom of the page.

Fluency and Number Sense

The new curriculum has a welcome emphasis on fluency and frequent practice in maths. This is something we also see as essential for success in maths.

Here’s what the new curriculum says:

“AIM:

become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately”

It’s worth remembering that the changes to the curriculum aren’t everything. More significant is their teacher, the school and last but by no means least, home and family support for learning. Meanwhile here at Komodo we’re incorporating the relevant changes to the curriculum to ensure we continue to complement classroom maths.

And the Roman Numeral answers are:

  • IV (4)
  • VII ( 7)
  • IX   ( 9)
  • XI  (11)
  • MCXII   ( 1112 )  the primary curriculum goes up to 1000  ( M) but most Y6 pupils will be able to work this out.

 

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Parent’s Tips for Summer Holiday Learning

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tramore

Having returned from a great weeks holiday in Donegal on the North West tip of Ireland I’d like to share a few thoughts and – hopefully useful –  tips on learning in the summer holidays.

Our annual holiday to Donegal is always tinged with trepidation because the weather, even in July, can be appalling. This year, thanks to a last minute shift in the jet stream, we lucked out on blue skies and freak temperatures in the low twenties. Add this to the usual beautiful clean empty beaches and who could ask for more! This year James and Kate’s holiday highlight was a trip to Tory Island. Not so much for the island itself, but for being tossed around and drenched by the swell on the tiny ferry boat that took us there and back. It was refreshing that the boat’s Captain had an old fashioned attitude to health and safety – or the fun would have been missed.

The Summer Slide

“The summer slide” is the term given to children’s educational gains evaporating during the summer holidays. Some writers have described this in a pretty alarmist way. In his book Outliers Malcolm Gladwell makes much of the “agricultural school calendar” being responsible for the US and European education systems falling behind Asia. His solution – have a two week break instead.

It’s no doubt true that 6 weeks – or 8 weeks in Northern Ireland & Scotland -  of summer holidays without stimulating our children’s brains is not going to do them any favours when they return to school. That said, having say 2 weeks of complete down-time while away from home is invaluable for de-stressing our kids and ourselves. Like all things parenting it comes to common sense and moderation. Here are a few tips & ideas for learning activities that will keep little minds active during the summer holidays - apologies in advance for stating the obvious:

2014-07-24 09.49.54

Reading Hour

Reading is one of the best habits we can pass to our kids and its educational value is immense. Of course these days kids will default to grabbing the ipad or watching TV – so I think it’s important to switch all screens off for a while each day. Here are some some reading suggestions from James – suitable for ages 9,10,11:

  • The “Percy Jackson” Books by Rick Riordan – no cover photo because he’s passed them all on
  • The “Alex Rider” books by Anthony Horowitz
  • Everything by Michael Morpurgo

Kate’s favourites include:

  • The “Pippi Long Stocking” Books by Astrid Lindgren
  • The Borrowers books by Mary Norton
  • everything by Michael Morpurgo too
  • Matilda – Roald Dahl

What about the 5,6,7  year old reading list?

I’m a big fan of clearing out the cupboards so we’ve passed most of our early reader books on to younger cousins. I would certainly recommend everything Roald Dahl, especially The Twits, Matilda and Charlie and the Chocolate Factory, but beyond that I’m hoping you guys might help by posting some suggested reading on our Facebook page or using the comments below - please add the age too!

All Things Crafty

Kids love a craft project but it can be difficult for parents to organise. The good news is it gets easier as kids get older. Here are a few great craft products that require little parental organising.

Kate, and lately James, are fixed on creating multi-coloured bracelets with her rubber bands and loom. The patterns are quite intricate and need a bit of mathematical thinking – and there are hours of dedicated weaving ahead!

loom

 

As you may already know we’re big fans of the Paper Toy Monsters book. This was a life-saver a few years ago when we weren’t so lucky with the Donegal weather. Suitable for age 5 to 9, all you need is glue and scissors and away you go.  Here’s a nice French site with some great free paper-toys to get you started:

Papertoy-Monsters

There are endless crafty possibilities – here’s a site with hundreds of craft projects split into age ranges. If you have any crafty tips please post them on our facebook page or in the comments below.

 

chess

Chess

Chess is a great way to develop mathematical thinking because it’s all about patterns and strategies. If your kids are new to chess it’s useful to start by using an app which shows you all the possible moves when you select a piece - this is a great way to learn the rules & moves while playing. Here’s a great free chess app for android and here’s one that looks good for ipad / iphone.

Komodo

Komodo is a great way to avoid sliding back in maths during the summer holiday. There’s no need to double the effort just because there’s no school. I’d recommend – after two weeks of complete downtime - continue using it as normal for twenty minutes, five times per week. Komodo is designed to be effective in a short time – minimising the time kids spend at the screen – so once they’ve used it your kids can get outside to burn off some energy.

Happy Holidays!

Jane,

Co-founder of Komodomath.com & mother of James & Kate

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The Mathematical Brain – How Children Learn to Count

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Learning to Count

 

Counting is easily taken for granted but there’s a lot of fascinating research into how we learn to count – and there’s more to it than you may think.

The Mathematical Brain

It’s first worth considering where our capacity to do mathematics comes from. Neuropsychologist Brian Butterworth in his book “The Mathematical Brain” suggests we’re born with an innate sense of number hard wired into our brain and he attributes this to a small region of the brain behind the left ear he calls “the number module”. He compares this idea to colour – in the same way we perceive the “greenness” of a leaf we can also perceive the “twoness” or “threeness” of a group of objects. Take counting. Like times tables and algebra, we tend to think it’s something kids have to be taught. Wrong, says Butterworth – it’s an instinct. Sure, we have to learn the names and symbols of numbers to develop that instinct, but, because the number module is hard wired into the brain, basic counting comes naturally. Remote tribes can count even when they have no words for numbers. In maths as in language he believes, “kids start off with little starter kits” And their maths starter kit is the number module. There are other theories too – such as maths being an extension of our spatial awareness – but there’s something nice in the idea of a “little maths starter kit”.  A Word of warning – All this doesn’t mean a child is predestined to be either good at maths or not. Far from it, we’re all born ready to learn maths – and it’s what happens in the first 10 years or so that sets us up.

Counting With Toddlers

Research suggest that toddlers – even as young as 12 months – have a sense of how many there are in a set – up to around three objects. This comes from their innate sense of number. Counting is learned when the toddler starts making the connection between this innate sense of “how many there are” and the language we use to count “one, two, buckle my shoe”. This is the first stage in learning maths and it’s the building block for many early concepts. Should parents count with their toddlers? Absolutely, using a variety of real objects. And since counting and language are interlinked reading to your toddlers is equally if not more important.

Counting – early learning milestones

Here are some stages of learning to count that you may notice your child going through at ages 3 to 5:

  • Recognising how many objects are in a small set without counting. So if you show your child four apples they won’t have to count them to tell you there’s four.
  • Knowing the “number words” from one to ten and their order.
  • Know the sequence regardless of which number they start on. So if you say “start counting at four” they will count “four, five . .” as opposed to always counting from one.
  • Conservation of quantity – This is where children realise that the number of objects in a set stays the same unless any are added or removed. So if they count six cans of beans in a straight line, then you rearrange the beans ( in front of their eyes ) into say two stacks of three – they will realise there’s still six without recounting.
  • Counting non-visible objects – your child will realise they can count things they can’t touch or even see – such as sounds, members of someone else’s family, or even ideas.
  • Cardinality, not to be confused with carnality - This is knowing that the last number counted is equal to the quantity of the set. If your child counts six oranges 1,2,3,4,5,6 and then you ask “how many oranges are there”? and they count them again then they haven’t grasped “cardinality”.

Counting on – as a step towards adding

Learning to add comes as an extension of counting. Here are some stages a child goes through to make this connection:

  • Counting all – For 3 + 5, children will count “one, two, three” and then “one, two, three, four, five”  to establish the quantity of the sets to be added – for example, three fingers on one hand and five fingers on the other. The child will then count all the objects “one, two, three, four, five, six, seven, eight”
  • Counting on from the first number – Some children come to realise that it is not necessary to count the first number to add. They can start with three, and then count on another five to get the solution. Using finger counting, the child will no longer count out the first set, but start with the word ‘Three’, and then use a hand to count on the second addend: ‘Four, five, six, seven, eight’.
  • Counting on from the larger number –  It’s more efficient when the smaller of the two numbers is counted. The child now selects the biggest number to start with which is “five”, and then counts on “six, seven, eight”.
  • The final stage isn’t really counting – it’s where learners know their number facts and skip the time consuming counting altogether.

Number lines are great visual tools for making this connection between “counting on” and addition or subtraction – we use them in Komodo a lot. Here’s an earlier blog article all about number lines.

The number line

Beyond basic counting

Counting is the first mathematical pattern learners encounter. From here they soon begin to count backwards which is a step towards subtraction and they’ll also count in twos, fives and tens which is a foundation for multiplication. The next big step is the idea of place value and counting to base 10. Learners often make this leap simply because it’s an obvious and efficient way to count large numbers. In Komodo we use practice examples like this to help learners make the connection to counting in tens and ones.

counting in tens

 

It’s easy to forget that counting is a key concept in maths with many stages before it’s mastered. There’s certainly a lot more to it than one, two, three!

I’m Ged McBreen, Co-Founder of Komodo and a qualified Maths teacher. If you found this article interesting sign up to our email list.

 

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