You don’t need to work in education to know how important it is for children to read for 10 minutes every day. Primary school teachers carefully assess reading ability and send home graded reading books. Parents and carers listen to children read for 10 minutes or so, and each day or week the level of challenge increases.

The National Literacy Foundation found that just 10 minutes of reading each day leads to a child being 13x more likely to read at or above their expected level and makes a dramatic difference to their educational attainment.

Chip & Book
Until now, there hasn’t been a way for teachers to send home 10 minutes of daily maths tailored to the individual needs of each child – the photocopying, marking and feedback alone make it unfeasible. But, DoodleMaths does just that – the app understands the personal strengths and weaknesses of each child and delivers work pitched at the right level and pace; it’s marked, provides feedback to the teacher and can be done on any smartphone or tablet so no photocopying either. Parents just need to provide a quiet moment and access to a smart phone or tablet.* If 10 minutes a day can make such a big difference in reading, just think what we can do in maths.

This rise in standards isn’t just important for student’s confidence in maths, but it’s vital to our economy as a whole. Research conducted by KPMG in 2009, estimated that the failure to master basic numeracy skills in primary school costs UK economy £2.4 Billion per year. Yesterday, GeekWire reported on the jobs report from CareerCast, where 7 of the top ten best careers are in a STEM-related field. These  top jobs included actuary, mathematician, statistician, biomedical engineer, data scientist, software engineer and computer systems analyst.**

DoodleMaths can be purchased as a site licence for schools from £245 or by parents for £6.99 in the the Apple and Android app stores.

*Ofcom statistics show that in 2014 84% of 25-34 year olds have a smartphone or tablet whilst PC ownership has dropped to 34%. http://bit.ly/1qY2YWa

** http://bit.ly/1CRIg9J

We left classroom teaching in 2007 to set up a tuition business in Bath. We taught from a converted shop, which became a small classroom equipped with the best maths resources I could lay my hands on. The business quickly took off, and soon we were teaching more students than we could manage, so the natural next step was to employ a tutor. And then a couple more. By 2008 the small classroom was full every evening and every Saturday morning, but parents were still knocking at the door.

We opened a second centre on the other side of Bath, and ran it remotely, employing tutors and a centre manager. Not quite as successful and the first, it still saw over 100 students per week pass through its doors. But by 2010, the business was stagnating. For a while we couldn’t understand it: we’d experienced 3 years of rapid growth, and we envisaged opening a third and perhaps fourth centre – after all, we were still only hitting 1% of the addressable market in Bath. Why had we stopped growing?

The answer is simple: the students being tutored in 2010 were receiving good tuition, but not the outstanding tuition that our first customers had received. As the business scaled, it became harder and harder to find really good tutors, and harder and harder to ensure our initial exacting standards were being met. And you are never under more scrutiny than when you are teaching a child maths. If we had opened a third centre, it could have been catastrophic for our business.

As I have said in previous blogs, the single most important factor when it comes to raising standards in maths is to ensure that every child is working at their threshold of understanding. And this is harder than you may think. Tutors do not do this reliably – even when you put processes in place, they need to be followed. The biggest issue we faced with tutors was the constant defaulting to teaching children what they were doing at school, which, by-and-large, was not what the child needed because it wasn’t their threshold.BIGENLARGEMENTS1

As we build DoodleMaths, the opposite is happening. Increased revenues mean we can invest more and more back in to creating the resources that work best for a child. The vast data we collect is vital to driving this: last month, 600,000 questions were answered. We know exactly what the average time taken to answer each question is, which questions are too hard, which ones are too easy. This allows us to refine our work program with greater and greater accuracy. And outcomes are immediately tangible: we can demonstrate progress transparently to parents, teacher and children in real time, so if a child is finding something difficult, there should be no reason for them to sweat on it for weeks at a time

As our technology-based tutoring system evolves, it will become better and better through scaling in a way that our human-based equivalent never could.

Threshold training is a common term in distance running. It’s one of the most productive types of training that an aspiring athlete can do. The proper pace for threshold training is about 90% of maximum heart rate, and training in this way can significantly improve a runner’s speed.

Martin Pettitt (CC2.0 Generic license)

Martin Pettitt (CC2.0 Generic license)

I sometimes like to think of maths, as a tree of increasingly difficult concepts. Every learner is at a different point in climbing the tree. Every learner has their own threshold, having made their way to a certain point up the tree. It’s vital they don’t forget what they learnt lower down the tree, else they’ll fall back down. And equally vital is that they learn what is next for them personally on the tree, so they are working at their own threshold.

If a runner took a light jog every day for 15 minutes, she’d never improve. But on the other hand, if she trained at 95% of maximum heart rate every day, she may suffer exhaustion, and injury or perhaps a crisis of confidence.

If our mission is to significantly raise an individual child’s standards in maths, the single most important task is to establish that child’s threshold. Set the work too easy and they won’t learn anything new. Set the work too hard, and they will be learning concepts that are not underpinned by the necessary pre-requisites, meaning there’s a danger of the child not fully understanding the concept and then forgetting it soon after. This is what made Kumon the most successful supplementary maths provider of the 20th century: every child entered the program at their threshold, and the curriculum was carefully constructed to ensure pre-requisites were always in place and never forgotten. Children learned through doing maths, always at their threshold.

We know what happens when a child isn’t working at their threshold. We’ve experienced it ourselves as either a teacher, a parent or from our own memories of school. A year spent in a maths group where a subject-enthusiast teaches to the top of the class with great enthusiasm but to the extent that most get left behind, or understand only in bursts and forget what they learned a few weeks later. Alternatively, perhaps less commonly, is the wasted term that a child might experience if they are placed in the bottom group by accident.

Image by Fir0002

Image by Fir0002

Finally, it’s worth noting that as maths branches out into different disciplines, children may have different thresholds for Algebra, Shape and Space, Number or Data Handling for example. It’s difficult for a teacher to keep track of these thresholds, let alone teach individual children at the right level for each. Luckily, that’s where technology can make a difference.

There’s always a buzz word, and it the world of education technology at the moment it is probably adaptive. But what does this mean, and how does an adaptive product differ from a product that personalises?

pəːs(ə)n(ə)lʌɪz/
verb: personalise
design or produce (something) to meet someone’s individual requirements.

We personalise things ourselves by making them individual to us. Most products in edtech that claim to be personalised do so through allowing choice: as well as choosing motivational features such as avatars (fairly standard these days) you may also make choices about the work that you do. Alternatively, tasks might be selected by a teacher or a parent, either in the app or website itself or remotely through a dashboard.

əˈdapt
verb: adapt
1. make (something) suitable for a new use or purpose; modify.
2. become adjusted to new conditions.

For an edtech product to adapt to a new purpose or new conditions, first it is necessary to assess or measure what those conditions are. Learning systems that are adaptive will incorporate three elements:

  1. data collection on existing progress
    b. analysis of data, leading to
    c. adaptations in the child’s work program.

Easiest here to use DoodleMaths as an example:

  1. aside from the initial assessment, the following data is collected for every child for every question answered: time taken, attempts taken, and date stamp.
    b. this is then analysed to gain an understanding of both the child’s progress and also the population as a whole (as a basis for comparison)
    c. the work program is adapted in three ways: level (on a general basis, are the questions too difficult, too hard, or just right for the child?); strengths and weaknesses (e.g. what are they finding difficult? Do we need to remediate here? – if yes, add it into the work program); pace of learning (e.g. if they found the last topic easy, let’s crack on, but if it’s tricky, let’s stick with it until they’ve mastered it).

There are other ways a program can adapt, too, for example, confidence level (some children are disheartened getting lots wrong, others can cope) or learning style (some children will exhibit more success with questions delivered in particular styles).

In the future, it will even be possible to adapt according to misconceptions: if a child consistently believes that a negative multiplied by a negative is a negative, for example, a really smart system will be able to detect this, adapt, and deliver the correct lesson to address this misconception.

So personalised and adaptive mean very different things: personalising is done by the user, usually at the start of using a product; adapting is done on an ongoing basis by the product itself. You might say that an adaptive product is aspiring to make decisions on an individual basis in a way that a good tutor might. Most edtech products have some kind of personalisation feature, but very few are truly adaptive.

…and the release of Version 2.1 – actually it is such a big change – let’s call it Version 3.0!

The big news here is that DoodleMaths is being launched on Android and Kindle Fire tomorrow at the prestigious BETT Show in London.  A new version is being released at the same time containing a complete visual overhaul to the App.

As you can imagine, on the eve of the launch, the office is a hive of activity with everyone working hard to ensure the best possible product is presented as this really is a huge release.

As well as the visual overhaul, the App has new games and the pets have been through a thorough detox and makeover at the spa – a personal stylist has even kitted them out!  Even the football now bounces as one would in reality!

If you wish to download the App on Android or Kindle Fire and are already a user, you only need to download the App and log in as you did before and you can pick up where you left off. You can use the school iPads, mum’s iPhone in the car, grandma’s android tablet at the weekend and dad’s Kindle Fire on the train.

If you wish the children to cover a particular topic, for example, 2-D and 3-D shapes or perhaps short division, by logging onto the parent/teacher dashboard you can assign these to one, some or all of your children. The child is locked out of the rest of the App until they have completed these topics.

If a child hasn’t been using the app for a while or has suddenly made significant progress in the classroom, you may wish them to do a reassessment.  This can be accessed by logging onto the parent/teacher dashboards.  Additionally, you can adjust the work program up or down by going into the grown-ups section of the App.

The update also includes improved monitoring on the parent and teacher dashboards, as they now allow accurate real time monitoring thanks to improved communication between the app and the dashboards. Due to each child’s work program being backed up online, if you get a new device, have to change device or need to reset your device, the progress is not lost. By signing in again the work program is reloaded from the last time the device had a stable internet connection.

Finally, the App now has localisation so that you can specify from where in the world you are so you only have to cover the topics in your own national curriculum. We are happy to announce that DoodleMaths is now use all over the world, including Uzbekistan, Australia, Dubai and New Zealand!

Why not Download DoodleMaths FOR FREE today and try for yourself!
App Store  Google Play Store

PS. That’s not all – DoodleMaths Secondary Maths will be available for download shortly – for a sneak peek visit us at Stand BFG4 at the BETTShow!

On the assumption that your five-year old has a grasp of addition, these are the most important numerical facts a child can learn at this age.

Children who are good at maths have committed a lot of what they know to heart. By this, I mean that important number facts have been learnt and committed to long-term memory. Note that it is widely accepted that there are two ways to commit something to long-term memory: either learn by understanding (perhaps you’d learn the events leading to the start of WW1 in this way) or rote learning (times-tables must be learnt this way in my view.)

I digress… back to the point in hand. The more number facts a child has committed to long-term memory, the more they free up their working memory to perform more complex calculations. A child who can recall the doubles of numbers below ten can then also learn the following without much more effort:

– Near doubles: if you know that 6+6=12, you can instantly work out that 6+7=13.

– Adjusted doubles: to work out 6+8, change it to 7+7 and use your doubles. Doubles, near doubles and adjusted doubles account for the majority of addition facts to 20.

– Double 10, 20, 30 etc. and 100, 200, 300 etc. This innately teaches children place value, and excites them because they are using big numbers! You’ll get them doubling 1000, 20,000 before you know it.

– 2x table: same as your doubles!

– Halving: the reverse of your doubles. But you have to learn them off by heart: if you choose to teach doubles by adding a number to itself, whilst this is sensible in the short term, in the long term many children learning how to halve will attempt some kind of subtraction. Better to get them to learn off-by-heart early on.

– If they can halve, they can quarter. Teach it by halving, and halving again.

– And you can even lead in to percentages, because 50% is one half.

– Partitioning: if they know their doubles confidently off-by-heart, they can double any number by partitioning. Double 24? Well, double 20, double 4, then put it back together.

Of course, the other by-product of doing this is it gets children into the habit of committing numerical facts to their long term memory from an early age. Because maths is never duller than when you are still continually counting on your fingers at 9 or 10 years of age…Image

These are powers of 11. So the next number will be 11 x 11 x 11 x 11 = 14641.

The beautiful thing about the powers of 11 is that they follow Pascal’s triangle:

1

1       1

1      2        1

1     3        3      1

1     4       6        4       1

You add the two numbers above to obtain the numbers below. Pascal’s triangle has a number of applications in probability, binomial expansions of brackets and geometry. It contains an incredible number of patterns within itself. Take a look and see what each row adds up to for a start. And if you want to know more, the best explanation is here.