I’m delighted to have been asked by the lovely people at Magical Maths to guest blog a little about the thinking behind DoodleMaths. We very much appreciate the opportunity to write a little bit about our motivation for developing DoodleMaths, and our own personal philosophy on how children learn maths.

A quick introduction: we are a husband and wife team: our backgrounds both lie in maths teaching (cheesy bit: we met in a maths classroom). We wanted to build a maths resource that was purely focused on raising children’s achievement in maths. Right now, if a child is behind in maths and we want to raise their attainment, they are supported through tuition. Even if this is done in groups or outsourced by video-link to India, it is still prohibitively expensive for most schools or parents to access: less than 5% of children ever receive any tuition through school, and only 24% of children receive tuition paid for by their parents at any point. Cost is the by far the most significant barrier to schools and parents entering the tuition market.

So our aim with DoodleMaths was to create an app which mimicked the actions of a good tutor, identifying a child’s level, strengths, weaknesses and the pace at which they learn, and creating a work program specific to their needs. But, as a digital product, offer the benefits of a tutor at a tiny fraction of the cost (£3.99 monthly per child for parents, or £3.99 annually if bought through a school).

First, the work program is very prescriptive, offering very little choice in what children learn next. Our own experience with offering children a range of activities (be it differentiated worksheets in the classroom or mathematical activities on the computer) is that a significant proportion will rarely choose what’s best for them – more likely, they’ll choose what gives them most gratification. Currently, digital maths resources require a parent/child/teacher to select what they do next (parent doesn’t know what they should be doing/child chooses inappropriately/teacher chooses appropriately for the class as a whole but not necessarily for each individual). DoodleMaths selects the work according to what will make the child progress at the most rapid rate. To do this, we’ve written some very funky algorithms to which analyse progress to date to determine when and what will be learnt next.

Second, 75% or more of the work program is based on recap – reviewing what the child has already learned. Children – in fact we all – forget what’s been learned unless it’s regularly practised. As maths teachers we are all familiar with, say, teaching addition of fractions, only to find the bulk of the class have long forgotten about the concept of equivalent fractions that underpins it.

Third, the work program is very much based on learning through doing: children making decisions about maths and trying stuff out. I’ve always had an interest in questioning techniques, and inductive questions in particular, so we keep explanations to a minimum and instead focus on teaching a concepts through a succession of carefully-authored questions which get gradually, incrementally harder.

It’s a system that works. Children are encouraged to use DoodleMaths for about 10 minutes a day. As an app, this is easily achievable: children can use it anywhere, anytime, on or offline, on any touchscreen device. When the app gets a connection, it sends its data to the server for analysis on our teacher and parent dashboards.

I can’t deny it’s been a monumental labour of love: we spent most evenings for a year writing the 10,000 questions and accompanying help sheets that make up our content. But we are proud of what’s been achieved: our success in the App Store, and the positive feedback we get from schools and parents, has helped us secure more funding. This investment will enable us to continue to build DoodleMaths into something that competes with a tutor – but at a price that’s affordable to all.

Tom Minor

Co-founder, DoodleMaths

**Maths should be fun for everybody**

I “got” arithmetic at an early age. In my early teens, one of the things that attracted me to astronomy was the scale of numbers involved: billions and trillions! (In those days a billion had 12 zeros after the one.)

A 40 year career in software engineering has brought me into contact with people possessing a wide range of arithmetical abilities. I put this down partly to not paying attention in class and partly to the use of calculators and computers.

The 1960s saw the advent of the pocket calculator which presaged the mistaken idea that one no longer needed to be able to do arithmetic.

People use spreadsheets such as MS Excel and take the calculated figures for granted having no apparent awareness of the order of result they should be expecting.

At primary school around 1950 we were taught multiplication and division (a rose by any other name would smell as sweet) by drawing and counting virtual matchsticks. Counting the total number of sticks in several groups of the same number of sticks taught multiplication, and ringing groups of sticks in a given total taught division. I found for myself, by experimentation, that 5×7=7×5 and so on. We also used abaci for addition and subtraction. Both these tools helped give meaning to written numbers.

Most pupils learned tables by rote. Admittedly this gives an immediate answer to a posed multiplication question, but does not, of itself convey the meaning of the numbers, unlike the matchstick method. I’m not saying you need one rather than the other; you need both. Also, I realized, as you saw, that since 5×7=7×5 and 6×9=9×6 etc, so you only needed to learn half the table entries.

Where, however, the drawn matchstick method falls down is over division, if the pupil is mixed up about what division means. If you divide a cake by three you get three pieces. If you divide twelve matches by three, by ringing them in threes, you get four groups, so surely you have divided by four. OK, you have because the division works both ways, but the process does not match (sorry!) the expectation of some pupils.

The problem goes away, if you use physical matchsticks, because you can physically move matches from the starting set into the required number of physical groups, and then you have demonstrably divided by the stated number. Having done that, the exercise is repeated the other way around so the student realizes how it works.

But matches are boring! Why not toy soldiers or, if you prefer, stormtroopers or Barbies? They can be arranged in ranks. The pupil can readily see how three ranks of four can be transformed into four ranks of three, and so on. 100 soldiers can be arranged in ranks of ten to demonstrate the concept of units, tens and hundreds. That’s if they don’t get pinched, of course. But this type of exercise can be replicated on computer screens.

A variety of scenarios can be posed: I have 12 commandos to deploy in taking out a machine gun emplacement. I want three equal teams to attack from left, right and centre. And so on.

Maths should be fun for everybody!

]]>**A Vedic multiplication method**

For some students the column method for long multiplication is enough for them to master. This equips them with a skill to use and apply in ever increasing magnitude even up to multiplying by eleventy billion.

For some students who struggle you, as the teacher, may need to pull another tool out of your toolbox and show them a different method such as the lattice method (Napiers Bones) or the noughty method (grid method). And then they get it and off they go off willy nilly, merrily multiplying with their preferred method.

Both methods thus far rely on times tables knowledge and that for some is a massive problem. As time goes on and the student gets older this becomes a big barrier and also can demoralise and demotivate. Those with SEN/ memory issues will always struggle with it where there is a reliance on times tables factual knowledge.

Vedic multiplication is one method that does not rely on prior times table knowledge – it simply relies on counting intersections.

If you know Napiers Bones then you can see how this Vedic method works. Bottom right is the multiplication of the units, middle section is the tens and top left is the hundreds.

It will work with bigger numbers and it will work with decimals. The only barrier is the ability to count.

Taking this one step further we can use shapes – virtually any shape.

We as teachers need a range of tools in our toolbox of maths methods. There are huge numbers of different multiplication methods to explore – Egyptian method, the Russian Peasant algorithm; Napiers Bones; Lattice method, Column method, Gypsy hand multiplication. Sometimes it’s time to say to a student “ that’s not how you learn it – let’s try this…or this…or even this”

By developing the “how does that work?” curiosity maybe that’s how we knock down some barriers

Teacher training should equip every teacher with the right tools and not necessarily the ones they thought they needed. There is a caveat to this – it is not for the teacher to decide whether they like the method or not. Just because you think it’s clunky, requires space, has limits does not invalidate it. Different methods are right for different children. And here we can celebrate diversity and difference.

So it’s not perhaps a simple method for multiplying eleventy billion by twelvety two but it allows students to explore and be curious; be creative yet challenged and gives them a method to do something that they couldn’t have hoped to have done otherwise. Instead of “I’m not doing that!” they may say “how does that work?” and then I’ve won.

There are many forms of Vedic maths and it is an area of particular interest to me – this method is but one presented from the sutras translated from Sanskrit texts.

You can read a little more from my NCETM Secondary Magazine article Vedic Maths

]]>**These cups should have a place in any classroom!**

Making the ordinary extraordinary… This picture was one I picked up a couple of years ago on Twitter and it sparked a creative note. Having experimented with the approach to place value and reading numbers in this way it has very good effect. Especially when the students make the tool themselves. Younger students can get to grips with the position of numbers and the zeros prompt them to say the correct magnitude if they are a little unsure. You could write the words too underneath the numbers if necessary. Its a lovely class project for year 3 and 4 and it’s cheap too. It is also great for intervention at a later stage, with older students.

Moving this on a stage you can move into decimal numbers and multiplication and division by 10, 100 etc as demonstrated below by Ed Southall @solvemymaths (unless that is a hand model)

As a teacher trainer this set me thinking to add this approach into my session called ‘making the ordinary extraordinary’ in which I give ITT students a series of ordinary objects – paper plates, wool, sweets, clothes pegs, knitting needles – to see what maths they can demonstrate and play with…working in a very different way in which they usually do or are encouraged to. This is challenging for quite a few new teachers in training. One chap, ex army, openly stated “I’m not creative…this will be awful” yet he produced this with his cups. It has a scale along the rim for positive and negative numbers which twists round – simple but very effective and something he was quite proud of. Celebrated on twitter it caused a stir and had some good feedback too.

So one relatively simple idea can spark an element of creativity. Making the ordinary extraordinary…have a go.

]]>Do you have more iPads than places to either safely store or charge them? MultiPad may have the answer…

iPads have grown in number in classrooms everywhere faster than places where they can be safely stored, or charged. Moving them around has proved problematic too. They’re robust, but only up to a point, very desirable things to be sure, and they’re needed in locations often a long way removed from where they are stored or charged.

Where there’s a need, invention finds a way so it wasn’t long before solutions to the growing problem began to appear. Where a population of iPads could be tied to a single location, lockers, usually wall-mounted were installed. Each locker location provided a secure home for an iPad, kept it safe and in a good state of charge. The more advanced solutions also helped keep content synchronised. At a price.

Portability is one of the iPad’s more valued features and so solutions that helped manage iPad populations but gave them a degree of freedom to move from place to place were introduced. Such solutions typically comprised a trolly, often compared to the sort of thing seen wheeled along the aisle in aircraft, with locations for around thirty iPads. The units are secure, keep the iPads in good health, but, as many adopters have discovered, are in fact, far from portable with even a single step presenting an Everest to negotiate. They’re heavy too. Some are known that tip the scales at over a hundred kilos.

Nailsea based Protechnic took a long look at what was available and determined that, locked up in the DNA of its UK designed and manufactured products, was a potential answer to the needs of people who have to work with multiple iPads.

Protechnic is no stranger to protecting valuable assets. The company designs and manufactures in the UK a patented range of transit cases which keep customers in the world’s military, industry and government establishments coming back for more. The cases offer an incredible level of protection and yet manage to cast themselves in the lightweight sector.

Protechnic has turned the art of protection into a science and built on those foundations superior potability. A Protechnic case is in its element when its being bumped up and down stairs, wheeled over rough ground or rattled around in the hold of a coach or boot of a car. The cases’ contents are happy with the ride too.

How does this apply when iPads are the subjects needing protection? Military grade protection comes at a price after all. It does. But thanks to Protechnic, it’s a price that practically anyone can afford.

The company’s new Juiceit 10 and its bigger brother the Juiceit 20 offer secure, highly portable protection and storage for ten and twenty iPads respectively and define a new class of product in the market for secure iPad transit and storage. The Juiceit keeps its valuable loads charged as well. By using the charging hardware supplied with the iPad and cleverly integrating it in the Juiceit case, the price is kept very low without compromising either security or portability.

Protechnic supplies the Juiceit case direct and through selected distribution partners and backs the product up with a solid warranty and technical support if needed.

]]>**Educating Ruby**

The school curriculum consists of several different kinds of things: things that are intrinsically interesting (to all young people of a certain age); things that can be made interesting by a good teacher; things that are self-evidently useful; things that, while neither useful or interesting in their own right, are effective ‘exercise-machines’ for developing useful life-skills and habits of mind; and things that everyone agrees are such ‘cultural treasures’ that everyone ought to just know about them, even if they are directly useful or interesting.

And then there is the rest of the curriculum: stuff that’s just there because its always been there, and some influential people, without a shred of evidence, insist that they be taught and examined. Why French irregular verbs (rather than Mandarin, say, or Hindi)? Why adding fractions (rather than computer coding, or Bayesian statistics)?

We have a FREE Signed copy of @GuyClaxton and Bill Lucas's Educating Ruby. Just RT or comment in post to enter! https://t.co/DLKNCCpJ98

— Magicalmaths.org (@magicalmaths) April 26, 2015

We need a real re-think of what we teach – and Maths is no exception. Despite a lot of hot air, there is scant evidence that learning maths makes you spontaneously more rational in non-mathematical or non-educational contexts. Nor do I know of any evidence that says we have to teach all young people algebra just in case they might need it, rather than ‘just-in-time’, when they do actually need it. With out the turbo-charger of real need, and in the absence of intrinsic interest, learning is weak, formulaic and usually disagreeable.

And we need a re-think of how we teach as well. As Jo Boaler and others have shown, you can teach ‘area’ or ‘fractions’ in a way that develops passivity, compliance, mindless application of procedures and fear of mistakes – and also gets good results. Or you can teach the same topics in a way that gets even better results, but develops attitudes of curiosity, collaboration, creative experimentation, and critical thinking. The pedagogy is crucial for these deeper aims.

Our new book Educating Ruby (‘us’ is Guy Claxton and Bill Lucas) argues really strongly that we owe it to all kids to explain why what we are teaching, and how we are teaching it, will add to their confidence and capability as adults – whether they are destined to be carers, cooks, mechanics or neurosurgeons. We think thousands of parents, and thousands of teachers, know in their heart-of-hearts that way too much of school is boring and pointless – and not knowing how to change things, we all fixate on the grades. We want all those people to start talking, tweeting and blogging about the need for a real re-thjink – so politicians will get off thier backsides and start to think about what really needs to be done. have a look at educatingruby.org, read the book, tweet (@educatingruby) and join the groundswell. We want whoever wins the election to be thinking hard about how to spread the good practice that exoists in many schools faster and wider. we owe it to the kids – especially the ones who are not going to do well in the competitive Examinations Game.

Guy Claxton

]]>I would so love to be in the position of being able to do this out in a restaurant and see the face of the waiter. : )

What a way to give a tip, share this with your lesson as a starter and see if they can work out why this is such a #mathsfunny!

Comments are FREE, please leave one below.

One for the mathematicians i guess… http://t.co/HHGy47D3Sq pic.twitter.com/yE2ZLLP7br

— Magicalmaths.org (@magicalmaths) April 25, 2015

]]>

The video below makes an engaging starter, assembly theme, or form discussion about the how we have been manipulated to desire bottled water over the conventional supply of tap water. A manufactured demand has been used to develop a multi billion industry that is actually causing a great deal of harm to our environment. The video is amazing, as it makes the audience really think about their actions and attitudes towards bottled water and generates some great discussion points.

Comments are FREE, please leave one below.

]]>Comments are FREE, please leave one below.

If you have not seen it, then the overnight internet viral Maths problem goes something like this;

*Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is.*

*Cheryl gives them a list of 10 possible dates.*

**May 15, ****May 16, ****May 19, ****June 17, ****June 18, ****July 14, ****July 16, ****August 14, ****August 15, ****August 17**

Cheryl then tells Albert and Bernard Separately the month and the day of her birthday respectively.

**Albert:** I don’t know when Cheryl’s birthday is, but I know that Bernard knows too.

**Bernard:** At first I did not know when Cheryl’s birthday is, but I know now.

**Albert:** Then I also know when Cheryl’s birthday is.

**So when is Cheryl’s birthday?**

**The solution Explained**

Going through the problem line by line it shows the following logic;

*Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.*

All Albert knows is the month, and every month has more than one possible date. Therefore he does not know when her birthday is. The first part of the sentence is complete waste of time.

The only way that Bernard could know the date with a single number would be if Cheryl had told him 18 or 19. Of the ten date options only these numbers appear once, as May 19 and June 18.

For Albert to know that Bernard does not know, Albert must therefore have been told July or August, since this rules out Bernard being told 18 or 19.

*Second Line: Bernard: At first I don’t know when Cheryl’s birthday is, but now I know.*

Bernard has worked out that Albert has either August or July. If he knows the full date, he must have been told 15, 16 or 17, since if he had been told 14 he would be none the wiser about whether the month was August or July. Each of 15, 16 and 17 only refers to one specific month, but 14 could be either month.

**Third Line: Albert: Then I also know when Cheryl’s birthday is.**

Albert has therefore worked out that the possible dates are July 16, Aug 15 and Aug 17. For him to now know, he must have been told July. Since if he had been told August, he would not know which date for certain is Cheryl’s birthday.

The solution has to be **July 16**.

This is a great looking activity that I found on twitter and can not wait to have a go at;

You could do this during form time to try and know your tutees better or use it in a lesson to identify and develop learning. Make sure you emphasise that all responses can not be kept private as due to child protection protocol you may have to report what a pupil may disclose.

All teachers should have a go at the “I wish my teacher knew activity”! http://t.co/S33OnJampi #usedchat #ausedchat #nzedchat

— Magicalmaths.org (@magicalmaths) April 6, 2015

Comments are free, please leave one below!

]]>One of my Year 5 kids answers to 'I wish my teacher knew' @ASTsupportAAli #nrocks a deeply affecting activity to do pic.twitter.com/SlwsLneKf5

— Jonny Walker (@jonnywalker_edu) June 13, 2015