Marcus and the Maths in the City team want YOU to contribute. Everyone, mathematicians or otherwise, is invited to submit mini-sites describing places of mathematical note in their city, and enter a competition in the process.

Submitted sites will eventually form part of walking tours focussing on hidden city maths, starting in Oxford and London. Check out the video below for more info.

The venture is sponsored by Oxford University’s Department for Continuing Education and the EPSRC.

If you see a little maths in your corner of your city why not add a site? Your city doesn’t have to be Oxford or London. The Maths in the City people are looking for:

• interesting examples of maths in the urban environment,
• clear explanations of some maths you see in your city,
• great demonstrations of your mathematical ideas on the street.

To give you some inspiration, there’s a great example of maths in St. Paul’s Cathedral, London, written by du Sautoy.

Maths in the city sites will “…become part of our virtual mathscape of cities around the world and will help Marcus and the team develop their walking tours.” If you’re successful, you can win some of the following:

1. a subscription to Nature, kindly provided by Nature Publishing Group,
2. best-selling popular science books, including the “Last Word” series kindly donated by New Scientist,
3. having a mathematical object named after you,
4. and showcasing your entry with other finalists at an event in Oxford on 18 June with Marcus and his team.

I’m going to check it out myself, if only so that future mathematicians have to refer to the ‘n-dimensional Duncagon’ in the years to come…

The competition ends in the first week of May. So, Maths-Whizzers, get spotting!

Innovation award winners!

The Education Resource Awards (ERA), held on the 18th March, and organised by the British Educational Suppliers Association, were created to:

…celebrate the innovative approach to learning and teaching by teachers, institutions and organisations from all levels of education.

Whizz has been thrice-nominated in previous ERA categories but fourth time, it seems, was the charm (as the vid on the Whizz Youtube channel shows)!

The response of the Whizz team at Birmingham’s Motorcycle Museum pretty much sums up our excitement and pride in this award.

In a more sober fashion, Ray Douse, Whizz CFO, said:

This win means a lot for our business both in the UK and internationally. The objective of Maths-Whizz is to bring together teachers, children and their parents and we feel the judges clearly recognised and valued this feature.

We can now add this to the stack of other awards in the Whizz Awards Cabinet, along with two other finalist positions at this year’s ERA.

You can read the official BESA press release here.

Alison Gopnik, writing at Slate.com, comments on the increasing tendency to teach pre-school children, rather than allow them to play. She suggests that this approach, at least for the youngest children, might be stifling not just creativity, but the ability to learn, and she cites two new papers that draw from computer science to prove her point.

Adults often assume that most learning is the result of teaching and that exploratory, spontaneous learning is unusual. But actually, spontaneous learning is more fundamental. It’s this kind of learning, in fact, that allows kids to learn from teachers in the first place.

The key seems to be the way children learn about learning. A child will learn about the teaching method in order to understand better how to learn. Two recent papers in the journal Cognition explore the nature of that process by giving groups of children toys with hidden features and starting them off with either an exploratory approach or a taught one.

The understanding is that a purely demonstrative, instructional teacher implicitly conveys the understanding that the student can only learn by doing as she does, following her instruction. Whereas, a teacher who explores with the student (or even no teacher at all) brings with her the belief that experiment and investigation are just as useful as instruction, and that not all knowledge is directed.

Both research groups found that the less-directed students discovered more, and explored for longer. The differences between being instructed and encouraged to explore in both studies were subtle – a teacher might demonstrate an action (or set of actions) that produces a result in a toy and tell children to do likewise, or the teacher might explore the toy to produce an action as if by accident and encourage the children to see what they can find for themselves.

The research Gopnik refers to is new, and devoted to pre-school subjects, so it may be inappropriate to extrapolate this to primary age children. But these findings point to what she describes as a common intuition amongst teachers: that play can be just as powerful a learning tool as instruction if not, at least for the youngest, more so.

So what, if any, conclusions can we draw for the primary and early secondary children who use our online maths tutor Maths-Whizz? The first might be that there is such a thing as too young to study – we tend to discourage parents who want to use Maths-Whizz for their more advanced four year olds.

Second, we built into our maths lessons an implicit understanding of a child’s learning style at different ages. Earlier lessons at ages five and six are more exploratory and playful, and are devoted to the concepts that underpin maths rather than the more ‘math-y’ material in ages seven and up.

Finally, our recommended usage patterns reflect the need for younger children to have a more varied and undirected experience, away from a computer.

Gopnik echoes indirectly the call for creativity in education, given memorably by Sir Ken Robinson at a TED talk some years ago:

…it’s more important than ever to give children’s remarkable, spontaneous learning abilities free rein. That means a rich, stable, and safe world, with affectionate and supportive grown-ups, and lots of opportunities for exploration and play. Not school for babies.

Maths-Whizz, as numerous awards, hundreds of testimonials, and tens of thousands of online users prove, is a fabulous and enjoyable tool for building numeracy and boosting confidence in maths.

But we know there is always room for play in maths learning and we encourage students to step away from their online tutor now and then. So, how can you encourage your Maths-Whizzers to make the most of their creative instincts? Without second-guessing the results of future research in this field, here’s an informal selection of ideas:

• Explore maths concepts with the Whizz Tools Board (accessible from the bedroom). Play with cards, dice, counters, shapes, number grids and number ‘machines’.
• Ask your child to teach you. This is a great way to encourage students to marshal their knowledge and creatively convey what they know.
• Find maths in the real world. Look for shapes and angles in the house, think about how to estimate the number of leaves on a tree, and make your own graphs and charts.
• Tell stories with maths. Imagine you’re a number or a shape, and describe your day!

With Maths-Whizz, a little play can go a long way!

In a report which looks at the limited impact of the money spent on the Skills for Life programme, author Dame Mary Marsh points out that poor numeracy is somehow far less shameful than poor literacy – a sentiment echoed by NIACE Director of Operations Carol Taylor.

The parents who come to Maths-Whizz to give their children a boost in numeracy are the opposite of the bad maths ‘badge of honour’ wearers. They are the parents who recognise the importance of maths not just for passing exams but for the life that follows the school years.

Even so, we still sometimes see an attitude which may be behind the problem outlined by NIACE. I once spoke to a parent who told me she was an accountant, and used maths every day. “Bravo!”, I thought. The mother was certainly keen on her son improving his maths, but she was angered that he was required to do so much pencil and paper-style working out (roughly 10% of the Whizz curriculum at his age). This was because, to use her words, “he can just use a calculator”.

At this point I confess I wanted to throw the telephone across the room and go for a long walk. But hers is an all-too-common sentiment that maybe is at the heart of our ‘problem’: namely, that whilst maths is A Good Thing To Know, we don’t really need to know it.

This attitude may be less a function of maths per se, and more a function of an advancing technical society. Maths skills are no less in demand than they were, and sectors like software, finance, research and business require good maths; but almost all of us can rub along with the very basics.

In fact, the NIACE report points out that only one in 10 adults with numeracy skills lower than an 11-year-old had taken a numeracy course. I don’t find this remotely surprising, because the maths required of a 10-year-old is often adequate for adult life.

The Whizz curriculum, which is based on the Primary National Strategy for Maths, teaches ratio, percentages, basic statistics, coordinate geometry, relatively tricky mental maths, and long division (amongst other subjects) to its maths age 10 students.

If we could all do long division and understand the difference between mean, median, and mode we would be a damn sight better off than we are now. So I suspect NIACE is pointing at the wrong statistics. In my opinion it’s less about whether we’re better mathematicians than our year 5 students, and more about whether we truly understand, or use, our year 5 maths skills.

If we fail to spot the right change in a shop, or work out the best interest rates for our savings, or understand the health statistics associated with lifestyle changes we may end up considerably less healthy and wealthy, but we won’t attribute such mistakes to poor maths. Instead, we put this failure down to others’ lack of scruples.

Government and industry should work harder to convey numeric information better (such as medical test reports and mortgage documents) in an age in which we are bombarded with data. But the very quantity of such data has made us passive, trusting, recipients. Whether or not we have the maths skills of an 11-year-old is irrelevant if we don’t know when to use those skills.

To take our accountant’s son, he doesn’t need to know how long division works, only that he can put the numbers into a calculator in a particular order to get the right answer. And since calculators never fail, he’ll be fine. But, as any good software developer knows, GIGO – “Garbage In, Garbage Out”. In other words, even the best calculator in the world can’t give you the right answer if you type the numbers in the wrong order.

And this is why a technologically advanced society risks losing an appreciation of maths skills just as it risks losing an appreciation of basic engineering or science. Despite being surrounded by electronic appliances, and the fruits of centuries of scientific development, we really only need to know that such appliances work, and not why, or even how.

Sixty-odd years ago, CP Snow decried an equivalent embarrassment gap to the one described by Dame Mary. He compared being asked to name, say, a Shakespeare tragedy and the Laws of Thermodynamics. He was right that this was a massive imbalance of priorities, but wrong to focus on shame, because once you’ve established that the Laws of Thermodynamics explain how the refrigerator works, the conversation generally ends. Which is a pity, but we take the fridge on trust. We don’t do the same for Hamlet.

So, to cut a long blog post short – NIACE is right, and yet they might be fighting the wrong battle. If we bang on too much about whether we have the necessary maths skills we might not stop to wonder whether we’re actually using them.

The OECD (Organisation of Economic Co-operation and Development) is a kind of fancy club for 34 countries committed to “[stimulating] economic progress and world trade” (Wikipedia).

Part of its remit is to follow trends in education, particulary literacy, numeracy, and scientific understanding. Pisa (Programme for International Student Assessment), the OECD’s body devoted to this task, has released results from its 2009 assessments, comparing those three skills across member nations.

As any fule kno, learning is good for you, and good for the country, too. So the latest Pisa educational rankings make for depressing reading.

According to The Guardian’s Datablog, the UK has fallen several places since the 2006 study (the first to include the UK):

The UK is ranked 25th for reading, 28th for maths and 16th for science. In 2006, when 57 countries were included in the study, it was placed 17th, 24th and 14th respectively. Poland has stretched ahead of the UK in maths, while Norway is now ranked higher in reading and maths.

This translates, according to Pisa’s prosaic rating system, as ‘average’ in mathematics and reading, and marginally ‘above average’ in science.

That three countries have ratified the OECD treaty since 2006 (and might, therefore, have shot ahead of us) provides cold comfort – Slovenia, Israel, and Chile all rank below the UK.

The Pisa findings don’t quite match the 2008 report of the other international education rating body, TIMMS, which indicated that the UK was rising up the leagues in key subjects.

But these results nonetheless do little to burnish our self-described reputation for excellence in education, and they throw up some depressing additional facts.

You can find these in their UK-specific report which points to the UK’s larger-than-normal difference between best and worst students, and includes a sad aside:

…77% of the between-schools differences in student performance in the United Kingdom is explained by differences in socio-economic background.

Only Luxembourg surpasses us for class-based educational inequality. So, in fact, you CAN get a top-flight education in the UK – as long as you’re wealthy.

Worse still, according to Pisa “only seven OECD countries spend more per student than the United Kingdom.” This poor performance seems to be in spite of expensive efforts to improve education, and the constant tinkering of politicians.

Is there any good news? The UK is at the forefront of investment in educational methods, and Maths-Whizz Tutoring is part of that progress.

We can’t – yet – take any credit for any rise or fall in the UK’s international reputation, but we can say that we know what we do works, and we know that we do it at a fraction of the cost of private tutoring – the kind that gives children better life chances and greater confidence in such a vital subject.

But, returning to the Pisa results: If, as we’ve said before, maths skills mean a stronger economy, then this news bodes well for none of us.

Einstein explains Relativity to his gran in order to understand it better...

This sentiment attributed to Albert Einstein is no less true of Relativity than it is of primary maths. And it is the thinking behind some sound advice reported in a recent article in Education Week sent my way by Whizz US’s Kate Vincent:

Teach in order to learn.

This is what’s known as the ‘protégé effect‘ (or, more prosaically, ‘peer-mediated learning’ and ‘reciprocal teaching’). Learning a subject in order to explain it to someone else forces the learner to remember and understand the material better.

Education Week reports on findings from studies in which children are required to ‘teach’ computer avatars that question the students, make mistakes, and so forth. Such students, compared to those who were learning only for themselves, spent more time studying the material and checking their work and “…As a result, the student-teachers performed better than learners…”

This effect is explained in common-sense terms by David Schwartz, director of a California-based learning research centre:

When you are looking at something yourself, you can fool yourself into thinking you know everything, but when you have to communicate it to someone else, you realize that you’re really not being precise enough.

Now, of course, you can take the teach-in-order-to-learn approach only so far. We’re not suggesting Whizzers do what a recent nominee for the 2010 teaching awards did by sitting the same Maths GCSE as her students.

But we are suggesting – if you’re the parent of a Maths-Whizzer – that you ask your child to tell you what he or she has learned, to explain the subject to you.

This isn’t simply a matter of saying “What did you learn today?” but, rather, asking your child to take the role of teacher, with you as student. Ask your Maths-Whizzer questions; make mistakes a novice maths student might make.

This is not an approach for the parent in a hurry. But a little bit of role-reversal might encourage your child to think more deeply about what he or she is learning, in order to be able to show their knowledge convincingly when you chat over the dinner table.

It is in both these respects that BETT has chosen to shortlist us for their 2011 BETT Awards:

BETT Awards 2011

BETT, as any fule kno, is “the world’s largest technology in education show.” The awards fall on the first night of the four-day show. Any fan of ed. tech. who has been to the awards or the show in recent years will attest to the scale, snazziness, and the impressive number of Madonna-style headsets worn by shiny-faced presenters in front of tennis-court-sized interactive whiteboards.

In the time since Whizz started attending – first as guests, and for the last five years as stand-holders – we’ve seen the event get glossier and more corporate. We don’t yet have Madonna-style headsets (The God of Whizz wouldn’t be seen dead, etc.) but we always have interested packs of teachers, parents, and students stopping by, some just to say hi, and many more to find out what makes us tick.

This interest goes both ways, and that’s why we come every year. We love to find out what we’re doing right, and what we can improve on. So if you want to bend our ears about Maths-Whizz, or tell us what you love, or just put faces to names in the Whizz team, then make sure you’re at BETT 2011 at London’s Olympia, 12-15th January.

Who knows, we may even have a shiny award to show you!

You can read up about our 2010 BETT Show and our previous triumphant BETT Award showing.

UPDATE (22/10/10): Bett Awards official shortlist now available to view online.

As with the legendary Ramanujan and his disappearing numbers, if you haven’t heard of Mandelbrot and his set, you need to get reading.

Mandelbrot gave his name to a famous fractal ‘set’, whose image has adorned thousands of student bedrooms, science labs, and psychedelic paraphernalia, but he has contributed a huge amount to maths in particular, and science in general.

Mandelbrot, who died of cancer last Thursday aged 85, was one amongst many for whom the Nazis’ loss was Britain’s, and America’s, gain. His family fled occupied Poland before WWII and young Benoit landed up in the USA.

Whilst a research mathematician for IBM Mandelbrot produced the 1980 book The Fractal Geometry of Nature, which illustrated such fractals with fascinating graphics. The Mandelbrot Set has since become one of the most famous images in modern science, instantly recognisable and fascinating.

You can get a taste for the Mandelbrot Set with this wonderful video. Zoom from the classic multicoloured bubble view deep into apparently random nooks and crannies to reveal another, tiny, set. Carry on zooming to see another set, and yet more, demonstrating one of the beautiful features of fractal images – self-similarity.

Self-similarity is everywhere, when you look. It is the same way that vast lines on the ocean seen from a passenger jet look similar to the wave sets visible from a few hundred metres, which look similar again to ripples in the water seen from a few feet. Look closely enough at many natural objects and you might see this self-similarity.

Even the humble Romanesco broccoli looks as though it was devised by a mathematician.

Self-similar Romanesco broccoli

In fact, Mandelbrot used the ‘complicated and yet simple’ broccoli to illustrate his point at a charming TED talk he gave earlier this year, weaving in the ‘roughness’ of mountain ranges and the fractal qualities of lungs.

This is fascinating stuff for yours truly. The equally humble fern is another great example of self-similarity, first described by British Mathematician Michael Barnsley, and animated in a computer program which the God of Whizz remembers with some fondness running on his venerable 8086 PC.

But Mandelbrot’s famous 1967 paper – ‘How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension‘ – showed how apparently trivial observations in geography can prompt quite deep questions.

In the 1967 paper Mandelbrot studied earlier measurements of coastlines which had found that their length increased with shorter measuring increments. For example, the coastline of Britain measured with a 200km stick is 2,400km; measured with a 50km stick the coast gains another thousand km.

Mandelbrot, in effect, noted that such coastlines exhibit a kind of self-similarity – they can behave like fractions. The further into a coastline that you look, the more detail you see; and the coast of Britain is wiggly enough to ensure there’s lots to look at. The seminal paper paved the way for Mandelbrot’s later observations about fractals in nature.

We can only give you a tiny taste of Mandelbrot’s work and the influence it has had on our understanding of nature and natural processes, so why not mug up on the great man and carry on reading…

[via the Register]

August institutions of learning and news reporting go on proving that the Maths-Whizz way is great for learning, and great for learning maths in particular.

The New York Times late last month reported on findings in education which may seem obvious, but help resolve a question still under intense debate, namely: “What is the best way to learn stuff?”

And, according to the Times’ piece, it is:

The Maths-Whizz maths tutor either directly encourages, or supports, all three techniques.
- First, by incentivising students to use 30-minute sessions every other day.
- Second, by presenting a huge variety of maths lessons weighted towards the student’s ability profile, so that students rarely address the same topic more than twice in a row.
- Third, by permitting Maths-Whizzers to log in wherever they can get to the internet – at home, in school, on holiday, etc. And given how many of our users log on using laptops there is even more scope to vary the learning environment.

The Times points out that these little-and-often, varied subject and varied setting approaches seem to strengthen learned information, and ensure its careful organisation in the brain:

Cognitive scientists do not deny that honest-to-goodness cramming can lead to a better grade on a given exam. But hurriedly jam-packing a brain is akin to speed-packing a cheap suitcase, as most students quickly learn — it holds its new load for a while, then most everything falls out…

…When the neural suitcase is packed carefully and gradually, it holds its contents for far, far longer. An hour of study tonight, an hour on the weekend, another session a week from now: such so-called spacing improves later recall, without requiring students to put in more overall study effort or pay more attention, dozens of studies have found.

No one knows for sure why. It may be that the brain, when it revisits material at a later time, has to relearn some of what it has absorbed before adding new stuff — and that that process is itself self-reinforcing.

“The idea is that forgetting is the friend of learning,” said Dr. Kornell. “When you forget something, it allows you to relearn, and do so effectively, the next time you see it.

Interestingly, the Times also suggests that trying to focus learning methods on visual vs. verbal student styles is pointless:

In a recent review of the relevant research, published in the journal Psychological Science in the Public Interest, a team of psychologists found almost zero support for such ideas. “The contrast between the enormous popularity of the learning-styles approach within education and the lack of credible evidence for its utility is, in our opinion, striking and disturbing,” the researchers concluded.

At Maths-Whizz we don’t fixate on personal learning styles, we focus on what the student does, and doesn’t know, about maths – and we let the student take it from there, in their own time and their own way!

Read the full article to find out more.

In the meantime, if you haven’t already signed up to our online maths tutor, do so! The New York Times would approve!

Policy wonks have found that summer learning loss, an established side-effect of long school holidays, is particularly pronounced in some groups:

…children from the poorest backgrounds suffered most with ‘summer learning loss’ because they were the least likely to practise reading and writing during the six-week break.

The Education Guardian has reported on plans from think-tank The Institute for Public Policy Research (IPPR) to shorten the long summer holidays. This should interest parents from any wealth bracket – without the right attention even the most expensively educated can suffer.

Further to this, long term times might be causing ‘burn out’ in some students.

A co-author of the IPPR study, Sonia Sodha, calls for a five-term system, with two-week breaks between eight-week terms, and a month for summer hols.

Many parents remember their long summer holidays with fondness, even though the original purpose of the long break – to allow children to return to farms for the picking season – has almost entirely been forgotten, certainly in practice.

Margaret Morrissey of the National Confederation of Parent Teacher Associations argues that children may also need “…a chance to recharge their batteries”; but one could well argue that if the terms weren’t so long, children’s batteries wouldn’t need recharging in the first place.

(As of 2010) Former Children’s Minister Kevin Brennan said the IPPR report (which also includes recommendations on increasing the role of play in classes for 5 and 6 year-olds and suggestions that secondary and primary schools employ in-house counsellors or use counselling networks) matches commitments made in the coming ‘Children’s Plan’.

Keeping children constructively entertained over summer is an issue, whether or not the Children’s Plan includes shortening the summer holidays. The finding that unstructured holidays can lead to ‘learning loss’ is still relevant, and is something we recognise. In 2007, Whizz Education launched our Summer Adventure – featuring the Professor lost in the jungle. Students were charged with helping him escape, by solving maths puzzles and playing jungle-themed games.

(a maths puzzle from the 2007 Summer Adventure)

The Summer Adventure was a huge success – Maths-Whizz students at Mead School, Kent, had a great day helping the Professor escape from the jungle when Toni Burkett and Monique Kleinschmidt from Whizz visited with prizes for their top-performing students.

(Our 2007 Summer Adventure in use at the Mead School, Tunbrdge Wells)

Our Summer (and Christmas) adventures encourage students to continue learning with Maths-Whizz; students must finish lessons before they can try the themed games, and they get to learn about jungle creatures with our colourful worksheets.

We’ll be bringing back the Prof and his rainforest antics each Summer, with brand new features. If you’re wondering how to keep your child occupied this summer, make sure he or she logs onto Maths-Whizz, because the Professor isn’t going to escape from the Mayan jungle all by himself…

[UPDATE: Read a study of 39 investigations into Summer Learning Loss]

[Read more about summer learning loss - Wikipedia]