Announcement: our first CBM country

I'm very excited to announce that computerbasedmath.org has found the first country ready for our completely new kind of maths education: it's Estonia. (...and here's the press release).

I thought Estonia could be first. They are very active on using technology (first to publish cabinet decisions immediately online, first to include programming in their mainstream curriculum), have ambition to improve their (already well respected) STEM aptitude and lack the dogma and resistance to change of many larger countries. There aren't so many countries with all those characteristics.

In our first Estonia project we will work with them to rewrite key years of school probability and statistics from scratch. This is an area that's just crazy to do without a computer, even harmful. It's an area that's only come to the fore since computers because it only makes sense with lots of data. No-one in real life does these hand analyses or works with only 5 data points, so why do we make our students? Why get students emulating what computers do so much better (computing) rather than concentrate on imaginative thinking, analysis and problem-solving that students ought to be able to do so much better even than today's computers?

Worse, in a subject like probability and statistics, current maths education often forces you to learn the wrong tools for the job.

Take the Normal Distribution--one of very few options taught to students for data analysis. Approximating your data with it rarely gets you the most accurate solution; it can be wildly wrong. Instead why not learn to select the best of 100+ other distributions and test their predictions against each other? Or why use a distribution at all, when you can work out results directly from each and every data point?

The reason is historical. Normal Distributions (and Poissons) are easiest to calculate, appear appropriate in over-simplified problems and you can't practically compare lots of distributions or work directly with data by hand. But with a computer you can and you should.

Out in the real world, there are real consequences to drilling students in de- or mis- contextualised techniques--and with the idea that each school problem has one right technique, and each technique has particular patterns of problem. Take the miscalculating of large swathes of financial risk analysis: people applied Normal distributions because they knew of them, had been trained to expect them but that didn't make for effective representations for the data.

This reminds me of an old adage. "If all you have is a hammer, everything looks like a nail". In maths context--the fact that every school problem can be solved with a small subset of maths tools leads to a false expectation that in the real-world this same subset will suffice. CBM broadens the toolkit dramatically by not insisting students should make all the tools that they use, freeing time for using more in a wider variety of situations.

Estonia is the first place where we're starting to change all of this though many other countries have voiced interest in pursuing CBM and being within the first group.

But it's slow work on several fronts for a little while. Even though several of us have been thinking along CBM lines for ages, we're constantly questioning whether a particular way of thinking or doing is in fact now the best way or simply a legacy of the pre-computer era. Indeed what outcomes are we trying to achieve and how does learning tools of maths fit with learning how to solve problems?

And education changes slowly, though now is the most vibrant and exciting time of change in my lifetime. Even with this, I expect it to be a couple of decades until the world's mainstream maths subject is universally computer-based maths rather than today's "history of hand-calculating". But today is an important step.

Countries that start the change early will reap many benefits from being first--a bit like the changes that universal education brought to countries who were first, but in microcosm for maths.

In fact it's more of a macrocosm. It affects lucrative problem-solving STEM jobs where pushing the boundaries of modeling is crucial to success. But it can make happier citizens too--able to assess risk, understand complex finances better, have an in-built mathematical 6th sense by which to understand life.

Where does programming fit in education?

It's great that programming is coming to the fore in UK education and that this new-found enthusiasm is starting to spread to the US.

But where does programming fit with ICT, computer science and maths? How central a subject is it?

What's termed ICT seems to be "how to operate your computer...or generic applications on it...or even past computing forms like calculators". Frankly children are often good at operating the latest tech--usually better than their teachers. Primary schools need to help, verifying that they can do basic operations and offer remedial, individual help if not, but this "operating your computer" should not be a subject per se and is far from programming in subject-matter and required skillset.

What about computer science? It's the specialist subject of how you optimise programs, programming, build large-scale software or even design new programming languages. Important though this is, attaching programming only to CS is too narrow a viewpoint.

Instead, programming is much more fundamental to STEM: it's the way you communicate technical ideas and processes in the modern world. It's as central as that.

You can view it as a superset evolution of mathematical notation, far more general and with the immediate consequence of machine computable results. Programs are the way you write down maths.

And so I believe programming is an integral, core part of maths education. It's the hand-writing of technical ideas and just like hand-writing is in the early years attached to learning English (if you're in England!), so core, basic programming should be attached to maths.

To be clear, I'm not talking calligraphy, but basic hand-writing. Calligraphy is the CS end--the subject in which you study programming in its own right, its nuances, detailed optimisation. Hand-writing is the basic tool, to let everyone communicate. Just like hand-writing is more generally applied than in English, programming is more generally applicable than is today's perception of maths' applicability in schools (though not than maths' actual utility). Whether in geography, economics or science, technical problem solving needs maths and the way you write down and do anything but trivial arithmetic is with programming.

I'm not knocking the new efforts with programming. Far from it. I'm all for getting programming into education under whatever guise is easiest. If making ICT "rigourous" is the politically expedient way, starting there is fine so long as we recognise it just as the start.

It would be folly indeed if in the very country where a mathematician invented the computer and effectively the concept of programming, we should fail to see the crucial integration of programming with maths education.

(Perhaps if Alan Turing had lived longer, computer science would have been generally considered a part of maths, not a separate discipline--just like mechanics or statistics usually are today).

Rebuilding finance...one platform at a time

We've just released Wolfram Finance Platform with a simple aim: take all the experience we've built up in computation and as a development platform from other areas--whether biology, knowledge or rocket science---and apply it in finance.

It's amazing how little cross-pollination there is between computational areas. Each area has largely had systems with their own lingo and customs and only the types of computation with which they have become familiar.

We can do a simple demo of graph layout of stock correlation to a group of financial engineers and they are impressed. Well, we do have a very nice implementation, but the algorithms are well established and standard fitment in areas like social network analysis.

Finance is clearly an area where the analytics needs rebuilding, particularly for risk. In truth, it's a mixture between questionable analysis and antiquated reporting. So it's not just straight computation we're talking here either. It's high-level language, instant interactive reporting and linguistic interfaces to name a few. But what it really needs is the coherence of having an all-in-one system with intelligent automation that builds trust.

This is just the start of taking Mathematica technology and doing much deeper deployment in finance and other, different verticals.

Should long-division be the pinnacle of primary maths education?

Many people asked me to comment on the UK government's draft primary curriculum in maths, and the Department of Education's response letter. Rather than compare computerbasedmath.org with the new curriculum, I'll instead make a few initial observations for those who've followed its ideas.

When governments talk maths, they seem intent on convolving hand-calculating with rigour, rigour with understanding, calculating with numeracy, maths with calculating, rote-procedure learning with the vital conceptual and intellectual requirements of today's real-world maths.

I read the response letter first. It fitted this mould rather too well.

Then I scanned the curriculum itself. It seemed much better. I agree with many problem-solving aspirations and indeed many of the skills cited. I like its not-too-prescriptive approach, as I understand it, giving leeway for lots of different ways to achieve the teaching outcomes including (though this is not specifically cited) basing it on technology. Yes, I'd like this to be much more radical and programming to be included as a core skill, but I understand the difficulty of hard-coding it at this stage. I also understand why there's little reference to technology on the basis that its use isn't an outcome but a highly appropriate (I'd argue essential) tool to reach the outcome--outcomes which I think could have been bolder if computers were the default assumption for calculating.

Where my support starts to diverge is with procedures for multiplying fractions (when did you last use this formally eg. 3/16 x 7/8?) and there's a gaping chasm by the time we get to long-division (ever need to use that?).

Not only are these examples mechanics-led outcomes, not problem-centric (in the end it's problems that maths is there to solve not its own mechanics), but the mechanics in question is in practice obsolete ie. it's not in use in the real world nor do I believe it empowers understanding that is.

This saps student's time, energy and motivation. But I'm concerned about a far more serious problem: the lowly government portrayal of maths.

Should placing long-division or learning your times tables really be portrayed as the pinnacle of achievement in maths at primary school? Worse still, why imply that those tedious procedures are what maths is primarily about?

This is about the worst maths marketing you can do to prospective students--and in the long term to parents. Perhaps it's a good short term vote-winner for some, like brands that consistently do special offers improving sales short-term, but it's not a good long-term strategy for building a quality image of maths in our society or one that's aspirational. It's using long-division as a badge of honour of what the government call rigour when in fact it's a prime example of mindless manual processing.

And more than ever, it presents a broadening chasm between government's view of maths and the real-world subject.

The nub of real maths isn't rote-learning procedures nor does it depend upon them. It's not calculating, but the highly challenging mathematising of ever more complex situations for a computer to calculate, de-mathematising the results and validating their worth. It's creative, applied, powers some of the most successful ideas and developments of recent centuries and can even be fun and engaging!

A useful analogy is with survival skills. In the past your life would depend on rubbing sticks together to make a fire. Now those aren't likely to be life or death. Instead basic survival is how to cross the road or  handle money. What are today's maths survival skills? What's at the pinnacle of today's maths?

Instead of rote learning long-division procedures, let's get students applying the power of calculus, picking holes in government statistics, designing a traffic system or cracking secret codes (so topical this month with Alan Turing's anniversary and his computer-based code breaking). All are possible, all train both creativity, conceptual understanding and have practical results. But they need computers to do most of the calculating--just like we do in the real world.

Examples from Wolfram Demonstrations site.

I hope these sorts of examples will all be encouraged under this new curriculum, and crucially that the assessments will highly value the skills they require, utilising computers so problems can be harder, more realistic and far more engaging.

One country will take this computer-based approach first and leapfrog others' technical education. This change will happen. The question is when not if. I worry that the UK won't be in the leading edge of this, but in so many ways it still could be.

Meanwhile, I won't be much help with my daughter's long-division homework. I've actually never learnt how to do long-division; I don't think it's disadvantaged me one iota.

P.S. Paradoxically, I would include times tables in a curriculum: they're still useful. Surrounded as I am by computers, I still find mentally hand-estimating helps me make quick judgements on information and I often do approximate multiplications to achieve that. Of course I could get my computer to do this---but for the moment, it's that bit slower. I do not think times tables give one valuable inherent understanding; but they are useful. Long-division doesn't and it isn't.

A visit from the Prime Minister

It was great to welcome David Cameron, British Prime Minister, officially to open our new Wolfram Centre in Oxfordshire, UK today.

Rather than a traditional plaque unveiling, we went virtual: an iPad button wirelessly firing off a sequence on a nearby TV, the ending "plaque" presenting live data captured at the moment of unveiling--the current weather, FTSE level, star chart and even the PM's age of 16562 days.

More seriously, we talked two topics I believe are key Britain's hi-tech role: making government data truly accessible (to citizens and government(!) alike) and resetting maths education to be computer-based--both more conceptual and more practical.

It's interesting how much the first chimed with the PM's 2010 TED talk about people empowerment in a "post bureaucratic age". It was fun showing how Wolfram|Alpha queries and interactive CDF could serve this agenda (including through Siri), and how the problem-centred approach of computerbasedmath.org might give the UK an opportunity to leapfrog other countries in STEM.

It's clear that the PM is keen to see Britain as a bold new tech and information hub, able to punch above its weight in reshaping the value-chain of knowledge, or what I've described before as the "computational knowledge economy".

In our unusual kind of way, I believe we can contribute unique facets to driving this agenda.