Evidence: let's promote not stifle innovation in education

Evidence: let's promote not stifle innovation in education

Earlier this week I was part of a high-level discussion about maths and computer science education, how we could improve their reach and effectiveness. Rather quickly the question of  evidence came up, and its role in driving innovation.

It's taken me a few days to realise that there were actually two very different "importance of evidence" conversations--one with which I completely concur, and one with which I vehemently disagree. In the end, what I believe this exposes is a failure of many in charge of education to understand how major innovation usually happens--whether innovation in science, technology, business or education--and how "evidence" can drive effective innovation rather than stifle it. In an age of massive real-world change, the correct and rapid reflection of this in education is crucial to future curricula, their effective deployment, and achieving optimisation for the right educational outcomes.

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Computation meets Data Science in London, Thursday 5 March

Computation meets Data Science in London, Thursday 5 March

I'm usually going on about "computation" or in education, "maths". But I've come to appreciate just how much of computation's utility in modern life centres around data (rather than, say, algebraic modelling).

Clearly data science is a major, growing and vital field—one that's relatively new in its current incarnation. It's been born and is driven forward by new technology, our abilities to collect, store, transmit and "process" ever larger quantities of data.

But "processing" has often failed to elucidate what's important in the data. We need answers, not just analytics, we need decisions not just big data.

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What are the modern areas of maths?

Traditional areas of maths like algebra, calculus or trig don't seem a good way to think about subdividing the subject in the modern world.

You might ask, why subdivide at all?

In a sense, you shouldn't. The expert mathematician utilises whichever maths areas helps them solve the problem at hand. Breadth and ingenuity of application is often key.

But maths represents a massive body of knowledge and expertise, subdividing helps us to think about different areas, for curricula to focus their energies enough that there's sufficient depth of experience gained by students at a given time to get a foothold.

However I believe the subdivisions should be grouped by modern uses of maths, not ancient divisions of tools.

So here goes with our 5 major areas:

  • Data Science (everything data, incorporating but expanding statistics and probability).
  • Geometry (an ancient subject, but highly relevant today)
  • Information Theory (everything signals--whether images or sound. Right name for area?).
  • Modelling (techniques for good application of maths for real world problems)
  • Architecture of Maths (understanding the coherence of maths that builds its power, closely related to coding).

Comments welcome!

PISA results: Let's win on the right playing field, not lose on the wrong one

PISA results: Let's win on the right playing field, not lose on the wrong one

Today's maths PISA results are predictable in the successes that many Asian countries show and the mediocrity of many of the traditional Western countries--like the UK. 

I believe PISA is meticulous in conducting its tests and reflects a good evaluation of standards of today's maths education. And yet I think if countries like the UK simply try to climb up today's PISA assessment, they'd be doing the wrong thing.

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Excited: Raspberry Pi gets free Mathematica + Wolfram language

Excited: Raspberry Pi gets free Mathematica + Wolfram language

I was very excited at our CBM summit this morning with Eben Upton to announce that Mathematica will be bundled on the Raspberry Pi computer for free, and so will the new Wolfram Language--also announced today.

This really has at least 4-dimensions of consequence:

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Collaborating with UNICEF: next month's CBM summit on fixing world's maths

Collaborating with UNICEF: next month's CBM summit on fixing world's maths

Fixing maths education is becoming ever more central to individual life-chances and our societal needs.

So I am very pleased that we're able to collaborate with UNICEF on our 3rd CBM summit, holding it at their headquarters in New York City on November 21-22.

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Maths v. Music Education

Maths v. Music Education

I was debating Computer-Based Maths education (CBM) with a sceptic before the summer and he brought up the analogy of music education to support various claims he was making of maths.

As I understood his central point it was that practising hand calculations is akin to practising music pieces--it's simply the way to learn to play. Also there was some attempt to draw the analogy between listening to music and CBM, whereas playing was like traditional hand-calculating maths.

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Announcement: our first CBM country

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.

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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.

programing.png

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.

WFP_Diagram_065.jpg

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?).

long-division.png

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.

Computer-based math eduation summit

Just a quick posting that we had a terrific first computer-based math education summit at the Royal Institution in London. We made good progress at an early start to charting out a new direction for the world's math students both for formal curricula and for the multitide of other ways that learning takes place.

Over the coming months you'll see topics and modules showcased alongside video of discussions from the conference. We haven't worked out our full plan yet, but for something destined to take a minimum of 10 years, we're thinking it through carefully. Watch this space!

Call me a control freak...

...and many would...but I like my environment to be set-up right. In particular, I'm pretty fussy about being at the right temperature. Yet inadequate control plagues our office and particularly home heating systems, wasting huge amounts of energy and making us uncomfortable into the bargain.

This came up in specing the HVAC system for our new office. Optimising zones v. heat recovery v. control sophistication is pretty complex and more control can be quite costly. Moreover, just modelling each room to answer questions like "will we always be able to get it to 21C within 1 hour" is surprisingly fraught. What outside temperatures to assume? How insulating are the room's walls, floor and ceiling? What are their heat capacities? How many people will be there?

(I can't help noticing this would be a great computerbasedmath.org module. It's exactly the sort of real-life maths question that today's curricula don't equip students well for and for which learning intricacies of hand-calculating won't help you).

Next step: see whether we can get to the system's API and use Mathematica to make a nice interface to it.

For the home, there are an increasing range of retrofit, wireless solutions for traditional wet central heating systems that have only a few years of payback. I've for some time had a Honeywell CM-ZONE and now an EVOHOME I put in. One of the worst marketed piece of tech, it's a pretty nice system that most plumbers don't know about.

It's a new Wolfram Research Europe...

17 years ago, we moved into our current Oxfordshire offices---yup, one year after I started doing non-stop email. Well, today we're moving to a custom built new office just up the road. The site is kind of an interesting place actually--where pioneers in wildlife filming Oxford Scientific Films set-up in 1968. Strangely I had had a school trip there in around 1982 and I'm pretty sure they told us they'd just finished filming a Cadbury's "glass and a half" ad with a then new micro video camera moving along many chocolate bars. None were left by the time we arrived!

Even though this is an exciting, positive move, there's a strangely eerie, reminiscent feeling sitting where I am now at my desk: all my stuff packed up, my monitor, phone and desk, the last to go. I was decidedly young when we moved in; I'm quite a bit creakier now...

And oh has the technology changed. 17 years ago I was equipped with a fine if monochrome NeXTStation computer. I wondered whether I really needed a colour monitor; it seemed unnecessary. And I needed lots of filing and a complex system of trays to manage my paperwork. Clearing up this morning, I realise that I haven't accessed physical files for 3+ years for anything. They're not moving with me.

It was here I was sitting when I first heard about "the world wide web". The keen Mathematica user from CERN on the phone was surprised that I hadn't tried it yet and hadn't understood how much it was going to change the world.

Over the years my desk size has reduced, as has the volume of my monitor and filing cabinets (even my waistline has shrunk, though it's now past its minimum!). Only my screensize has grown.

Time for my computer to get packed now...Off to the next (hopefully also prime) 17 years from Monday--a new era for Wolfram Research Europe Ltd.

Just finishing CDF rollout...

Thought I'd take a quick breather from getting everything ready for our rollout of the Computable Document Format (CDF) technology. Rather than tell you about the tech (just authoring a blog on that for the Wolfram blog), I'm thinking of the process.

And gosh there's lots for the team to think about.

First there's the technology and workflows for it. That's got to be right or all bets are off. Then there are all the websites, their technology, their testing. The press releases, briefings, talks. The blog items, examples and questions. Internal announcements, external announcements.

We're kind of used to this with Mathematica but we know our audience well. Here we're into uncharted territory, not just for us but for everyone.

In the end, what I will worry about is whether we've explained what we're doing well enough. Will people get CDF's significance? Have we spoken both to people from document and from software backgrounds---they're very different. Have we missed some crucial part of the story, some important nuance because we're so close to it?

Watch this space (literally)...and see "Documents come alive with the power of computation"!

P.S. You'll want CDF Player installed. It's free here.

 

Happy 18th, non-stop email

Yes, I know it's sad, but I have looked at email every single day, regardless of where I was, for 18 years.

Achieving email access everywhere is now pretty easy, but back in the early 90's it wasn't. I used to pride myself on figuring out how to do it on my own computer, carrying adapters, cellphone hook-ups---whatever I needed. I remember rewiring hotel phones in China and often having to plug into reception desk fax machines. But collect email I did.

My psychology is such that I prefer knowing that I'd know, to worrying about not knowing (not to mention enjoying the technical challenge)! Apparently that addiction has gripped most of the population too. Wonder how it changes us?

 

Phew! New Demonstrations site up...

A little tougher than I thought it was going to be to get everything lined up for release.

Our "knowledge app" site demonstrations.wolfram.com was completely redesigned to use the inline Mathematica 8 or free Wolfram Player plug-in rather than having to open a separate window (alongside various other changes).

This apparently small plug-in change makes a big usability difference and by the same token, it changed the site workflow quite a bit. It also required the latest version of Player--just releasing too--and itself quite a feat of engineering.

One of the complexities has been to work through all the cases of different machines, installations and therefore optimal operation. What should the site show if someone has Mathematica 7 (no plug-in capability) installed? Or they're on an iPad (no Player for now on iOS)? Or it's a complex demonstration that takes some time to compute? Each has its own adjusted workflow.

Hopefully, we've ironed out these cases but with the traffic we get, I'm sure we'll find out anywhere we haven't soon. Getting this optimised is a high priority: Demonstrations is one example of much broader interactive publishing plans codenamed CDF.

Amazing: iPhone app got my father a pacemaker

Heart rate.PNG

Last week I had downloaded this heart monitor app, intrigued at how it used a finger placed over a phone's camera to work out your pulse.

My father was visiting so I showed him the app for fun. He's 86 and has had a few issues with walking etc. but that wasn't on my mind. The app read 36bpm--way low (as Wolfram|Alpha confirms). My wife, ophthalmologist Stella Hornby, checked. It really was 36bpm; she was sure he had a heart block. After some effort we pursuaded him to hospital. They confirmed the diagnosis where this morning he had a pacemaker fitted (rather a quick turnaround by the UK NHS, I thought).

This result is all the more amazing as 3 years ago my wife thought my father might have carotid sinus syndrome, and that a pacemaker would be the likely treatment. But on visiting the cardiologist, he couldn't find anything (heart rate was fine while they were measuring it) and so nothing was conclusively diagnosed, and no treatment given.

What an example of the power of interactive apps and the future of self-monitoring!