Today's Power of Disenfranchisement: Are Data Scientists the New High Priests?

Today's Power of Disenfranchisement: Are Data Scientists the New High Priests?

Computational Thinking—The New Literacy

Our democracies face a massive challenge today. The battleground for electoral success is based on information that few are equipped to question. A small elite manages our thoughts through knowledge only they possess, to the exclusion of most citizens.

I am talking about the overriding effect of modern data science and more generally computation in our societies. Just a tiny fraction of our populations are educated in directly applying computational thinking to information, arguments and decisions they have to take. Including about government. Including about voting.

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Has the math(s) brand become toxic?

Has the math(s) brand become toxic?

For once I'm not talking about the contents of school maths but the name and its associations.

The question I'm asking is if our core technical subject wasn't termed "maths" but "nicebrand" would things go better in and out of education?

Sadly, I've started to conclude the answer is yes. I now suspect that using the brand of maths is damaging core technical education, its reform, and efforts to equip society for the AI age.

Believe me, this is not the conclusion I want. I've spent years of my life somehow connected with the word "maths". But much as I might not like my conclusion, I want the essence of subject maths to succeed; so I don't want the name to kill the subject—a much worse outcome.

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Post-truth: shocking indictment of today's maths education

Post-truth: shocking indictment of today's maths education

Listening to debates pre-Brexit, one of the most familiar cries from the British public to politicians was "we need more information, a more informed debate", implying "tell us more accurately how our vote will play out, you must know!" but then when trends or figures were presented "you can't believe any expert".

Unpacking these sentiments is enlightening. Effectively the clamour was for a detailed model and computation of what leaving the EU versus staying in might mean, particularly in practical financial ways like affordability of housing.

The fact is, no-one knows, even approximately. In practice you can't predict it. The ecosystem is too complex, with huge numbers of feedback loops and linked components, many of which even individually are almost unknowable.

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Anchoring Computational Thinking in today’s curriculum

Anchoring Computational Thinking in today’s curriculum

There is a lot of talk of "Computational Thinking" as a new imperative of education, so I wanted to address a few questions that keep coming up about it. What is it? Is it important? How does it relate to today's school subjects? Is Computer-Based Maths (CBM) a Computational Thinking curriculum?

Firstly, I've got to say, I really like the term.

To my mind, the overriding purpose of education is "to enrich life" (yours, your society's, not just in "riches" but in meaning) and different ways in which you can think about how you look at ideas, challenges and opportunities seems crucial to achieving that.

Therefore using a term of the form “xxx Thinking" that cuts across boundaries but can support traditional school subjects (eg. History, English, Maths) and emphasises an approach to thinking is important to improving education.

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Enterprise Private Cloud: the core solution for Enterprise Computation

Just a quick entry to say we released a product I've been involved with--Enterprise Private Cloud--a few days ago. It's a dramatic feat of engineering, built on the uniquely extensive base of the Wolfram Technology Stack.

I'll leave my main blogpost to do the talking, but suffice it to say that I'm pleased there's a clean, powerful, modern way to put computation at the heart of the enterprise--what I call Enterprise Computation.

It's important for organisations to start to think now about how they manifest this new opportunity which will rapidly become a necessity--one driven particularly by data science.

How Significant is Significance Arithmetic?

How Significant is Significance Arithmetic?

Central to our mission at computerbasedmath.org is thinking through from first principles what's important and what's not to the application of maths in the real, modern, computer-based world. This is one of the most challenging aspects of our project: it's very hard to shake off the dogma of our own maths education and tell whether something is for now and the future, or if really it's for the history of maths.

This week's issue is significance arithmetic, similar to what you might know from school as significant figures. The idea is when you do a calculation not just a single value but bounds that represent the uncertainty of your calculation too are calculated. You can get an idea of how accurate your answer is or indeed if it has any digits of accuracy at all.

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Computers in education: Great machines, Wrong results

Computers in education: Great machines, Wrong results

I am not the slightest bit surprised at the recent OECD report that use of computers in education hasn't improved PISA results − and indeed that many countries with the best technology provision have mediocre performance.

Why? Because the world's most transformative machines have been used for entirely the wrong purpose in most classrooms: automating pedagogy not changing the subject taught.

Countries with the most attentive teaching are also likely countries where there is least pressure to computerise pedagogy for teaching today's school subjects. They do best in PISA because they are best at helping students through those subjects.

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China: from omnipotent to impotent?

China: from omnipotent to impotent?

I've been struck in the last couple of weeks by China's apparent fall from global economic wonder-kid to the latest problem child.

Neither characterisation is true in my view.

What really seems to have spooked people is the psychological turnaround from apparently omnipotent Chinese government, able to command and fix at will, to a government that's apparently largely as financially impotent as any other.

Haven't we seen this same "country on a pedestal" culture that saw Japan fall from grace in the 1990s, the US in 2000s (along in a small way with the UK) and now China?

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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.