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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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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How Significant is Significance Arithmetic?

How Significant is Significance Arithmetic?

Central to our mission at 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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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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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 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.

Why "fair" maths tests aren't fair...

How should one define fairness of testing? There are countless ways to make tests unfair, but achieving fairness surely involves aligning what's being tested with the purpose of the education. And isn't the main purpose of education to give you skills for life?

Yet in the modern US-UK concept of fairness, questions with complete reproducibility of assessment trump questions that more accurately simulate real life but can't always get every marker awarding exactly the same marks.

For example, multiple choice tests can be marked with complete reproducibility, but when in real-life did you last pick from 4 or 5 answers one of which you knew "has to be" right? Rather, questions which need explanation and judgement calls can be much fairer tests of the student's ability at the real-life subject, even if they might garner some subjectivity of marking.

All this was brought up today when I looked at a book which helps testers set tests. Within the narrow confines of how US testing works, it was no doubt very helpful.

But thinking bigger picture, it was deeply frustrating--like castigating a question with "irrelevant information" ie. more than the minimum needed to calculate the answer, because it wasn't solely testing one core ability [doing a manual calculation]. Since when does real life only have exactly the amount of information you need--no more, no less? And isn't sifting information and using what's relevant a crucial, core ability---particularly since the internet?

Something that makes this all worse: today's tests have assumed an importance beyond their capability to judge. And that's had the unfortunate feedback of putting huge emphasis on reproducibility of marking...and therefore questions with definitively right or wrong answers.

Governments, others setting test guidelines, please remember: fairness ≠ reproducibility (and while you're about it, math ≠ calculating (!))

Or as a London cabby put it on not getting a tip "it may be correct but it ain't right".