Conrad Wolfram


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Announcement: our first CBM country

I'm very excited to announce that 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.

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Reader Comments (4)

Hello, very good blog post. Helps to understand what You really mean - example of lognormal distribution vs. normal distribution. For example, I also learned normal distribution in university, and some others, but I am mainly ignorant of the others and did not know that I am missing something :)

But, for me it seems too harsh to say "Stop teaching calculation". It is valuable to know how to do the calculations. I would emphasize the "Start teaching Math/Computing" part, and teach computation and calculation together. Of course, here is where Wolfram | Alpha comes in, as way to provide visual feedback about calculations.

What I want to say is that I think that Your message should bring out more clearly answer to this question: do You think, that calculation should be teached not at all, or that You believe just that it is not main focus?

For example, the distributions. I see, that students could be teached in this way: they take real-life data (about something they are interested about), they find the nearest type of distribution by some automated tool, for example Wolfram|Alpha; and then they learn the mathematical details of this distribution. And for example, students could make presentations to each other about what they learned (both real life consequences and mathematical apparaturus), because everyone ends up with different data and different distribution. Teacher could also present, which distribution was the most common.

Or should the teaching stop when students have learned how to use computer tools to find answer? I think not. But on the other hand, some distributions could be mathematically so complicated, that they are just not the right ones to start teaching from. They would only scare the student away. But on the other hand, teacher could minimize this effect by helping to choose the student from the "easier" ones, that still represent the data nicely.

Did I express my question clearly? Just saying "stop teaching calculation" sounds like "stop teaching 2+2=4". It is still necessary. It can just be boring, because it is not applied or connected with real life. This is where computer-based curriculum can help - to spark interest and show, how learned knowledge can be applied in real life.

Maybe You could say "concentrate on teaching math" or "empower math, not calculation". "Stop" seems to much and is likely to raise unnecessary prejudice, I think.

Let me know what You think :)

April 24, 2013 | Unregistered CommenterRauni Lillemets

I am happy to see that someone is willing to make this change, at first I put the phrase "take this risk" then realized it really is not a risk but just feels like one. We as people are slow to embrace new ideas typically, and they sometimes feel risky when first seen. But the idea that we hand over the tedium and mindlessness of computation to a machine that has no concept of the tedious is way past due. It will require the curriculum to radically alter. Problems will come to the forefront, skills to the backseat. Thinking and analysis of results will still require an understanding of technique and why a technique produces the result it does. I am anxious to see what work is accomplished in the Estonian curriculum. Bravo!

April 30, 2013 | Unregistered CommenterChris Brownell

I started buying resveratrol in my late fifties and decided to investigate what it does. That started me learning cellular chemistry backwards. I started with a relevant interest and hyperlinked down to understandable concepts (got my BA in 1970) and then worked my way back up to more related chemistry. It seems chaotic but works in it's own organic way. I thoroughly endorse learning by relevance first rather than studying principles and dynamics outside of any meaningful context. Math never had the relevance to encourage me to study it for it's own sake. Now I love the numbers because they tell me what works and what the score is. The computational algorithms highlight information that I would have had to sort out with painstaking analysis on paper. Getting rapid confirmation, my mind has the freedom to move to the next consideration.

May 6, 2013 | Unregistered CommenterJim Lew

Dear Conrad

Despite you don't know me just a friendly greeting as I think we need to stay closer in touch. Estonia is by far the first. I am not sure if Denmark - you know another small tiny cold nordic country with a lot of happiness - was first, but we have had the use of computer algebra in secondary schools mandatory for a couple of years and the use of i(c)t mandatory on all levels. We also had programming back in the 1980ies in our school programs but it was left behind due to different reasons. I am convinced it will be back next summer.

What is more strange to me is that I am aware that the math teachers union in primary and lower secondary has been collaborating (or at least workning with) Mathematica fro around 10 years by now, so I wonder where that ended up being a first or not. I must admit I a little on the edge here as I was behind the use of Mathcad (from 1996) in primary school and before this we actually used a Danish software Multimat as early as 1988. Never mind all that it is history today.

More in perspective I am doing a ph.d. at the moment on potentials from i(c)t and among other things I have a reworked version of statics on primary and lower secondary level. This can probably be improved so I would like to suggest to you that we collaborate on this. And maybe we will have to take this up more private than in a blog, but on the other hand this is new times.

Beside this most of my efforts is within making the learning of math playful to more students. I have several principles I try to invoke to study if this makes positive attitudes among the pupils towards mathematics. I am not so much into STEM, more STEAM, as the science area is not ao attractive to young people in Denmark. It has got an even lower x-factor than mathematics. So I am more into gamification and different things in that area.



October 30, 2013 | Unregistered CommenterSteen Grode

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