Science of science standards

Abandon your moderate smugness about your academic skills and try to answer any of these old maths and chemistry exam questions:
Old mathematics paper
5 decades Chemistry papers

Well, I think I could get a few right, especially with a bit of a run-up to revise and some practice. But I would still have failed dismally. I couldn’t even get near to passing an exam that I’ve actually got the paper qualifications for – from the days when it was “harder”.

The Royal Society of Chemistry has petitioned the government about a fall in school science standards.

Armed with the first hard evidence of a catastrophic slippage in school science examinations standards, the Royal Society of Chemistry (RSC) has launched a Downing Street e-petition calling for urgent intervention to halt the slide.
And tomorrow morning a devastating RSC report demolishing the myth of record-breaking science education performance will land on the desks of all Members of Parliament.
The RSC report, also being supplied to industrialists and educationalists, raises major concerns over the disappearance from schools science examinations of vital problem-solving, critical thinking and mathematical manipulation…..
… Even bright students with enthusiastic teachers are being compelled to “learn to the test”, answering undemanding questions to satisfy the needs of league tables and national targets. The RSC has powerful evidence of the decline in standards, adding to the revelation that students are able to receive a “good pass” with a mark of 20%.

I’m not saying that they are wrong. They make very valid points in the report .

However, the public face of their “first hard evidence” seems more like a publicity stunt than science. In its pop-science media version, it certainly looks like the application of poor social science The RSC “hard evidence” is their exam test (5 decades Chemistry papers)

The RSC ran a competition based on exam questions culled from 50 years of chemistry O Level/GCSE exams. They found that the students (identified as “the most promising scientists” by their schools) who sat the tests “averaged just 25% of available marks.”

“Although the winner of the RSC competition got 94%, the fact that many highly intelligent youngsters were unfamiliar with solving these types of questions, obtaining on average 35% correct from recent papers from the 2000s and just 15% from the 1960s, points to a systemic failure and misplaced priorities in the educational system, rather than shortcomings in individual teachers or students. (From the RSC website)

Hmm. The content of the Chemistry curriculum has surely changed over 50 years. The percentage of correct answers fell as the questions went further back in time. This suggests at least one alternative explanation – the less familiar they were with the material, the worse the students did.

(Which is not surprising, given that teachers have had to “teach to the test” whenever they have prepared students for public exams. Students would be quite annoyed if they found themselves being prepared for exams from 50 years ago, because – however good their knowledge might be, it still wouldn’t allow them to do well on a 2008 paper.)

Surely, control samples should have been used. For instance, groups of students who weren’t already identified as the science stars; groups of students given only recent questions; groups of adults asked to sit the same tests and/ or recent exams. It would also have been more convincing if they hadn’t marked and set the tests themselves.

Not worth the bother? Obviously, because this would imply it was a real investigation, not a way to get their petition some public interest. (Such as I am showing here…. D’oh. Chemists:1 Me:0)

The RSC aren’t stupid. Their full report shows that they are aware that changes in the subject make it impossible to draw easy conclusions. They point out that they aren’t blaming teachers or students.

However, unless they are almost too unworldly to shop for their own pipettes, they would know that this will get publicity only because the whole report will be presented in terms of “exams are getting easier”.

This is an ongoing debate. It’s sometimes seen as a bit churlish to suggest that exams are easier, presenting some implied insult to the efforts of current students.

However, by very simple mathematics, if education policies are qualification-driven, demanding very high target levels of achievement, exam qualifications must get easier.

It is not possible to demand that 100% of 16 year-olds pass exams unless those exams are so easy that anyone can pass them (By definition. The clue’s in the target figure, for the mathematically-challenged.)

What teacher in their right mind would enter their dimmest or least interested students for a tough chemistry exam? Why would they encourage any students whom they think won’t get a good exam mark to develop an interest in science, when their school will go tumbling down the league tables if only 5% manage a pass?

The RSC is actually saying this. Their real argument is about the system not the easiness of exams.

But who’s going to notice that while we are all feeding our own prejudices about the youth of today getting dumber? (Try one of those exam papers if you ever start to believe that.)

Mathematically Challenged Education Authority

What hope do the children have?

In the UK we suffer a very bad obsession with league tables in which the performance of every public body is graded (on an arbitrary scale) and compared against others – rarely in a like for like but that is another matter.

As you can imagine, schools bear the brunt of this. Parents are understandably determined to get their children the best education possible, often moving across the country to be in the catchment area of their chosen school. Most of this one-upmanship is derived from the school tables, helpfully published on the BBC website.

All the trust has to be placed in what ever body is responsible for collecting these numbers. Are they up to the task?

Idly surfing the web, I came upon this educational report on the BBC. It is the stats for an infants/primary school (ages 3 – 11) in Shrewsbury. All normal. Have a look at the stats and it seems like its a reasonably good school – it performs above the average for its educational authority, which is also above the average nationally.

Then have a look at this:

PERFORMANCE
37 eligible, 18.9% of whom had special educational needs

At first glance it seems normal and slightly low compared to some schools.

Then look at the numbers.

18.9% of 37 is 6.993.

This means that 6.993 students have special educational needs. How is that possible? Is this just a rounding problem? No, because 7 pupils would be 19% in any normal formulation.

Either the organisation who collates the stats is mathematically challenged, or they have massaged the numbers to make it look lower than it is (and are ethically challenged).

Whichever it is, how much faith can you have in this system?

Banks Fumble, Taxpayers Punished

The current “banking crisis” has been pretty hard to ignore of late, but here in the WhyDontYou ivory towers, we have tried. Partly this is because both of us are in (largely) economy immune employment sectors and partly (mainly) because neither of us can really fathom the nonsense being thrown about in the news. Given that both of us are required by profession to be mathematically astute (yes, really) it could be taken to imply that the average citizen would be even more lost.

With this in mind, it is entertaining to watch the news about the crisis when it pretty much only shows scared-to-death financial experts going on about weird ways of selling things you dont have (short selling) and how important the banking risk takers are to society. They are so important that the rest of society has to protect them should their risk taking go wrong. Being ignorant of the financial wizardry, this strikes me as being totally insane, let alone unfair. This post (long, sorry) is pretty much a way for me to let off steam about something that is destroying peoples lives and, basically, really annoys me. I would welcome your comments and feedback on my take – if I am wrong, please educate me.

There are two headline examples today (in the UK at least) – The UK Government take ownership of the crap part of Bradford & Bingley, after selling the good bits to a Spanish bank; The American government fails to secure a $700bn line of funding for its banks to keep them safe. (Neither are good news items. Neither are going to reassure people that their future is safe. Do not mistake a light tone here for a lack of concern)

Some Background

UK first. Starting about 20 years ago there was a big rush for building societies to become banks – changing from being basically there for a group of people in one area (eg. Bradford, Halifax) where everyone who paid in was a member to becoming a limited company, where some of the members became shareholders. In the process, especially throughout the 1990s the drive was on for these banks to press hard and return massive profits for the shareholders (often a tiny subset of the Building Societies membership). At the time (and in principle it still does) this seemed a good idea. Most people got a bit of money (sadly for most of the members this was just a bit – around £100) and a few people got lots and lots of money. Everyone was happy.

From this, there was a drive in the finance sector to target more and more high risk trades, where often the winnings were large beyond the avarice of mortal man. City bonuses in the millions ceased to be newsworthy and sales of high end sports cars went through the roof. Being a “risk taker” became the nicest thing you could say about someone. We (the public) were dimly aware that there was a risk it could fall down on the bank (Barings) so we accepted the ostentatious lifestyle of the successful. For some reason we were convinced it was down to skill and intelligence rather than basically throwing dice and hoping for the best. These were people who worked hard predicting the markets and had a rare skill in knowing where the trades were. Or so we thought.

Hidden for most of the time were the downsides to this.

Insane wages in London made the already insane prices there spiral out of control. People began to think that paying £750,000 on a one bedroom apartment was a “good investment.” In turn, this priced even well paid people out of the city, so prices near London went up (often even faster if it was commutable and “nice”). For the last ten years it has been impossible for anyone on less than twice the average wage to even think of buying a house in the south of England, without a hugely fiddling their application – so they did. People overstated their income, understated their expenses, and took insane repayment terms hoping they’d get on the gravy train before they had to pay the capital. Lots of these people had “normal” jobs and were not aware that they were bearing the same risk that the Ferrari driving millionaires living in central London appartments had. The public never benefited from the wins so, rightly you would think, assumed it was safe from the risks.

Wrong. (More on that in a minute)

A similar story in the US (I assume, I have no idea of the background). From my visits, the gulf between rich and poor in America vastly outstrips that in the UK. I have always thought that if you were filthy rich, there is no better place to live than the US, but if you were penniless poor the UK wins. Rich people in America are really rich. I am amazed the poor survive one day to another.

In recent years, the risk loving traders have really had a few field days in the US. Massive windfalls made rich people richer. They took huge risks, which often paid off. People applauded them for having the guts to risk so much, making it hard to condemn them for their salaries and bonuses. As with the UK, most Americans had some fallout from this (house prices going up for example) and people begin to think that property is the best investment, so take some personal risks to buy a house. In turn the bank takes a bit of a risk lending to them, but often at crippling interest rates that will see the bank get its money back in spades.

Eventually, as everyone with hindsight knew it would, the whole system explodes. That is the thing with taking a risk, sometimes you get hurt.

Here is where my understanding and reality part company.

Current events

I have always thought that you took a risk, gambled something for example, sometimes it would pay off and other times it wouldn’t. Some risks are “low risk”: for example, betting that a tossed coin will land on either heads or tails rather than its side is quite a low risk bet – you are a lot more likely to win than lose. Some are “medium risks”: betting on heads in our example. Some are “high risk”: betting the coin will land on its side. They all make sense to us and we live with this sort of understanding on a day to day basis.

The world banks have paid their “High Risk takers” absolute fortunes because they take high risks. This is fair. If I bet £1000 on the coin landing on its side and I won, I would expect to win big, if I bet £1000 on the coin not landing on its side, I would expect to win a tiny amount simply because I wouldn’t expect to lose.

For most of the last two decades, the amazing thing is the risks have (on the whole won). The coin has landed on its side a lot. People have won big.

The problem is people then forgot what a risk it was. If you win something that is high risk enough times, you forget that it is high risk and assume the opposite. The merchant banks have been so successful with high risk ventures, they forgot that “high risk” meant dangerous and plowed more and more money into it. They still throw around the terms, they certainly still paid the bonuses, but everyone assumed it would never happen.

Then the coin came up tails and everyone lost. Everyone who had bet big, lost big.

Oddly, this came as a shock. The great and bold risk takers were mortified. Nothing hits a herd as fast as panic and the trading centres of the west are no different. Contagious fear spread everywhere and a generation of “risk takers” who actually had no idea about risk were the most affected. The less scrupulous traders saw a chance to strip the foundations of fragile structures and asset rich, stable organisations took a massive hit (Bye, bye HBOS). The wonders of a free market allowed short-selling and a few scares to destroy a company with solid resources – can you imagine how scared the rest must have become.

Risk?

So, in the interests of a free market, the government steps in and saves the companies. The government spends billions of the taxpayers money to rescue institutions that have, basically, gambled themselves out into the street.

This is where I am confused.

In the UK, the government has reportedly taken over a £50billion debt on behalf of Bradford and Bingley. That is effectively £1000 per person so that the demutualised, risk taking, company can survive. Although we were not aware of the risk we were taking, nor did we share in the rewards, everyone of us in the UK was involved in the gambles these people were taking.

The US has the same problem. The $700bn bail out (good idea or not) is a phenomenal sum of money. The high flier financial wizz-kids and their high risk lifestyle would cost every one of the 300 million people in the US over $2000. For someone on federal minimum wage, that is 321 hours work – 40 working days – to save the rich from becoming poor (I know it is not quite that simple). Instead, the poor get a little bit poorer. Wonderful.

The US must be the only modern democracy where funding the rich bankers is a more appealing proposition than giving healthcare to the sick. That confuses me.

To confuse me even more, the news today had lots of talking heads on both sides of the Atlantic saying how it might seem strange but it was vital that the taxpayer (poor) bail out the bankers (rich) because. Often simply because. Sometimes there were vague, dire, warnings about the economy, but most of the time it was just a simple statement. We have to do it.

Why?

I don’t doubt that letting one or two banks slip will cause even more panic which will destabilise the economies, but if the US has $700bn and the UK has £20bn going spare, then surely we can weather some rough times. When the average person on the street still has money for shops to take off them, then the economy will still work. In my mind that is where the salvation needs to be pointed.

Equally odd, is this new definition of risk.

If I gamble my house on a high risk deal and lose, I lose my house. Will the government bail me out? (Well, in the UK we have social housing but that is different) It is unlikely. For me, betting on high risk stocks is just that – high risk. I stand to gain but I also stand to lose everything.

If a bank gambles the houses of 20 million people and loses, well they really lose nothing. Poorly paid staff will get laid off but the “risk takers” are immune. The organisation is immune because as long as it cries loudly enough the government helps. For the banks, betting on a high risk is actually risk free. They will either gain a lot, or lose nothing.

Why is this acceptable? Why is this considered normal? Why are we still hearing that it is all down to the taxpayers to save these banks? Why not claw back the multimillion bonuses? Why not fine the fund managers? Why are they allowed to gamble without risk, yet still be thought of as “cool” risk takers?

Crime and Punishment

The most sickening thing about the whole deal is not just that the taxpayer has to suffer.

If, through negligence or design, I caused someone to lose out to the tune of £1000 there are laws that would punish me. If I gambled £1000 of someone else’s money without their knowledge and lost it, I would expect the police to visit me and to end up in jail.

It seems, however, if you do it with enough people then not only does the government step in to cover your debts, but you dont even get punished. In the middle of the credit crunch, UK stockbrokers were still getting massive Christmas bonuses (just not as massive… poor things).

While it often smacks of unscientific voodoo, I accept what the “finance experts” say and that the state has to prop up these failing institutions. However, why should the people who have caused this problem be allowed to walk away? If, for example, the fund managers and directors of each organisation were to be fined in proportion to their participation, the rescue plan’s tax burden would be a sweeter pill.

Alternatively, if this heralds a new era of tightly controlled financial markets, where crazy risks are punished, and these people are not simply able to start ripping the world off again in a few years then, again, it becomes a bit more acceptable.

I think the problem is, this will never happen. The hint that the US bail-out would be followed with government involvement meant that the Republicans stood against the great George Bush and turned down the bill (*). It seems the only way a rescue plan will be approved is if it carries no strings or punishments. Basically, the bankers are free to risk all our money without having to worry…. (Slightly better over here, where we are more accepting of government control and oversight).

What a wonderful world.

(*) This adds an ironic twist. I strongly think that the Republican party expect to lose the next election. McCain/Palin are their idea of a joke. They know the country and the economy is about to tank, and the war in Iraq has gone badly. If they lose the election, Obama will be handed a hospital ball of a presidency. Unless he is truly Odin’s chosen one, come the next elections people will still be smarting from the economic crisis and will be ready to turn to the Republicans once more. Taken in this light, both Bush’s plan to asset strip the country, and the parties refusal to do something that (on the surface) benefits the public makes sense.

Can you be too cynical?

Shares for all

On the BBC Tech pages a blog by Kate Russell recommends a site called Gnu Trade where you can gamble on the world’s stock markets.

Now everyone will have their own take on whether gambling on market movements is a good or bad thing but even if you do not want to risk a penny it is possible to make money here.

That is because the site allows people who bet with cash to back players who are playing for fun. If you attract a real money player to back you and you make a profit – then some of that real cash gets sent to your account.

If you are sh*t hot (belatedly decided to think of family-friendly filters) at online poker you could probably make a lot of money, There are plenty of maths geniuses out there. It’s got to be easier than the lottery,

I can think of a few other potential unforeseen consequences, whether “good” or “bad”.

My grasp of economics is pretty shaky (as witnessed by my lifetime failure to even try to be rich) but I thought the things traded in stock markets related to people’s livelihoods. Food? Manufactured goods? Oil?

Stocks and shares aren’t just numbers. Entire national economies and people’s lives rest on them.

Aren’t international markets supposed to be “sensitive” to the slightest event? Share prices fluctuate within moments with the impact of a mysterious set of forces – from changes of government to the wildest rumours.

Wild rumours on the Internet? Surely not. Bizarre misunderstandings across cultural and language gaps? No, they can’t happen on the Net. The Internet isn’t allowed to lie. It’s like television (It said so in the Simpsons.)

Might not the international markets become ever more volatile? Easier to manipulate? Might not the implications be ever more destabilising?

It’s been so long now that economists have been saying that “free trade” is the answer to everything. Maybe we will soon find out if this is the case. Alternatively, you could think of it as a scientific test of chaos theory.

Moebius strip

Moebius strips are wonderful. There’s an image at http://images.salon.com/comics/tomo/2003/08/29/tomo/story.jpg
showing Bush’s foreign policy as a Mobius strip. I couldn’t save it here so I borrowed this one from mcescher.com

Escher’s mobius strip

Seed magazine says that two mathematicians – Gert van der Heijden and Eugene Starostin – have resolved the shape algebraically. I’ll have to take that on trust. I can’t even grasp what the problem is, so I doubt I’ll understand the solution..

What determines the strip’s shape is its differing areas of “energy density,” they say.
“Energy density” means the stored, elastic energy that is contained in the strip as a result of the folding. Places where the strip is most bent have the highest energy density; conversely, places that are flat and unstressed by a fold have the least energy density.

Stats cant lie

Five days ago I talked about the odd statistics which were showing up in my BOINC client for Einstein@Home. Sadly in the intervening five days, nothing has become any clearer.

BOINC Client - User Total 19 Feb BOINC Client - User Average 19 Feb

Now, the BOINC client has been running constantly (with the exception of one 9 hour period) for the last five days, yet the increase seems minimal and the average is plummeting like a stone. Looking at the client stats page there are still 82 work units “pending” credit (at around 53.4 credits per unit) so eventually this should change.

Even so, I am still not sure how the two sets of numbers compare to each other. I cant work out how the averages are calculated at all. Any comments welcome.