Y Safle

The percentage of A grades at ‘A’ level rose sharply again last year as the number of candidates hit an all time high. The most stunning rise was in the percentage of top grades at A level mathematics, reaching an amazing 43.5% as the new “more accessible” syllabus settles in. Not surprisingly many are suggesting this is just dumbed down.

To be fair, Mathematics was a hard ‘A’ level, and there is an obvious danger that if an ‘A’ level is too hard, that people will opt for easier subjects. But the pendulum may swing the other way, when we are approaching the point where half of all entrants for the exam get the top grade!

I have updated the graphs I have created over the past weeks with the results announced today. This first graph shows the ever increasing pass rate plotted against the number of candidates. We see here that the argument that those who do badly at AS level are not taking the A2 exam is getting more and more tired, as the number of candidates taking A2 reach a new high.

But this next graph, updated for 2006 shows the most alarming trend. More people are getting grade A than any other grade, and the histogram of grades which was more or less normall distributed in 1992 now looks as if it is anything but a normal distribution, as results are so strongly biased to the top grades that anything below grade C is now largely irrelevant.

So finally, my grade comparison chart, updated for 2006. Remember that grade boundaries prior to 1992 are estimated, and so use this graph with caution. But look up the year that you took your ‘A’ levels and you can now “convert” them to 2006 rates.

I wrote some posts about A Levels last year. This was amongst them:

My third post on ‘A’ level standards, and this time the issue is a report carried by the BBC that schools are ‘letting down UK science’.

UK schools are letting down business by producing too few scientists, the Confederation of British Industry says.

Director-general Richard Lambert said bosses had “serious anxieties” …

Even universities had to offer remedial classes to science students to help fill gaps in their knowledge, [the CBI] added.

The CBI said the number of A-level students taking physics had fallen 56% in 20 years. In chemistry the decline was 37%.

Indeed this is all part of the current trend in ‘A’ levels, and perhaps part of the reason that ‘A’ levels seem to be getting so much easier – the harder subjects are being shunned by students.

In the following graph I have plotted the number of candidates for physics GCE ‘A’ level between 1992 and 2001 and then added the pass rates at grades A, A-C and A-E. I have also added (in green) the A-C pass rate for all subjects.

Notice the trend in number of candidates for physics is downwards (as the CBI have noted). The pass rates are increasing ahead of the trend for all subjects. This may indicate that the weaker students are primarily the students avoiding the subject, encouraging the improving trend.

But what does this do for UK science? Why are people shunning physics and other hard sciences? Could it be that GCSE has already failed these students? Before GCSEs replaced the old ‘O’ level system, students would choose from various sciences, typically physics, chemistry and biology. This was replaced with a generalist system where all science was taught together under a single GCSE that would count as two GCSEs.

Notice that we did not decide to amalgamate all language teaching into a “languages” GCSE. Neither did we sweep the rest of the subjects up under an “arts” heading.

So why did we do away with the various sciences at GCSE? Could it be because science is more expensive to teach? thus if we teach less of it, we can save money? Could it have been related to chronic shortages of physics teachers?

Whatever the reasons for the decision, it was wrong and it is failing children who consequently will not even attempt the science ‘A’ levels, and thus the talents of a generation of young potential scientists are being lost to the UK economy and culture.

It is time to return the traditional three sciences to the UK national curriculum.

Next week we are expected to be told that ‘A’ level exam results have improved for the 25th successive year.

Following on from my post last week, I have been collecting more data and extending my analysis of A level results. One of the points I made in my original posting was that since 2002, the new ‘A’ level syllabus and the split between AS and A2 ‘A’ levels has caused a definite jump in the figures. This jump in pass rate is presumed to be caused by the fact that weaker candidates who do badly at AS level will not go on to take the A2. This would be expected to go hand in hand with a drop in overall candidates at A2.

In this graph, it is possible to see this drop in candidates in 2002, but the numbers are picking up quickly and are not sustained. Meanwhile it is not only pass rates that jump in 2002, but also A grades. Take a look at this graph to see the effect.

If the jump in numbers passing were simply due to weaker candidates not taking the exam, then why is there a sudden jump in A grade candidates? It is possible that this jump is related to more people starting A level courses so that the candidates continuing to A2 are stronger as a population, but this seems unlikely.

We can see this same effect in the graph of all grades, which I have updated with data for 2002 and 2003 from the one I produced last week:

I have also updated the graph with estimated data from 1982 to 1991 and actual data from there on. The estimate was based on what data we have for 1982 and a (somewhat unsound) assumption that the years 1983 – 1991 showed linear trends. This graph is really a bit of fun, but if you took ‘A’ levels in the 1980s you can run your finger along from your grade boundary to the current grade boundary to “translate” your results to today’s values! If you took your ‘A’ levels prior to 1982, use the 1982 values, which were broadly similar for previous years.

Don’t read too much into this graph. The ‘A’ levels are different exams to what they were in 1982. Schools are different too, and people have much greater access to information. There may be plenty of reasons why grade inflation is happening, and those who did well or badly in the 1980s may have failed to thrive or exceeded their expectations if they were sitting the exam now.

What is unfortunate, however, is that with so many people passing at grades A-C, the other grades are largely suprfluous, and it is hard to distinguish the best candidates. In this, ‘A’ level is no longer the gold standard it used to be, which is a pity.

It is almost that time of year again where we in the UK go into a period of collective angst about rising pass rates in the A level exams being a sign of the dumbing down of our education system.

Since 1982 the A level pass rate has risen every single year, and whereas only 68.2% of candidates passed in 1982 (grades A to E), the pass rate was 96.2% in 2005, and we are moving ever closer to 100% – if you sit the exam, you pass it.

However, that is not the whole story. I obtained figures from the Qualifications and Curriculum Authority web site for 1992 – 2001, and also 2004 and 2005, and produced the following histogram:

You can see the gradual improvement of grades from 1992 onwards, but there is a sharper improvement for 2004 and 2005, even allowing for my two years of missing data. This is explained by the introduction of the A-S level, because now those who should not be entering the exam are being weeded out before they take A2. It is therefore not surprising that there is a sharp improvement for those years, although it seems likely that the same general improving trend is continuing.

Government and those with an interest in the A level system argue that the year on year improving trend demonstrates rising standards. There may be some truth to this – or at least it may be that technology such as the Internet has provided students with much greater access to information than before, and has thus allowed improved educational attainment. However it is noteworthy that other exams such as the International Baccalaureate do not demonstrate this improving trend. It is also not reasonable to suppose that even with an improving ternd, there would not be the occasional year when pass rates would actually fall, or at least rise imperceptibly.

No, it seems much more likely that what we are seeing is grade inflation.

That does not mean that (a) A levels are easy. They most certainly are not. Nor that (b) the harder A level was more desireable. It may be that a 96.2% pass rate is actually more desirable than an exam that failed a third of the people that took it.

The problem lies with attempting to use the results to make judgements about the academic abilities of students. With 23% of all students taking the exam now getting a grade A, how do you discern the top class students? And how do you compare a student now with a student 25 years ago?

Unfortunately neither the QCA nor any other body has accurate figures prior to 1992. Consequently I have made some extrapolations based on the 1982 figures that we do have, and assuming a rather simplistic steady rise between 1982 and 1992 I have estimated grade boundaries for all of these years. The resulting histogram is here:

Now you can look at this chart and make the rather bold (if not entirely sound) assumption that, say, a grade B in 1985 would be a grade A now. If you took your exams in the 1980s, you can convert them to new currency! (If you got straight As in the 1980s, then this will be particularly accurate!)

Now pass rates are rising year on year, but it turns out that A grades are rising even faster. There is something quite interesting going on here. Look at this third histogram I have produced, this time comparing the spread of grades for three different years:

Notice that in 1992 the spread of grades, whilst slightly skewed, is broadly what one might expect: a normal distribution. The mean grade tallies with the mode and median, so that by each type of average we see that grade D is the mean/mode/median average. This is what one might expect from a mixed ability age group going into these exams.

But notice the trend – increasingly the mean and mode averages are being squashed towards the higher grades, with more and more students achieving As, Bs and Cs and fewer and fewer achieving lower grades.

This is problematic, as the division between D and E becomes increasingly irrelevant, and it becomes harder and harderto recognise which students have really achieved the gold standard in this exam.

But it is only fair that I add some caveats. Not all subjects show these trends, and at least part of the uplift in grades can be attributed to students choosing subjects in which they are more likely to do well. Grade inflation makes it hard to tell good candidates from the best candidates, but it does not necessarily indicate a falling in the standards on the exam paper itself.

So tell me what you think. Is this analysis flawed? Should I add in other graphs (e.g. number of candidates, or the uplift in pass rate?) Have I misrepresented the facts here? Please leave comments and I’ll try to take this analysis further.

From the Daily Telegraph:

The examinations system is embroiled in a fresh row over “dumbing down” following claims that A-levels are easier than they were 20 years ago.

Academics said that pupils capable of getting a C in exams two decades ago can now expect an A grade.

Researchers found that on average A-levels for pupils of the same ability improved by two grades between 1988 and 2006.

In maths – one of the core subjects – scores increased by more than three grades, it is claimed.

The findings, in a report written for the Office for National Statistics, come as thousands of students prepare to receive their examination results week

Not my usual fayre for this blog, but there is an excellent issue of the Journal: “Library Philosophy and Practice” available. Nearly the whole issue speaks about how Google can be coupled with traditional library services in a manner that benefits both (i.e., none of the hit and miss nature of Google, whilst enhancing the work of librarians).

There is also a very enthusiastic article about the benefits of Open Source and Open Access Journals to libraries. Wel worth a look

The BBC writes:

One in 10 web pages scrutinised by search giant Google contained
malicious code that could infect a user’s PC.

That may seem a worryingly high proportion! Fortunately it is also nonsense.

Looking at the actual paper, it seems that Google in fact analyzed several billion pages, and sifted these with a preliminary analysis tool called MapReduce

“MapReduce processed all the crawled web pages for properties indicative of exploits”. As it says in the paper, “MapReduce allows us to prune several billion URLs into a few million”. This process left around 4.5 million pages that were likely candidates. Out of *those*, they found 450,000 pages that they were confident were correctly identified as malicious.

So it is not 1 in 10 pages. It is perhaps 450,000 pages in several billion. It’s more like 1 in 10,000.

The BBC failed to spot this – although perhaps that is not surprising, considering some examples of previous sloppy scientific reporting by the corporation (and most other media corporations of course).

In the news this week, as Tony Blair plans to step down from his role as Prime Minister of the UK, he has indulged in one final round of constitutional change and agreed to move parliament to Aberystwyth. See News Biscuit for the full story.

Should children be present in the communion service? This was a question recently on MInTheGap’s weblog. It is also a question I have come across before regarding practices in churches where infant baptism is practiced. The question is asked, “if baptism is the mark of a Christian, what right do we have to refuse communion to children?”

As I understand it, membership of the Christian Church is through
baptism. This is, I think, a subtlety that is important to protestant congregations that practice infant baptism. Because those who believe in baptising children too young to answer for
themselves, do so on the belief that there is some special benefit of
so being a part of the Church, whilst not actually a believer. c.f. 1
Cor 7:14 (which is talking about marriage partners, but it perhaps
conveys the same idea).

Now if this accepted, then it follows that when one comes to faith,
the promises made for them at baptism are now owned by them. Their
membership of the church is confirmed in some sense by their faith.

On the other hand, those of us who hold to believers baptism say that faith should precede the baptism, and the baptism itself is the symbolic or sacramental enactment of our new birth. But even so, we can still hold to a view that the children present in our church are in a priveleged position, benefiting from teaching and nurture and the love of our community. Churches that practice believer’s baptism usually have some kind of dedication ceremony symbolising the special responsibility of the church to that child.

Now communion is a feast for the believer, and only for them. If
people are baptised into the Church, and properly instructed as to the
purpose and meaning of communion, then the act of taking communion
itself is a declaration of faith. Thus, someone who might say that the
eucharist defines the church is quite right. The true Church, the body
of baptised believers is self defined by the very act of taking communion.

This being so, it seems to me that any age limit applied by us on the
taking of communion simply says that we do not believe anyone under
that age can be a true believer, or sufficiently capable of making a
declaration of faith.

Now we might argue that this is so, but I wonder how this differs from
the argument that is thrown against “believer’s baptism”, which
argues that very young children are either unjustly denied baptism, or
else the believers baptism is virtually infant baptism in any case.

One minister I spoke to recently suggested we don’t *baptise* the children until they are eight, but this still suggests we do not believe the statement of faith of a
seven year old, if they should make one.

It is all something of a knotty issue, but I think the key issues are
flexibility, a good understanding of grace, and the ability to believe
the testimony of young children, without falling into gullibility.

But one thing is clear: if we don’t allow children at the communion table – if we just ship them off to their own age specific activities – then we are making a statement that these people are *not* believers.

The solution, as practiced in many churches, is to allow children to take part in the communion service but suggest that they receive a special prayer rather than the bread and the wine.

Now in churches with believer’s baptism, we have a good date for when they first take communion – at the first opportunity after their baptism. Churches that have infant baptism, or believer’s baptism only after a certain age have a thornier problem. But if children are really to benefit from the worship of a communion service, and if they are to understand how deeply we feel about Christ’s sacrifice, and the glorious hope that we will one day drink from the fruit of the vine with Christ in His Father’s kingdom, then however we deal with this issue, we are wrong to take them out of the service altogether.

You may not have known it, but Moore’s law appears to have reached its limits.

If you don’t know what Moore’s law is, it is a law proposed by Gordon Moore (a co-founder of Intel) that the number of transistors on an integrated circuit would double every two years. Double the number of transistors on a chip and you essentially double the speed by halving distance between transistors. This he predicted in 1965.

And he was right! What a star!!!

So essentially since 1965 we have seen chip speeds (including, of course, processor speeds) doubling every two years (or less). And now we have processors that run … well .. very fast.

There have been some problems on the way. The technique of etching a circuit into silicon is based essentially on a photographic technique, but at some point the transistors got so small that the wavelength of photographic light required was so tiny that it was in the X-ray spectrum. The result – the X-rays passed right through the silicon. But clever people solved these and other problems.

But now there is a new problem. Each transistor gives off a tiny bit of heat, and all those transistors working together are running the chips too hot. Heat dissipation is a major issue, and of late we have not seen the big increases in chip speeds – which is why we are going to parallel multi-core designs.

But wait a minute! Does an increase in the clock rate really increase the speed of the chip? Perhaps we could keep the clock speed static with more intelligent chip designs.

Why? Because of pipelining. One instruction is not executed each clock cycle any more. Instead, processor pipelines are created and in a clock cycle, one part of one instruction and another part of another instruction is executed.

Consider a launderette which opens with just one washing machine, spin tub thing (whatever that bit is called) and one dryer. I go in and wash my clothes in the first wash cycle. In the second wash cycle I use the spinner thing and Fred washes his clothes. In the third was cycle I dry my clothes, Fred spins, and Mary washes her clothes.

This is the way processor pipelines work.

And Apple made an excellent point about processor speeds and pipelines here:

Megahertz Myth

Their point – run the chips slower with shorter pipelines and you could improve performance.

But I guess the question is: if PowerPC architecture is so much better than the Intel arhitecture, why did Apple switch to Intel chips?

Hmmm.