I went to a very good technical high school in the late 70's, and I don't remember doing any calculus, surds or any of the other stuff mentioned in this thread in my 'O' levels, physics or maths. Just basic manipulation of log tables in calculations. It certainly wasn't part of the exams, (I got a B in maths, and an A in Physics, so I would have noticed.
)
)
But they may have been marked harder. My JMB maths, further maths and physics A levels, taken around 1970, can't have been very hard to pass, and general studies must have been very easy because there was no course.
I'm always impressed by how much people in places like this know about the maths of feedback systems. My grasp of transforms is really shaky, and partial fractions drive me up the wall. If standards have been falling for years, how come so many people know so much?
Looking back, it's amazing that the expansion of higher education around the time of the Wilson government actually worked. How did so many more students pass their A levels so suddenly?
I don't see what politically-acceptable arguments drove the recent expansion. Unlike in my time, there isn't a credible vision of a future in which universal HE will be useful. The idea that a few countries will be fully occupied with clever stuff, whilst the others do all the menial tasks, should have perished ages ago. Assuming capitalism stumbles along indefinitely, we need to recreate our own downtrodden class of manual workers.
China may radically change the world. What's education like there?
The smartest people still know a lot in every generation. However, their education may still have taught them less and less while not destroying their ability to learn more. I was surprised to hear a communications professor tell a combined MSc/MEng 4th year class (in response to a question) that radio receiver spurious responses were too complicated for the course - stuff which I began to learn as a teenager 30 years earlier. People capable of understanding stuff will still understand it if they find a need to do so, but they may no longer be taught it at university.PlasticIsGood said:
For example, servo systems was not part of my physics course but the required complex number stuff was. When I had to learn it in industry I managed OK, then realised that it also enabled me to understand negative feedback in audio.
They didn't. What happened was that university entrance criteria were relaxed, especially at the newer universities. The gradual A-level grade inflation then meant that over the next few decades the entrance criteria were 'increased' again. In the early 1970s you could get into Imperial College with 2 Bs; now you would probably need 3 As - which may actually be a reduction in requirements.
Suggestions would stray too far into politics for DIYaudio so I won't go there.
It's the algebra of surds that's important. Use whatever symbol you like. It's a surd for as long as you don't convert it into a number.
You covered the ground at school, I'm sure. At the most obvious level, you treat them algebraically so you can combine and simplify before evaluation, so avoiding the accumulation of error. You learned the rules.
Revision:Surds - The Student Room
I guess their peculiar rules of manipulation allow them to be used in transforms, rather like complex numbers? I vaguely remember some trick related to a proof of the binomial theorem.
What? Ours has been an epoch of immense technical and scientific achievement. If the quality of general education was not important for this rate and breadth of advancement, then surely it quite simply doesn't matter at all. In that case, we may as well forget about it and do something else instead. If it is important, then it did a good job.
I don't feel we are close to agreement on grade inflation. At the very least, your highlighting of the issue seems reductionist: you are projecting a complex system onto too few axes
eek: that's my first ever pun).One key element of the expansion in the 60s and 70s was the grants system, which made university free. Kids from poor families had something to aim for. Funding for schools, welfare benefits, women's emancipation, and advances in the technology of education were a few of many other factors.
I'm still hoping someone will chip in from somewhere that's still making progress. What's education like in Brazil, Ghana, China, ROK?
Quaternions or Gibb's abortion, the cross product, "axial vectors" lets you use one more axis - but you really want Clifford Algebras with exterior product, multivectors, Spinors...
(complex numbers are the "spinors" of the 2-d plane)
a really good education system could sieze on ideas like Hestenes' "Geometric Algebra", introduce it at the same time as complex numbers, vectors
Last edited:
More precisely it is two possible numbers in the case of a square root ,
hence the surd cant be always removed since it would forcibly cancel
a solution , thus leading through intermediary operations to a false result.
Anectdoticaly , any entire number can be written as a never ending
decimal number in such a way :
1 = 0.99999999......
thus , 2 = 1.99999999......
And so on.....
Strictly mathematicaly , they are equal , mind you....
1 = 0.999999999.................
Let s divide both side by 3 :
1/3 = 0.3333333333.....................
Let s take again 1 = 0.999999999.................
Try to ad the necessary quantity for the expression on the right
to allegedly reach 1 , it will be :
0.000000000000000000000 hey but there s an infinite serie of 0 ,
when thinking about it.....
OK, here are a few axes:PlasticIsGood said:
1. Difficult stuff like calculus and logarithms were removed from the normal 16-age exams. As a result bright kids in good schools now take the GCSE at age 15, and the FSAMQ at age 16 (as that more closely aligns with the old O-level).
2. Entrance to elite universities now requires higher exam grades, yet staff report that students actually know less than they used to. (and there is evidence from long-term studies to back this up).
3. A Masters degree in 2002 contains material which was taught as 2nd-year undergraduate in 1974.
4. The proportion of Firsts awarded has steadily increased, in parallel with a rising complaint from industry and commerce that recent graduates don't seem to know very much.
5. In the 1970s it was expected that about 20-25% of an age cohort would get a set of reasonable GCE O-level passes. It is now expected that about 40% of an age cohort will get an honours degree. I have met university students who are too dim to find the right page in a handout; they have no chance of understanding what it says.
6. Older university staff can recall the stuff they used to teach which has now been removed from the courses as modern students can't cope with it. Even on my own Master's there were times when we were told "You used to have to know the derivation of this formula; now you just have to know how to use it".
The evidence for grade inflation is clear. Much of it has to be anecdotal, as there are obvious reasons why many people would not wish to seek for hard evidence. I realise that many find this unpalatable, even unacceptable, but it is true.
How could we make so much technical progress with declining education? A good question. The best people are still as bright as they ever were. However, how much more progress might we have made with maintained educational standards? Look at where the world economy is shifting, and you will find it is a lagging indicator of true education quality.
Back in the day EE students only had to learn analog, and maybe some primitive digital, so there was plenty of time to make people learn derivations.
But nowadays they have to learn analog, some fairly advanced digital and computing concepts, and how to program in multiple languages. You simply have to cut out the really non-essential stuff to fit an electronics degree into 3 years, these days.
I find it ironic that I would now be unable to secure admission to the University from which I graduated with honors... Every time they come calling, asking for donations, I point this out and tell them that I'll be happy to contribute when they revert to their old policy (relatively open admissions, very strict passing requirements, high attrition rates).
They still explain the derivations during the university course, but students are not expected to memorise them and be examined on them. As long as I know roughly where the derivation comes from, I can always look it up.
One of my university lecturers said (with some humour) there are two differences between a physicist and an EE:
1: A physicist memorises his formulae, an EE only learns were to look them up.
2: EE's get paid more.
Last edited:
This is why we are starting a Sudbury school.
Jefferson Sudbury School | where children direct their own learning
Jefferson Sudbury School | where children direct their own learning
Yes, that is the best way to run a university. Funding regimes in the UK put a stop to that, as universities faced a huge financial penalty for every student who 'failed to progress'. Here we have 'completion' targets i.e. you are not allowed to throw out more than a certain (small) fraction; I would insist on a 'completion band' i.e. you are required to throw out a certain fraction in order to maintain standards and call yourself a university!SY said:
When I went back to university, after a long gap, I found myself appointed to the department's student-staff liaison committee. I innocently asked "Why are there so many dim students in the 2nd-year lab classes?" I was told that they were not allowed to throw them out at the end of the first year; the university insisted that the department keep them, because of pressure in turn from the government.
- Status
- This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.