Declining Standards

[Severian]

The guy teaching dynamics to our first year undergrads can into my office for a rant today. He was giving his first lecture to the new intake and was going over all the stuff they should know. He mentioned the velocity was obtained by differentiating the position vector with respect to time, and someone put up their hand to ask 'what is differentiation?'

 

He was rather stunned, so conducted a straw poll asking who doesn't know what differentiation is. Out of a class of about 170, 19 people stuck up their hand. On later investigation it was claimed that differention is no longer in the A-level sylibus (I am in the UK) unless you take further maths. I was a bit shocked by this.

 

Since we have a few people here who took A levels this year, could you tell me if you met differention, and where. In maths, further maths or physics?

 

(I am slightly surprised, because the government keeps telling us that improving A-level results are due to better teaching - not taking things out of the course.)

[swansont]

In my experience in the US, calculus is either a prerequisite or corequisite for calculus-based physics, and this is generally explicitly stated in the course listings. So, no excuses for not knowing it.

[insane_alien]

its still standard in highers(scottish equivalent of A-levels) according to the few guys i know have that done that last year

[ecoli]

It's hardly surprizing if it's true. In the US, better test scores don't mean smarter kids, it means lower standards.

[Genecks]

It's hardly surprizing if it's true. In the US, better test scores don't mean smarter kids, it means lower standards.

 

I think it means that kids are learning the system, becoming more intelligent by doing so, and making the standards raise because of their behavior. Then again, it depends on many factors. I don't think a hasty generalization will do.

 

Anyway, if educators have a problem with students being unlearned, maybe educators should teach the students more than work them. There are always going to be people who don't know what someone else does. Educators need to compensate for these differences. I'm glad that the educator was willing to find out the information right away. Now that information is known, the next step would be fixing the problem.

 

We can't rely on institutions to make sure everyone is at the same level.

[Severian]

Anyway, if educators have a problem with students being unlearned, maybe educators should teach the students more than work them. There are always going to be people who don't know what someone else does. Educators need to compensate for these differences. I'm glad that the educator was willing to find out the information right away. Now that information is known, the next step would be fixing the problem.

 

We can't rely on institutions to make sure everyone is at the same level.

 

There have to be limits. Do you think someone should be accepted to university to study English Literature if they can't read or write?

[rajama]

In the UK during the '70s 'O' level math - usually taken at age 16 - included differentiation : the limit / continuous curves, finding min / max / turning point of a curve etc., all the basic but useful stuff for applied math and physics... but not integration as I remember.

[JohnB]

He mentioned the velocity was obtained by differentiating the position vector with respect to time, and someone put up their hand to ask 'what is differentiation?'

Just count your lucky stars they can add and subtract. We get a lot of young guys in my industry and numeracy and literacy are not among their strong points. (And yes there are quite a few Uni students in there.)

 

I came across this recently and thought it rather accurate.

 

1960's Arithmetic test:

"A logger cuts and sells a truck load of lumber for $100. His cost of production is four-fiths of that amount.

What is his profit?"

 

70's New Math test:

"A logger exchanges a set (L) of lumber for a set (M) of money. The cardinality of set M is 100. The set C of production costs contains 20 fewer points.

What is the cardinality of set P of profits?"

 

80's education reform version:

"A logger cuts and sells a truckload of lumber for $100. His cost is $80, and his profit is $20.

Find and circle the number 20."

 

90's version:

"An unenlightened logger cuts down a beautiful stand of 100 old growth trees in order to make a $20 profit.

Write an essay explaining how you feel about this as a way of making money.

Topic for discussion: How did the forest birds and squirrels feel?"

 

I can't speak for other places but here we don't have an "Education Department". We have a "Department of Education, Training and the Arts" and therein lies our problem.

 

From the Front page of their website.

 

Welcome to the new Department of Education, Training and the Arts. Our purpose is to engage Queenslanders in life long education and training and to build a strong arts and cultural sector which enriches the lives of Queenslanders.

 

Students

Student life is a never-to-be-repeated experience. Daily challenges redefine your understanding of the world and your place in it. Enjoy the ride with valuable resources, support groups and activities.

 

Didn't reading that make you feel sooooo good?

[abskebabs]

Since we have a few people here who took A levels this year, could you tell me if you met differention, and where. In maths, further maths or physics?

 

(I am slightly surprised, because the government keeps telling us that improving A-level results are due to better teaching - not taking things out of the course.)

Hi Severian, I suppose I am a bt late to reply to your post, but I am pretty surprised you have 1st year physics students(I assume they are) who haven't heard of differentiation. I know 1st years can be pretty dopey(I am one myself:embarass: ), but these ppl shud have studied differentiation and integration as it is still on the A level and AS level syllabus, and the core math modules are compulsory.

[Severian]

Thanks for the info abskebabs. I can use any ammo I can get.

[the tree]

Since we have a few people here who took A levels this year, could you tell me if you met differention, and where. In maths, further maths or physics?

Yes in maths, yes in further maths and I don't do physics but I would assume so.

I would imagine that under some board it could get called a different name, "find the rate of change" or whatever, but I'm sure it must be on the syllabus for all boards. It's one of the first things to get taught that isn't just a continuation of GCSE maths.

[husmusen]

Well speaking of the Australian school system, we did it in the last two years before university in Victoria.

 

Husmusen

[Klaynos]

I'm pretty sure when I did a-level maths a couple of years ago (now in my third year of uni) that differntiation was at the end of my first year, and a bit more complex stuff was at the end of my second year.

 

I know for certain I could do trig functions and knew the chain rule etc...

 

But since then they've put in a no calculator paper so claimed that made it alot harder so had to make it easier for alot of sylabuses :@

[ed84c]

Basic (i.e. Polynomial) differentiation is mid way through the first year.

 

Chain, Quotient, Product rules are all at the begging of the second year.

[Genecks]

Ah, nevermind.

[ajb]

Last week I had a student ask about how to differentiate something like [math]\frac{x}{x^{2} + y^{2}}[/math] wrt [math]x[/math]. He was sure a log function should be there somewhere!

 

This guy was a level 2 mathematics student!

[Klaynos]

This saddens me greatly

 

Shocks me how many of my fellow second year physicists last year didn't know the trick with double integration by parts of substituting in I = original integra, and then solving for I

[CPL.Luke]

hmm klaynos what is this trick you speak of?

 

I tried googling for it and couldn't find anything. And I don't think its in my textbook

 

 

You guys seem to start everything alot earlier over in the UK, in the US we don't usually start calculus until our senior year of highschool (18 years old) if we even do it then.

 

Out of curiosity when do you start your mathematics studies? and when do you do all of the trigonometry?

 

I know that the in the US the standards have been falling through the floor ever since the "no child left behind" act was passed. It made it so that every student who goes through a school system must do so well on a standardized test, or the school could lose its accredidation (and this does include people with mental handicaps).

 

This leads to school systems catering to the bottom fourth of their student body, and the States lowering the standards in order to reduce the strain on underfunded school systems.

[Klaynos]

Well you integrate by parts once to get

 

Integral = somefunction - another integral

 

You then use by parts on the second integral to get

 

integral = somefunction +someotherfunction + orignal intetral *something

 

you then do (1 - something) *integral = somefunction + someotherfunction

 

and then divide through by 1-something

[CPL.Luke]

oh you meean a recursive integral. (I think thats what they called it)

 

I thought you were talking about double integrals for some reason. Second year physics majors didn't know how to do that?

[Klaynos]

oh you meean a recursive integral. (I think thats what they called it)

 

I thought you were talking about double integrals for some reason. Second year physics majors didn't know how to do that?

 

The term major is not entirely true as it's all we do. But yes they didn't know how to do that.

[GutZ]

I had Basic diff. calculus section for my math credit in my 3 year technology program, even before than I knew about it though.

[5614]

ajb, the LaTeX isn't working, if you can get it to work I'd be interested to see what it was.

 

Severian: I know this was from two months ago (to the day, as it happens) but I can assure you differentiation is in the syllabus. It is in C1, or Core 1, the first thing you get taught in year 12. Found here:

http://en.wikibooks.org/wiki/A-level_Mathematics/C1/Differentiation

You then get more in year 13, found here:

http://en.wikibooks.org/wiki/A-level_Mathematics/C3/Differentiation

and a little bit more in year 13:

http://en.wikibooks.org/wiki/A-level_Mathematics/C4/Advanced_Differentiation

 

As well as plenty of integration to top it all off. And that's all for just maths, if you're doing further you get loads more.

 

Klay/CPL: I know what you mean. It's not that hard, you just notice your original integral appearing in your answer...

 

Out of curiosity when do you start your mathematics studies? and when do you do all of the trigonometry?

Erm, what kind of trig? We start learning what trig functions are, the real basics, at the age of 15 or 16. At that age you're expect to use it to calculate lengths and angles.

 

Then that's developed all the way through your education. I suppose there's all sorts of differentiation, equalities, integration and introduction to new functions (arcsin, arccos, arctan, sec, cosec, cot) at the age of 17 and 18. Although if you take further maths you go further (no pun!) still with advancing all previously mentioned areas and more trig functions (cosh etc.).

[CPL.Luke]

hmm i think I see the difference, in the US you learn the basic trig functions and all when you first enter highschool (age 15) in a course called geometry which covers lengths and angles and such.

 

then the following years involve alot of extra algebra and trigonometry. So we learn all of the trig identities before going into calculus.

 

I was starting to think that in europe you guys were two years ahead of us.

[ajb]

ajb, the LaTeX isn't working, if you can get it to work I'd be interested to see what it was.

 

 

The function was something like [math]\frac{x}{x^{2} + y^{2}} [/math]