Calculus in Lower Education

Since Calculus is a sort of "big picture" view of what everything in Highschool Math actually means and looks like, should there be some kind of Pre-PreCalculus or Calculus Concepts that can be introdeuced around first year highschool?  So people could perhaps actually understand what it is they're learning?

I don't think so.  First, a lot of people in high school still need to grasp and get a firm understanding of the basic concepts before being shown the "big picture."  The people who already have a solid understanding are probably taking calculus already, through some accelerated program.

I think it ought to be offered to those who want it, but making it mandatory doesn't work well because at the high school level not everyone is ready for it.

If all students entered high school ready for calculus, it would be appropriate to make it mandatory for everyone.  I believe that in Japan, they do this.  No one gets out of the 8th grade without a solid grasp of algebra and trigonometry, no one gets out of high school without calculus.  It seems to work for them, but the rest of the world does a lot of other things we don't do in America.  In America we have high-school graduates who can't read their diplomas and can't make change without a calculator.

For instance, in the US, we only have classes 9 months out of the year.  The rest of the world doesn't do this "summer vacation" thing and never did.  It's a holdover from frontier days when the children would be needed at home to work on the farm all summer.

Also, in the US, we have had since the early 1970s this dubious concept of "mainstreaming" and "the least restrictive environment" for the mentally retarded and the severely emotionally disturbed.  Which means basically that schools by law are forced to put drooling Down's Syndrome cases and shrieking, disruptive, severely mentally ill children into normal classes, then slow everyone else's progress down to allow the 'tards to pass.  This is a disservice to every child in those classes, including the 'tards themselves (who are never going to be able to benefit from education anyway).  They really need to go back to the pre-1973 system of segregating the 'tards and the other "special" children in the boiler room and giving them some coloring books (just don't let them eat the crayons) and letting the other 99% of students get on with the business of learning.

We need to start taking discipline and safety seriously in the schools, too, and start permanently expelling dangerous or disruptive children.  If they won't behave and let the others learn, let the lifetimes of flipping burgers to which they've condemned themselves serve as examples, pour encourager les autres.  At the very least, segregate them and put them in reform schools, and let the other 99% of children learn.

The American educational establishment is in love with every harebrained fad that one of their members can imagine.  Just now it's toys and gadgets.  American schoolchildren need fewer laptop computers and calculators and more strict discipline and the three R's.

We need to raise standards for teachers, not just students.  Teaching children is one of the most important jobs in any society, yet most American schoolteachers could make more money waiting tables.  This is why the field of education doesn't attract the best candidates.  Any present or former college student may have noticed that "early childhood education" majors are invariably the very bottom of the intellectual barrel--they just don't have the mental horsepower for science, engineering, business, or law, so they go for the very easiest major with the very easiest classes because they "love children" (i.e., math is too hard).  We need to increase wages for teachers to attract people other than these barrel scrapings to this vital profession.

The teachers' unions are not unaware of this, and want to protect their monopoly on education, without which most all their members would be flipping burgers or scrubbing toilets for a living.  Changing state laws to allow otherwise qualified people who lack ECE degrees and educational certification to teach classes would really light a fire under the teachers' unions.  I'd like to see high school science courses taught by real scientists, courses in foreign languages taught by real linguists, math courses taught by real engineers.  There are a lot of people in these fields who genuinely want to teach part-time because they know how vital education is, and it's brutally obvious that a Ph.D chemical engineer with thirty years experience in industry can do a better job teaching high school chemistry than some education major who just reads one chapter ahead of the students and doesn't understand all the big words.

Go to a system of year-round schools, make classes 8 hours a day instead of 6 or 7, and you'll be able to raise standards all the way around.

So, to recap:

strict standards for achievement at all levels, no more "social promotion"
year-round schools with longer school days
get the 'tards out of the normal classes and let the normal kids learn
strict discipline to maintain classroom order, up to and including permanent expulsion of problem cases
fewer laptop computers, thicker textbooks with fewer pictures and bigger words
more money for teachers to attract someone to the field other than the absolute bottom of the intellectual barrel
break the teachers' union monopoly and allow qualified and experienced laymen to teach in their fields

Well, yes.  Has anyone here ever read the old McGuffey Reader?  Everything there is to know about teaching children to read and write, as well as mathematics, has been known for a hundred and fifty years, or more.

We already know what works.  We knew what works before anyone reading this was born.  Yet for some reason, we don't do what works.  In American education, we do what we know doesn't work, because the NEA says so, and no one dares to defy the NEA.  So in American education today, we do what we know doesn't work, and everyone from the NEA on down agrees that American schools are utterly failing on every level.  So, are we going to give up the laptop computers and the self-esteem classes and go back to the paddle and the three R's?  Hell no.  The NEA likes it the way it is, except that they want more money and bennies.  They want to keep their little gravy train rolling, and if they send America back to the Dark Ages in the process, they couldn't give less of a shit if they tried.

In Finland we have a 2,5 month summer break, a teacher's union, pretty shitty wages at least for teachers teaching pre-secondary school (16 years and younger), no private schools... most of the time tards have their own special classes, however.

Our kids usually rank pretty high. From what I've understood it's because our curriculum is more demanding from early age on.

>>6

there are no black and mexican people in finland

The rest of the world doesn't do this "summer vacation" thing

Yes we do.

Japan is not "the rest of the world".  Not all Canadian high school students graduate with an extensive knowledge of calculus.  In the US, the opportunities are there for those that want to learn.  Most US high schools have AP programs; AP calculus and AP chemistry can get you out of the analogous freshman university courses given a good AP test score (although many US universities do not allow this).  If the AP classes are not there, just about any local community college will have at the very least first and second year university-level courses in those areas. 

And if that's not advanced enough for you, check out the results of the Intel science talent search (http://www.sciserv.org/sts/64sts/winners.asp), and keep in mind that these are *high school students*.

Sorry if this comes off as abrasive, but it sometimes irks me to hear people talk about all US students being idiots.  The truth is, the "problem" isn't 100% education system.  It's also culture.  If students *want* to learn, they have to go out there and do it.

Finland has gypsies and somalis.

Gypsies still scare me. Never met a somali. There are a couple of thai(or vietnamese) girls in my HS, and there's also a thai massage parlour a few hundred meters from aforementioned school - right on the pizza street - name given by me as there are so many pizzerias there. I shall not part with the name of the city, though - finns might guess it. Finland's cheapest pizzas. Well, känkky anyway.

>...it is brutally obvious that a Ph.D chemical engineer with thirty years experience in industry can do a better job...

Brutally obvious until you actually try it. What many people forget is that teaching, at any level, requires a lot more than just knowledge of the subject. If you can't effectively control and communicate with a class, then you might as well go back to your six-figure engineering job because you're a failure as a teacher.

<anecdote>
When I was still at school, our chemistry teacher transferred to another school half way through the year. His replacement was a man who had been a chemical engineer for twenty-five years, and then decided to go into teaching as a change of pace. After two weeks, we ran out of patience with his utter fucking ineptitude in the face of looming exams and put a petition round the class to get us another teacher. Everyone signed, and he was gone a week later to be replaced by a girl fresh out of university who could actually TEACH. We did great on the exams, and she stayed with us for the next two years, and everything was sweet. And she was SO FUCKING HOT oh my god seriously you should have seen her.
</anecdote>

Clearly knowledge of the subject you are teaching, in excess of the syllabus, is essential, but it's meaningless unless you are talented or trained in communicating with the kids.

>>11
you are correct sir

bump

>>9
did you notice that half the kids in that link have at least one parent with the title "Dr."?

gotta love these 3 year old threads, can it really be that nothing has happened in science in 3 whole years? thats all the years i've been in college, wtf

I'd be more interested in introducing discrete structures early on.  Unfortunately without the use of calculus and high-level algebra it's very difficult to do anything in DS though.  It might be helpful if you could get people to listen, but most don't even listen in algebra.

A significant problem in American education is a general contempt for math, and excess focus on breadth, rather than depth (especially in math/sci).

Case in point: in 7th grade, there was algebra (advanced students), pre algebra (less advanced students), "7th grade math" (regular students [retard students, if you think about it]).  Where was my "easy" English, "easy" history...?  All these other subjects have a minimum standard, but we're allowed supposed to be dumbasses in math.

With regards to the breadth/depth issue, consider China.  They don't offer calculus until college, but the high school mathematics curriculum is far more demanding, and requires more thought than in America.  In fact, the math portions of the college entrance exams are at the AMC/AIME level.  Any idiot can memorize the derivative of sin(x), but > 2/3 of my high school calculus (and probably my recent college analysis)classes would probably fail these entrance exams horribly.
[As a side note, a few years ago, the test makers decided to add an IMO level question to the college entrance exam for the lulz.  Needless to say, most people bombed it.]

America does indeed offer tons of options, but when's the last time you heard of physics/bio/computational/chem Olympiad in high school?  The USAMTS?  If the schools don't tell the students about the options available, then it doesn't really matter.  The schools are afraid that if we take something beyond our level, we'll phail, and they'll look bad.  They would much rather we go through the grind, and do well.

It is probably worth mentioning that despite the low reputation of America's high school education, its undergraduate and graduate education is renown world wide.

>(and probably my recent college analysis classes)
I thought Berkeley was a good university?

>>18
We should ship boatloads of 6 year olds to Finland and China, and pay for their return trip only when they can pass an university entrance exam. You just can't go wrong with specialization!

>>19
It's good, but not that good.  Most of the students are still educated in America, and they've never been trained to do complicated problems.  To be honest, I'd probably fail too.

>>20
An interesting idea, but I think a lot of parents are going to BAWWW when their kid never comes back.

>>18
its undergraduate and graduate education is renown world wide.
It's dropping quickly.
American universities got really good immediately after WWII when all the intellectuals fled Nazi Germany and the countries they invaded, and then managed to sustain itself on academics coming over to study under those later on (and attract intellectuals fleeing the communist countries), but nowadays more and more are moving to Canada or Europe, in no small part due to ever-increasing budget cuts for universities and scientific research.

Id say the English curriculum could be more challenging early on, but our limey, communist ways means under no circumstance will a child be told they suck ass, despite them sucking whole acres of it

I went from picking my arse in year 9 to having to learn algebra ( pretty much quadratics and up, including simultaneous equations), trigonometry and a whole load of other stuff in the two year GCSE course becuase top-set mathematics before that was limited to colouring in things under the pretense of 'introducing loci'.

The A-level course is the ifrst time calculus is mentioned, and it pretty much becomes a course in calculus

Its not like kids are going to break down if you introduce things earlier, and use the right terminology instead of hand-waving around the issue

>>22
wrong way round. the flow of academics is still from Europe to America because of the greater wealth of American universities. That said, ugrad education is better in the UK than US, especially in technical subjects.

>>23mathematics before that was limited to colouring in things under the pretense of 'introducing loci'.

haha yes, and rolling dice to introduce probability. everything useful I learned in year 7 - 9 could have been compressed into one year. top-set kids could be doing a-level work by the start of year 10.

>>24
It's kinda funny, but though I'd always been top-set at school (except for one erroneous term) I probably would have flunked out and lost interest if I was introduced to A-level material at Year 10. I didn't really show that much promise until year 11, and only really excelled towards the end of Sixth Form. Now I'm doing better at Cambridge than my old teacher, a PhD. You have to allow for slow burners.

Err, A level Maths may be a joke but it most certainly not a calculus course.

The only decent thing we have to offer in terms of a 'challenge' at a level for Maths is STEP and AEA.

WARGLGARGL.