From my experience, calculus is not required for business majors at some schools. I have a degree in accounting, and the year before I attended college, our "Calculus for Business Majors" requirement was replaced with Intermediate Algebra. While nothing in my coursework required calculus, I think that the calculus I took in high school better prepared me to understand economic relationships.

I'm currently working at another college which requires analytic geometry & pre-calc (not calculus) for its business majors.

I advise mechanical engineering students at a college. We've found that 60% of our incoming freshman are unprepared for calculus (which we, of course, require). It boggles my mind that this figure doesn't include all incoming freshmen--just those who think they're suited to become engineers!

-- KtmGuest - 22 Aug 2005

Yes.

46% of Singapore kids were in the top 10% of all test takers.

That we know.

Oh!

Good grief.

I used the wrong figure. I was using 505 as their average, not 605.

Unbelievable.

THEY HAVE AN AVERAGE SCORE OF 605.

I'm completely blown away.

Obviously, I couldn't keep that in my brain because it's so outrageously high.

Absolutely, you're right. The bell curve centers on 605 which is just 20 points shy of the HOTSHOT IN MATH cut-off.

This country, which was dirt poor about 5 seconds ago, has put probably at least 40% of its students in position to major in math-related subjects in college.

-- CatherineJohnson - 27 Jul 2005

I think he said that 46% of all Singapore kids definitely are in the top 10% of all kids, right?

Let me check.

-- CatherineJohnson - 27 Jul 2005

OK, here's my assumption, since it's probably easier for you to follow my reasoning ...

I'm assuming a normal distribution for the Singapore kids, with the top of the curve centered on the 505, which is their median score.

That means 50% of Singapore kid, or 49%, will be above 505....but since 46% of Singapore kids were in the top 10% of all test takers, that tells me that not all of that group could have scored above 605. A bunch of them would have had to score between 505 and 605, right?

Or is that wrong?

I'm going to figure out your comment now.

-- CatherineJohnson - 27 Jul 2005

I'm too hot to read this.

OK, let me think.

I'm assuming a normal distribution, which I vaguely understand.

-- CatherineJohnson - 27 Jul 2005

I think you're confusing two different populations here -- one is the population of all kids who took the test, and the other is the population of kids in Singapore who took the test.

The information you're missing is the standard deviation for all these populations -- the 'spread' of the bell curve. You can't figure it out without that bit of info.

Assuming that the distribution for the Singaporeans is a bell curve centered at 605, with a spread-out standard deviation (i.e. a 'fat' rather than 'narrow' bell curve, it is possible that 46% of the Singapore population earned a score above 625.

And it's likely (even without knowing the standard deviations!) that 46% of the Singapore kids were in the top 10% of the population of all kids who took the test, simply because the Singapore average was so high.

-- CarolynJohnston - 27 Jul 2005

top students in England, U.S., & Singapore

The British report, Where will the next generation of UK mathematicians come from?, (pdf file) includes this passage about the TIMSS study (Trends in International Mathematics and Science Study):

[a score of] 625 was fixed as the “Advanced benchmark”. In the “Comparison group” of countries [essentially, all countries with advanced economies], 13% of 14 year olds scored at this higher level – which might be taken as a rough indication of those who are well-positioned to subsequently study mathematics and other highly numerate subjects with some prospect of success post-16, or at university.

Naturally some countries in the “Comparison group” had a larger percentage performing at or above this level, while some fared worse. A mere 7% of the USA sample scored at or above this ”Advanced benchmark” level. And the International average was just 6%. But the results for England should have struck Ministers and officials as far more disturbing: the percentage of English 14 year olds scoring above the “Advanced benchmark” was just 5%!