American Innumeracy

[merithyn]

While this is a bit late, now, blame your 10th-grade math teacher.  I was taught trigonometry both in physics and in math.  The physics version was very concrete, and directed towards triangle-based problem solving; the math version was more abstract, and directed towards interesting circle properties.  Really, though, calculus is a different idea based solely on limits (as noted by dguller).

This would have been very handy. However, because I dropped out of Trigonometry, I wasn't allowed into Physics. Trig was taught the year before Physics. So, all I learned was theory, not application.

[grumbler]

No I'm pretty sure I've heard of that shit and suffered the horrors of it. I think the lack of multimedia presentations is less of a problem than the fact that many children are lazy fucks who don't really want to be in school.

Nice non-requiter!

You may or may not have been a lazy fuck who didn't want to be in school, but I can assure you that many lazy fucks who didn't want to be in school had no particular problems with maths.  And some very hard-working students who loved school did.

Whether you were lazy, ugly, or whatever doesn't change the fact that differentiated instruction works, so if you "suffered the horrors of it" I suspect that that is because you were a lazy fuck who don't really want to be in school.

[Syt]

Most trigonometry we did in 10th grade was based on real life problems. The classic was, "A ship sights the top of a lighthouse at an upward angle of x degrees. The lighthouse is known to be y meters high. How far is the ship from the lighthouse? Solve with both calculations and drawing."

Similarly, "Lightouses x and y are sighted with angle z between them. They are known to be x meters apart. How far is the ship from each lighhouse?"

[DisturbedPervert]

You are really making the argument that a lot of people are just innately stupid.

A lot of people are just innately stupid.  Some of them are good at math, some of them are not.

[grumbler]

I don't think getting good grades in math courses is all there is to it.  You can certainly improve your math test scores with more work.  Russians and Asians in general are much better at math mainly because math is drilled so much harder there.

What I'm not sure about is the abstract thinking part (which I think is the essence of "getting math").  You can get your good grades in math without ever learning to think abstractly, at least up to a certain point.  However, it's certainly a lot easier to do well in math if you're predisposed to think abstractly. 

Is abstract thinking just a talent given to some and not others, or is it a skill that math develops?  I don't know.

Maths is a language.  Some people think better in non-native languages than other people do.  Maths is not generally taught in high school as a language, though; it is taught as though , say, French were an entirely abstract concept, with no people actually speaking it and no utility in communications, just a bunch of connected ideas.

Part of the problem is that maths teachers, IMO, aren't very good teachers nor mathematicians.  They know they pretty much cannot be fired because they are so hard to replace (teaching is just about the least lucrative thing one could do with a maths degree) and so they tend to be pretty inflexible - and since the more advanced maths teachers are teaching optional courses, it is easier for them to chase away the students who need more help than it is to help them.

[grumbler]

Most trigonometry we did in 10th grade was based on real life problems. The classic was, "A ship sights the top of a lighthouse at an upward angle of x degrees. The lighthouse is known to be y meters high. How far is the ship from the lighthouse? Solve with both calculations and drawing."

Similarly, "Lightouses x and y are sighted with angle z between them. They are known to be x meters apart. How far is the ship from each lighhouse?"

I agree trig can be a lot of fun, if taught that way - especially if presented as a problem that the students cannot answer yet, but which they can answer if they just learn the new rule.  It isn't always done that way, unfortunately.

[ulmont]

Just out of curiosity, do you "get" math? Is it a relatively easy subject for you?

Interestingly, I "got" math up through the second semester (well, quarter at the time) of college math, Calculus II.  Calculus III was ok, and after that I struggled through about a million more quarters of calculus and proofs.

So I've done it both ways.

[Ed Anger]

I was lazy. 2 trains traveling to some location? Who cares? Nobody rides trains in America.

[merithyn]

Maths is a language.  Some people think better in non-native languages than other people do.  Maths is not generally taught in high school as a language, though; it is taught as though , say, French were an entirely abstract concept, with no people actually speaking it and no utility in communications, just a bunch of connected ideas.

Part of the problem is that maths teachers, IMO, aren't very good teachers nor mathematicians.  They know they pretty much cannot be fired because they are so hard to replace (teaching is just about the least lucrative thing one could do with a maths degree) and so they tend to be pretty inflexible - and since the more advanced maths teachers are teaching optional courses, it is easier for them to chase away the students who need more help than it is to help them.

Thank you, grumbler. This makes perfect sense to me.

[Syt]

I agree trig can be a lot of fun, if taught that way - especially if presented as a problem that the students cannot answer yet, but which they can answer if they just learn the new rule.  It isn't always done that way, unfortunately.

I agree. Many math tasks in German schools during my time (between 1982 and 1995) were presented in that way. Of course that also required a different skill from the students: reading comprehension.

Math became theoretical in grades 12 and 13 for us (calculus), and that was when I slipped from being an A student in math to being a B student. They still tried to inject some real life stuff into it occasionally, though, such as calculating the volume of a yoghurt cup that's shaped like a hyperbola.

I admit, though, that I've forgotten much of the more advanced math stuff because I simply don't use it. I still can do force vectors, and - the single most useful everyday life stuff they teach you in math - the rule of three.

[garbon]

so if you "suffered the horrors of it" I suspect that that is because you were a lazy fuck who don't really want to be in school.

True.

[Jacob]

Yeah, I think there's a "getting" and "not getting" part of math understanding.  Math was easy for me for most of my education, until I hit a certain point and I just couldn't get it right.  I mean, I could get it right after lots of hard work but it was qualitatively different from all the prior math where I just sort of glanced at it and figured it out and got it right 95% of the time.

This was independent of any laziness factors, because I was equally lazy before and after hitting that point.

[Razgovory]

Maths is a language.  Some people think better in non-native languages than other people do.  Maths is not generally taught in high school as a language, though; it is taught as though , say, French were an entirely abstract concept, with no people actually speaking it and no utility in communications, just a bunch of connected ideas.

Part of the problem is that maths teachers, IMO, aren't very good teachers nor mathematicians.  They know they pretty much cannot be fired because they are so hard to replace (teaching is just about the least lucrative thing one could do with a maths degree) and so they tend to be pretty inflexible - and since the more advanced maths teachers are teaching optional courses, it is easier for them to chase away the students who need more help than it is to help them.

Thank you, grumbler. This makes perfect sense to me.

Well it is nice to for someone who actually knows something about the subject to chime in.  Personally I believe that some people are in fact good at certain things and not so good at others.  Some people have to work much harder to be able to accomplish the same task as other people.  There are for instance many people who will do very well in math classes but still not be very good at mathematics and never feel comfortable with it.  Others might find it comes easy for them and still do poorly in their studies cause they don't like it.  Remarkably not all people's brains work the same. I invite anyone one who disagrees with me to spend some time in a mad house.  You'll meet plenty of people who's brains don't work like yours.

[Duque de Bragança]

Maths.

Colour.

Fucking Rebels

Le keske vire sa cuti ?

[DisturbedPervert]

Yeah, I think there's a "getting" and "not getting" part of math understanding.  Math was easy for me for most of my education, until I hit a certain point and I just couldn't get it right.  I mean, I could get it right after lots of hard work but it was qualitatively different from all the prior math where I just sort of glanced at it and figured it out and got it right 95% of the time.

This was independent of any laziness factors, because I was equally lazy before and after hitting that point.

Yeah.  Once I reached university it became a skill that required practice in order to solve many of the problems, rather than just something that came.  For some people it still just came easily to them.