21–30 of 60 posts
> That student who breezed unchallenged through algebra, geometry, and trigonometry, will breeze through calculus, too. I took calculus last year (AB Calc BC, 10th grade), and I can say that my experience was certainly a counterexample. I did OK, but it was definitely a marked difference from "breezing through" algebra.
> "For an avid student with great skill in mathematics, rushing through the standard curriculum is not the best answer. That student who breezed unchallenged through algebra, geometry, and trigonometry, will breeze through calculus, too." That was me. I was great at calculus type things, but Matrix Theory hit me like a ton of bricks. I still have that text book, sitting on my other desk, staring menacingly at me from…
Earlier quoted context omitted.
> That was me. I was great at calculus type things, but Matrix Theory hit me like a ton of bricks. I still have that text book, sitting on my other desk, staring menacingly at me from across the room; Matrix Analysis, Horn and Johnson. Geometry in High School gave me a taste, but would have been nice had we had available another proof based class in the math curriculum; Formal Logic or Discrete Maths at a high school…
I didn't say that Linear Algebra and Matrix Theory were separated. I said that Matrix theory hit me like a ton of bricks. I took Linear Algebra in college prior to that, obviously. I further stated that I think Linear algebra might benefit students if taught earlier, in high school.
My impression of three semesters of calculus in college was that much was a waste of time. It was probably useful for a mechanical/electrical engineer circa 1950. But today no one solves problems that way.
I think more linear algebra and matrix theory would have been better.
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I don’t know about the rest of the world but in Quebec calculus is not taught with any epsilon-delta formalism. You don’t encounter that until mathematical analysis, which is in the curriculum of a very few majors in uni.
This differs throughout the USA. "Best" schools ( "Very Good" schools ( "Decent" schools will teach how to compute derivative/integrals by rote and maybe talk a bit about the physical intuitions in a very hand-wavy way. Calculus is very much a continuation of Algebra or Trig where you learn some rules and how to pattern match and don't ask too many questions about why. The other half of USA high schools? They don't e…
That's a bit misleading. There are many districts where one school serves as a magnet school where anyone interested in taking more advanced classes can go. So yes while it may be true that half of all schools don't offer calculus--far less than half of all students can't readily take calculus.
Earlier quoted context omitted.
I don’t know about the rest of the world but in Quebec calculus is not taught with any epsilon-delta formalism. You don’t encounter that until mathematical analysis, which is in the curriculum of a very few majors in uni.
This differs throughout the USA. "Best" schools ( "Very Good" schools ( "Decent" schools will teach how to compute derivative/integrals by rote and maybe talk a bit about the physical intuitions in a very hand-wavy way. Calculus is very much a continuation of Algebra or Trig where you learn some rules and how to pattern match and don't ask too many questions about why. The other half of USA high schools? They don't e…
As a high school student who took AP CS last year, I agree, but in reality the course isn't even about Java. Code is written by hand on the free response portion and Java syntax is mentioned but not really emphasized (things like missing brackets and semicolons are okay on the FRQs). I finished all the questions in about 25 minutes, with over an hour left to twiddle my thumbs.
Even questions about algorithmic analysis (in APCS's case, just sorting algorithms) are done without proper big-O notations, which is just plain stupid IMO.
For a student that has done CS on their own for years now, APCS feels like the fake, industrialized, watered-down version.
Earlier quoted context omitted.
This differs throughout the USA. "Best" schools ( "Very Good" schools ( "Decent" schools will teach how to compute derivative/integrals by rote and maybe talk a bit about the physical intuitions in a very hand-wavy way. Calculus is very much a continuation of Algebra or Trig where you learn some rules and how to pattern match and don't ask too many questions about why. The other half of USA high schools? They don't e…
>The other half of USA high schools? They don't even offer a Calculus course of any kind [1] That's a bit misleading. There are many districts where one school serves as a magnet school where anyone interested in taking more advanced classes can go. So yes while it may be true that half of all schools don't offer calculus--far less than half of all students can't readily take calculus.
Earlier quoted context omitted.
This differs throughout the USA. "Best" schools ( "Very Good" schools ( "Decent" schools will teach how to compute derivative/integrals by rote and maybe talk a bit about the physical intuitions in a very hand-wavy way. Calculus is very much a continuation of Algebra or Trig where you learn some rules and how to pattern match and don't ask too many questions about why. The other half of USA high schools? They don't e…
> AP CS is the epitome of a "Java School" course. As a high school student who took AP CS last year, I agree, but in reality the course isn't even about Java. Code is written by hand on the free response portion and Java syntax is mentioned but not really emphasized (things like missing brackets and semicolons are okay on the FRQs). I finished all the questions in about 25 minutes, with over an hour left to twiddle m…
All of the AP tests are roughly comparable in my opinion. Just not too many high school kids are as overprepared for the tests in chemistry, physics, statistics, economics, etc.
Ideally, by an expert in calculus, who has done the whole KA course on it (though why an expert would do that, I don't know...)
It is unfortunate that the prevailing educational trends are to get rid of tracks, lanes, and advanced classes, and dumping all the kids into mixed ability classes.
Earlier quoted context omitted.
This differs throughout the USA. "Best" schools ( "Very Good" schools ( "Decent" schools will teach how to compute derivative/integrals by rote and maybe talk a bit about the physical intuitions in a very hand-wavy way. Calculus is very much a continuation of Algebra or Trig where you learn some rules and how to pattern match and don't ask too many questions about why. The other half of USA high schools? They don't e…
> AP CS is the epitome of a "Java School" course. As a high school student who took AP CS last year, I agree, but in reality the course isn't even about Java. Code is written by hand on the free response portion and Java syntax is mentioned but not really emphasized (things like missing brackets and semicolons are okay on the FRQs). I finished all the questions in about 25 minutes, with over an hour left to twiddle m…