### 2.07.2006

## Multivariate calc in American high schools? The mind boggles

It's true. And apparently it's not just in these high schools either (though the article does focus on Montgomery County in MD and Fairfax County in VA, the homes of the last two schools I just linked).

Once you get through epsilon-delta limits and the conceptual meaning of the Fundamental Theorem of Calculus, single-variable calc is pretty mechanical -- you just memorize a bunch of derivatives, employ some pattern-matching skills to decipher integrals, get the hang of a few word problems, and so forth. Multivariate calc isn't conceptually much more difficult. Usually the sequence for good students goes like this: algebra in 8th grade, geometry in 9th, algebra II in 10th, trig/pre-calc in 11th, calc in 12th. I'm sure that in the better school districts in the US, there are enough students who are qualified to take algebra in middle school and can ace calc in 11th grade or earlier that a class beyong single-variable calc should be a standard offering. When I was in 6th grade at this private school, there were a bunch of 6th graders taking algebra, and a good number of 10th and 11th-graders taking calc, though they didn't offer anything beyond calc. I think schools could get kids more interested and better prepared for the algebra-through-calculus sequence if they stopped giving it such an aura of mystique.

Of course, the sad fact is that this advanced math track is really quite standard in other countries (scroll down to page 7 of the article). (Actually, the main reason I like this article is because half of the Math 55 class I TA'd last year was interviewed in it.)

And I'll bet none of these kids in the WaPo article reads at a 78th grade level.

Once you get through epsilon-delta limits and the conceptual meaning of the Fundamental Theorem of Calculus, single-variable calc is pretty mechanical -- you just memorize a bunch of derivatives, employ some pattern-matching skills to decipher integrals, get the hang of a few word problems, and so forth. Multivariate calc isn't conceptually much more difficult. Usually the sequence for good students goes like this: algebra in 8th grade, geometry in 9th, algebra II in 10th, trig/pre-calc in 11th, calc in 12th. I'm sure that in the better school districts in the US, there are enough students who are qualified to take algebra in middle school and can ace calc in 11th grade or earlier that a class beyong single-variable calc should be a standard offering. When I was in 6th grade at this private school, there were a bunch of 6th graders taking algebra, and a good number of 10th and 11th-graders taking calc, though they didn't offer anything beyond calc. I think schools could get kids more interested and better prepared for the algebra-through-calculus sequence if they stopped giving it such an aura of mystique.

Of course, the sad fact is that this advanced math track is really quite standard in other countries (scroll down to page 7 of the article). (Actually, the main reason I like this article is because half of the Math 55 class I TA'd last year was interviewed in it.)

And I'll bet none of these kids in the WaPo article reads at a 78th grade level.

### Comments:

It's a good trend to see. I remember going to a suburban middle school and being told by the school system that I couldn't take algebra a year early because then I would run out of math courses. At the start of my freshman year in high school, I was told by the school system that I couldn't take both Algebra II and geometry at the same time because it would be too hard. Luckly, I transfered to city schools, where they let motivated students do their own thing.

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