Gifted Issues Discussion homepage Forums General Discussion Is Algebra Necessary?

I agree wholeheartedly with Mathwonk. Is calculus beyond some otherwise well-educated people? Probably-- it includes certain abstract concepts that I think some people probably aren't hard-wired to grasp. But I don't think that algebra is in that category.




?? How does that follow from anything that anyone has thus far stated? If you look at my post, my statement was that any scientist needs a working understanding, and that any scientifically literate person needs to know-- well, basically they need to understand what it is that calculus does.

That's the difference between understanding how an internal combustion engine is put together versus the fact that it converts chemical fuel into useable mechanical work. A mechanic needs to know the former, and anyone that uses a car probably needs no more than the latter.

And yes, maybe we SHOULD stop teaching scientific "facts" without the context of the underlying scientific process, quite honestly. That's not what science is fundamentally, and it leads to no end of abysmal reporting and lawmaking that there is such confusion on this point.

A 95% confidence interval clearly means that the science has received an "A".

Maybe if scientists would study more and work harder, they could finally get to 100% and get that A+.

Fortunately, most people are just fine with getting an A and don't worry too much that it wasn't an A+. It's a good thing too, or few peer-reviewed studies would even be published.

Except for Tiger Moms.

They want the confidence interval to be 100% every single time.

I may be misunderstanding your position. Perhaps it would help if you explain what you mean by "scientifically literate."


So... you're saying we SHOULD stop teaching children science before calculus?

No. I'm saying that taking the math OUT of science leaves us with little but vague, hand-waving explanations and memorization. That's not good science education at all.

The scientific method isn't as 'glamorous' nor does it lend itself so well to flashy demonstrations or class projects to eat (a personal pet peeve, sorry)... but it's more authentic in terms of educational value than playing with liquid nitrogen or watching a thermite volcano. ::Sigh::

Absolutely not - if I get completely real! However, that is not to say that it is not nice to have that knowledge/skill. I speak from the perspective of someone whose part-time jobs as a sophomore, junior and senior in college were to grade homework (and sometimes tests) for classes in Calculus, Differntial Equations and Statistics. However, I don't use math (beyond arithmetic) in my professional life. To be (embarassingly) honest, I don't think that I remember all that much from Calculus, Differential Equations, Statistics or any of the math courses that I studied although it would be very easy for me to pick up the concepts if I see them again. In my professional life, I see lots of intelligent educated people who are math-phobic and probably unable to recall much of anything from Algebra.

here is my suggestion for one of the most basic ideas of calculus: if two plane figures are such that all horizontal slices have the same length, then they have the same area.

it follows that two triangles of the same base and height have the same area.

the next case of this principle is that two solids all of whose horizontal plane slices have the same area, have the same volume. archimedes used this cleverly to show that a sphere inscribed in a cylinder has 2/3 the volume of that cylinder.

in a calculus class they combine this with algebra to show how to compute a formula for the volume formula of a figure from the formula for the slice area.

by the way, a mathematician is not someone who knows a lot of math facts, but someone who knows how to deduce them. I.e. the prime compliment for a mathematician is that she "knows nothing but can do anything".

...and this is also generally true in the physical sciences. Oh, sure, there is a base of knowledge, but ideally, it's about using familiar tools to DO unfamiliar things. Or to find answers to questions, I suppose.

Math is a foreign language. Some people need to be fluent in some dialects (statistics, vector calculus) more than in others. What's really, really COOL, though, is that math is truly an international language throughout most of the world.

Not to rain on your parade, but the basic of idea of calculus is to sum up an infinitely small number of things to get a finite quantity, and then to do this in reverse, divide a finite quantity into an infinite number of small things. Once you can show that you can do this reliably, then the next trick is to extend this idea to where you can sum up across functions that produce an infinite number of small things. Historically, the basis of this approach had its root in addressing Zeno's Paradox.

http://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus

http://en.wikipedia.org/wiki/Zeno%27s_paradoxes

As for your statement that a mathematician does not know a lot of facts. Its the exact opposite. Mathematicians know an enormous amount of facts and know how to operate a lot of intellectual tools, too. Its this combination of knowledge and operative ability that allows them to work a large set of problems and to attack unknown ones.

FWIW, I discussed this with my husband, who did take basic calculus, and he was bemused by the idea that calculus was necessary for basic scientific literacy. He felt that stats were much more important (I agree) and said that what little calc he remembers (not much) is not relevant to him on a daily basis.

Well, understand that I did qualify that statement-- significantly. I stand by it, but for the physical sciences, and with the understanding that "principles" there means methodology and conceptual understanding. I'm repeating that statement again, since it keeps getting oversimplified. Pretty sure that anyone who has taken Physics recalls "Newton's Laws" have something to do with motion and macroscopic objects, yes? That's what I mean by "literacy" in this context.

I was also very bemused by the notion of "vectors/calculus" being the STEM track, and not "statistics" instead.

My DH and I have both used our stats backgrounds far, far more than any other area of math we've ever learned-- including calculus. Diff-Eq and matrix methods are more useful when you get right down to daily use. If you don't use it, you do lose a lot of the nuance of the mechanics, however. I think that isn't a big surprise.