Gifted Issues Discussion homepage Forums General Discussion Is Algebra Necessary?

I agree completely with everything you wrote here.

Old Glory Insurance.

For when the metal ones come for you.

Because they will.

http://www.hulu.com/watch/2340

>>SNORK<<

In all seriousness, I'm a professional physical scientist, and I'm deeply confused by the 'multiple emphasis paths' thingy in that article.

Frankly, I can't imagine being a scientist-- or really, even being scientifically literate-- without a rudimentary understanding of both statistics and of calculus. By rudimentary, I mean enough to recognize methodological flaws in sampling and analysis, and to know that 'integration' involves area under a curve, and that 'differentiation' is the other side of that coin.

So I'm very puzzled by the notion that only 'industrially' oriented folks would need to understand QA/QC statistical methods. That's simply not so.

:sigh: Physical science is a series of discussions about the natural world-- in the language of mathematics. Fluency is not just 'desirable' there. It's essential.

Do I get to continue to play the dumb monkey in this thread? Very well; carry on....

I do actually have a rudimentary understanding of stats, but it's really quite rudimentary. I need to have some basic comprehension of it for work. Fortunately, I live with a scientist, so he is called upon from time to time when I need help, although he doesn't always know the social science stats mumbo-jumbo I often encounter.

While I am certainly not a scientist, nor do I play one on TV, I consider myself more scientifically literate than 90% of the American public. That's a rough guess. Okay, maybe not WRT physics. But still.

I think we need to be rather wary of implying that it's necessary to pass calculus to be, what, worthy of basic intellectual respect?

Honestly, even if I had taken it, I doubt I would retain anything of value at this point. I took trig. Can I do trig? No. I haven't used it since I was 16.

I think precisely what HowlerMonkey was doing was avoiding that recall problem - that this is roughly what the words "integration" and "differentiation" mean is about what you would expect someone to retain if they took calculus decades ago and haven't used it since. And that level of knowledge is of value, I would argue; it helps someone to have a very rough idea of what kind of thing scientists might be doing when they make a model of climate change incorporating data and use it to make predictions, for example, which is one example of an idea a scientifically literate person needs to have these days.

On the "respect" question: "having passed calculus" is something with a lot of US-specific cultural baggage because of calculus's status as the peak of school maths education. There's no reason why everyone shouldn't have the basic ideas HK refers to, and in some countries everyone who has completed compulsory education will have - this is not a claim that in some countries the population is better educated, but a comment on sequencing within school syllabuses. I would hope that even people who don't take calculus in the US system come across the basic ideas HK refers to, later, if they are scientifically interested and want to be scientifically literate - don't they? If not, I do think that's a problem.

How is what HM said all that useful, though? I can't say that knowing that "'integration' involves area under a curve, and that 'differentiation' is the other side of that coin" does anything for my scientific literacy. It sounds like a Trivial Pursuit answer. I'd need to know a lot more than that for it to be meaningful to me.


I would certainly classify myself as scientifically interested. I'm married to a scientist and have edited many scientific journal articles. I have taken intro-level college biology and geology, intro- and mid-level ecology, and upper-level psych classes. I also worked as a biological research assistant in the field for many years. Calculus did not come up.

I'm trying not to take too much offense, but you know, I honestly don't think the people I went to HS with who took calculus are retaining some vast store of scientific literacy that I do not possess. I would never claim to have the background of someone *with a science degree*--but that's not what we're talking about here. I actually read scientific studies every day for work.

I'd agree with you that your background (which lacks calculus) is entirely appropriate and adequate to provide you with scientific literacy.

The problem is that the concepts taught in calculus all-too-commonly come as revelations which are presented solely in that venue. Similarly, statistical methods. Possessing a conceptual (as opposed to comprehensive or working) understanding of the concepts underlying calculus is exactly what I meant by "knowing the terms" at issue. I didn't mean verbal definitions, but conceptual ones. Honestly, that is a simple enough thing that I've taught middle schoolers what "integration" is in about twenty minutes; I find it horrifying that people can graduate from high school, much less college, without understanding that.

That would be akin to not understanding what a "subject" is in a sentence, or how a Democracy differs from a Republic. Is that merely a parlor trick or trivial pursuit answer? Well, maybe-- at least in isolation it is-- but it's still part of being literate in the relevent area.

Truly, statistics are probably more critical than calculus to the average person, and nothing more than algebra is actually required to understand the methodology of at least 80% of that. Oh, sure, you may not be able to follow the derivations completely, but that's fine if you know how to use the results and what they mean (or don't).

The fact that most people have no idea what a 95% confidence interval actually means is deeply distressing to me, because that means that while they may have access to peer-reviewed studies in journals, they lack the competence to actually understand them.

Even an auto mechanic ought to be capable of understanding the difference between quality assurance statements from two parts companies when they are made in statistically correct verbiage.

Does one have to acquire this understanding via formal instruction? Certainly not. I acquired my own linear algebra skill set via self-study in college. Colinsmum is absolutely correct about how oddly insular the view on this is in north America. Those who have taken calculus in the US tend to have a propensity to lord it over those who have not for some bizarre reason. I find that rather incomprehensible, too. Differential equations was ultimately far more interesting and useful. More to the point-- none of it is alchemy any more than German or Cantonese is. LOL.

Maybe we should stop teaching our elementary school-aged children about basic scientific principles, since they can't be "scientifically literate" until they take calculus.

The thing about statistics is that sure, you can sort of understand statistics, but without a lot more work and sweat, you don't REALLY understand statistics. I have some grasp of the basics. (I know what a confidence interval is, for instance.) This is unhelpful to me when trying to parse much of what happens in the Results sections of the papers I read for work. I can grasp whether the results look decent to some extent, but there's a lot of "And then a miracle occurred" handwaving going on that I suspect the authors don't even understand, having called in a stats expert and a fancy computer to do it for them.

With all respect, to me it is almost irrelevant whether or not one is gifted in a subject, or whether one finds it easy or not. I believe algebra e.g. is an important subject for every educated human being, and that if one finds it difficult, one should be especially encouraged to take it and master at least the basic tools. I am troubled by the idea that a student should not be required to take a subject he/she finds hard. I also firmly believe that college students do not generally fail freshman math because they are ungifted in math.

After 40+ years of teaching math, I have found that all that is needed in 99.9% of cases, to master a reasonable amount of any mathematical subject, is motivation and dedication, and hopefully a qualified teacher. My gifted students who tried to slide by by have regularly underperformed, even failed, while my less gifted ones who applied themselves have consistently over performed, even excelled.

Many people on this forum who admit they find math challenging seem to me like wonderful examples of motivated students who refuse to let their challenges in math shut them out from its benefits. I love to have such students. The gifted student who won't work is my frustration. I myself failed out of college before learning this lesson.

I was ungifted in English and maybe poorly taught in high school, but fortunately for me I went to a college where everyone was required to take expository writing and where every course (except math) emphasized essay writing on every test. Although math was my specialty, my greatest pride, after committing myself to working and studying and going to class, was in finally achieving an A- on a single English paper (about Portrait of the Artist as a young man) as a senior.

If we come out of college with skill in only the same subjects as before entering, I think we have somewhat wasted our tuition.