In response to Jay's post

That children are allowed calculators in 3rd grade to help them with fractions, is a crime. 8x7 doesn't take a calculator and yet most adults I encounter pull out their cells to figure it out. I think that calculators shouldn't be allowed until high school and not at all in algebra and geometry. When I have kids, I'm home schooling them, because I don't want them to learn math that way. They won't need to memorize, but they should be able to understand that 8x7 is also 4x14 or 2x28 and that 4x14 is 4x15-4 and that 2x 28 is 2x30-2x2.

Not all kids are great at math, but I hate the fact that I went from elementary through high school thinking that I was terrible at math, when instead the teachers didn't understand the math enough to show relations between what we were learning and things we already learned.

If you want to get a math education degree in this state (VA), you have to go through differential equations and while I don't have a problem with that, I do have a problem with the fact that many of Fairfax County's math teachers have degrees in psychology, history, business administration, and astronomy and not even minors in math. In the Fairfax County Public School system, West Springfield high school is by far the worst.

Math needs to stop being treated like one subject, because it's not. Algebra, while helping you in geometry is not the same thing as geometry, just as chemistry will help you with biology but they are not the same subjects. Yet, for some reason, the US does not allow for algebra degrees or geometry degrees in the way they allow for biology and chemistry degrees. When we start talking about theoretical math, algebra is nearly non existent, going from calculus to trig to arithmetic almost immediately, it is for precisely this reason that I say that I study maths and English.

Some may respond that English is not a single subject either and yet it is a single degree in colleges. Except it isn't. There are creative writing degrees, technical writing degrees, linguistics, literature and plain English degrees. Yet, there is no distinction for Math, a math major is a math major with a concentration, minor or specialty. They still graduate with a BS in Math, not in Theoretical Mathematics. Now you may ask,"what about statistical degrees, applied math degrees and business math degrees?" Even at Purdue University, which has all of these curricula, when a person graduates, it is a BS of Math with a concentration or specialty in one of the previous.

I was actually pleased with the US' placement in the PISA this year. In 2003, We were only the 5th worst OECD country, well above Mexico. In 2006, we were, again the 5th worst country, with a score 20points lower than the 2003 assessment and only holding ground because Portugal, Italy and Greece back slid so much. Isn't that great? I mean, at least we didn't lose a rank. 2003 Graph can be found here. 2006 data can be found on pg12 (25th sheet) of the NCES report.

Have fun crying and be sure to look at our fabulous science and problem solving scores as well. Suddenly, I understand why I am the stupidest person in my family and yet significantly more educated than many of my peers.

This will be made public for easy reference.

Cited Works
"Baird" West Springfield High School. 6 Oct 2007. 14 Apr 2008. [http://www.fcps.edu/westspringfieldhs/academic/math/staff/baird.shtml]
"Embrey" West Springfield High School. 6 Oct 2007. 14 Apr 2008. [http://www.fcps.edu/westspringfieldhs/academic/math/staff/embry.shtml]
"Highlights from PISA 2006" National Center for Educational Statistics. 8 Jan 2008. 14 Apr 2008 [http://nces.ed.gov/pubs2008/2008016.pdf].
"Lindsay" West Springfield High School. 6 Oct 2007. 14 Apr 2008. [http://www.fcps.edu/westspringfieldhs/academic/math/staff/lindsay.shtml]
"Math vs World" Stop the FCAT. 20 Oct 2007. 14 Apr 2008 [http://www.stopthefcat.com/math_vs_world.html]
"Murray" West Springfield High School. 6 Oct 2007. 14 Apr 2008. [http://www.fcps.edu/westspringfieldhs/academic/math/staff/murray.shtml]




Responses:
Frank wrote:
Apr. 14th, 2008 04:19 pm
OK, not 100% certain I agree with your premise that "Math needs to stop being treated like one subject, because it's not."

Here's the difference, as I see it. The various mathematical iterations build upon one another. Geometry builds upon and uses concepts taught in algebra, as does trigonometry, calculus, probability and Statistics, etc. Algebra is built upon "lower" (I use that term for lack of a better one ATM) mathematical iterations.

Now, as you pointed out, knowledge of chemistry will usually assist with learning higher biology, but it doesn't build upon that. The bio classes I have taken (admittedly, they were not both fairly basic-level classes) have required little to no knowledge of chemistry. Nor have either of those sciences had much of an impact on my physics classes. This is not to say that they do not have an impact on each other, because I know that they do.

Here's the important part: They do not *build* on each other the way that the mathematical concepts do. If I do not have a firm grasp of Algebra, Trig is gonna kick my butt from here to eternity. I don't have to have as firm a grasp of chemistry to continue my studies of biology.

Now, does math branch out? Certainly! But, even some of the higher branches of mathematical studies have a close relation to each other. And, they still require grounding in the same foundation.

Let me try this tree analogy I've got brewing in me head and see where it goes.

You state above that Biology and chemistry are not the same subjects. Think if them as two trees then, close to each other, and occasionally, the branches become entangled. Those entanglements are where the sciences cross or collide. But they start with different trunks - and only meet in places.

(Throwing Physics in as a third tree is not that far a stretch either.)

But, the various disciplines of mathematics ALSO all start from the same trunk. The person studying advanced geometry and the theoretical mathematician share the same base trunk, just as the environmental biologist and the veterinarian share the same trunk.

Now, here comes the part I may need to don flame-proof armor for. For the record, it is not my intention to denigrate math, math majors, mathematicians of any stripe, math geeks, or asaia.

It would be correctly pointed out that there are "specialist" degrees in each of the "hard" sciences (1) listed above; biochemistry, astrophysics, etc., while none exist for mathematics. Very true.

Now, answer me this: For most, if not all, of the "hard" science specializations, there is a specific field of study and endeavor which their knowledge will be used in. The biochemist may go into pharmaceutical research, while the astrophysicist may go work for NASA, etc.

What does the theoretical mathematician to after graduation, besides teach?

I ask this because a: I honestly don't know and b: it is a common conception (and probably a MISconception) that there is little practical use for theoretical math - that it has little to no impact on the lives of the everyday Joe Blow and his family, so why should it be taken too seriously?

The fact is that at this moment, Mathematics will remain a single field in most "institutions of higher learning" until there is compelling reason for a change. And I'm sorry to admit that so far, I don't see it.

(1) "Hard" Science refers not to the difficulty of the subject matter in question, but rather to the fact that these fields of study generally have more quantifiable, precise, and objective data and methodology. This term is generally used in opposition to "Soft" Sciences, such as Political Science.

Then I wrote:
Apr. 14th, 2008 05:04 pm
In the same way the maths build on themselves, so do sciences. "Life science" as taught in the state of va is the introduction of scientific thinking and processes. The basic of biology, chemistry and applied physics and the familiarization thereof. An analogy can be made that arithmetic, algebra and planar geometry are the same introductory processes. Euclidean geometry is not needed for trig. Nor is trig necessary for calculus. trig will certainly help calculus make however. By you're previous statement, where does math place itself on the science tree? Algebra is necessary for chemistry and calculus for physics. That is not to say that either can be done without these maths but the finding of information is impossible otherwise.

Then Frank wrote:
Apr. 14th, 2008 05:31 pm
Never argued that the Math tree doesn't intertwine almost incestuously with at least 2 of the three trees mentioned (not so much with Bio, IMHO, but I digress). I am in agreement wholeheartedly.

While euclidean geometry may not be needed for trig, I would argue that algebra is, *and* that arithmetic is required for algebra. Arguing whether or not Trig is required for calculus (maybe not strictly or theoretically, but I would argue it is on a practical level) (1) is not necessarily the point here, either. I think for purposes of the tree analogy, we're in agreement that it is its own tree - I just think the main trunk goes a lot further up before it *really* starts splitting up.

Again, there is, for better or worse, a perception issue that while theoretical math is nice and all, it has little practical application. Not saying I agree with the statement, but it's out there.

Ultimately, the various branches of physics (or bio or chem) are merely subsets of their base science. In that respect, math is no different.

Except that late at night, when studying for a pre-calc test, the numbers on the page will start armign themselves for battle. They use square root signs as catapults, and decimal points for ammunition. "1"s are launched Ballista-like across the page by "3"s, while carats are spread about to slow the advance of the "5"s, who wield "7"s like scythes...

To which Jay wrote:
Apr. 14th, 2008 05:30 pm
Assuming "theoretical math" is equivalent to "pure math", Craig's suggestion is one of the prominent ones. Honestly, it would really depend on which branch of math one was in. In more applied math, there are a variety of programming, scientific, and engineering jobs which are relevant right from the bachelors. For the others, unless you got at least an masters, employment would be tricky; but then, it usually is in the sciences (and math is a rational science). Once you have the masters, noneducational opportunities include the aforementioned No Such Agency, other gov't jobs in techy areas, various companies doing comp sci or sci or eng research (IBM, Google, Microsoft, etc), and financial groups.

Honestly, I think that as much as it's true for bio, chem, physics, and geology (what I'd consider the traditional "hard" sciences) that there are nonacademic options, I'd say it was true for math. Admittedly, I say this as a person getting degrees in geology and math, who currently is leaning towards academia, and who plans to go into geology related industry if that doesn't work.

Also, I very much disagree that it is correct to point out that there are no specialist degrees in math. Statistics, Applied/Computational/etc Math, Mathematical Finances, etc plus the more traditional degrees all say you're wrong. The whole point of adding those other degree types is because people who take them are more specialized. And also usually don't know any Topology. Honestly, sometimes it makes me wonder if some of these specializations were created specifically so people could avoid topology. But that's another story.

Then Frank wrote:
Apr. 14th, 2008 05:43 pm
(and math is a rational science)

Never argued that one.

Once you have the masters, noneducational opportunities include the aforementioned No Such Agency, other gov't jobs in techy areas, various companies doing comp sci or sci or eng research (IBM, Google, Microsoft, etc), and financial groups.

Which is why I asked the question. As I said, I honestly had no idea what opportunities were available to someone with such a degree.

But that brings up another point. So far as I know, neither of us knows each other from Adam. The other people who have responded to this would (I hope) consider me a reasonably intelligent, educated and informed individual. Certainly more so than what seems to be the majority of America. If I don't know about these facts, how likely is it that *they* know them?

Also, I very much disagree that it is correct to point out that there are no specialist degrees in math.

On this one, I am taking my cue from asaia's original post, where she states the following:

Yet, there is no distinction for Math, a math major is a math major with a concentration, minor or specialty. They still graduate with a BS in Math, not in Theoretical Mathematics. Now you may ask,"what about statistical degrees, applied math degrees and business math degrees?" Even at Purdue University, which has all of these curricula, when a person graduates, it is a BS of Math with a concentration or specialty in one of the previous.

I freely admit I have done little to no research on the subject; I am but taking her statements at face value.

As far as the job market goes, again, without doing any research, I'd venture to guess that there are more jobs out there looking for people in fields of bio, chem and/or physics than in math.

Maybe when job hunting tonight, I'll take a look. Again, I have no idea, I'm just hazarding a guess...

Then Jay wrote:
Apr. 14th, 2008 06:16 pm
Oh, I agree that most people in America don't know about these job opportunities, or how math enters into so many things. Hell, I know other math majors who don't know about them. While with the other math majors, it comes from lack of effort into planning for their futures, I suspect for many people, it comes from not wanting the math to be important. There is a strong strain of anti-intellectualism in America, and pure math definitely makes one a bit of an intellectual. Since frequently it takes about 30 to 50 years for a pure math idea to really get an application (and even then, it's usually something like Einstein using manifolds, which isn't much of an application from a lot of people's perspectives), it's hard to really understand what they pay off is.

With regards to the specialization, while that's mostly true at the undergraduate level, the same holds for many chem, physics, bio, and math programs. The fact that someone holds an undergraduate degree in bio doesn't usually distinguish between someone who got a genuinely general bio education from a molecular/biochem, an ecology/evolution, or a premed specialization. Some programs make a distinction at the undergraduate level, rather more do at the graduate, though some don't.

With regards to the job stuff: hmm. It would depend on which degrees you restricted it to. However, I'd strongly suspect that at a given degree level, math and physics had similar job numbers. Chem probably has more, especially once graduate degrees are reached. Biology probably has more, but only once graduate degrees are reached, and has a lot more people for the slots, so I'm not sure how that works out. I'm assuming that engineering disciplines heavily leaning towards a particular one of the hard sciences/math are being excluded, because otherwise software engineering, computer science, and systems engineering say you lose.