Basic Math Concepts
 

Do you understand? Just taking an informal poll.

Eh? It's Saturday night man! I've got a pint of ale in hand here...

Alright. I understand change, rate of change, and differences in rate of change...but as applied to what? Derivation? Maybe I don't understand after all.

I did at one point, when I earned my BSc. Years of rock and roll have eroded that knowledge, sadly. :D :P

I'd say you do. Well done. :)

i am pretty good at making change. does that count?

tom w

smooch... smooch

LOL..:D

Yep, but are you faster than the next guy?

usually. seven years as a paper boy made me a permanently impressive change figurer.

my specialty is figuring out how to make it work when neither party has the correct amounts to make change and you have to pay extra so as to return an amount that will make it all wash.

i am usually ahead of the cash register.

tom w

I've been on two Math search committees. The candidates had to explain, What is a limit?. That's two full days, 15 candidates lecturing on that topic.
It's amazing how many mathematicians can't explain rate of change.

As a paperboy, I had one of those metal change holders that attached to my belt and kicked out the change as I pushed a lever. Did you have one of those?

I can just about do Algebra. Such a drag why learn such a useless subject in school.

Warren Buffett doesn't put much stock in it. Some professions need it but mine certainly does not.

Algebra II is as far as I will find math to be useful :) I had a terrible time with Pre-Calculus. That's as far as I got in high school. I never found rate of change to be very hard of a concept though..

That's an interesting point. There are tens of thousands of students in the US struggling to pass College Algebra to meet a basic Math requirement. Most of them will never use those concepts again. But the will retain a basic resentment against Math and very likely pass it along to their children.

Is this a waste of valuable human resources?

no i just used one of those green cloth bags with the zipper on top. i always thought the change thingies looked pretty cool but i think i tried one once and found it too bulky.

my favorite thing was taking all the change to the bank and watching them run it through the change counter.

tom w

What the hell is rate of change?When I was 16 and dropped out of school I could measure and grind crank journals,C&C cylinders and calculate projected horsepower ratings,semi-size bottom end bearings and fit valve guides for engine rebuildings,also how to buy cheap and sell dear,so what is this rate of change and why would it affect me?

Well....
 

It sounds like: The speed at which something is becoming not what it was before. :silly:

In an airplane. It tells you when you’re going to be very high. :D
Or a yard-dart.:eek:

I'm an Engineer.

What kind? I have two BIL's who can't draw wiring diagram for a stair light, you know where there is one switch at the bottom of the stairs and one switch on top, and no matter which way you flip the switch the light either turns on or turns off.

I ask because you really don't need to take math class to understand these things do you? After all, acceleration is rate of change and so is the rate at which your garden grows.

I LOVE Open Discussion!!!

Where else in my hum drum world can I observe such discussions as this?

Kerry Edwards asked a very leading question about whether requiring math in university is a waste of human resources.

Algebra is to calculus what grammar is to language.

IMO, if you cannot pass calculus you shouldn't be in a university. The same goes for other fundamental analytic skills in other liberal arts disciplines. That's what the "university" word is all about -- once through with it, you can apply your knowledge universally -- to all problems.

Go to a JuCo or trade school if you want a curriculum that doesn't require analysis in the major fields of human endeavor.

So no, it's not a waste, if we set low educational goals for our most advanced education, we'll get students of exactly that quality. Kind of like what we have.

B

Math am hard

rate of change of what with respect to what? rate of change of distance WTR time gives you one thing and stuff like that?

Word! You can be successful not know where to put a comma but you can never make sound decisions without a solid understanding of mathematical problem solving. Since schoolin the main thing I constantly brush up on is math rithmitic scillz.

There are three kinds of people. Those who can count and those who can't.

Exactly! For my degree I need to take four math courses. Math 095, Math 100, Math 120, and math 139. It took me two tries to pass 095, and another two to pass 100. Now I am going into 120 which is pretty much Algebra two, and 139 is calculus for liberal arts majors, or business majors like me.

But in the mean time I hate math with a pasion, and will complain about it to anyone who will listen. It burns me that I have to expend to so much time, effort, and money banging my head into a wall to learn a subject that is useless to me. I feel my time and money could be much better used taking business courses, and english courses.

Oh just one more point. I can do math, I am a wiz at accounting and can do some neat stuff in my head. I can also calculate inflation and the time value of money equation. Advanced economic principals I can do.

Exactly!

What percentage of the population needs to understand and use calculus? Why? Who are they?
Why should Hatty have to take Alegbra if he has a clear grasp on the Math skills necessary for his field?

It seems to me that of all the things we can learn and teach, Math is the kind of thing that is most influenced by the hard wiring of the brain. We have idiot savants in Math but none in sociology or literature. Would it possibly be better to tailor education to meet these differences?

Calculus is helpful in estimating the value of an income stream or the payout of an investment (really the same problem), by considering it as continuously-compounded. The computation then becomes simple, if you understand the relationship.

Let me add that I've seem some idiot savants who can do arithmetic, but never mathematics. Arithmetic is to mathematics as spelling is to literature.

Need and understand calculus? Small group. However, to understand concepts and thinking strategies? Probably a large group.

I would say that math is way more marketable than sociology or literature. More useful too. I'd rather go thru 2 math courses than one soci or lit.

Why take a philosophy or history course? I have yet to have a need to know what happened in 1066 and where it was that something happened that year. Nor has anybody asked me about 'Meno' in since ... ever. For that matter, I can't think of a time when it was important whether or not I split an infinitive or read a work of "Great Literature."

Fundamentally, learning is it's own reward, or not, depending on whether one values it.

What is of practical importance is a different question, which is why for those folks who need a practical application to make education worthwile, I suggested a JuCo or trade school (or business college like Remington). It is disrespect that some folks prefer practicality to general learning and vice-versa. On the contrary, I would like to see stronger Juco's & trade schools so that folks who want a practical education can get one without being burdened with courses that are of no use to them --- allowing the student to concentrate more effectively on those courses that are of practical value.

B

I'm not arguing the value of practicality over learning for its own sake.
You don't find tens of thousands of students struggling semester after semester to fulfill a History, Philosophy or Sociology requirement. You don't even see it in the hard sciences.

There's something different about Math. Is this difference worth modifying its role in the curriculum?
I suspect that Math is somehow hard wired in the brain in a manner similar to the way in which language is hard wired although the differences in the quality of wiring differs more with Math than with language.

There are millions of dollars being spent in higher education on remedial classes necessary to get students through their college alegbra course. Would this money be better spent on higher level math courses for students who actually want to study Math?

*** Expand the options... ***
 

Kuan:

Expand the options to include: First, Second and Third - I understand...

I understand exactly what Bot is saying...being well-rounded in the math field is better than being structured in one disipline-vs.-another.

I had 8 years of business math (accounting) through Jr./Sr.-High School and in college, two years of calculus and algebra - I hated the college years - too "free-thinking" for my tastes.

Turns out, in my chosen field of endevor, I use the calculus/algebra math more than the business math. (Although, my business manager has NEVER thrown my Expense report back at me for errors! :D ).

.

I agree.

Obviously a grasp of basic math and geometry concepts benefits EVERYONE... You need to be able to balance your checkbook, do your taxes, count change... and at least have enough of a grasp of geometry to be able to fit a few boxes or pieces of luggage into the trunk of your Mercedes... ;)

But for someone who is not going into advanced engineering, programming, or other highly technical fields... Is highly advanced knowledge of calculus, trig, etc. really of any use to them? It certainly has not been of any practical use in my life.

For many students, I think that the time and effort that is too often spent pointlessly beating such subjects to death could be put to much better use.

Mike

Mightn't there be hard-wiring (and lack thereof) for any subject or discipline? Why not call it "a college for people who like sociology and art and stuff but think mathematics is too hard"?

This might be of benefit to people interested in science, engineering, and mathematics. They would no longer be burdened with smarty-pants PhD's forcing them into trivial classes like sociology and music and philosophy and other crap and could thus, concentrate on what is important to them.

Then we could have colleges separate from each other and get rid of that whole notion of universal education. The chances are we would be embarking on a new tower to replace the Ivory ones of Pointy-headed fame. It would be a tower of mutual incomprehensibility, where seemingly intelligent people would be unable to communicate, having no common educational paradigm. Instead, they would Babel.

B

Not picking on you Mike but your point pretty much sums up how a lot of folks feel about math.

And as an IS expert who minored in Math, even my most challenging career projects required at best, high school algebra know-how.

But the analytical requirements of the theoretical maths like differential calculus and such, allow a select few who choose to go the next level to think "outside the box".

Leading-edge technology is not developed by minds who are simply adept at balancing their checkbooks...

Agreed.

....But not everyone goes into a career where the goal is to "develop leading-edge technology".

I just think that the advanced math requirements are over-emphasized and pushed too far in many college and university curriculums.

For instance, I was in college for a BA in Music Performance. To require me to take advanced calculus, trigonometry, and other such nonsense (my university didn't, fortunately) would have been a big waste of time, money, and resources. COMPLETELY unrelated and not useful to my chosen field. I didn't need it then, and I don't need it now.

Mike

When Universities became "job training" instead of centers of education, this argument was lost.

A legitimate point to a degree, but....

As much as a college education costs nowadays, one should be able to tailor the course of study to fit one's goals and career choices as one sees fit, at least to a reasonable degree.

As Kerry already pointed out, math--highly advanced, specialized areas of math in particular--are not nearly as "universally applicable" to everyday life as language, psychology, and other common general-requirement courses.

Mike

That's sure the reality. And as we "dumb-down" so that more people can matriculate, we devalue that which they seek to accomplish. Welcome to the world of everybody's a genius.

There are some few things for which there is no substitute. Aristocracy of the intellect is one of them. Egalitarianism in education is self-defeating bull*****.

B

Bot..can you translate that for me??

My goodness.

B

LOL .. :D ...Its good see your back to normal!!..;)

I'm certainly not arguing that Universities should become job training centers, nor am I arguing that Math is not one of the greatest accomplishments of the human intellect or that Math is not central to almost all of modern technology.

I'm just saying there is something different about Math. We never hear of Sociology phobia or Welding phobia or History phobia, but we all know of Math phobia. Ask anyone who teaches Math at the kind of level we are talking about.

Take Art as a counter example. Most universities require some kind of exposure to Art in their core curriculum. However, since artistic talent is something that is often inborn, we don't require students to produce good paintings or sculpture, we allow them to study the history of Art instead of doing Art. We don't do this in Math. We don't allow students to study the history of Math (indeed such courses are extremely rare at the undergraduate level). We make them DO Math. Is this the equivalent of requiring students to DO sculpture or painting or play an instrument, rather than learning about these things?

Should we require a History of Math course as the logical equivalent of Art History? Maybe we could get people to go to Math museums the same way we get people to go to Art museums and get rid of the phobia at the same time?

That's not really fair is it? A philosopher querying a Mathematician about the notion of a limit? A Mathematician's standard answer to Zeno's paradox goes something like... "it's all solved with calculus." Trouble is, Zeno's paradox (and Heraclitus' too) is empirically shown to be false every single time we set something in motion, a la G.E. Moore's "plain man" philosophy. How do we know a hand exists? SLAP! There, it exists.

I was playing the role of 'guy who doesn't teach Math' to see if I concurred that one or more of the candidates could explain an idea to the non-expert.
Turns out that on one of those committees, the candidate who stood out beyond all others, was a undergraduate Philosophy major who got a graduate degree in Math to make some money. He's become one of my best friends. He'd far prefer to discuss Moore's (unconvincing) argument than solve a Calculus problem.

As an aside, the English dept at our school came up with a great interview question that gives interesting insights into the candidates. "What famous historical figure (or 3 historical figures) would you invite to dinner and why? What would you serve?

The last time I was on a search committee (for an English professor) I talked them into including a famous scientist in the list. Believe it or not, there was a person with a graduate degree in English who could NOT name a famous scientist. This is an example of the kind of problem with which Bot is concerned.

I've only been on one search commitee, and it was probably more fun than any you've been on. My wife and I were on the commitee to hire a resident oenologist at the University of Illinois. Amazingly enough, there were only four candidates so we "interviewed" all four. Although the school had a strict no alcohol policy at official University events, we managed to break that rule all four times. :D :D

That's a reasonable argument and I am not sure that it has a global answer.

The reason that I defend calculus is precisely in-line with Kuan's original query -- to analytically understand rates one must understand the calculus (limits, derivatives, integrals, etc). I don't think one needs to be an accomplished analyst but the insight gained from learning and demonstrating the concepts is so fundamentally illuminating to every aspect of the physical sciences and engineering (and increasingly, the biological sciences) that I find it hard to conceive of a universally educated person NOT having been exposed to it. Golly, I left out mathematics.

The argument about the humanities is a good one: Why should a brilliant expert in Assyrian art be required to take the calculus? He should not, unless he wants to claim a university education. If all he wants is mastery of Assyrian art then let him have a degree from an entity that does not claim educational universality as it's accomplishment.

B

when i was in architecture school we had to take one quarter of calculus.

i just didn't get it at all. it is the only math class ever that i got less than a b in. i am not sure but it is possible i never got less than an a in other math courses. and i got all a's in my structures as well i am pretty sure.

the calculus was totally worthless. i have never needed it ever before or since.

and it is no longer required for the architecture degree.

tom w

Architecture is one of those wonderful professions which so seamlessly blends art and science. Although it seems to me like a lot more science at times, I bet it's more often than not an art, a black art so to speak.