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Author Topic: Why calculus?
philnotfil
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Why is calculus THE end game for high school math? Calculus is fairly useless for the general population. Not that calculus is useless, it is incredibly useful for engineers, physicists, and mathematicians. However, outside of the fields, it really doesn't get used, and those limited uses don't require any understanding of why it works.
I think statistics should be a socially acceptable math for students preparing for college. An understanding of statistics is more important for voters and consumers, which is a much larger group than engineers, physicists, and mathematicians.

[ April 14, 2010, 11:50 AM: Message edited by: philnotfil ]

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TomDavidson
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I don't think you can be said to have an understanding of statistics without an understanding of basic calculus.
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The Drake
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Interesting point. But you don't have to be a physicist to take physics, and physics is much easier to understand if you have some calculus under your belt.

Basic statistics is part of algebra (mean, median, standard deviation) - so what are you talking about?

In fact, you will find statistics and probability questions on the SAT, but not calculus.

[ April 14, 2010, 01:00 PM: Message edited by: The Drake ]

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Clark
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My high school (I graduated 11 years ago) offered both calculus and statistics. A lot more students took statistics than calculus, but the vast majority of students stopped well before that. Some stopped at the minimum, completing Algebra II and geometry. Others took pre-calculus and then stopped. I think the answer to your question lies in looking at why the various groups acted as they did.

Group I: Stopped after Algebra II & Geometry
Reasoning: These are the kids that either have no interest in math, or are not very good at it. They completed the minimum requirements for high school graduation and may not be planning on pursuing a university education.

Group II: Stopped after Pre-Calculus/Trig
Reasoning: This is the largest group of kids (at my high school). They intend to go to college but do not intend to pursue a science/engineering degree. In the case of the university I attended, a sufficient score on the ACT math section (which should be achievable with a decent understanding of pre-calculus/trig) fulfills the basic requirement for graduation. These are students with no plans for high math in their future. In my opinion, pre-calculus is an essential course which locks in the lower courses already taken.

Group III: Calculus
Reasoning: This group is fairly small. I took calculus in high school, as did many of my friends, so this group felt large to me, but it really isn't. (A number of people on ornery are probably in this same boat.) This group is almost exclusively college-bound and, for many of us, we were planning on pursuing degrees that would require calculus. The AP tests allowed me to skip past the first year of calculus in college. This group includes the engineers, physicists and mathematicians phil mentioned, but also includes most physical and biological science degrees (chemistry, biology, etc.), as well as business and finance.

Group IV: No calculus, but took statistics
In my high school, this group was quite small. There was 1 AP statistics course each year. I didn't take it, and looking back, I don't know why I would have. (I started as a chemistry major and ended up with a degree in physics. My decision to take calculus over stats in high school made lots of sense. But back to the general populace.) A high school junior or senior looking to take an optional math class might well be looking to the future, so the question is: what sort of student would see a need to take statistics? What groups use statistics more than calculus? Well, the statisticians, obviously, as well as social scientists (psychology, sociology, etc.). And students interested in those paths should take stats over calculus.

The decision students are making isn't between statistics and calculus. It is between statistics, calculus and no math. (Or statistics, calculus and some-other-thing-I-am-interested-in.)

Finally, toward the point of educating "voters and consumers" in statistics, would a whole year of statistics really be useful for that purpose? What concepts from statistics are people going to use in their every day lives? Mean, median, mode, bell curves and standard deviations, sampling concepts and basic probability? (I've probably missed something there?) I learned about some of these concepts in other math classes along the way. Maybe a better answer would be adding a small amount (2 weeks?) of basic statistics ideas to both Algebra II and pre-calculus/trig courses, which would be much more likely to reach large portions of students anyway.

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threads
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I think our education system should aim to give students a basic understanding of probability and decision theory by the time they graduate high school. While our cultural values provide a decent substitution for decision theory in day-to-day life, having a populace that understands how to evaluate theories and how to update based on evidence would improve national debate considerably. Our political debates are infested with bull**** because there are many people who "care" about political issues while still remaining too lazy to evaluate them. People tend to judge new ideas based on their immediate affectual response to them without realizing that the affectual response (related to bias) is what needs to be overcome to objectively evaluate the idea in the first place.

Minor addendum: a basic understanding of decision theory would hopefully also help people understand how little we know about damn near everything. If people understood that then perhaps we could have levelheaded discussions on topics that necessitate them (ex: healthcare).

edit: The connection between "knowledge of lack of knowledge" and levelheaded discussions being that it becomes harder to throw one's confidence fully behind one idea or another which, in turn, makes it more difficult to become emotionally attached to the ideas in question.

[ April 14, 2010, 01:18 PM: Message edited by: threads ]

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Hannibal
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calculus basically is the study of functions and how they behave.

min/max, limits etc

take economy, how do you find the balance point of a market? -- using calculus
take statistics, how do you find the total probability of a non discrete probability function ? -- using calculus

Everything leans on calculus

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JWatts
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quote:
Originally posted by philnotfil:
Why is calculus THE end game for high school math?

I think your question is looking at it from the wrong point of view. Calculus isn't the end game of high school math, it's the first step for serious college math.

If you can't do Calculus you're not going to be able to get an Engineering/Science degree. Isn't it much better to learn that fact before you get to college, rather than spend a very expensive year at college coming to the same conclusion?

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philnotfil
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quote:
Originally posted by JWatts:
quote:
Originally posted by philnotfil:
Why is calculus THE end game for high school math?

I think your question is looking at it from the wrong point of view. Calculus isn't the end game of high school math, it's the first step for serious college math.

If you can't do Calculus you're not going to be able to get an Engineering/Science degree. Isn't it much better to learn that fact before you get to college, rather than spend a very expensive year at college coming to the same conclusion?

Except that calculus is what schools push all of their bright kids towards, whether or not those kids want to go into Engineering/Science.

What percent of high school students go on to a college? (50-60%) What percent of those students get a degree that they need calculus for? (15-18%)

Why push something to so many that so few need (or want)?

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Greg Davidson
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quote:
I don't think you can be said to have an understanding of statistics without an understanding of basic calculus
I took calculus in high school before statistics in college. Most applied statistics can be done without an understanding of the mechanics of calculus.

quote:
What concepts from statistics are people going to use in their every day lives? Mean, median, mode, bell curves and standard deviations, sampling concepts and basic probability?
There's so much cool stuff in your brief description - just the combination of sampling concepts and basic probability cover virtually every situation where you can make measurements to establish what is true and what is false. The fun is in all of the applications...
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Pyrtolin
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quote:
Originally posted by philnotfil:
Why push something to so many that so few need (or want)?

Because engineering and science are deemed desirable (read profitable) while other endeavors into arts and humanities are culturally considered to be a waste of time.
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Hannibal
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Guys you comepletley ignored me 10x alot.

As a person who finished a dual degree in two different fields, one in computer science and the other in buisiness administration I can gurentee you, that if you want to do ANY undergraduate degree that is not in psychology or history you will need to know calculus.

If you want to learn economics you need a much higher level of calculus than what is studied at school. you will need to know how to calculate minimum and maxium points of functions with many variables under constraints (you will need to use lagrange multipliers if you know what that is)

In statistics, as one of you suggested here, you also need to know how apply an Integral to a function.

Its not only that, you also do alot of linear algebra in operational research which is a cruicial course in a degree in management. though linear algebra is mostly studied in universities and not in high schools.


basically, unless you study psychology, or history (and more often than not, kids who do so will not study the highest level of math) you WILL require calculus in your walk of life.

In israel its even harder because there is usually a 3-4 years gap between the last year of high school and the first year at the university, so in the first year students are grinding math like there is no tommorow.

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The Drake
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I find it odd that everyone focuses on math/science here and ignore the obvious business/economic applications of calculus.

If you are going for literature or such, as others pointed out, you probably won't take either statistics or calculus regardless of which are offered.

And, the point I made, your algebra classes probably cover the basic mean/median/std dev/prob that are necessary for day to day life.

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PSRT
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Because calculus is the first level of math any student is going to take in college.
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Clark
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A quick googling turned up some numbers, which are fairly old:

quote:
The portion of college-bound students taking calculus, for example, increased from 16 percent in 1987 to 23 percent in 1997.
Link (with graph, and data for other math courses, too)

quote:
The percentage of graduates taking AP calculus rose from 1.6 to 6.7 percent over the same period (1982 to 1998)
Link Graphic

A small portion of high school students are taking calculus courses, which probably corresponds fairly well to those who end up in math, physics sciences, biological sciences, engineering, business and finance. Sadly, it is much harder to google statistics about statistics, and googling anything about high school students and statistics leads to reports on teen pregnancy and drug usage.

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philnotfil
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Thanks for the numbers. It would be nice to see what they look like now, that was a pretty big jump in both of those datasets.
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LoverOfJoy
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A lot of people who go to college aren't sure what they want to major in. It was generally recommended to take calculus your first semester (or even first two semesters) to give you the flexibility to shift to any of the many majors that required calculus.

So many of the majors that require calculus are so jam packed with required classes that it's very difficult to switch to the major later without seriously postponing your graduation. There just isn't room for many electives in the engineering program, for instance.

For kids that take AP calculus in high school it gives them that much more flexibility their first year in college to dabble in other majors they might be interested in. They can actually take a psychology course that may not require calculus without having to rule out a hard science major. Or it might give them the leg up to consider a minor or a dual major if they are really motivated. An AP stats class wouldn't be quite so beneficial in that way.

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Rallan
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quote:
Originally posted by philnotfil:
Why is calculus THE end game for high school math? Calculus is fairly useless for the general population. Not that calculus is useless, it is incredibly useful for engineers, physicists, and mathematicians. However, outside of the fields, it really doesn't get used, and those limited uses don't require any understanding of why it works.
I think statistics should be a socially acceptable math for students preparing for college. An understanding of statistics is more important for voters and consumers, which is a much larger group than engineers, physicists, and mathematicians.

So what, you're suggesting that highschool math would be better if they threw all the advanced stuff in the "too hard" basket and just taught students what they need to know to hold down an assistant manager position or fluff their way through a liberal arts degree?
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philnotfil
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quote:
Originally posted by Rallan:
So what, you're suggesting that highschool math would be better if they threw all the advanced stuff in the "too hard" basket and just taught students what they need to know to hold down an assistant manager position or fluff their way through a liberal arts degree?

Well, I thought I made it pretty clear that I was suggesting that they teach things with greater utility, but I guess you could look at it that way.
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NewYooper
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When I went to high school in the 80's, my school offered neither calculus nor statistics, so algebra II/Trig was as far as I was able to go. When I went thru Navy Nuclear Power School I got "some" calculus, but only enough to understand that I didn't really understand it at all. Now I find myself back in college full time as a Secondary Education Physics major, and having to relearn a lot of math. Because I hadn't had any formal math classes in 20 years I wanted to brush up before rushing into the hard stuff. So I took a College Algebra/Calc prep course this winter semester and will be doing Pre-calc this summer before taking Calc I in the fall.

One of the things that really bothers me about our educational system is that it assumes that everyone is/should/wants to go on to college. While I think that high schools should prepare students for college, I also think that they should prepare them for life should they chose NOT to go to college.

Based on what I see in classrooms on a medium sized university as a 40 year old Freshman, high schools are not doing a very good job of preparing students for college. There are far too many "kids" in my classes who should be in remedial classes and who are slowing down everyone else, because they don't have the background knowledge that the professors are asumming that all of the students should have. It's very frustrating when kid's who graduated high school last year, are slowing down the progress of someone who graduated high school before they were born.

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PSRT
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quote:
Well, I thought I made it pretty clear that I was suggesting that they teach things with greater utility, but I guess you could look at it that way.
After trig and algebra, I'm not sure I agree with your premise that there is a math option with greater utility than calculus.
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philnotfil
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Clive Thompson at Wired on the subject:

quote:
Statistics is hard. But that’s not just an issue of individual understanding; it’s also becoming one of the nation’s biggest political problems. We live in a world where the thorniest policy issues increasingly boil down to arguments over what the data mean. If you don’t understand statistics, you don’t know what’s going on — and you can’t tell when you’re being lied to. Statistics should now be a core part of general education. You shouldn’t finish high school without understanding it reasonably well — as well, say, as you can compose an essay.
quote:
There are oodles of other examples of how our inability to grasp statistics — and the mother of it all, probability — makes us believe stupid things. Gamblers think their number is more likely to come up this time because it didn’t come up last time. Political polls are touted by the media even when their samples are laughably skewed. (This issue breaks left and right, by the way. Intellectually serious skeptics of anthropogenic climate change argue that the statistical case is weak — that Al Gore and his fellow travelers employ dubious techniques to sample and crunch global temperatures.)

Granted, thinking statistically is tricky. We like to construct simple cause-and-effect stories to explain the world as we experience it. “You need to train in this way of thinking. It’s not easy,” says John Allen Paulos, a Temple University mathematician.

That’s precisely the point. We often say, rightly, that literacy is crucial to public life: If you can’t write, you can’t think. The same is now true in math. Statistics is the new grammar.


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JWatts
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quote:
Originally posted by philnotfil:
Why push something to so many that so few need (or want)?

I don't think that's a really valid question. Generally you have a choice of taking one class in calculus in 4 years of high school. In my high school class 9 kids out of 70 took calculus. (The number might be higher now, but I bet it's still less than 50%).

Nearly all kids (US system) have to take 4 YEARS of English, of which the last 2 are mostly literature. I agree that English/Language/Literature is more useful than Calculus, but I doubt my last year of English was as valuable as my single year of Calculus. Furthermore, English is a requirement whereas Calculus is always an elective class.

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Chris W.
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I am currently majoring in nursing and every teacher biology/gen. science teacher I ever talk to about it was very happy that I took AP Calculus (and physics and chemistry).
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