Fear of Mathematics

Great Debates
61

I made the simple comment regarding the failure of the system and it’s turned into this.

Sorry fellow posters. But if I can get through her rather thick skull, she’s the one that will benefit in the long run.

Pepperlandgirl, do me (and yourself) a favor – use the cut and paste features of your Windows environment to save your last reply. Then reread it after each year in college and after your first year in the workforce. You’ll be amazed at how your attitude will change.

High school is supposed to do more than just teach you enough to get into college. Apparently yours is failing you in several different ways.

It doesn’t work that way in real life. You have to finish what you start. Bombing the final is a very good indicator that you didn’t learn what you were supposed to learn. The last time that I checked, that is why the give an “F”. You’ll find next year that in some classes your entire grade is based on one test. Others will be more forgiving with the final counting only 60% of your grade. What you won’t find is someone asking you to turn in homework every day so that they can grade it.

Your grade is supposed to be a measurement of success, not of your motivation.

Except in Advanced Math class where it means that you showed up.

You’ve again proven my point. While you’re very proud of your 4.0 average, it appears that it’s been achieved through aptitude, work, reputation, and a lax grading system.

How in the world does someone in Honors English acquire a 4.0 average with such horrible writing skills? Granted, we all make typos, have brain cramps, get into a hurry, and have other distractions that keep us from properly expressing ourselves, but repeatedly making the same spelling errors suggests that English classes are graded a bit more subjectively on the west coast.

“Guarantee” is not spelled “guarentee”.

“Calculus” is not spelled “calculas”.

Your “Freshmen” year? Help me with California grammar – was there more than one year or is there more than one of you?

Is “mean time” what happens if you miss “happy hour”?

“I think I did a damn good job”. Past tense – “damned good job”.
And lets parse your rebuttal.

“The choral example happens all the time.” This makes it right?

“Two of which are life and death situations, which Calculas is clearly not.” Tell that to the guy that’s dropping the shuttle out of orbit.

“Otherwise I would never, ever even think about taking an advanced Math class.” A “C” in the class screws your GPA sufficiently to ruin your guaranteed acceptance by being in the top 4%, just as would an “F”, but you’ll take the class because of the guaranteed “C”? You don’t need to take advanced math, you need to take logic.
I hope that you understand that college will teach you exacly zilch. What it will do is steer you in the right direction. It’s up to you to be motivated enough to learn. For your sake, I hope that you’re ready for college. I wish you well.

I’m not going to waste any more time of the other posters to this thread. If you want to engage in a discussion, e-mail me.
SouthernStyle

62

I am with Southernstyle, a grade should reflect an objective capability and not how much your worked to get it.

A degree in Architecture should mean you can build a house that will not fall down, not that you worked really hard to design that house that just collapsed.

I don’t care how hard the surgeon studied, I want to know he can tell my liver from my spleen.

Regarding math, while some people may find it easier, for those that do not find it so easy, I do not think it is so much a question of working hard at it as it is a question of working on it until the concepts sink in to your brain and become familiar. At least that is the way it works for me.

I can explain to you how to drive a car in 5 minutes but you need hours until you are familiar and feel comfortable behind the wheel.

I can teach you a few words of another language in no time but you need to keep going over them for many days until they sink in and become familiar. It is not a question of working hard on them, just going over the same things over and over and over and over until your grain can do it in autopilot.

People who say they are no good at math generally just dislike the idea of spending time going over the same things but they are no worse than others. It just takes a little effort.

63

SouthernStyle, for shame!

You had a perfectly good position to argue on a perfectly legitimate topic: namely, that it’s not ultimately helpful to students to grade their math classes on anything but objective and consistent assessment of performance.

You could perfectly well have stuck to debating that point on its merits, and incidentally given pepperlandgirl an opportunity to appreciate the importance of being able to carry on a reasoned abstract argument.

Instead, you chose mostly to waste your remarks on 1) being patronizing (“you’ll agree with me when you grow up”), 2) debasing the argument to personal criticism (“the system must be lousy if you’re succeeding in it, because you can’t spell”), and 3) making insolent gibes. I put it to you that you would not dare treat an adult poster so contemptuously.

Yes, pepperlandgirl is a very young person (although apparently a bright and thoughtful one, whom I bet most of us consider entitled to a place on the MB) who will be benefited by learning more about many things, including the techniques and etiquette of constructive argument. You might try to set her a better example in that regard.

[simmering down] Now then. goboy said:

Not having a rigorous chain of deductive reasoning by which you can logically prove something incorrect isn’t the same thing as being purely subjective. Is there a mathematically exact way to demonstrate that Jane Austen didn’t secretly intend her novels as a study of lesbian relationships? No. Are there bodies of knowledge about Jane Austen, her works, and early nineteenth-century English society and literature that would make most if not all scholars reject that interpretation as highly implausible? Absobloodylutely. In the humanities, you can’t simply say “well, my interpretation is as valid as anyone else’s because you can’t PROVE I’m wrong” and be respected as a serious scholar.

That’s an aspect of “the two cultures” that I’ve noticed before: scientists are (justifiably) consciously proud of what’s called “the scientific method” but they often seem naively unaware that there’s anything that might be called a “humanistic method.” Sometimes they seem to imagine that humanities scholarship is all just sitting around BS’ing into the blue (they’re aided in this by the nature of most instances brought up in popular media, which is much more interested in reporting on the stupid and absurd because they’re more eye-catching).

Humanists have to deal with reams of data (e.g., this is an inscription of Hulegu, this is a Shakespearean sonnet addressed to a man), just as scientists do. When they construct theories and interpretations (e.g., about the Mongol sphere of influence or Shakespeare’s sexuality), they have to take those facts into account, just as scientists do. “Theories are discarded” all the time in the humanities because they don’t adequately fit the known facts, or because new facts are found which invalidate them. To take an example from my own line of country, a nineteenth-century Indologist named Bentley (a cuckoo if ever there was one) came up with the idea that all medieval Sanskrit astronomical treatises were late forgeries by a Brahmana conspiracy. These days, we know so much more about these treatises that Bentley’s notions are completely discredited (not that they were ever very widely accepted even in his own day). What is that if not a process of “self-correction”?

Yes, humanities scholars don’t have the advantage of being able to repeat historical or literary events under controlled conditions, and there are lots of data we’ll never have access to and lots of aspects of our models that we’ll never be able to test. But we do pay a lot of attention to the quantity and quality of our data, we do consider it important to refine our models to fit the data, and we do discard theories for not fitting the data. Sure, it’s necessarily more subjective and disputable than the results obtained by most scientists, but the processes really have a lot more in common than you seem to think.

(And thank you! coffee sounds great, but do we hafta talk about Lacan? :))

And zut said:

Sounds good to me. (Though as RTFirefly won’t be surprised to learn, :slight_smile: I think it would be very useful to present these subjects also with an eye to their historical development, to lessen the sense of alienation that many people feel when confronted with abstract concepts. I’d like to get p-girl in my “History of Calculus” class and see if the concepts make more sense to her when attached to the concrete ways that people actually dealt with things like change and increment and infinity in different periods of history; it works for many.)

But I think this is missing something that Indiana Jones, goboy and others touched on earlier: the beauty and power of deeper mathematical concepts. Consider the way we teach students English: we give them grammar and vocabulary and spelling and syntax, all the language tools that they need for the demands of formal communication. But we also give them literature courses: we ask them to think about issues like “what is a poem?”, “what is a metaphor?”, “how does an author use language satirically/ironically/dramatically/etc. to convey emotion or opinion or character?”

Why don’t we do this in math too? By all means, give them the quantitative tools they’ll need for the basic demands of life, but also give more exploratory courses about concepts. Make them think about issues like “what is a function?”, “what is a prime number”?, “what is dimension?”, “what is a group?”, “what is a transformation?”, “does math really describe reality?”, “how do we reason mathematically?”, “what do we mean by proof?” All the cool stuff. :slight_smile: This would not only give them a better conceptual grounding for the higher-level courses they may take in college, but would allow them another perspective on what math is really about. I’m sure that we’d still end up with many students who have trouble using the basic math tools like geometry and algebra—just as there are many articulate people who never really master spelling or syntax—but I bet we’d get a lot fewer people willing to dismiss all of mathematics as “a subject that just isn’t important for me to know anything about.”

Kimstu
(whoo, long post)

64

Excellent post Kimstu

I would be very interested in taking a class like that. I didn’t even know a class like that existed. When I move on to college, I will look into such a class.
I never understood algebra or certain other concepts until I began to apply them to daily life in some way. Then everything was clear. I’m sure that learning the “History of Calculas” would have the same effect.

And I probably would have been more than happy to agree with him if he would have stuck to arguing the legit topic, instead of seemingly personal attacks. However, via email, we worked everything out (I hope) so there are no hard feelings.

Thank you, I try. :slight_smile:

65

Kimstu,

Damn! I was hoping that the “rambling from my soapbox” would come off differently.

Before posting my last installment, I read it over and over trying to figure out how it was going to sound to everyone else. My intent was to show how the system was flawed, but having only Pepperlandgir’s offerings to use as examples, the tone apparently came off more personal than it should have. I missed the mark.

My offer to take the discussion offline was meant to return the thread to the other posters. Pepperlandgirl took me up on the offer, and we exchanged a couple of civil e-mails. I don’t believe that she sees things any differently than she did 48 hours ago, but she will one day.

Thanks for the critique,
SouthernStyle

66

Now that we’re thru picking Pepperlandgirl apart, can I put my two cents in?

I have an extensive interest in math, and have since grade school. Up until high school, I did fairly well in it. What changed that was my school district’s attitude that any moron can teach math.

For my freshman year, the golf coach taught my pre-algebra class. (I was forced into that one because my school records hadn’t shown up from out of state when I had to register.) I had a year’s worth of learning to fill out checks, do simple math, and really not much more than that. Consequently

My Algebra I class was taught by an assistant football coach. This man sat at the front of the class, showed us how to do one, maybe two, sample problems, then sit for the rest of the hour diagramming football plays while we students worked out our assignments. When I asked for help, he told me to re-read my notes and made it clear I was not to bother him, and discouraged outside help. That year, my high-school football team won the state finals. I also flunked algebra. Twice.

I ended up with a good geometry teacher, who took the time to make sure we understood what was going on, and why we were doing what we were doing.

It’s not that I HATE math, I just have to have a teacher who’s patient and good at explaining how to do things. I think that one of the failings of the educational system is that schools put too much emphasis on the theory of teaching, and not enough on the actual content. I don’t care if my teacher aced Pedagogy, I want to know if s/he can do math.

Robin

67

oops… that should say “Consequently, I was so bored, I kinda zoned for most of the year.”

68

I’ll agree with your first point, but not with the second. Reading any good literature can make you a better teacher by exposing you to different thought patterns, and making you more aware of creativity. I flunked math until I found an instructor who could see things my way and explain the concepts to me in a way I could understand. I’m not stupid, I just need different motivation for learning math.

If more math instructors opened their minds to their artsy students, more artsies would enjoy math. On this note, I recently read an article in the Notices of the American Mathematical Society discussing ways to interest arts majors in math. IIRC, his theory was not to teach the methods of calculus and algebra, but to teach the purposes of higher math. I believe the article was in the March or April issue. I can’t find the issue, so my husband must have it at school. It’s not on their website; sorry for the vagueness.

I have a somewhat unique perspective on this issue. As I said earlier, I darn near flunked high school math; I got C’s in grades 9-11, and dropped grade 12 math with a grade of 42%. My problem is that I can’t do arithmetic in my head. I can perform very simple calculations (sometimes having to use my fingers) and I can generalise broadly for percentages, but I need a calculator for any subtraction, multiplication, or division with higher-than-two-digit numbers involved. I can reason out how to do a geometrical problem, but need a calculator to actually get the results. Interestingly, I took grade twelve physics at the same time as the math, and got a B, even though the two subjects involved the same algebra.

I’m good at visualisation, not at abstraction, and I didn’t care at all about the algebra. Physics was cool, though.

After a year of a rhetoric degree however, I decided I wanted to switch majors to biology, so I dropped out and went to Sylvan Learning Centre (shameless plug follows). My instructor was very good, and helped me to understand the relationships of the various mathematical types. I got perfect scores on my quizzes. Four years and one rhetoric degree later I’m back to my original problem of needing a calculator.

Long story short (too late!) I married a topologist, and although I have no clue how the algebra he uses works, I’m continually fascinated by what he does, and I can understand the basic concepts and issues. If I knew in high school that mathematicians could visualise four-or-more-dimensional objects, I might have been more interested.

Wow, and I actually got that to wrap around to my opening comments! I’m a better rhetorician than I thought! (No comments on that statement, please.)

69

Kimstu said:

Not too hijacky. It was not a completely formulated thought.

Perhaps I am seeing the situation thru my science-colored glasses. At the height of the Cold War science was definitely emphasized as part of competition with the Soviets. But with the coming of detente right after the cultural shift of the late 60’s, even though the government still funded science at high levels the philosophy in academia changed. Greater emphasis was placed on humanities programs. Not that the emphasis wasn’t necessary. It just seems to some of us science types that the shift of emphasis is a loss of science dominance.

Or maybe I’m barking up the wrong tree.
Suo Na

Don’t know if I fully agree with you there. Seeing as I have read Shakespeare I cannot use myself as a counterargument. However, if what you say is true, then should not humanities instructors take more math and science in order to better explain their fields to the science types?

70

Thanks SouthernStyle, sorry I snarled at you.

Indiana Jones:

I don’t disbelieve you, I just still don’t know what quantifiable data you’re basing that claim on. You know what bears we humanities scholars are for hard evidence. :slight_smile:

Yes, yes, yes!!! The fundamental concepts of mathematics and science should be as important for an educated person as the great achievements of history or literature. (That doesn’t mean that we have to whip everyone through classes in multivariable calculus and complex analysis; as I suggested in my earlier post, we could also have “concept” courses that pay more attention to ideas than to algorithms.)

This would have many beneficial effects. For one thing, we’d see less of one of my pet peeves, namely writers using math and science buzzwords in a totally meaningless way as mere literary flourishes. (I.e., don’t say “non-binary equation” when you mean “unequal relationship”, and don’t say “chaos theory” when you just mean “chaos”! Grrr, that sort of thing annoys me.)

Also, how are lit professors going to teach plays like Arcadia or Copenhagen or The Five Hysterical Girls Theorem, or other literary works with significant mathematical or scientific content, if they have no clue about the topics? I think the idea of erudition as something separate from knowledge of math and science is becoming rapidly outdated.

Kimstu

71

Here’s some math and literature all rolled into one
A MATHEMATICAL PROBLEM

72

The thread that just won’t die.

And maybe it shouldn’t. People get over their fears by talking about them. Maybe more people should talk about math.

So a bit more trivia about the problem.

Besides causing tremendous pressure on school aged persons (is that PC enough? oh, wait. “person” implies gender. How about “school aged perpeople”?)

Sorry … not awake yet. Back to the point.

Besides causing tremendous pressure on schood aged perpeople, math now causes tremendous consternation in the scientific community.

For centuries, math was far ahead of science. Mathematicians and theorists continued to study math, its patterns, and beauty. But science wasn’t advanced enough to know how to use all of the known math. Tools, measuring devices, and manufacturing techniques went largely unchanged from 1 A.D. to the early 1800s.

Now that mechanical measurements are accurate to less than 1/10,000 of an inch and we can count the number of atoms in a shoebox, science has caught up with, and in some ways passed the math that is its tool.

The scientific community screams for the mathematicians of today to improve the tool, all the while, the tool causes headaches to the very group that should be lining up to deliver the next advances in math.

Ironic, huh?
SouthernStyle

73

Ahhh…math… I thought I was done when I finished Calc IV. Guess not. I’m an EE major, so every class I take is a mathematics course in some sense. For those of you in pre-calc (or just finishing)…even if you hated pre-calc and found it hard, give plain old calculus a chance. I found Pre-calc extremely long, hard, and boring, but then when I took AP Calc, I was just pissed…learning that all the stuff that took a page of work in pre calc can be done in one line with calculus…(Derivatives, anyone?)

I am pretty amazed that most people in the world can’t do basic computation in their heads…but I’ve always been very good at math and science, so who am I to judge. One thing I found interesting about the progression of my math courses was what was truly covered…my progression:

Math, Pre-Algebra, Algebra I, Algebra II, Geometry, Pre-Calc, AP Calc (derivation, simple integration, some sums), Calc II (very difficult integration, infinite sums, etc.), Calc III (double, triple integrals, differential equations, more junk than I can remember), Linear Algebra.

Strange to go deep into calculus…then hit linear algebra…always thought that was strange…but of course, L.A. is probably the most used of the stuff I learned, even if it is done by programs like Matlab most of the time. Then there’s the EE specific junk that I’ve done as well…more of a convoluted combination of everything else.

Basically, I don’t expect anyone to subject themselves to the amount of math an engineer or a math major (uck) takes…but I do expect people to be able to multiply by 10 and add single digits.

Wow…long post without much of a point…sorry.

Jman

74

That was the way it was approached where I went to school, too. IMO, the reason they order it that way is that linear algebra is often one of the first classes where students are expected to learn some of the theory, rather than just follow the basic formulas to differentiate or integrate. It’s been my experience that many students have more trouble with a basic linear algebra class than with a basic calculus class; many of them don’t have trouble understanding what constitutes a “proof”, such as “prove this is a vector space”, or “prove that is a linear transformation”. Having calculus first, then linear algebra, makes sense to me.

I do think it’s odd that you took differential equations before linear algebra, though. I personally wouldn’t order it that way, there’s a lot of linear algebra to be found in diff. eq.'s, and I think it’s much more natural to take linear algebra before diff. eq. But maybe that’s just me.

75

Personally, I hated having to do proofs in mathematics. Bleah. Just show me how to do a surface integral or a second-order nonlinear differential equation so that I can use it for something practical. Don’t try to prove to me that it works – I believe you, all right?!

76

Oops, I meant for that to read “many of them do have trouble understanding what constitutes a ‘proof’”.

77

Math sucks.

Actually, I was always good at it, top of my class, until Junior year of high school. I moved, got stuck in the wrong class, messed me up good. I went from having all As in math to nearly flunking Calculus. I dropped out and tried it again my Senior year and dropped out again. Personally, I think I just wasn’t developmentally ready for it. I was never so intimidated by a subject in my life. Maybe I could do it now, if I had to take it all over again.

I can remember some basic stuff from Geometry, Trig and Algebra II, but I never use anything past Algebra I. Therefore, I remember very little of the math I learned. And I’m forgetting more every day. Since college, I think all I’ve ever used math to do is addition and subtraction, multiplication and division, fractions and percentages. Period. Working in the humanities area, I don’t plan to ever have to use math beyond that.

78

Number/math ignorance is one more form of ignorance and you may think you don’t need that knowledge but if you do not understand certain things you are in the hands of others. The main reason there are scammers out there is that they have a permanent supply of ignorant victims.

That gadget mentioned in another thread that you plug into the lighter and it starts your car? Do you really believe that? Do you really believe a battery with a capacity of 1/20th what your car battery has can do the same job? Why would car manufacturers overdimension the battery like that?

Another example: I was in a meeting of about 20 people and we were discussing the viability of heating a small warehouse and how this might be done and the energy needed. There was a lady who kept insisting in “these new electric heaters”. We tried to explain to her that electricity was not the way to go as too much power would be needed. She was talking of a small space heater of about 500 w which would not even begin to heat the place. She would bring it up again and say “but it’s ceramic!” and we would all roll our eyes again. This comes from number ignorance and people like this are prime suckers for scammers.

Lady, a 500 watt space heater puts out 500 watts of heat no matter how you slice it and our needs here are something like 20 or 30 times that.

And if she can’t grasp that how can she grasp the national debt? I have a friend that, every time someone says something really dumb will whisper to me “remember, these people vote”.

79

I don’t think they took “differential equations”, they just took Calculus III, which contains an intro to differential equations. As far as I know, that’s a pretty standard progression.

80

I’ve heard stories of primary grade teachers who
were so innumerate that they had to work to keep ahead of the lesson schedule by a page or two. How can people like
this instill in anyone the wonder of numbers of the elegant beauty of a proof?

And the situation tends to be self-perpetuating since primary grade teaching as a profession tends to attract exactly those who, because of their own innumeracy, never
considered becoming electrical engineers or physicists.

I was one of those kids who wanted to be a scientist or astronaut, until someone explained to me what Algebra was.
I struggled with math from about the 4th grade on, had to
take Algebra I twice and never made it to Algebra II. Then
in college I had a fairly easy version of Calculus (for humanities majors) which was actually pretty interesting.

To make a long story short, in spite of all that I eventually became a programmer analyist and have been doing that for about 16 years now. And in the meantime, I’ve actually gotten a lot better at math, even though I’m still
very weak in a lot of areas. I don’t know how it happened,
but about 10 years ago I sat down with a pencil and paper
and decided to prove rigorously the formula for the volume of the sphere, and what do you know, I did it. You probably remember seeing the headline in the papers: “30-Year Old Former German Literature Major Proves the Volume of the Sphere: ‘Giant Leap for Math Idiots!’” Well, from there I’ve been dipping into an old college algebra book, learning
much of what I would have gotten in Algebra II, and it’s
really interesting. My enthusiasm does frequently outpace
my ability and my preparation, but I do now have a liking for and an understanding of math that I never would have
thought possible.

Except Trig. Call me a gonophobe.