# Useless math

matt grime
Homework Helper
"My philosophy has been: If a student asks "So what?" and you cannot respond, then step down from the podium."

What other answer than: because mathematics is important, it is used in.... used for...? can we offer? Exactly the same reasons as why we teach French, History, Biology and so on. The difference seems to me to be that students expect some better answer in respect of mathematics because it is perceived to be geeky and dull, and they need to be convinced before they'll study it. It is perhaps the indirect nature of the application of mathematics that is the problem.

However, we should draw a distinction between why we learn mathematics as subject, which we should explain, and why you are taught are particular technique, which shouldn't need an explanation.

Math Is Hard
Staff Emeritus
Gold Member
My little sister (in high school) has the same gripe about her English classes. She says, "I don't care about this, I don't want to be a writer, and I have all the English and writing skills I need."
She sees absolutely no pratical reason for her composition classes, and she's stubborn as a mule.
I think math teachers aren't the only ones who have to put up with this attitude.

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JohnDubYa said:
RE: "Why is it assumed that teaching students "practical" uses of math is the best way to motivate them?"

Well, what IS the best way to motivate a typical high school student to study math?

So they can calculate the life-long expense of their drug habits.

The typical high school student (in this country anyway) not only doesn't care, but won't ever. You can't convince them, its beyond their understanding.

RE: "My little sister (in high school) has the same gripe about her English classes. She says, "I don't care about this, I don't want to be a writer, and I have all the English and writing skills I need."

Her English instructor has probably not done his or her job very well. I teach an English course right now and every one of my students knows exactly why they need to work hard in my class. I craft my assignments to demonstrate the importance of solid English skills.

And if I can do that in an English course, why shouldn't I be able to do that in a math course?

RE: "She sees absolutely no pratical reason for her composition classes..."

Probably because she has never been shown a reason, yes?

RE: "Exactly the same reasons as why we teach French, History, Biology and so on. "

And what are those reasons? And are these reasons likely to motivate a student? If not, what do you do to motivate students.

So put yourself in the role of the teacher. The school principal is sitting on your course for an annual review. You have just finished a lecture on (say) polynomial long division, and a student says "So what?"

What do you say in response?

RE: "The typical high school student (in this country anyway) not only doesn't care, but won't ever. You can't convince them, its beyond their understanding."

I would guess about 5% of the class will study mathematics for its own sake. They have genuine interest in the subject on its own merits, irregardless of practicality.

Roughly 40% of the students are probably unreachable. They will not put out any effort no matter how important they perceive the subject.

"Screw 'em! If they don't see that mathematics is the most wonderful subject in the whole world, then let them drift off while I teach my beloved 5%."

Is that the attitude that a high school teacher should adopt towards his students? Would you hire that teacher?

Math Is Hard
Staff Emeritus
Gold Member
JohnDubYa said:
Probably because she has never been shown a reason, yes?

Either that or she hasn't been shown any consequences for not doing the work. She managed to squeak by with a D minus, and was satisfied with that.

Maybe I'll pack her up and send her to you!

p.s. after Algebra 1, I never thought I'd see polynomial long division again, but it made a cameo appearance in Calc 2.

I see it every now and then, but most of the time i'm using it, i'm using maple anyways.

Hurkyl said:
Some things that a computer scientist will specifically find useful from calculus are limits (asymptotic analysis), infinite summations, and the general method of estimating functions by finding good upper and lower bounds.

Furthermore, some techniques of discrete math bear strong relation to those of continuous math; for example, differences correspond to derivatives, finite sums correspond to definite integrals. The techniques are often easier to learn in the continuous setting.

Statistics is also generally useful. Many very useful algorithms have abysmal running times; the most prominent example is that quicksort, in the worst case, is a $\Theta (n^2)$ algorithm... absolutely horrible for sorting techniques... but it almost always beats out "better" algorithms like heapsort and mergesort. Why? Because, statistically, quicksort has an average case running time of $\Theta (n \ln n)$.

Also, many problems simply cannot be solved in a reasonable amount of time... but probabilistic algorithms can be effective. Without knowledge of statistics, how could you design or analyze such an algorithm?

As for linear algebra, it's just so pervasive throughout mathematics that you'd be disadvantaged without it.

But what if I'm just going into a job where I program all day at a cubicle or be part of a software engineer team. Where would all of this math stuff come in? I mean I would just have to know how to write good documentation and good code. And as far as sorting algorithms go, couldn't I just use a built-in sorting function (or choose from different ones) for Java or whatever language I happen to be coding in? I wouldn't even have to know how the sorting algorithm itself works or how efficient it is.

Hurkyl
Staff Emeritus
Gold Member
Then don't call yourself a computer scientist, and hope you're never expected to write efficient code.

krab
JohnDubYa said:
irregardless of practicality.
BTW, that should be "regardless". English does have some mathematical rules: e.g. a double negative becomes a positive.

JohnDubYa said:
I would say, make sure you have the respect of your students. Teach enthusiastically and if they cannot be made to see the beauty of mathematics, then at least they will come away with an impression that there is something there that some people can appreciate.

HallsofIvy
Homework Helper
krab said:
Teach enthusiastically and if they cannot be made to see the beauty of mathematics, then at least they will come away with an impression that there is something there that some people can appreciate.

Very well said. They may think you are a fool but they will remember that you care!

Speaking of useless maths., whatever happened to Lamba Calculus? There are very few universities offering this course and all the books I know on the subject are getting old now. The only thing I remember from Lamba Calculus is the wierd symbolism.

RE: "BTW, that should be "regardless". English does have some mathematical rules: e.g. a double negative becomes a positive."

Groan.

RE: "I would say, make sure you have the respect of your students."

Respect must be earned. The best way to earn respect is to show your students that you are acting in their best interests. When I teach English, I show my students why the material we learn can help them. (One of my first assignments is a letter of inquiry. They learn immediately that they would be in real trouble in the real world unless they pick up significant writing skills.)

RE: "Teach enthusiastically and if they cannot be made to see the beauty of mathematics, then at least they will come away with an impression that there is something there that some people can appreciate."

Teaching enthusiastically with no regard for the benefit to the students is called "self-absorption." Have you ever had such a professor? They go on, and on, and on. At some point you wonder if they would continue lecturing if everyone left the room.

Again, how do you respond when a student says "So what?"

BTW, that should be "regardless". English does have some mathematical rules: e.g. a double negative becomes a positive.

sorry to interrupt but this is NOT true.
Irregardless means regardless. As inflamable means flammable. There are other cases too. These are somewhat informal but they were never meant to be antonyms.

Not the best authorties but:

irregardless definition

more

http://web.uvic.ca/wguide/Pages/UsIrregardless.html [Broken]

scroll down

http://www.wsu.edu:8080/~brians/errors/irregardless.html

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arildno
Homework Helper
Gold Member
Dearly Missed
I quote the entry from the dictionary in full:
"ir·re·gard·less ( P ) Pronunciation Key (r-gärdls)
Regardless.

--------------------------------------------------------------------------------
[Probably blend of irrespective, and regardless.]
Usage Note: Irregardless is a word that many mistakenly believe to be correct usage in formal style, when in fact it is used chiefly in nonstandard speech or casual writing. Coined in the United States in the early 20th century, it has met with a blizzard of condemnation for being an improper yoking of irrespective and regardless and for the logical absurdity of combining the negative ir- prefix and -less suffix in a single term. Although one might reasonably argue that it is no different from words with redundant affixes like debone and unravel, it has been considered a blunder for decades and will probably continue to be so.

When a tutee of mine is expressing their dislike for math, if they are not persuaded by whatever example I can come up with where they would use the subject matter in real life, I show them some renderings of the mandelbrot set that I always have handy. Many students in earlier math classes do not understand how conceptually meaningful and elegant math is, but few fail to see the beauty in the graceful curves and swirls of a fractal set. Being shown that math is not all rote and pedantry can soften them up towards the subject.

Of course, the ultimate "reason why I should learn this garbage" is, "because you would like to pass the class." That's a perfectly valid response, if someone has rejected the other possible motivations for studying the material.

RE: "When a tutee of mine is expressing their dislike for math, if they are not persuaded by whatever example I can come up with where they would use the subject matter in real life, I show them some renderings of the mandelbrot set that I always have handy."

And the tutee then asks "How is this related to polynomial long division?"

No one has answered my question: You are lecturing on (say) factoring of polynomials. A student asks "So what?" (A perfectly legitimate question, I might add.)

What do you say in response? Because it's beautiful? Because I'm interested in it?

RE: "Of course, the ultimate "reason why I should learn this garbage" is, "because you would like to pass the class." That's a perfectly valid response, if someone has rejected the other possible motivations for studying the material."

Well, that will motivate them to reach at least a D.

BTW, I'm not trying to antagonize anyone. Those who teach will encounter this situation, and I think it behooves future teachers to be prepared. Showing pictures of Mandelbrot sets is not going to motivate someone to learn factoring.

JohnDubYa said:
RE: "When a tutee of mine is expressing their dislike for math, if they are not persuaded by whatever example I can come up with where they would use the subject matter in real life, I show them some renderings of the mandelbrot set that I always have handy."

And the tutee then asks "How is this related to polynomial long division?"

No one has answered my question: You are lecturing on (say) factoring of polynomials. A student asks "So what?" (A perfectly legitimate question, I might add.)
I was not bringing up the fractals in response to a specific topic, like polynomial long division, but rather as a response to someone who is frustrated with math in general and has not experienced its elegant side. Resenting a subject makes it much more difficult (or impossible) to learn that subject. When someone discovers a subject has an appeal that they were previously unaware of, it can reduce their level of resentment towards it, making it easier for them to proceed.

You are correct that some of what is taught in math classes will not be of direct use to most of the students who take the class, and that polynomial long division fits into this category. However, even if you never actually wind up wanting to divide one polynomial into another, it's still good practice at manipulating algebra, and can be viewed as a "case study" in following an algorithm to arrive at a result.

JohnDubYa said:
No one has answered my question: You are lecturing on (say) factoring of polynomials. A student asks "So what?" (A perfectly legitimate question, I might add.)

What do you say in response? Because it's beautiful? Because I'm interested in it?

What generic answer could possibly be of any use?

A "why should I learn this" question is impossible to answer without knowing more about the student (other than the "to pass this course" answer, which isn't a very good answer; even then, you are assuming that the student cares about passing the course).

Motivating students by telling them why something is important is actually just telling them why you think something is important. This works if the students are like you; but given the wide variety of interests among high school students, it's not very often that you can give a good answer that works for almost everyone.

And what do you do in a situation where there is no widespread, immediate practical use for something? Almost everything you learn in high school has no immediate value; this includes what you learn in core courses like math and english.

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RE: "What generic answer could possibly be of any use?"

Well, as a teacher you better think of something. You can't just stand up there and say "Oh, nothing, I suppose." (Well, you could, but it wouldn't go over well.)

RE: "A "why should I learn this" question is impossible to answer without knowing more about the student..."

I think it is safe to say that the student wants to know why this particular topic will possibly (but not necessarily) affect his future. I also think it is safe to say that the student is not a born mathematician, otherwise he probably wouldn't be asking the question.

RE: "Motivating students by telling them why something is important is actually just telling them why you think something is important."

I think you tell them how it CAN be important for certain people. The student can decide for himself if he falls in the category. (I don't think calling something important because it is beautiful will fly. It doesn't even fly with me.)

RE: "Almost everything you learn in high school has no immediate value; this includes what you learn in core courses like math and english."

The lessons you learn in core English do have immediate value. But I never said anything about IMMEDIATE value. I have no problems with topics that will not become handly until they are late in their college career, as long as you can express that importance.

Keep in mind that we are talking about middle and high school students.

Most of the things a person learns in high school do not have immediate value to them; if they did, people would tend to remember a lot more of what they learned.

Of course there are things that will be of immediate value to some people, and there are a lot of things that will be of future value to some people. However very few things will be of either immediate or future value to everyone.

But we can't predict what will be of value to who; and even if we could, it isn't really practical to try and ensure that nobody has to learn something that is of no value to them. So we try and teach a wide breadth of material, hoping that everyone will learn at least some things that are useful.

JohnDubYa said:
I think it is safe to say that the student wants to know why this particular topic will possibly (but not necessarily) affect his future. I also think it is safe to say that the student is not a born mathematician, otherwise he probably wouldn't be asking the question.

But unless you know more about the student, it's difficult to be sure what kind of impact a subject will have on their life. I can think of reasons why everyone should learn how to read and write, or why they should learn simple arithmetic. It's much harder when the knowledge they are learning becomes more specialized.

And what good is a response that explains how something may possibly affect his future going to be? If a student wants an answer, they probably won't be satsified with you just making up some hypothetical situation where the subject material will benefit them.

JohnDubYa said:
I think you tell them how it CAN be important for certain people. The student can decide for himself if he falls in the category. (I don't think calling something important because it is beautiful will fly. It doesn't even fly with me.)

The lessons you learn in core English do have immediate value. But I never said anything about IMMEDIATE value. I have no problems with topics that will not become handly until they are late in their college career, as long as you can express that importance.

In your previous posts you expressed dissatisfaction with other responses because they would not be effective at motivating students. But now your standards seem to have changed - you don't seem to care if the response is worthless as motivational material, as long you provide a "correct" answer.

Of course, a well thought out explaination of why learning Y is useful in life for people in career X might look good to the school principal. That's probably useful for getting good evaluations.

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RE: "And what good is a response that explains how something may possibly affect his future going to be? If a student wants an answer, they probably won't be satsified with you just making up some hypothetical situation where the subject material will benefit them."

Sure, but if you point out that biologists use XXX for doing YYY, a student will appreciate the topic more then if you say "because it's beautiful." The student may not know whether or not he is going to be a biologist, but at least he realizes the mathematics isn't simply being taught for its own sake.

RE: " you don't seem to care if the response is worthless as motivational material, as long you provide a "correct" answer."

When did I ever say anything remotely like that? Let's not put words in my mouth. I have always maintained that the practical importance of material should be stressed as much as possible. I never said that the relevance needed to be immediate. That was a straw man stated by someone else.

JohnDubYa said:
RE: "And what good is a response that explains how something may possibly affect his future going to be? If a student wants an answer, they probably won't be satsified with you just making up some hypothetical situation where the subject material will benefit them."

Sure, but if you point out that biologists use XXX for doing YYY, a student will appreciate the topic more then if you say "because it's beautiful." The student may not know whether or not he is going to be a biologist, but at least he realizes the mathematics isn't simply being taught for its own sake.

RE: " you don't seem to care if the response is worthless as motivational material, as long you provide a "correct" answer."

When did I ever say anything remotely like that? Let's not put words in my mouth. I have always maintained that the practical importance of material should be stressed as much as possible. I never said that the relevance needed to be immediate. That was a straw man stated by someone else.

You said that is doesn't matter if your example of how the material is important shows that it is important to the student...just that it is important to someone.

Your very first post included a remark about theoretical physicists that suggests you want examples from a career you consider to be "practical", and not just an example from any career. So why would the student be any different? What makes you think they care about the fact the a biologist uses something, unless you know they want to be a biologist?

If a student wants to know about the importance of something, they probably want to know why it's important to them. Not why it's important to a career that you think is important, but they care nothing about.