Most Useless Math Topics for Experienced Scientists & Educators

[krab]

regardless of practicality.

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

What about the other 55%?

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]

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!

 

[e(ho0n3]

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 weird symbolism.

 

[JohnDubYa]

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?"

 

[styler]

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

scroll down

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

 

[arildno]

I quote the entry from the dictionary in full:

"ir·re·gard·less ( P ) Pronunciation Key (r-gärdls)
adv. Nonstandard
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.

 

[Zorodius]

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.

 

[JohnDubYa]

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.

 

[JohnDubYa]

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.

 

[Zorodius]

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.

 

[master_coda]

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.

 

[JohnDubYa]

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.

 

[master_coda]

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.

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.

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 explanation 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.

 

[JohnDubYa]

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.

 

[master_coda]

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.

 

[JohnDubYa]

Theoretical physicists are so rare and study at such a high level that very few students would appreciate math topics that are relegated to their discipline. Biology is unlike theoretical physics in this regard. If I show how solving simultaneous differential equations is used to model wolf populations, students will understand that and appreciate it. Quaternions? Probably not.

 

[master_coda]

Theoretical physicists are so rare and study at such a high level that very few students would appreciate math topics that are relegated to their discipline. Biology is unlike theoretical physics in this regard. If I show how solving simultaneous differential equations is used to model wolf populations, students will understand that and appreciate it. Quaternions? Probably not.

What do teachers do in an ordinary high school where the majority of students have no appreciation or interest in either physics or biology? Most teachers will not be lucky enough to work at a school where the students are specializing in biology.

Quaternions are sometimes used in computer science to do 3D modelling.

 

[futb0l]

Rather than a specific subject, I'd like to nominate the generic set of all problem solving techniques where students are taught something incredibly overspecialized simply to solve one certain class of problem.

For instance, "mixture" problems. (John has two containers of punch. One is 5% juice, the other is 10% juice. How much of each should John mix together to get a 10-liter solution of 7% juice?) Rather than using these problems as general examples of how to describe and solve mathematical relationships involving percentages, students are frequently taught to set up specialized grids that include the given information, and then compute the missing information using the pattern of the grids. Essentially, rather than being taught problem solving skills, students are taught yet another step-by-step process to follow, without understanding why it works or how they could develop a similar process on their own for a different sort of problem.

I can understand why this would be appealing to math teachers - anyone can learn a process through repetition and reproduce it on demand, given sufficient practice, but teaching someone a concept is harder. Still, I think it's a disservice to students to do it that way.

Also - unrelated to the previous point - quaternions are a subject that will be of no use to most people, even in the sciences, although they do produce elegant solutions to certain problems.

Wow, I totally agree.. u couldn't explain it better.

 

[JohnDubYa]

RE: "What do teachers do in an ordinary high school where the majority of students have no appreciation or interest in either physics or biology? Most teachers will not be lucky enough to work at a school where the students are specializing in biology."

Students don't specialize at the secondary level. But students, by and large, are interested in biological applications, even if they never plan to study biology.

There is no way around it. Modelling wolf/sheep populations is simply more interesting, and accessible, to high school students than gauge field theory. And those students who don't even find population modelling interesting? Well, they belong to that 55% who are completely unapproachable. They may as well not even be there.

RE: "Quaternions are sometimes used in computer science to do 3D modelling."

Yes, I'm aware of that. Good point. As long as the connection can be explained to students, I have no qualms about teaching subjects like quaternions to high school students (although it is a pretty advanced topic in algebra). Without the connection, forget it. They will just think you are wasting their time.

 

[master_coda]

Students don't specialize at the secondary level. But students, by and large, are interested in biological applications, even if they never plan to study biology.

There is no way around it. Modelling wolf/sheep populations is simply more interesting, and accessible, to high school students than gauge field theory. And those students who don't even find population modelling interesting? Well, they belong to that 55% who are completely unapproachable. They may as well not even be there.

Do you actually have any evidence to back up these assertions, or are you just talking out of your ass? I'm not just going to believe that students are interesting in biology or biological applications just because some teacher says so.

You aren't even consistent. One moment, you're complaining that students deserve a proper explanation for why they have to learn something, instead of just getting a dictatorial "because we said so". Then you're making sweeping statements saying that students who aren't interested in applications you consider important are unapproachable.

Yes, I'm aware of that. Good point. As long as the connection can be explained to students, I have no qualms about teaching subjects like quaternions to high school students (although it is a pretty advanced topic in algebra). Without the connection, forget it. They will just think you are wasting their time.

I sure hope they don't get taught. Whenever any kind of difficult scientific or mathematical subject gets taught to high school students, they always get a watered down version of the real thing. It might work better if teenagers were taught as if they were intelligent people instead of generic faceless children.

 

[JohnDubYa]

RE: "Do you actually have any evidence to back up these assertions, or are you just talking out of your ass? "

I think you are taking this a little too personally. So maybe it is best we end the discussion here.

 

[Hurkyl]

He has a point; you seem particularly biased towards what you find interesting. You call quaternions advanced, though they are just barely beyond complex numbers. You compare solving a ridiculously simplified toy population model with differential equations to gauge field theory, hardly comparable as techniques. I wouldn't have said anything, but you seem to be attempting to offload criticism onto Master Coda rather than address it.

 

[JohnDubYa]

RE: "He has a point; you seem particularly biased towards what you find interesting."

Actually, I'm a theoretical physicist, not a biologist. You won't find a single post from me the biology section of this forum. If anything, my stance runs counter to my background. Physicists tend to elevate the importance, meaning, and beauty of their work. I do, but I have enough experience with high school students to know when I am doing them a disservice for the sake of my own interests.

RE: "You call quaternions advanced, though they are just barely beyond complex numbers."

Yes, and we are talking about middle school and high school levels here, not college level.

If you want to teach quaternion algebra to high school students, go for it.

RE: "You compare solving a ridiculously simplified toy population model with differential equations to gauge field theory, hardly comparable as techniques."

Which was my point all along --- that some issues are far too advanced to be concerned with at the middle school and high school levels and that we should concentrate on those issues that are more accessible. Obviously I exaggerated for effect.

RE: "I wouldn't have said anything, but you seem to be attempting to offload criticism onto Master Coda rather than address it."

I have not criticized him one iota. And what criticism have I not addressed?

 

[Math Is Hard]

I find all your comments very interesting, JohnDubYa. I am studying to become a teacher one day, and I know that one of the biggest challenges I'll face is holding students' attention. I am particularly interested in learning what will make a subject or technique meaningful for them.
I think that in the society we live in we are bombarded with so much information that a lot of kids are programmed to instantly filter, filter, filter everything as it comes in and only hang on only to the small amount of information that think will be relevant later on. Anyway, I find your comments on your first-hand experience with teaching very informative.

 

[techwonder]

The most useless math I have learned so far is fraction calculation.

 

[master_coda]

And what criticism have I not addressed?

Well, you haven't backup up your assertion that a lot more students will be interested in a biology example than a physics one.

And you haven't addressed the fact that you are very understanding when students aren't interested in a physics example, but if they don't appreciate your biology one then all of a sudden you classify them as unreachable.

To me that makes it sound like you have a much higher opinion of biology compared to physics (despite your specialization in biology). Otherwise why would you consider it to be normal for students to be uninterested in physics, but unacceptable for them to be uninterested in biology?

 

[JohnDubYa]

RE: "Well, you haven't backup up your assertion that a lot more students will be interested in a biology example than a physics one."

I base it on personal experience (I have taught physics at the high school level) and common sense. Students can relate to biology because they interact with biological examples. They know wolves and sheep. They don't know abstract algebra.

And I referred specifically to THEORETICAL phyiscs in my examples. Practical physics DOES interest them to a significant degree.

RE: "And you haven't addressed the fact that you are very understanding when students aren't interested in a physics example, but if they don't appreciate your biology one then all of a sudden you classify them as unreachable."

The key word is UNDERSTAND. Yes, I do understand when they don't appreciate topics in theoretical physics. I probably wouldn't have at that level either.

RE: "To me that makes it sound like you have a much higher opinion of biology compared to physics (despite your specialization in biology)."

Who cares?? Why are you trying to turn this into a personal issue? It doesn't matter what *I* like, appreciate, understand, or respect. What matters is reality. And when you step into a class filled with 30 high school students who are wondering why they need to take a math class, reality rules.

RE: "Otherwise why would you consider it to be normal for students to be uninterested in physics, but unacceptable for them to be uninterested in biology?"

Again, it's all about reality, not my personal wish. Sure, I would love high school students to become interested in theoretical physics. Not gonna' happen.

In essence, whenever I try to cite examples of the practical applications of mathematical topics, I look for biology, economics, psychology, and so on. If the only application I can surmise appears in theoretical physics at an advanced level, I have to wonder if the topic is worth teaching.

 

[remcook]

about Quaternions: They are very much used (not sometimes, often!) in Satellite Control and other control problems! Definately not useless!
(excuse the exclamation marks)

 

[master_coda]

I base it on personal experience (I have taught physics at the high school level) and common sense. Students can relate to biology because they interact with biological examples. They know wolves and sheep. They don't know abstract algebra.

And I referred specifically to THEORETICAL phyiscs in my examples. Practical physics DOES interest them to a significant degree.

The key word is UNDERSTAND. Yes, I do understand when they don't appreciate topics in theoretical physics. I probably wouldn't have at that level either.

Who cares?? Why are you trying to turn this into a personal issue? It doesn't matter what *I* like, appreciate, understand, or respect. What matters is reality. And when you step into a class filled with 30 high school students who are wondering why they need to take a math class, reality rules.

Again, it's all about reality, not my personal wish. Sure, I would love high school students to become interested in theoretical physics. Not gonna' happen.

In essence, whenever I try to cite examples of the practical applications of mathematical topics, I look for biology, economics, psychology, and so on. If the only application I can surmise appears in theoretical physics at an advanced level, I have to wonder if the topic is worth teaching.

Except you're missing the whole point I was making...I'm not saying that you're using biology examples because you love biology and wish that all students would study it. I'm saying that you have this strange idea that certain subjects like biology are "practical" while other subjects are not, and then are assuming that students are reachable if and only if they can relate to your chosen subjects.


Students do not generally specialize into their fields of interest until after high school, although it starts to happen a little bit in the last year or two of high school. That means that in any given class, it is unlikely you will be able to pick a specific field of interest and find more than a handful of students who actually care about it. So examples drawn from a specific field are not going to interest very many students in your class. The fact that biology is straight from the real world doesn't change that; we're utterly dependant upon the state of the economy for our survival, yet even most college students can't be bothered to learn anything about basic economics. Being in the real world does not magically mean that people are going to better relate to a subject, or have an easier time understanding it.

Of course, you don't seem to be drawing examples from just a single field. You probably can reach a lot students by exposing them to uses in a wide variety of fields - almost everybody gets at least one example that interests them. But then why are you presupposing that students are going to be interested in a select group of subjects? Do you actually never have students who are interested in fields you don't consider practical?

 

[JohnDubYa]

RE: "I'm saying that you have this strange idea that certain subjects like biology are "practical" while other subjects are not, and then are assuming that students are reachable if and only if they can relate to your chosen subjects."

No, I think that there are subjects that STUDENTS think are more practical than others. It isn't about ME, ME, ME. It's about the STUDENTS, STUDENTS, STUDENTS and what THEY value.

High school teachers need to work within that framework. Those teachers that try to turn their high school courses into college courses do the students a disservice, because the students (by and large) have not developed an attitude that appreciates esoteric subjects. If you ignore that reality, you will see nothing but glazed-over eyes in the room and the students won't learn a damn thing.

RE: "Do you actually never have students who are interested in fields you don't consider practical?"

Yes, but you cannot just teach to those students. That is why you must consider whether or not a mathematical topic has interests beyond the esoteric. And if it doesn't, then you should consider whether or not the subject is worth discussing at that level.

That is all I have been saying. And there is no need to parse every last word I write looking for an inconsistency somewhere. This isn't about ME.