Most Useless Math Topics for Experienced Scientists & Educators

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Discussion Overview

The discussion centers around the perceived usefulness of various mathematical topics for experienced scientists and educators. Participants explore specific mathematical concepts, their applications, and the teaching methods associated with them, including polynomial long division, problem-solving techniques, and the relevance of certain mathematical structures like quaternions and functions.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants question the practical utility of polynomial long division, suggesting it may only be relevant for specific theoretical applications.
  • Others argue that polynomial long division can aid in identifying factors and simplifying expressions, particularly when dealing with higher-order polynomials.
  • A participant criticizes the teaching of specialized problem-solving techniques, such as those used in mixture problems, arguing they do not foster true understanding of mathematical concepts.
  • Quaternions are mentioned as potentially elegant but largely irrelevant for most practitioners in the sciences, although one participant suggests they may have applications in theoretical physics.
  • There is a discussion about the practical applications of polynomial division in computer science, particularly regarding efficiency in calculating remainders.
  • Some participants express skepticism about the necessity of certain mathematical concepts, such as functions being defined as subsets of relations, suggesting alternative views may be more useful in specific fields like computer science.
  • Concerns are raised about the limited applicability of certain integration techniques learned in calculus, with some participants favoring computational tools over manual methods.
  • There is a recognition that understanding various mathematical techniques can be beneficial for comprehending more advanced topics, even if those techniques are not frequently used.

Areas of Agreement / Disagreement

Participants express a range of views on the usefulness of specific mathematical topics, with no clear consensus on which topics are truly "useless." Disagreements exist regarding the relevance of certain techniques and concepts, as well as the effectiveness of teaching methods.

Contextual Notes

Participants highlight limitations in the teaching of mathematics, including the potential overspecialization of problem-solving techniques and the challenge of fostering deep understanding versus rote learning. There are also references to the evolving nature of mathematical education and its practical applications.

  • #91
JohnDubYa said:
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.

Then why don't you teach based on what they are interested in, instead of insisting that we only use examples that you think they should be interested in? I've been saying that you should decide upon examples based on what students actually care about, and that you shouldn't just use examples based on subjects you've predetermined to be "interesting". IF YOU CARE ABOUT STUDENTS THEN STOP INSISTING THAT THEY CAN ONLY BE INTERESTED IN CERTAIN SUBJECTS.

JohnDubYa said:
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.

I don't care about you. I care about the unfortunate people you are going to teach who aren't interested in what you care about. You're telling us it's wrong to use esoteric examples because we're ignoring all those students who want "practical" examples, whatever the hell that means, and then you go on to tell us that we should only use practical example, thereby ignoring all the students who don't care about practical examples.

If you cared about the students, you wouldn't insist they be taught using only certain examples, automatically excluding a whole bunch of students.
 
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  • #92
I don't care about biology, okay? I am not a biologist. I have no personal reason to use biological examples. I have no reason to insist that students must be interested in biology.

I resort to biology because in my experience that is one of the topics that students find most interesting. And in my experience, they are not intersted in esoteric theoretical physics. I play with the hand that is dealt me.

I go by my experience teaching the subjects to actual high school students and common sense and I have yet to meet a high school student who wasn't interested in practical examples.

I mentioned earlier that you were starting to take this to the personal level. Now you are claiming that I don't care about my students, and that any student that enters my classroom is unfortunate. I have more important things to do then to read personal attacks on my character, so I suggest you change your tone if you want this conversation to go any further.
 
  • #93
I suggest neither continue this conversation further, in this thread.
 
  • #94
JohnDubYa said:
I resort to biology because in my experience that is one of the topics that students find most interesting. And in my experience, they are not intersted in esoteric theoretical physics. I play with the hand that is dealt me.

I go by my experience teaching the subjects to actual high school students and common sense and I have yet to meet a high school student who wasn't interested in practical examples.
Since when do they teach theoretical physics in high school!? I think most of what one learns in primary and secondary school is practical knowledge (expect for philosophy, theology, etc.), so when a student asks you "So what?", your answer should immediately be "Because you will most likely need this later in life if you don't want to become an uneducated bum."

I believe that teaching is not only about transfering knowledge. I think a teacher's prime responsibility is to develop a student's problem solving ability regardless of what is being taught. Giving only practical examples will only get you so far.

I believe most high schoolers will prefer practical examples since they are 'easier' to digest than some deep abstract result (which would require them to think abstractly and most high schoolers (as I've experienced) are lazy to do so).

This is what I believe.
 
  • #95
Hurkyl said:
I suggest neither continue this conversation further, in this thread.

Agreed. Clearly my experiences are very different than those of JohnDubYa, so there isn't much progress that we can make going back and forth like this.

And JohnDubYa, I really don't know why you thought I was taking it so personally. I don't hold back from attacking any point of view I disagree with; if someone introduces their personal experience into the argument, it doesn't get any special treatment from me.
 
  • #96
RE: ""Because you will most likely need this later in life if you don't want to become an uneducated bum.""

That's the same argument their parents have been using on them since Day One. If it doesn't work for their parents, it most likely won't work for you.

RE: "I don't hold back from attacking any point of view I disagree with;"

You didn't just attack my point of view, you questioned my motives.

I am finished with the discussion.
 

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