[mxlm]

"Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary."

I'm sorry, I prefer my "imaginary" 7'2" tall about 250 lbs lean with lavender skin, long ears projecting about 10 inches behind the head with 'huge tracts of land'.

.....the f*ck?

World of Warcraft?

[CP5670]

I always like to work on math problems coming from applications (and would even say I prefer them), but I have seen enough of pure math that I can appreciate it. At a high level, there is little difference between pure and applied math anyway.

And I was like, without physics, what is the POINT of math???

There are many applications of math outside physics. EE and computer science have their own set of problems that are somewhat different from the ones in physics, and which I think are more interesting.

[Uchuujinsan]

After reading the first pages I have to say he is both absolutely right and absolutely wrong.
Math is fantastic and interesting because it's an art, an art with practicable applications, but still one with endless creativity. On the other hand, only mathematicians will see it that way. Some like Freespace 2, some don't - some like The Sims, others hate it. It's just a matter of taste, and different people have a different taste. Teaching the "interesting" stuff won't change that many people still simply won't like it.
But some knowledge is almost required in life, and school has to teach you that knowledge, no matter if the teaching itself is (or can be) fun.

You should try to make the subject interesting for your students, but in the normal school there is no simple solution. You have to look at the people in your class and teach in a way that manages to motivate exactly those individuals.

[Ghostavo]

As it stands, you don't encounter much in the way of genuinely interesting math until the graduate level (so most people never see it at all), but that is really an issue with the way the math education system is structured.

I disagree. There is some very basic and beautiful math way before you hit that level.


I had the good fortune to like playing with numbers when I was younger and participating in many math olympiads. To me, that method of learning math was very satisfying, even more so, since many problems were rehashed to be solved with a completely different path of thought and assumed knowledge in latter years.

Once I hit graduate level, there were lot of new interesting subjects, but the time required to play with them was too short unfortunately to have a sort of native understanding of them.

[CP5670]

I disagree. There is some very basic and beautiful math way before you hit that level.

I had the good fortune to like playing with numbers when I was younger and participating in many math olympiads. To me, that method of learning math was very satisfying, even more so, since many problems were rehashed to be solved with a completely different path of thought and assumed knowledge in latter years.

Once I hit graduate level, there were lot of new interesting subjects, but the time required to play with them was too short unfortunately to have a sort of native understanding of them.

Actually, that was precisely my point. You learned interesting math by doing it outside classes in some way, just like I did. I didn't mean that all interesting math is graduate level, but that you only encounter it at that point if you stick to learning it through classes. There is certainly a lot of good stuff that is accessible and easy to get into, but is simply never done in classes at lower levels.

[Mongoose]

If you've ever walked into a store where the cash registers weren't working (and sometimes even when they are), you've probably experienced it in vivid detail.  At least it gives the rest of us something to laugh at.

That isn't exactly a typical example, and even then nobody would want to sit there and add numbers together. I certainly wouldn't do it.

Okay, let's make it even simpler.  Think about the cashier who looks at you with an utterly clueless look on their face when you hand them a $20 bill and a quarter for a $15.25 charge.

I'd posted last night after reading only about half of the document, and I found some of the later discussion to be even more interesting (though who knows how much of it I can recall right now).  I do rather vehemently disagree with the notion that "teaching can't be taught," though, or that a "planned lesson" isn't valuable; while enthusiasm and passion for the topic is obviously a huge asset, there are valuable skills that can be conveyed and practiced involving handling a classroom of diverse students, and an enthusiastic off-the-rails class session can possibly do more harm than a standard directed one.  I did sympathize with the "Simplicio" perspective on geometric proofs, since that was honestly one of my favorite areas of high school math and one that came quite naturally to me, but the alternate method of looking at that triangle-in-a-semicircle problem completely blew my mind.

For anyone looking for more discussion on this, a Google search turned up some interesting back-and-forth in the comments of this blog post.

[CP5670]

Okay, let's make it even simpler.  Think about the cashier who looks at you with an utterly clueless look on their face when you hand them a $20 bill and a quarter for a $15.25 charge.

They usually just put it into their cash register's calculator if they can't figure it out instantly. It's not just a matter of doing it right, but of making that clear to the customer.

For anyone looking for more discussion on this, a Google search turned up some interesting back-and-forth in the comments of this blog post.

I recognize one of the names there. I think she was a student in a class I was TAing last year.

[Mika]

I think the original lamentation was, I don't know, unsurprising in the content. The outlined problem not only affects Maths, but pretty much all other areas of education also.

Reading through the PDF, it seemed that the main point is to remind that there are multiple ways to teach stuff to students, and teacher has to be able to see what is the best way to answer the question by a student. Different people, different methods - should be nothing new to a good teacher.

Besides, I don't consider any of the Maths stuff I got my hands on during High School "unnecessary". All of that **** has found a way to be applied in my work. However, courses held by Department of Mathematics during my stay in University could best be described by that lamentation. Luckily, I realised quite soon (probably second lecture of Linear Algebra) that I didn't have to attend the lectures... and that was an eye-opener of the University world. I could read and learn stuff all by myself.

Later on I cursed the Department of Maths to deepest pits of Hell for allowing to lecture the Linear Algebra course in about the dumbest possible way imaginable and providing worst possible learning material. Writing proofs down from the black board had to be one of the best ways I have yet seen to waste students' time. Even today when programming computers, I find my capabilities severely lacking in Linear Algebra, or in Matrix manipulations. How I wish it would have been possible to attend the Maths courses by the Faculty of Engineering, but no.

Luckily, Physics courses gave a lot more reasonable explanations of those fancy mathematical terms I heard during those torture lectures. And I'm still wondering afterwards how well could I have actually understood all that stuff had the approach been different.

[Liberator]

You know, it might be that it's never been presented right, but I'm going to sit here right now and tell you that despite all your lamenting on how the material is taught.  Kids hate math because IT IS boring.  I'm 31 years old and am more scared of an algebra(nevermind calculus!) class than I would be walking down a side street in Brooklyn or Harlem wearing a swastika.  I get lost when they try and teach me how to factor an equation to solve it, and they can't wait for me to get it because there's 29 other people in the class that do get it, so I get left behind and that's that.  The highest grade I ever made in a math class was a C, and that was a geometry class where I could use a little imagination to think of the problem in real, concrete terms.

I'll reiterate, kids don't hate math because it's presented boringly, kids hate math because IT IS BORING.

[Thaeris]

I happen to enjoy math, Lib. Boring or not boring is merely a matter of opinion.

Like any subject, it's a matter of adapting to that subject. It's surprising... you might hate a subject initially because it's rather foreign to you. Because it's so foreign, you have difficulty adapting to and assimilating the data. However, once you're familiar with it, you might actually enjoy the material.

We often tend to like or dislike something due to our ability or inability to do it. If we never adapt to and assimilate a skill, we'll of course tend not to like it. And because we don't like it, why would we waste our time doing it? Because we never do it, why would we be good at it?

There are exceptions to this, of course. Natural curiosity also make it easier to achieve competance in an area because the mind is now engaged on that topic. But still, you get good at doing something because you do it. 

If said kids aren't interested in math, which is often foreign... somehow (it just is... I remember not being great at math as well...), why would they bother to become proficient? Of course those kids will hate the subject!

[Polpolion]

You know, it might be that it's never been presented right, but I'm going to sit here right now and tell you that despite all your lamenting on how the material is taught.  Kids hate math because IT IS boring.  I'm 31 years old and am more scared of an algebra(nevermind calculus!) class than I would be walking down a side street in Brooklyn or Harlem wearing a swastika.  I get lost when they try and teach me how to factor an equation to solve it, and they can't wait for me to get it because there's 29 other people in the class that do get it, so I get left behind and that's that.  The highest grade I ever made in a math class was a C, and that was a geometry class where I could use a little imagination to think of the problem in real, concrete terms.

I'll reiterate, kids don't hate math because it's presented boringly, kids hate math because IT IS BORING.

  You've just admitted ignorance over the subject, and yet you claim to know that it's boring?

[Liberator]

I think I can tell if something is boring or not, initmate knowledge is not always required to make that determination.

[Thaeris]

As already stated, boring is a matter of opinion. 

[General Battuta]

I think I can tell if something is boring or not, initmate knowledge is not always required to make that determination.

Math definitely isn't boring. I'm not the biggest math guy in the world, though I'm good at it, but a few of the proofs I've seen - especially in combinatorics - took me aback with their beauty and elegance.

It could be fun for kids if it were presented as secret superpower knowledge. It's just not.

[iamzack]

I like math because I have moods where I actually want to do something tedious and boring. I can't even imagine how math could be considered 'beautiful.' It's just useful, like roads or mattresses. "Fun" I can understand, because some people do like fixing/solving things, or just playing with numbers. But beautiful? Ugh, are you a philosophy major?

[General Battuta]

Nope. You're just still mired in the level of math where nothing elegant has yet appeared.

[Ford Prefect]

The type of pattern analysis and manipulation involved in music theory can be highly mathematical, and I find it extremely aesthetically pleasing.

I don't wish to sound dogmatic-- I realize people's aesthetic sensibilities vary widely-- but I suspect that people who see math as purely utilitarian don't fully appreciate how much it imbues absolutely everything in the universe.

[iamzack]

Math *is* purely utilitarian. Math only exists because it is needed to help us understand the universe.

[Scotty]

Math *is* purely utilitarian. Math only exists because it is needed to help us understand the universe.

And that is why you fail.[/Yoda]

[General Battuta]

Math *is* purely utilitarian. Math only exists because it is needed to help us understand the universe.

No. Math is an art form as well.