Math thread

[jtwcornell91]

Maybe we should move the math talk over here, rather than continuing the Cornell-Clarkson thread ad infinitum.

Also, it gives me a place to post this.

[Trotsky]

And this:

[ftyuv]

Math is just one theory, and I think schools should be allowed to teach alternative theories as well.

[ursusminor]

Maybe we should move the math talk over here, rather than continuing the Cornell-Clarkson thread ad infinitum.

Also, it gives me a place to post this.

Slide 6. ::banana::

[billhoward]

Nice post. Us liberal arts types hustled over to Wikipedia to look up Riemann-Zeta Function. More than the math geeks had to go look up herpes.

[Robb]

Friend of mine just posted this on Facebook.  Liked it.  Linked it.
Math is not linear.

[Trotsky]

Friend of mine just posted this on Facebook.  Liked it.  Linked it.
Math is not linear.

This is great, thank you for posting it.

[David Harding]

Friend of mine just posted this on Facebook.  Liked it.  Linked it.
Math is not linear.

I like this very much, too.  One major obstacle to the approach advocated here is that it requires math teachers who are comfortable with a broad base of math concepts, not just the linear material.  I fear that many are well-intentioned, but just not sufficiently well educated.  I remember parents night, or whatever they called it, when my daughter's math teacher apologized for having to spend a week on polar coordinates, which he said were totally useless, just because they're in the book.  I refrained from screaming at him, but afterward told him that I disagreed with that assessment.  He acknowledged that he had heard that they were used in electrical engineering, but as his college major was economics, he had not had any exposure to their applications.  A couple of days later I sent him a couple of examples of ways in which I had used them recently.  Two years later, when my second daughter had the same class, he was using my notes as handouts.

[Robb]

Friend of mine just posted this on Facebook.  Liked it.  Linked it.
Math is not linear.

I like this very much, too.  One major obstacle to the approach advocated here is that it requires math teachers who are comfortable with a broad base of math concepts, not just the linear material.  I fear that many are well-intentioned, but just not sufficiently well educated.  I remember parents night, or whatever they called it, when my daughter's math teacher apologized for having to spend a week on polar coordinates, which he said were totally useless, just because they're in the book.  I refrained from screaming at him, but afterward told him that I disagreed with that assessment.  He acknowledged that he had heard that they were used in electrical engineering, but as his college major was economics, he had not had any exposure to their applications.  A couple of days later I sent him a couple of examples of ways in which I had used them recently.  Two years later, when my second daughter had the same class, he was using my notes as handouts.

Ha.  Well, this presentation would be how to teach math excellently.  Sadly, very few people in any field are really destined for excellence...

My math teacher was great - more than 10 out of our class of 20 got 5s on BC calculus.  However, even she was largely unaware of the practical applications for many of the topics.  In my experience, high school teachers tend to be teachers first, and subject matter experts second.  Clearly, a balance is needed.

Since it's anecdote time, yours reminded me of my physics teacher, who was terrible.  Almost nobody ever even bothered to take the AP exam.  I worked my butt off for 6 weeks (spending upwards of 20 hours per week on my own) to get myself ready for the exam.  Three years later, when my sister took the class he was introducing himself and said something along the lines of, "I think I do a pretty good job.  I even had one student who got a 5 on the AP exam..."

[Jeff Hopkins '82]

My high school physics teacher was also terrible.  He quit teaching a couple years after I graduated to become a priest :-O

[ftyuv]

This conversation reminds me a bit of a suggestion I heard on NPR a while back on reforming universities. The person pointed out that professors in universities are often extremely specialized; they'll know their one (sometimes esoteric) field through and through, but most useful applications require application of various fields. The person's suggestion was that majors be focused on problems rather than specific academic fields; one might major in water shortage problems in poor countries, for instance -- rather than in biology, or politics, or economics, or operational engineering, or any of the other fields that go into solving water shortage.

I don't think the idea should be taken to its full extreme, but I thought it was an interesting idea nonetheless.

[Trotsky]

The person's suggestion was that majors be focused on problems rather than specific academic fields; one might major in water shortage problems in poor countries, for instance -- rather than in biology, or politics, or economics, or operational engineering, or any of the other fields that go into solving water shortage.

I don't think the idea should be taken to its full extreme, but I thought it was an interesting idea nonetheless.

Interesting idea, though one problem comes to mind.  Generally, we organize work around a problem and then call in experts from a lot of fields who bring field-general principles to bear on a reality-specific phenomenon.  Those experts are useful for an infinite number of "accidental" problems in real life.

The suggestion strikes me as training architects to build the Sears Tower.  You'll wind up with a great Sears Tower when you're done, but not much else.

And for that matter, if you already know enough about a problem to teach to it... it's not really a problem.

But it's probably a decent perspective to keep in mind.

[Robb]

The person's suggestion was that majors be focused on problems rather than specific academic fields; one might major in water shortage problems in poor countries, for instance -- rather than in biology, or politics, or economics, or operational engineering, or any of the other fields that go into solving water shortage.

I don't think the idea should be taken to its full extreme, but I thought it was an interesting idea nonetheless.

Interesting idea, though one problem comes to mind.  Generally, we organize work around a problem and then call in experts from a lot of fields who bring field-general principles to bear on a reality-specific phenomenon.  Those experts are useful for an infinite number of "accidental" problems in real life.

The suggestion strikes me as training architects to build the Sears Tower.  You'll wind up with a great Sears Tower when you're done, but not much else.

And for that matter, if you already know enough about a problem to teach to it... it's not really a problem.

But it's probably a decent perspective to keep in mind.

I think this actually already occurs in a number of fields.  For example, my sister-in-law is working on a masters of public health degree.  Her courseload is incredibly diverse - everything from pure statistics to virology to economics to vaccine policy to international relations.  It's a real mashup of all the tools and knowledge that it would take to be a proficient problem solver in the field of public health. This certainly doesn't bring to mind your overly-specific "Sears Tower" fear.  In fact, it's really the exact opposite - they're delving into such a wide variety of topics that they aren't being trained how to solve any specific problem.

[Trotsky]

The person's suggestion was that majors be focused on problems rather than specific academic fields; one might major in water shortage problems in poor countries, for instance -- rather than in biology, or politics, or economics, or operational engineering, or any of the other fields that go into solving water shortage.

I don't think the idea should be taken to its full extreme, but I thought it was an interesting idea nonetheless.

Interesting idea, though one problem comes to mind.  Generally, we organize work around a problem and then call in experts from a lot of fields who bring field-general principles to bear on a reality-specific phenomenon.  Those experts are useful for an infinite number of "accidental" problems in real life.

The suggestion strikes me as training architects to build the Sears Tower.  You'll wind up with a great Sears Tower when you're done, but not much else.

And for that matter, if you already know enough about a problem to teach to it... it's not really a problem.

But it's probably a decent perspective to keep in mind.

I think this actually already occurs in a number of fields.  For example, my sister-in-law is working on a masters of public health degree.  Her courseload is incredibly diverse - everything from pure statistics to virology to economics to vaccine policy to international relations.  It's a real mashup of all the tools and knowledge that it would take to be a proficient problem solver in the field of public health. This certainly doesn't bring to mind your overly-specific "Sears Tower" fear.  In fact, it's really the exact opposite - they're delving into such a wide variety of topics that they aren't being trained how to solve any specific problem.

I'm not going to argue against people getting training outside their cubbyhole; that's always good.

[David Harding]

The person's suggestion was that majors be focused on problems rather than specific academic fields; one might major in water shortage problems in poor countries, for instance -- rather than in biology, or politics, or economics, or operational engineering, or any of the other fields that go into solving water shortage.

I don't think the idea should be taken to its full extreme, but I thought it was an interesting idea nonetheless.

Interesting idea, though one problem comes to mind.  Generally, we organize work around a problem and then call in experts from a lot of fields who bring field-general principles to bear on a reality-specific phenomenon.  Those experts are useful for an infinite number of "accidental" problems in real life.

The suggestion strikes me as training architects to build the Sears Tower.  You'll wind up with a great Sears Tower when you're done, but not much else.

And for that matter, if you already know enough about a problem to teach to it... it's not really a problem.

But it's probably a decent perspective to keep in mind.

It's hard to argue that we don't need both the specialists and generalists.  The trick is finding the right balance, even within a field like medicine.  One of the beauties of Cornell is the breadth of really deep expertise that can be brought together.