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Teaching Kids to Love Math

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Re: Teaching Kids to Love Math

#31

Post by 5xz41s0P8T5N »

walrus wrote: post #27
lutusp wrote: post #20

Earlier quoted context omitted.

> The only people who love math are math majors. Most humans don't love math. Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end. > This is like trying to become smarter by listening to classical music. Granted the problem with the basic idea, this has it all over trying to become smarter by listening to Country & Western music.…

> Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end. Can you elaborate? To me, the interesting part of mathematics is the process of manipulating expressions, not the expressions themselves. For example, the number pi would be pretty boring if it weren't for the theorems related to it.

That argument confuses 'loving math' with 'loving things made of math'. I enjoy eating cake and playing video games, that does not make me a chemist and developer.

Your parent comment missed the point of his parent.

Re: Teaching Kids to Love Math

#32

Post by walrus »

5xz41s0P8T5N wrote: post #31
walrus wrote: post #27

Earlier quoted context omitted.

> Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end. Can you elaborate? To me, the interesting part of mathematics is the process of manipulating expressions, not the expressions themselves. For example, the number pi would be pretty boring if it weren't for the theorems related to it.

That argument confuses 'loving math' with 'loving things made of math'. I enjoy eating cake and playing video games, that does not make me a chemist and developer. Your parent comment missed the point of his parent.

Maybe. I'd like to hear back from lutusp before I jump to that conclusion.

Re: Teaching Kids to Love Math

#33

Post by debacle »

lutusp wrote: post #22
debacle wrote: post #13

Earlier quoted context omitted.

You can't justify a $200 price tag for a 100 page text book.

That might sometimes be true, but the textbook the OP referred to is less than $16.00: http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/d...

Which is why no one will ever use it, because you can't justify a $200 price tag for a 100 page text books.

e.g. no college will ever endorse this book as a text, because they need to sell 60k in calc 101 text books each semester so they can get their cut.

Re: Teaching Kids to Love Math

#34

Post by 5xz41s0P8T5N »

As a math undergrad dealing with mathematical anxiety (how silly, I know), I wish math education started with logic.

Is there evidence that learning discrete math first leads to better skill, or that it is easier/more fun for kids? or even teachers?

I suspect I only feel this way because discrete math seems so foundational now, but perhaps what is taught matters less than how it's taught.

I wish education was more empirical.

Re: Teaching Kids to Love Math

#35

Post by lutusp »

debacle wrote: post #33
lutusp wrote: post #22

Earlier quoted context omitted.

That might sometimes be true, but the textbook the OP referred to is less than $16.00: http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/d...

Which is why no one will ever use it, because you can't justify a $200 price tag for a 100 page text books. e.g. no college will ever endorse this book as a text, because they need to sell 60k in calc 101 text books each semester so they can get their cut.

> ... no college will ever endorse this book as a text ...

Yes, fair enough, however I think the discussion is not so much about schooling as education. Not all education takes place in college -- and with costs rising as they are, I predict a future with many more autodidacts -- self-educators.

"I have never let my schooling interfere with my education." -- Mark Twain

Re: Teaching Kids to Love Math

#36

Post by eli_gottlieb »

lutusp wrote: post #20
stephengillie wrote: post #9

The only people who love math are math majors. Most humans don't love math. Teaching kids to love math is pointless. Math is a tool, like a hammer or a DLL. Do you love your screwdrivers and methods? Let's teach kids about how math is useful to them in their lives, and let them take it from there. Ongoing research is shedding new light on the importance of math to children's success. Math skill at kindergarten entry…

> The only people who love math are math majors. Most humans don't love math. Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end. > This is like trying to become smarter by listening to classical music. Granted the problem with the basic idea, this has it all over trying to become smarter by listening to Country & Western music.…

Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end.

Do you mean the computer-graphics movie, or The Last Airbender? None of those really has any mathematical interest for the viewer -- though The Last Airbender rocks.

Re: Teaching Kids to Love Math

#37

Post by [deleted] »

lutusp wrote: post #20
stephengillie wrote: post #9

The only people who love math are math majors. Most humans don't love math. Teaching kids to love math is pointless. Math is a tool, like a hammer or a DLL. Do you love your screwdrivers and methods? Let's teach kids about how math is useful to them in their lives, and let them take it from there. Ongoing research is shedding new light on the importance of math to children's success. Math skill at kindergarten entry…

> The only people who love math are math majors. Most humans don't love math. Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end. > This is like trying to become smarter by listening to classical music. Granted the problem with the basic idea, this has it all over trying to become smarter by listening to Country & Western music.…

[deleted]

Re: Teaching Kids to Love Math

#38

Post by lutusp »

5xz41s0P8T5N wrote: post #31
walrus wrote: post #27

Earlier quoted context omitted.

> Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end. Can you elaborate? To me, the interesting part of mathematics is the process of manipulating expressions, not the expressions themselves. For example, the number pi would be pretty boring if it weren't for the theorems related to it.

That argument confuses 'loving math' with 'loving things made of math'. I enjoy eating cake and playing video games, that does not make me a chemist and developer. Your parent comment missed the point of his parent.

> That argument confuses 'loving math' with 'loving things made of math'.

That might be a fair objection if they could be separated. If I say y = cos(x) * e^-x^2, when expressed in two dimensions I get this:

http://i.imgur.com/MePPy.png

And in three dimensions I get this:

http://i.imgur.com/9gr4u.jpg

But I'm still looking at y = cos(x) * e^-x^2 -- the picture only confirms the mathematical identity. So it is with Avatar -- when we watch Avatar, we're looking at math.

And much of nature is defined using math -- note that I said, not described, but defined. Here's an example -- there are species of locusts (cicadas, actually) that reproduce at 13-year and 17-year intervals. Until recently, no on knew why. It turns out that both 13 and 17 are prime numbers, and this ties into a survival strategy hatched by natural selection (quite by chance). All explained here:

http://arachnoid.com/prime_numbers/index.html#Mathematical_L...

In other words, the locust survival strategy is math speaking out loud.

If you read a book in which a seashore is described, do you argue that the description isn't germane to the thing being described? If the writer isn't skilled, or the reader is lacking in the capacity for visualization, then that is perhaps a legitimate objection, but for most people, words convey meaning. So does math. Math is a language in much the same way that words are a language.

The distinction between "loving math" and "loving things made of math" is dubious at best. When P.A.M. Dirac wrote his now-famous equation that describes how relativistic electrons behave, he noticed that it had two solutions -- sort of like a quadratic equation.

At first he doubted that there could really be two kinds of matter, as his equation suggested. But within a few years antimatter was observed, and Dirac forever afterward wished he had been willing to take his own equation at face value and predict antimatter himself.

My point? The math told him something about reality that no one knew, even him. To put it another way, the math was reality.

Re: Teaching Kids to Love Math

#39

Post by lutusp »

walrus wrote: post #27
lutusp wrote: post #20

Earlier quoted context omitted.

> The only people who love math are math majors. Most humans don't love math. Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end. > This is like trying to become smarter by listening to classical music. Granted the problem with the basic idea, this has it all over trying to become smarter by listening to Country & Western music.…

> Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end. Can you elaborate? To me, the interesting part of mathematics is the process of manipulating expressions, not the expressions themselves. For example, the number pi would be pretty boring if it weren't for the theorems related to it.

> To me, the interesting part of mathematics is the process of manipulating expressions, not the expressions themselves.

I think most mathematicians and physicists would disagree. I think such people wouldn't want distinguish between generating equations and studying them and their effects, especially with physical equations that must reflect reality to have any value.

For example, I can make elaborate predictions about a lot of physical reality with:

f = G M_1 M_2 / r^2 (gravitational force)

And if I want to study tidal forces, all I need to do is take the first derivative of the above:

f = 2 G M_1 M_2 / r^3 (tidal force)

I have just "manipulated" an equation, but with an awareness of the equation's physical consequences and effects, and I can now use the second equation to make predictions about ocean tides, the future position of the moon, and the temperature of the volcanoes on Io (which arise from the energy of tidal forces). So for me, the equation itself is immensely valuable for modeling reality -- it's more than a case of manipulating terms.

> For example, the number pi would be pretty boring if it weren't for the theorems related to it.

Pi, as it turns out, may serve as a source for random sequences of digits. So apart from its geometric meaning, Pi stays interesting.

Re: Teaching Kids to Love Math

#40

Post by lutusp »

eli_gottlieb wrote: post #36
lutusp wrote: post #20

Earlier quoted context omitted.

> The only people who love math are math majors. Most humans don't love math. Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end. > This is like trying to become smarter by listening to classical music. Granted the problem with the basic idea, this has it all over trying to become smarter by listening to Country & Western music.…

Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end. Do you mean the computer-graphics movie, or The Last Airbender ? None of those really has any mathematical interest for the viewer -- though The Last Airbender rocks.

> Do you mean the computer-graphics movie, or The Last Airbender?

I meant Avatar, the computer-graphics movie, although I really like The Last Airbender, and I wish it had gotten more attention.

Avatar is nothing more or less than a very long mathematical expression, sort of like a computer plot conducted very carefully for aesthetic reasons. When they watch Avatar, viewers are looking at mathematics.

> None of those really has any mathematical interest for the viewer

People who watch Avatar, who find it interesting, are appreciating mathematics even though they may not realize it. All the lighting, the colors, the motions, are expressed by the mathematics of physical reality.

When a real tree falls, it's very mathematical. When the big tree fell in Avatar, that was also mathematical. As to the first, mathematics could be used to predict exactly how the real tree falls. As to the second, the falling tree was the result of a computer solving a differential equation that described the tree and gravity.

They're really the same -- mathematics predicting reality, and mathematics generating an imaginary reality.

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