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- Thread starter JohnDubYa
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- #27

ahrkron

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Math not only gives you tools to solve specific problems, but also (and mainly) helps you develop abstract problem-solving skills, plus, the many techniques you learn can often be applied in quite different settings if you are able to establish solid analogies.

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I hope not, as I'm a theoretical physicist.

But keep in mind that my examples were aimed at the algebra/pre-algebra level. Is it really efficient to focus on techniques that only 0.1% of the students will ever use?

Consider polynomial long division. If a teacher never shows how polynomial long division can be used to help plot a function, or optimize a computer code, should they teach it at all?

What I find in most mathematics books is a complete disconnect between mathematical techniques and their practical use. (And contrived word problems don't count.)

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Calculus 2, Statistics, and Linear Algebra

Actually that's pretty skimpy. Aren't you required to take a few more discrete math, calculus III, and some numerical analysis.

Most of computer science deals with developping data types and algorithms. IT ISN'T about writting a text editor with pink and blue text.

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I don't know why Calculus is required for CS majors. Most problems in computer science make no use of Calculus at all. I think more Discrete Maths. would be appropriate. Of course, all of what I'm saying applies to undergraduate studies. I mean, if you're going to do research in quantum computing, the more maths. you know the better.Goalie_Ca said:Actually that's pretty skimpy. Aren't you required to take a few more discrete math, calculus III, and some numerical analysis.

Most of computer science deals with developping data types and algorithms. IT ISN'T about writting a text editor with pink and blue text.

"Writing a text editor with pink and blue text" does require knowledge of data types and algorithms, so I find this argument rather flawed.

- #31

matt grime

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JohnDubYa said:What I find in most mathematics books is a complete disconnect between mathematical techniques and their practical use. (And contrived word problems don't count.)

And in when learning the basics of French they don't teach you how to use metaphor and simile using the complexity of the language to enrich your written and oral style. There's no reference to Balzac, and you're not learning to act like Madame Bovary.

Finding a subject uninteresting and worthless because of these reasons seems peculiar to mathematics. You are presumably at University so the motivation should be yours. But I do sympathize as I have taught pointless courses, or rather potentially pointful courses (but the habit of setting partial credit ruined that) to some particularly odd sections of the undergraduate community. If anyone can tell me why an Architecture student was made to do multivariable calc I'd be grateful, it's been puzzling me for a while now.

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Hurkyl

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I mean I still have to take Calculus 2, Statistics, and Linear Algebra.

It takes more than basic arithmetic to analyze algorithms.

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No, I am talking about teaching these concepts to middle school and high school students.

Math for math's sake is another matter entirely. I have no problem teaching unpractical topics out of sheer interest to college students.

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matt grime

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Zurtex

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I know what you mean matt grime, I've always been talented at mathematics throughout my life so far and I've always had the automatic assumption from people that I must therefore be really clever and it's just not true lol.

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cookiemonster

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Why would I have to be able to determine when the function:

x^3 + 2x^2 - 5

Is concave up or concave down as a computer scientist? Or better yet, why would I have to be able to do a lot of this stuff without a calculator when I could just use a calculator at the place I happen to work at? I just don't get that.

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To impress your boss and freak out your coworkers, duh!

cookiemonster

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That seems a bit harsh to generalize all who couldn't pass high school math as morons. When I was in high school, I had other ambitions that were heavily at odds with physics and math. I couldn't stay awake long enough to read the first page of the chapter we were studying, let alone try to grasp the material. This kept me from getting past algebra II, since I couldn't even slide by with a D. This even led me to not being able to graduate high school, since I didn't meet the math requirements. It wasn't until some subsequent soul searching, that I realized physics

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matt grime

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Hurkyl

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Or better yet, why would I have to be able to do a lot of this stuff without a calculator when I could just use a calculator at the place I happen to work at? I just don't get that.

Because the calculator won't suggest to you that concavity might be something useful to use.

- #44

Hurkyl

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Furthermore, some techniques of discrete math bear

Statistics is also generally useful. Many very useful algorithms have abysmal running times; the most prominent example is that quicksort, in the worst case, is a [itex]\Theta (n^2)[/itex] algorithm... absolutely horrible for sorting techniques... but it almost always beats out "better" algorithms like heapsort and mergesort. Why? Because,

Also, many problems simply cannot be solved in a reasonable amount of time... but probabilistic algorithms can be effective. Without knowledge of statistics, how could you design or analyze such an algorithm?

As for linear algebra, it's just so pervasive throughout mathematics that you'd be disadvantaged without it.

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- #46

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I have taught physics, math, computer science, and English. I try to relay the importance of each subject I teach.

But you are correct -- we don't have to motivate our students. We don't have to teach in a manner that produces a quality learning environment.

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JohnDubYa said:

I have taught physics, math, computer science, and English. I try to relay the importance of each subject I teach.

But you are correct -- we don't have to motivate our students. We don't have to teach in a manner that produces a quality learning environment.

Why is it assumed that teaching students "practical" uses of math is the best way to motivate them?

While some people really are motivated by seeing an example of math being used in another, it's been my experience that most people who complain about a lack of practical uses are never satisfied. "Practical" is usually defined in such a way as to intentionally exclude math.

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matt grime

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I didn't say we shouldn't have to motivate, i said we shouldn't have to motivate with some higher reason, writing as a (university level) teacher of pure mathematics. I don't mean without reference to a practical application, but that there often is no high metaphysical/philosophical reason why something is true in mathematics.

Again, you are thinking of a college course. I am talking about mathematics as taught to middle school and high school children.

My philosophy has been: If a student asks "So what?" and you cannot respond, then step down from the podium.

After all, if you cannot relate the importance of a topic, then how can the student be convinced the topic is important? And if you cannot convince the student that the topic is important, then how are you going to motivate them to work hard?

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Well, what IS the best way to motivate a typical high school student to study math?

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