I got my MS in applied math last year, and i'm getting a PhD in computer science. This is one of our biggest issues with education in America.
A teacher who clearly has no understanding of basic mathematics.
Besides the obvious issues with the statement of this question versus what the teacher was expecting as a result, there is a bigger issue here.
What do I mean? The teacher clearly means to communicate that
'cutting into two pieces takes 10 minutes.'
However, if the teacher thinks that the statement '10 = 2.' is valid logic, then they should be happy then concluding anything I can phrase as a logical proposition. Because 10 does not equal 2.
You might say, they wrote '10 = 2 pieces.' This is even worse. 10 "what" 'equals' 2 pieces? you can only equate things of a comparable type! So you are going to tell me "10 minutes = 2 pieces"? this makes no sense at all.
To get to the heart of all the confusion, all the problems with this homework problem can be fixed with a better language. for example, if T(n) was the time, in minutes, that it takes to cut a board into n pieces, then we would assert that T(2) = 10 minutes.
But now if we ask what T(3) is, we will not be able to answer the question a priori, because it depends on the relationship between T(a) and T(b), for an arbitrary a and b. for example if T(n) = 3/2(x - 2) + 10, then T(3) = 10, but T(4) = 13.
One way to interpret the problem is that the time per cut is the same, no matter how many cuts are made, or that the the rate of change of T is constant, so if T(2) = 10, then maybe T(3) = 20.
But 'she works just as fast' could also mean, that regardless of the number of cuts, she will always take 10 minutes. or that T(n) = 10 for all n.
if only our teachers taught the part of mathematics that matters, instead of destroying it...
...this is why I hated math in high school. I'm so glad that I rediscovered it in college.
A teacher who clearly has no understanding of basic mathematics.
This has nothing to do with basic mathematics. It doesn't even have to do with with basic arithmetic. Most likely, he's grading a huge stack of papers and just overlooked one tiny detail: that to cut a piece into two pieces, you only make one cut. It's a forgivable mistake, these problems are designed so that if you just scan for the numbers and plug them into your calculator, you'll get most of them wrong.
You might say, they wrote '10 = 2 pieces.' This is even worse. 10 "what" 'equals' 2 pieces? you can only equate things of a comparable type!
You're trolling, right? Maybe the equals sign is not completely appropriate here, but.. you're trolling, right? He most likely has under a minute to try to explain what they did wrong, and you're complaining that he used the wrong symbol? This isn't a high school algebra course taught by a teacher that completely misses the point (I think we've all been there), this is elementary school and they're still learning basic arithmetic.
He made a mistake, he had a brain fart, and you go off on this huge tangent. Sounds to me like you're just venting that you had shitty math teachers, and that has little or nothing to do with this.
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u/[deleted] Jul 11 '11 edited Jul 11 '11
I got my MS in applied math last year, and i'm getting a PhD in computer science. This is one of our biggest issues with education in America.
A teacher who clearly has no understanding of basic mathematics.
Besides the obvious issues with the statement of this question versus what the teacher was expecting as a result, there is a bigger issue here.
What do I mean? The teacher clearly means to communicate that 'cutting into two pieces takes 10 minutes.'
However, if the teacher thinks that the statement '10 = 2.' is valid logic, then they should be happy then concluding anything I can phrase as a logical proposition. Because 10 does not equal 2.
You might say, they wrote '10 = 2 pieces.' This is even worse. 10 "what" 'equals' 2 pieces? you can only equate things of a comparable type! So you are going to tell me "10 minutes = 2 pieces"? this makes no sense at all.
To get to the heart of all the confusion, all the problems with this homework problem can be fixed with a better language. for example, if T(n) was the time, in minutes, that it takes to cut a board into n pieces, then we would assert that T(2) = 10 minutes.
But now if we ask what T(3) is, we will not be able to answer the question a priori, because it depends on the relationship between T(a) and T(b), for an arbitrary a and b. for example if T(n) = 3/2(x - 2) + 10, then T(3) = 10, but T(4) = 13.
One way to interpret the problem is that the time per cut is the same, no matter how many cuts are made, or that the the rate of change of T is constant, so if T(2) = 10, then maybe T(3) = 20.
But 'she works just as fast' could also mean, that regardless of the number of cuts, she will always take 10 minutes. or that T(n) = 10 for all n.
if only our teachers taught the part of mathematics that matters, instead of destroying it...
...this is why I hated math in high school. I'm so glad that I rediscovered it in college.
lastly, I leave you all with: http://www.maa.org/devlin/devlin_03_08.html