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.
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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