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Can someone check it over to make sure it's right?
Assuming it is, I'm dedicating this sheet to nowthatshockey, author of this observation:
Mathematical reasoning does not lie in the connection of mathematics to the real world, but in the connection within mathematics.
How mathematics is applied is its connection to your world.
We've all been talking about Liping Ma's notion of fragmented knowledge for two years now, off and on.
But nowthatshockey nailed it.
American students (and American math teachers) have fragmented knowledge of mathematics. We know things, but each thing is separate and distinct from every other thing. Most of us have no idea how it all fits together.
I, for instance, had no idea until 3 years ago that a fraction is also a division problem and a division problem is a fraction. (Remember when Carolyn quoted someone who remembered being happy as a boy to discover that a fraction was just a long division problem he didn't have to do? I never made that discovery.)
Teaching myself math today, I constantly have moments in which I think: oh.
Setting up ratios is a whole lot like setting up a dimensional analysis.
Whenever such a thought strikes me I stop and work whatever problem I'm doing both ways to make sure I'm right and to cement the connection.
Which brings me to constructivist math.
As usual they've taken the right idea and drawn the exact wrong conclusion.
Students don't need to make connections between math and everyday life. Making connections between math and everyday life is easy.*
What's hard is making connections between math and math.
* It stops being easy well before you get to college math, but that's irrelevant to the point I'm making here.
making connections
help desk
7 comments:
You've got an error under function. It should be:
N_G=f(N_M)=k*N_M
(It's a function of N_M, so your variable is N_M and 300 is a number of miles not gallons).
Other than that it looks correct. It looks like you've done a and b but not c.
"What's hard is making connections between math and math."
Yeah--that's the key.
thanks!
I'm too tired at the moment to put my brain through the function again -- and yes, I didn't do c.
I wonder if I should just take c. off.
I wasn't thinking about it when I typed it in.
Or....maybe I'll add a second sheet.
I don't think I follow your first comment, but I'll read again tomorrow morning and see if I do---!
oh!
I see it --- thanks!
function notation is unbelievably confusing
I'd never seen it before in my life, and suddenly had to teach it to myself AND to Christopher in one night.
Now I'm trying to teach it to myself for real -- and to him for real -- before the test.
"Making connections between math and everyday life is easy. What's hard is making connections between math and math."
That's a keeper.
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