algebra and driving Re: Hi...testing the waters...
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In a message dated 1/12/03 5:57:37 AM, fetteroll@... writes:
<< When we were flying from Boston to LA we stopped in Pittsburgh. It took us
an hour by plane. It takes us 11 hours by car. We had 5 more hours to get to
California. Kathryn, who was 10 at the time, said "Do you know how long it
would take to drive to California? It would take 66 hours." *That's*
algebraic thinking. (Which someone neatly described as using what you know
to figure out what you don't know.) The context of the problem supplied the
sense of how the numbers needed to be manipulated. Her curiosity supplied
the desire to manipulate them. >>
CREEPY CREEPY!!!
Yesterday Holly was asking how long it would take to drive to Florida. I
said four days (taking into consideration stopping and sleeping, and not
driving like a truckdriver). How long would it take to drive to California
(by which she meant "Disneyland"). I said "two drivers, not stopping? one
day" meaning there within 24 hours.
And yesterday I was thinking (without mentioning it to Holly) of Boston. She
had said "We should go on a road trip," and I was doing something else and
didn't say anything but said "Boston." And she saw a panel van with a little
window in the back, on the side (like a full-size Chevy without side windows)
and said "We should get one of those for trips!" I said it's not fun, I had
ridden to Pennsylvania and back in the back of a windowless van. Hot and
boring.
But my most obvious algebra story has to do with allowance.
When I was a kid my allowance was 35 cents for a while. The paperback books
I was reading that season cost 50 cents. (Doc Savage books. Weird.) So my
math had to do with two weeks, one book, four candy bars. Boring and
insufficient for my needs. But I still to this day know with no thought that
70 cents is divisible by 35 and that $1.05 is three weeks' allowance at that
long-ago rate.
My kids are aware of the others' allowance rates. It's 75 cents per year of
age per week. A ten year old gets $7.50, and there was a second wave
Schoolhouse Rock video about "$7.50 once a week" that Holly saw when she was
ten. That was cool.
But they have over the years calmly, efficiently and correctly calculated how
long it would take any one of them, or two or three of them together, to buy
this or that. And how much more quickly they could save a given amount if
they were a year older. Marty is especially quick at it. We've never
stopped them and shown them any algebraic notation to go with it. Someday
when someone does, they will get it immediately, without any hesitition or
bafflement, because it will be the writing system of a language with which
they are already familiar.
Kirby doesn't claim his allowance regularly because he has a job. It goes on
the calendar each Sunday like an oldtime passbook. When he needs a lump of
money he "withdraws allowance," but the goal is to save for the anime
convention in Denver in fall. This will be the third year that is his method
of savings.
Holly sometimes goes to calendar, but often takes it and keeps it herself.
She is the person most likely in this family to be able to change a $20 or to
lend someone $10.
I have seen Kirby's wallet, and Marty's. They usually have a little money,
and their wallets are immaculately organized. I'm impressed. Their dad's
is too. I guess it's genetic. I would use a wallet if I didn't lose them
so easily. I use little manila envelopes that fit into a jeans pocket, and I
can write on the outside when I use the debit card and for how much, and I
can note appointments and phone numbers, and then get a new envelope when
it's full or I've spent $200. That's a kind of algebra problem too, mixed
with other matters. But the best parts of life are mixed matters!
Sandra
<< When we were flying from Boston to LA we stopped in Pittsburgh. It took us
an hour by plane. It takes us 11 hours by car. We had 5 more hours to get to
California. Kathryn, who was 10 at the time, said "Do you know how long it
would take to drive to California? It would take 66 hours." *That's*
algebraic thinking. (Which someone neatly described as using what you know
to figure out what you don't know.) The context of the problem supplied the
sense of how the numbers needed to be manipulated. Her curiosity supplied
the desire to manipulate them. >>
CREEPY CREEPY!!!
Yesterday Holly was asking how long it would take to drive to Florida. I
said four days (taking into consideration stopping and sleeping, and not
driving like a truckdriver). How long would it take to drive to California
(by which she meant "Disneyland"). I said "two drivers, not stopping? one
day" meaning there within 24 hours.
And yesterday I was thinking (without mentioning it to Holly) of Boston. She
had said "We should go on a road trip," and I was doing something else and
didn't say anything but said "Boston." And she saw a panel van with a little
window in the back, on the side (like a full-size Chevy without side windows)
and said "We should get one of those for trips!" I said it's not fun, I had
ridden to Pennsylvania and back in the back of a windowless van. Hot and
boring.
But my most obvious algebra story has to do with allowance.
When I was a kid my allowance was 35 cents for a while. The paperback books
I was reading that season cost 50 cents. (Doc Savage books. Weird.) So my
math had to do with two weeks, one book, four candy bars. Boring and
insufficient for my needs. But I still to this day know with no thought that
70 cents is divisible by 35 and that $1.05 is three weeks' allowance at that
long-ago rate.
My kids are aware of the others' allowance rates. It's 75 cents per year of
age per week. A ten year old gets $7.50, and there was a second wave
Schoolhouse Rock video about "$7.50 once a week" that Holly saw when she was
ten. That was cool.
But they have over the years calmly, efficiently and correctly calculated how
long it would take any one of them, or two or three of them together, to buy
this or that. And how much more quickly they could save a given amount if
they were a year older. Marty is especially quick at it. We've never
stopped them and shown them any algebraic notation to go with it. Someday
when someone does, they will get it immediately, without any hesitition or
bafflement, because it will be the writing system of a language with which
they are already familiar.
Kirby doesn't claim his allowance regularly because he has a job. It goes on
the calendar each Sunday like an oldtime passbook. When he needs a lump of
money he "withdraws allowance," but the goal is to save for the anime
convention in Denver in fall. This will be the third year that is his method
of savings.
Holly sometimes goes to calendar, but often takes it and keeps it herself.
She is the person most likely in this family to be able to change a $20 or to
lend someone $10.
I have seen Kirby's wallet, and Marty's. They usually have a little money,
and their wallets are immaculately organized. I'm impressed. Their dad's
is too. I guess it's genetic. I would use a wallet if I didn't lose them
so easily. I use little manila envelopes that fit into a jeans pocket, and I
can write on the outside when I use the debit card and for how much, and I
can note appointments and phone numbers, and then get a new envelope when
it's full or I've spent $200. That's a kind of algebra problem too, mixed
with other matters. But the best parts of life are mixed matters!
Sandra