Arithmetic (was Deschooling competitive perfectionists)
Pam Sorooshian
On Thu, Jan 5, 2012 at 8:06 AM, JustSayin <mfcappella@...> wrote:
long it would take us to drive from Southern California to New York City -
she put 3,000 at the top of a page and started subtracting 450 over and
over. 3,000 is about how far away we are and 450 miles was what I told her
was the maximum I could drive in one day. So she was figuring out 3,000
divided by 450 by looking at the number of times she could subtract 450
from 3,000.
I learned that multiplication was a shortcut for repeated addition (I
realized this in high school). But I just thought of division as reversed
multiplication - not as a shortcut for subtraction.
Also, addition and subtraction are both shortcuts for counting....
It makes no sense to me to introduce addition and subtraction using really
small numbers - because with small numbers, like 2 + 3, it is easier to
just count up and that's what most people will naturally do.
Same thing with multiplication and division -- you don't need it for small
numbers - why would you multiple 2 X 3 when you can just add (or count up).
I used to feel like I was cheating - I remember this clearly - in 3rd grade
when we were supposed to be "multiplying" and I didn't have the "facts"
memorized by could count up really fast and fool my teacher. If I'd wanted,
for some real reason, to add up 2,346, 47 times, it would have made more
sense to learn a new cool shortcut for doing that.
-pam
[Non-text portions of this message have been removed]
> He and my husband started talking about why we use multiplicationAlso, division is a shortcut for subtraction. When Rox wanted to know how
> (shortcut for adding).
long it would take us to drive from Southern California to New York City -
she put 3,000 at the top of a page and started subtracting 450 over and
over. 3,000 is about how far away we are and 450 miles was what I told her
was the maximum I could drive in one day. So she was figuring out 3,000
divided by 450 by looking at the number of times she could subtract 450
from 3,000.
I learned that multiplication was a shortcut for repeated addition (I
realized this in high school). But I just thought of division as reversed
multiplication - not as a shortcut for subtraction.
Also, addition and subtraction are both shortcuts for counting....
It makes no sense to me to introduce addition and subtraction using really
small numbers - because with small numbers, like 2 + 3, it is easier to
just count up and that's what most people will naturally do.
Same thing with multiplication and division -- you don't need it for small
numbers - why would you multiple 2 X 3 when you can just add (or count up).
I used to feel like I was cheating - I remember this clearly - in 3rd grade
when we were supposed to be "multiplying" and I didn't have the "facts"
memorized by could count up really fast and fool my teacher. If I'd wanted,
for some real reason, to add up 2,346, 47 times, it would have made more
sense to learn a new cool shortcut for doing that.
-pam
[Non-text portions of this message have been removed]
Meredith
Pam Sorooshian <pamsoroosh@...> wrote:
---Meredith
>> > It makes no sense to me to introduce addition and subtraction using reallyOne of the interesting things about the way kids tend to learn or derive mathematical concepts naturally, as opposed to how math is taught, is that it's common for kids to divide Before they subtract. It makes more sense to a younger child to divide - one for you, one for me, rather than "take away one" - fractions and parts of sets make more sense than counting backwards. One of the downsides of math education is that young kids spend so much time focused on subtraction they forget how to divide or never get to learn it naturally.
> small numbers
---Meredith