Re: [Unschooling-dotcom] Unschooling Math
[email protected]
While on the subject of math, I was wondering if anybody has a source, in
their arsenal of information, for practical math formulas. For instance,
I need to buy wood chips to put in childrens play area. The mulch is sold
by cubic yard. The play area is approx. 25' by 40'. I think the mulch
should be at least 12" deep. How many cubic yards of mulch do I need? I
don't want the answer, just the formula, and a source for other formulas
like this.
Thanks,
Wende
________________________________________________________________
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their arsenal of information, for practical math formulas. For instance,
I need to buy wood chips to put in childrens play area. The mulch is sold
by cubic yard. The play area is approx. 25' by 40'. I think the mulch
should be at least 12" deep. How many cubic yards of mulch do I need? I
don't want the answer, just the formula, and a source for other formulas
like this.
Thanks,
Wende
________________________________________________________________
Sign Up for Juno Platinum Internet Access Today
Only $9.95 per month!
Visit www.juno.com
[email protected]
In a message dated 1/12/03 7:10:28 AM, love-it-here@... writes:
<<
While on the subject of math, I was wondering if anybody has a source, in
their arsenal of information, for practical math formulas. For instance,
I need to buy wood chips to put in childrens play area. The mulch is sold
by cubic yard. The play area is approx. 25' by 40'. I think the mulch
should be at least 12" deep. How many cubic yards of mulch do I need? I
don't want the answer, just the formula, and a source for other formulas
like this.>>
Probably someone else will answer that, but you might find them by looking
for "algorithms."
What I am going to share is some stuff my husband wrote in correspondence
with an unschooling mom a couple of years ago. It's been posted before, but
it's easier for me to find it on my computer than in the archives. This is
just his answers, not the questions. <g>
And the reason I've brought this up now is that he taught me (before we had
kids, when I was saying I only liked the word problems in math in school, not
the number problems) that the forumlas are not the questions, they are the
answers. So if someone does show you a list of how to calculate various
things, that won't be the math. That will be the product of someone else's
mathematical thinking.
It's hard to change school thinking enough to realize that "teaching math" is
to a large extent "memorizing answers" and not really helping anyone to think
mathematically.
From here down is my husband Keith's writing:
-------------------------------------
Math is a highly structured abstract modeling tool and requires a strong
sense of discipline, but ...
A true math student must possess a strong passion for discovery in a realm
which has little direct connection to the world of our five senses. My
experience says that the passion will grow in children if they are shown the
myriad of modeling applications in their everyday world (physics, chemistry,
finance, sports, arts, etc). All growth takes time and gentle nurturing.
Unschooling is about educating the parents as much as educating the
children.
Keith Dodd
(husband to Sandra)
-------------- my response 11/5 -----------------
I don't know the ages of your children (or yourself or your husband :) but
it doesn't really matter. Think of your everyday actions, then look at how
they can be represented with math. Scaling of cooking ingredients (ratios),
boiling water (physics or chemistry), bouncing a ball (physics), watching
the moon circle the earth (geometry), (as in why does a ball fall to earth
but the moon does not?). Find art with a protractor, compass, straight
edge, (like the Greeks) or just play with graph paper (geometry & trig).
Look for symetry in nature or man made artifacts (ratios again). Look for
applications of fractions (ratios, division, combinatorics). Talk about the
lottery or statistics in elections or sports.
Algebra and calculus are abstractions to be delved into once you see the
need for modeling in the first place. Interest in "the need" I find to be
hinged on a budding interest in some tangible format. Do they like
architecture or engineering (mud pies to model planes)? How about
competitive puzzles (board games, cards, video games)? My son (12) just
finished reassembling a TV. (The picture was cutting out.) He now knows
that the insides are not some kind of magic. We talked a little about
circuits and assembly and troubleshooting. In the process of finding the
broken circuit, we talked about TV signals and waveforms and how both audio
and video came from the same antenna. I didn't try to go into the math of
electronics (really complicated modeling), but he now is a little more
interested in just how that stuff works. It took him 3 days of putzing
around with it, (and a $20 part) and mostly all I did was encourage him to
be careful and take small steps.
I think the greatest thing I have learned from homeschooling, it the fact
that it is ok to say, "I don't know, let's find out." The other side of
that is being able to judge when the child is bored with the subject and you
can let it slide.
Good luck,
Keith
Combinatorics:
Consider a lottery drawing of 3 balls from 3 separate pots of 10 balls each.
The odds of picking a specific combination of numbers is:
1/10 * 1/10 * 1/10 = 1/1000 or one in one thousand combinations.
Now consider drawing the 3 balls from a single pot.
1/10 * 1/9 * 1/8 = 1/720 or one in seven hundred twenty combinations.
Combinatorics is the study of ratios.
Computer Programming:
This is more like logic than math, but the same principals apply. My
recommendation would be to buy your son a simple programming environment
(like Visual Basic or even better Microsoft Access) and a couple beginner
books on programming. Even so, it will require a rigorous effort because of
how 'dry' the materiel really is. The artistry of programming is in
conceptualizing just what it is you want to accomplish.
Glad you enjoyed this
Keith
<<
While on the subject of math, I was wondering if anybody has a source, in
their arsenal of information, for practical math formulas. For instance,
I need to buy wood chips to put in childrens play area. The mulch is sold
by cubic yard. The play area is approx. 25' by 40'. I think the mulch
should be at least 12" deep. How many cubic yards of mulch do I need? I
don't want the answer, just the formula, and a source for other formulas
like this.>>
Probably someone else will answer that, but you might find them by looking
for "algorithms."
What I am going to share is some stuff my husband wrote in correspondence
with an unschooling mom a couple of years ago. It's been posted before, but
it's easier for me to find it on my computer than in the archives. This is
just his answers, not the questions. <g>
And the reason I've brought this up now is that he taught me (before we had
kids, when I was saying I only liked the word problems in math in school, not
the number problems) that the forumlas are not the questions, they are the
answers. So if someone does show you a list of how to calculate various
things, that won't be the math. That will be the product of someone else's
mathematical thinking.
It's hard to change school thinking enough to realize that "teaching math" is
to a large extent "memorizing answers" and not really helping anyone to think
mathematically.
From here down is my husband Keith's writing:
-------------------------------------
Math is a highly structured abstract modeling tool and requires a strong
sense of discipline, but ...
A true math student must possess a strong passion for discovery in a realm
which has little direct connection to the world of our five senses. My
experience says that the passion will grow in children if they are shown the
myriad of modeling applications in their everyday world (physics, chemistry,
finance, sports, arts, etc). All growth takes time and gentle nurturing.
Unschooling is about educating the parents as much as educating the
children.
Keith Dodd
(husband to Sandra)
-------------- my response 11/5 -----------------
I don't know the ages of your children (or yourself or your husband :) but
it doesn't really matter. Think of your everyday actions, then look at how
they can be represented with math. Scaling of cooking ingredients (ratios),
boiling water (physics or chemistry), bouncing a ball (physics), watching
the moon circle the earth (geometry), (as in why does a ball fall to earth
but the moon does not?). Find art with a protractor, compass, straight
edge, (like the Greeks) or just play with graph paper (geometry & trig).
Look for symetry in nature or man made artifacts (ratios again). Look for
applications of fractions (ratios, division, combinatorics). Talk about the
lottery or statistics in elections or sports.
Algebra and calculus are abstractions to be delved into once you see the
need for modeling in the first place. Interest in "the need" I find to be
hinged on a budding interest in some tangible format. Do they like
architecture or engineering (mud pies to model planes)? How about
competitive puzzles (board games, cards, video games)? My son (12) just
finished reassembling a TV. (The picture was cutting out.) He now knows
that the insides are not some kind of magic. We talked a little about
circuits and assembly and troubleshooting. In the process of finding the
broken circuit, we talked about TV signals and waveforms and how both audio
and video came from the same antenna. I didn't try to go into the math of
electronics (really complicated modeling), but he now is a little more
interested in just how that stuff works. It took him 3 days of putzing
around with it, (and a $20 part) and mostly all I did was encourage him to
be careful and take small steps.
I think the greatest thing I have learned from homeschooling, it the fact
that it is ok to say, "I don't know, let's find out." The other side of
that is being able to judge when the child is bored with the subject and you
can let it slide.
Good luck,
Keith
Combinatorics:
Consider a lottery drawing of 3 balls from 3 separate pots of 10 balls each.
The odds of picking a specific combination of numbers is:
1/10 * 1/10 * 1/10 = 1/1000 or one in one thousand combinations.
Now consider drawing the 3 balls from a single pot.
1/10 * 1/9 * 1/8 = 1/720 or one in seven hundred twenty combinations.
Combinatorics is the study of ratios.
Computer Programming:
This is more like logic than math, but the same principals apply. My
recommendation would be to buy your son a simple programming environment
(like Visual Basic or even better Microsoft Access) and a couple beginner
books on programming. Even so, it will require a rigorous effort because of
how 'dry' the materiel really is. The artistry of programming is in
conceptualizing just what it is you want to accomplish.
Glad you enjoyed this
Keith
[email protected]
In a message dated 1/12/2003 9:10:22 AM Eastern Standard Time,
love-it-here@... writes:
in the future you'll NEED to know how many cubic yards you'll need! <G>
The important thing is that there's someone out there who can give you the
answer in no time (I married one who could answer that one! <G>).
Having the formula is good. Knowing whom to ASK is better! <G>
Joyce'll be along soon to answer that question! My non-mathy answer would be
about 35 bags.
~Kelly
[Non-text portions of this message have been removed]
love-it-here@... writes:
> While on the subject of math, I was wondering if anybody has a source, inThe biggest fallacy in schools is that you're learning this because one day
> their arsenal of information, for practical math formulas. For instance,
> I need to buy wood chips to put in childrens play area. The mulch is sold
> by cubic yard. The play area is approx. 25' by 40'. I think the mulch
> should be at least 12" deep. How many cubic yards of mulch do I need? I
> don't want the answer, just the formula, and a source for other formulas
> like this.
>
in the future you'll NEED to know how many cubic yards you'll need! <G>
The important thing is that there's someone out there who can give you the
answer in no time (I married one who could answer that one! <G>).
Having the formula is good. Knowing whom to ASK is better! <G>
Joyce'll be along soon to answer that question! My non-mathy answer would be
about 35 bags.
~Kelly
[Non-text portions of this message have been removed]
Colonel Newton
Having the formula is good. Knowing whom to ASK is better! <G>
~~~~
And, actually, knowing how to figure OUT the formula would be even better. :)
Teresa G.
[Non-text portions of this message have been removed]
~~~~
And, actually, knowing how to figure OUT the formula would be even better. :)
Teresa G.
[Non-text portions of this message have been removed]
Fetteroll
on 1/12/03 9:08 AM, love-it-here@... at love-it-here@... wrote:
problem that will lead you to the formula. (Though most almanacs have them.)
Basically what you're asking is if you had one size box and wanted to
reshape it into a bunch of cube shaped boxes of a particular size, how many
cubes would you have?
There's a number of approaches.
You could visualize slicing every cube 3 times so each is 3 flat boxes
stacked on top of each other. And then visualize (or draw it on graph paper)
how many of those slices would fit into the play area.
Since the slices from the cubes and the play area are both 1 foot deep you
can ignore that you're dealing with 3 dimensions.
So how many 3 foot squares fits across the 25 foot side? To make it easier
so you don't have to deal with fractions you can deal with "close enough"
and say more than 8, less than 9. And how many across the 40 foot side? More
than 13, less than 14.
8x13 is 104 and 9x14 is 126.
That's too broad a range, so I'd go back and fill in the real numbers and
use 8 1/3 x 13 2/3 = 113.8888 so call it 114. The trick is you need to
remember you used *slices* not whole cubes. So there's 3 slices per cube
whic means you need to divide 114 by 3 which is 38.
Or you could you could figure out the volume in cubic feet of the play area
and then keep subtracting 1 cubic yard's worth (3'x3'x3' is 27 cubic feet)
until you don't have any left. (That's also known as division ;-)
24'x40'x1'=1000 cubic feet
1000/27 is 38.
Joyce
> While on the subject of math, I was wondering if anybody has a source, inHmm. I'm not sure that a book of formulas would help. It's understanding the
> their arsenal of information, for practical math formulas. For instance,
> I need to buy wood chips to put in childrens play area. The mulch is sold
> by cubic yard. The play area is approx. 25' by 40'. I think the mulch
> should be at least 12" deep. How many cubic yards of mulch do I need? I
> don't want the answer, just the formula, and a source for other formulas
> like this.
problem that will lead you to the formula. (Though most almanacs have them.)
Basically what you're asking is if you had one size box and wanted to
reshape it into a bunch of cube shaped boxes of a particular size, how many
cubes would you have?
There's a number of approaches.
You could visualize slicing every cube 3 times so each is 3 flat boxes
stacked on top of each other. And then visualize (or draw it on graph paper)
how many of those slices would fit into the play area.
Since the slices from the cubes and the play area are both 1 foot deep you
can ignore that you're dealing with 3 dimensions.
So how many 3 foot squares fits across the 25 foot side? To make it easier
so you don't have to deal with fractions you can deal with "close enough"
and say more than 8, less than 9. And how many across the 40 foot side? More
than 13, less than 14.
8x13 is 104 and 9x14 is 126.
That's too broad a range, so I'd go back and fill in the real numbers and
use 8 1/3 x 13 2/3 = 113.8888 so call it 114. The trick is you need to
remember you used *slices* not whole cubes. So there's 3 slices per cube
whic means you need to divide 114 by 3 which is 38.
Or you could you could figure out the volume in cubic feet of the play area
and then keep subtracting 1 cubic yard's worth (3'x3'x3' is 27 cubic feet)
until you don't have any left. (That's also known as division ;-)
24'x40'x1'=1000 cubic feet
1000/27 is 38.
Joyce
[email protected]
In a message dated 1/12/2003 10:11:09 AM Eastern Standard Time,
colnewt@... writes:
bags of mulch I'll need. I did it last spring, and I'll do it again this
spring. I guesstimate---and I might have to go back for one more bag!). There
are other things I do VERY well. Things that people call on me for. I have no
reason to clutter up my brain for an hour "figuring" when it would take
someone with the knowledge/joy of cubic feet just a few minutes to figure
out. There are experts on every damned subject known to man---people who
devote their lives to topics I might just need a quick response to. I LIKE
that their are people who like cubic feet. And amortization. And car engines.
And lots of stuff!
~Kelly
[Non-text portions of this message have been removed]
colnewt@... writes:
> Having the formula is good. Knowing whom to ASK is better! <G>Yeah, but you know, that is SUCH a small part of my life (figuring how many
>
> ~~~~
>
> And, actually, knowing how to figure OUT the formula would be even better.
> :)
bags of mulch I'll need. I did it last spring, and I'll do it again this
spring. I guesstimate---and I might have to go back for one more bag!). There
are other things I do VERY well. Things that people call on me for. I have no
reason to clutter up my brain for an hour "figuring" when it would take
someone with the knowledge/joy of cubic feet just a few minutes to figure
out. There are experts on every damned subject known to man---people who
devote their lives to topics I might just need a quick response to. I LIKE
that their are people who like cubic feet. And amortization. And car engines.
And lots of stuff!
~Kelly
[Non-text portions of this message have been removed]
[email protected]
In a message dated 1/12/2003 10:17:17 AM Eastern Standard Time,
fetteroll@... writes:
G>
~Kelly
[Non-text portions of this message have been removed]
fetteroll@... writes:
> 1000/27 is 38.Ok, THREE bags! I probably would have picked up an extra one or two anyway! <
G>
~Kelly
[Non-text portions of this message have been removed]
[email protected]
In a message dated 1/12/2003 10:17:17 AM Eastern Standard Time,
fetteroll@... writes:
3/1000 is 33---plus a couple, just in case! <G>
[Non-text portions of this message have been removed]
fetteroll@... writes:
> 24'x40'x1'=1000 cubic feetAnd I figured that 25 x 40 is 1000 square feet. 3 square feet in a bag.
>
> 1000/27 is 38.
3/1000 is 33---plus a couple, just in case! <G>
[Non-text portions of this message have been removed]
[email protected]
In a message dated 1/12/03 8:23:02 AM, kbcdlovejo@... writes:
<< I have no
reason to clutter up my brain for an hour "figuring" when it would take
someone with the knowledge/joy of cubic feet just a few minutes to figure
out. >>
Well then you ask the guy who sells the whatever-it-is (I forgot the original
cubic-yards-of-what problem).
Or you go to www.google.com and put in enough to find it one more time.
No sense digging through an almanac or an old math book while google lives
and breathes.
Sandra
<< I have no
reason to clutter up my brain for an hour "figuring" when it would take
someone with the knowledge/joy of cubic feet just a few minutes to figure
out. >>
Well then you ask the guy who sells the whatever-it-is (I forgot the original
cubic-yards-of-what problem).
Or you go to www.google.com and put in enough to find it one more time.
No sense digging through an almanac or an old math book while google lives
and breathes.
Sandra
[email protected]
In a message dated 1/12/2003 10:31:26 AM Eastern Standard Time,
SandraDodd@... writes:
[Non-text portions of this message have been removed]
SandraDodd@... writes:
> << I have noYeah, he's PAID to know!
> reason to clutter up my brain for an hour "figuring" when it would take
> someone with the knowledge/joy of cubic feet just a few minutes to figure
> out. >>
>
> Well then you ask the guy who sells the whatever-it-is (I forgot the
> original
> cubic-yards-of-what problem).
>
[Non-text portions of this message have been removed]
Fetteroll
on 1/12/03 10:04 AM, kbcdlovejo@... at kbcdlovejo@... wrote:
You going to tell us how you got there?
Joyce
> Joyce'll be along soon to answer that question! My non-mathy answer would beDarn close!
> about 35 bags.
You going to tell us how you got there?
Joyce
[email protected]
On Sun, 12 Jan 2003 09:44:41 EST SandraDodd@... writes:
how to calculate
not just coming up with a sum, but in fact the method used to achieve
that sum? Don't you need a starting point from which to base your
equation on? For instance, using my mulch problem, in my mind's eye I can
visualize the play area broke up into little cubes, let's say 1' square.
But short of counting out each of the cubes one by one, and then dividing
this number by 3 to come up with the cubic yard measurement (if that is
even correct), I have a mental block as to how to finish the equation. I
tend to have the same problem figuring out volumes, masses, etc., but can
easily remember formulas once I've applied them. I feel like knowing your
strengths and weaknesses, and overcoming or using them to complete the
task at hand would be very much unschooling. Am I wrong in this
assumption? Or am I totally off base in what you were describing? How
does one think more mathematically in an unschooling way? I'm going to go
back and reread your husband's suggestions, maybe the answers will be
more clear now. Maybe I'm just looking for the easy way out and not
exercising my mathematical muscles. I, too, have always been better with
words.
Wende
________________________________________________________________
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> Probably someone else will answer that, but you might find them byThanks. I'll look that up. But now how have me thinking......
> looking
> for "algorithms."
> And the reason I've brought this up now is that he taught me (beforein
> we had kids, when I was saying I only liked the word problems in math
> school, not the number problems) that the formulas are not thequestions, they are the answers. So if someone does show you a list of
how to calculate
> various things, that won't be the math. That will be the product ofsomeone
> else's mathematical thinking.anyone
> It's hard to change school thinking enough to realize that "teaching
> math" is to a large extent "memorizing answers" and not really helping
> to think mathematically.I'm not sure that I understand you. Are you saying that learning math is
not just coming up with a sum, but in fact the method used to achieve
that sum? Don't you need a starting point from which to base your
equation on? For instance, using my mulch problem, in my mind's eye I can
visualize the play area broke up into little cubes, let's say 1' square.
But short of counting out each of the cubes one by one, and then dividing
this number by 3 to come up with the cubic yard measurement (if that is
even correct), I have a mental block as to how to finish the equation. I
tend to have the same problem figuring out volumes, masses, etc., but can
easily remember formulas once I've applied them. I feel like knowing your
strengths and weaknesses, and overcoming or using them to complete the
task at hand would be very much unschooling. Am I wrong in this
assumption? Or am I totally off base in what you were describing? How
does one think more mathematically in an unschooling way? I'm going to go
back and reread your husband's suggestions, maybe the answers will be
more clear now. Maybe I'm just looking for the easy way out and not
exercising my mathematical muscles. I, too, have always been better with
words.
Wende
________________________________________________________________
Sign Up for Juno Platinum Internet Access Today
Only $9.95 per month!
Visit www.juno.com
[email protected]
OK, so....
25x40x1=1000 cubic feet. And there are 27 cubic feet in a yard.
so 1000/27=38 cubic yards needed. Got it! Thanks!
Wende
On Sun, 12 Jan 2003 10:17:51 -0500 Fetteroll <fetteroll@...>
writes:
Sign Up for Juno Platinum Internet Access Today
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25x40x1=1000 cubic feet. And there are 27 cubic feet in a yard.
so 1000/27=38 cubic yards needed. Got it! Thanks!
Wende
On Sun, 12 Jan 2003 10:17:51 -0500 Fetteroll <fetteroll@...>
writes:
> on 1/12/03 9:08 AM, love-it-here@... at love-it-here@...________________________________________________________________
> wrote:
>
> > While on the subject of math, I was wondering if anybody has a
> source, in
> > their arsenal of information, for practical math formulas. For
> instance,
> > I need to buy wood chips to put in childrens play area. The mulch
> is sold
> > by cubic yard. The play area is approx. 25' by 40'. I think the
> mulch
> > should be at least 12" deep. How many cubic yards of mulch do I
> need? I
> > don't want the answer, just the formula, and a source for other
> formulas
> > like this.
>
> Hmm. I'm not sure that a book of formulas would help. It's
> understanding the
> problem that will lead you to the formula. (Though most almanacs
> have them.)
>
> Basically what you're asking is if you had one size box and wanted
> to
> reshape it into a bunch of cube shaped boxes of a particular size,
> how many
> cubes would you have?
>
> There's a number of approaches.
>
> You could visualize slicing every cube 3 times so each is 3 flat
> boxes
> stacked on top of each other. And then visualize (or draw it on
> graph paper)
> how many of those slices would fit into the play area.
>
> Since the slices from the cubes and the play area are both 1 foot
> deep you
> can ignore that you're dealing with 3 dimensions.
>
> So how many 3 foot squares fits across the 25 foot side? To make it
> easier
> so you don't have to deal with fractions you can deal with "close
> enough"
> and say more than 8, less than 9. And how many across the 40 foot
> side? More
> than 13, less than 14.
>
> 8x13 is 104 and 9x14 is 126.
>
> That's too broad a range, so I'd go back and fill in the real
> numbers and
> use 8 1/3 x 13 2/3 = 113.8888 so call it 114. The trick is you need
> to
> remember you used *slices* not whole cubes. So there's 3 slices per
> cube
> whic means you need to divide 114 by 3 which is 38.
>
> Or you could you could figure out the volume in cubic feet of the
> play area
> and then keep subtracting 1 cubic yard's worth (3'x3'x3' is 27 cubic
> feet)
> until you don't have any left. (That's also known as division ;-)
>
> 24'x40'x1'=1000 cubic feet
>
> 1000/27 is 38.
>
> Joyce
>
>
>
> ~~~~ Don't forget! If you change topics, change the subject line!
> ~~~~
>
> If you have questions, concerns or problems with this list, please
> email the moderator, Joyce Fetteroll (fetteroll@...), or
> the list owner, Helen Hegener (HEM-Editor@...).
>
> To unsubscribe from this group, click on the following link or
> address an email to:
> [email protected]
>
> Visit the Unschooling website: http://www.unschooling.com
>
> Your use of Yahoo! Groups is subject to
> http://docs.yahoo.com/info/terms/
>
>
>
>
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[email protected]
On Sun, 12 Jan 2003 10:21:59 EST kbcdlovejo@... writes:
response to.
I don't like to have to depend on other people to know things for me. I
think you can get taken advantage of a lot in life if you count on others
for those things. It would be very hard for an auto repair shop to take
advantage of me, because I can pretty much identify any part or the
function of the part on my car. I could do most of the repairs myself, if
so inclined and the right tools were available to me. I rarely ever have
to, because my husband takes care of that stuff. But, if I brake down on
the side of the road I will not be helpless. I try to educate myself
about all things, some of which I may never use. I taught myself how to
give CPR. Hopefully I'll never have to use that info, but if needed I
can. When I was in school, and didn't see any practical use for math, I
just did the work, got good grades, and quickly forgot any of the
information. I just want to relearn the basic principles for times like
now when I need to figure out how much mulch to buy.
Wende
________________________________________________________________
Sign Up for Juno Platinum Internet Access Today
Only $9.95 per month!
Visit www.juno.com
> I have no reason to clutter up my brain for an hour "figuring" when itwould
> take someone with the knowledge/joy of cubic feet just a few minutesto
> figure out. There are experts on every damned subject known toman---people who devote their lives to topics I might just need a quick
response to.
> I LIKE that their are people who like cubic feet. And amortization.And car
> engines. And lots of stuff!Kelly,
> ~Kelly
I don't like to have to depend on other people to know things for me. I
think you can get taken advantage of a lot in life if you count on others
for those things. It would be very hard for an auto repair shop to take
advantage of me, because I can pretty much identify any part or the
function of the part on my car. I could do most of the repairs myself, if
so inclined and the right tools were available to me. I rarely ever have
to, because my husband takes care of that stuff. But, if I brake down on
the side of the road I will not be helpless. I try to educate myself
about all things, some of which I may never use. I taught myself how to
give CPR. Hopefully I'll never have to use that info, but if needed I
can. When I was in school, and didn't see any practical use for math, I
just did the work, got good grades, and quickly forgot any of the
information. I just want to relearn the basic principles for times like
now when I need to figure out how much mulch to buy.
Wende
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On Sun, 12 Jan 2003 10:35:31 EST kbcdlovejo@... writes:
Wende
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> Yeah, he's PAID to know!Yep, and also has a vested interest in over-selling to you!
Wende
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In a message dated 1/12/2003 12:04:25 PM Eastern Standard Time,
love-it-here@... writes:
[Non-text portions of this message have been removed]
love-it-here@... writes:
> > Yeah, he's PAID to know!And I can return what I don't use---and HE has to restock it! <G>
>
> Yep, and also has a vested interest in over-selling to you!
[Non-text portions of this message have been removed]
[email protected]
In a message dated 1/12/03 9:11:26 AM, love-it-here@... writes:
<< I'm not sure that I understand you. Are you saying that learning math is
not just coming up with a sum, but in fact the method used to achieve
that sum? >>
Yes.
<<Don't you need a starting point from which to base your
equation on? >>
Of course. But that starting point will be in a non-numerical context.
Language, or spatial situation, or music, or art.
<<For instance, using my mulch problem, in my mind's eye I can
visualize the play area broke up into little cubes, let's say 1' square.
But short of counting out each of the cubes one by one, and then dividing
this number by 3 to come up with the cubic yard measurement (if that is
even correct), I have a mental block as to how to finish the equation.>>
You have a mental block because someone made you think that unless you could
memorize a formula you MIGHT need in twenty years, that it was none of your
business and too hard for you. They didn't teach you how to create the
formula. They showed you the formula and taught you how to plug other
numbers in and "solve" it.
<<I tend to have the same problem figuring out volumes, masses, etc., but can
easily remember formulas once I've applied them. >>
It's no crime to build on what others have discovered. But it's not
artistry, it's clerk's work.
<<I feel like knowing your strengths and weaknesses, and overcoming or using
them to complete the task at hand would be very much unschooling. >>
It's hard for people to even think about math without it becoming bound up in
personal worth and emotion, (NO) thanks to school.
Instead of worrying about overcoming, knowing or using strengths and
weaknesses, how about just encourage childs are?
<<How does one think more mathematically in an unschooling way?>>
By thinking less about numbers and more about patterns.
<<Maybe I'm just looking for the easy way out and not exercising my mat
hematical muscles. I, too, have always been better with words.>>
Then go on strike from numbers for a while and see how that goes!
The "formal" juncture (school-style) of math and words is logic.
But I don't even mean think in and of logic. Just think in words, even about
cubic yards of stuff. Don't fish around in your head for something that
looks like page 113 of an 8th grade geometry book. Keep that out of your
thinking until you can see math another way.
This is an odd case of "start where you're not."
If you start where you are, you'll be blocked.
Sandra
<< I'm not sure that I understand you. Are you saying that learning math is
not just coming up with a sum, but in fact the method used to achieve
that sum? >>
Yes.
<<Don't you need a starting point from which to base your
equation on? >>
Of course. But that starting point will be in a non-numerical context.
Language, or spatial situation, or music, or art.
<<For instance, using my mulch problem, in my mind's eye I can
visualize the play area broke up into little cubes, let's say 1' square.
But short of counting out each of the cubes one by one, and then dividing
this number by 3 to come up with the cubic yard measurement (if that is
even correct), I have a mental block as to how to finish the equation.>>
You have a mental block because someone made you think that unless you could
memorize a formula you MIGHT need in twenty years, that it was none of your
business and too hard for you. They didn't teach you how to create the
formula. They showed you the formula and taught you how to plug other
numbers in and "solve" it.
<<I tend to have the same problem figuring out volumes, masses, etc., but can
easily remember formulas once I've applied them. >>
It's no crime to build on what others have discovered. But it's not
artistry, it's clerk's work.
<<I feel like knowing your strengths and weaknesses, and overcoming or using
them to complete the task at hand would be very much unschooling. >>
It's hard for people to even think about math without it becoming bound up in
personal worth and emotion, (NO) thanks to school.
Instead of worrying about overcoming, knowing or using strengths and
weaknesses, how about just encourage childs are?
<<How does one think more mathematically in an unschooling way?>>
By thinking less about numbers and more about patterns.
<<Maybe I'm just looking for the easy way out and not exercising my mat
hematical muscles. I, too, have always been better with words.>>
Then go on strike from numbers for a while and see how that goes!
The "formal" juncture (school-style) of math and words is logic.
But I don't even mean think in and of logic. Just think in words, even about
cubic yards of stuff. Don't fish around in your head for something that
looks like page 113 of an 8th grade geometry book. Keep that out of your
thinking until you can see math another way.
This is an odd case of "start where you're not."
If you start where you are, you'll be blocked.
Sandra
[email protected]
In a message dated 1/12/2003 12:04:04 PM Eastern Standard Time,
love-it-here@... writes:
too many "things".
And I can always get a second or third opinion. Or ask someone I trust. I
don't get taken advantage of much, 'cause I ask a lot of questions. If I do,
then it won't happen again! <easy study>
I think it's better for me to focus on what I do well and rely on those who
do what I can't/won't.
CPR's a cool thing to know, no matter what. And hopefully you'll never need
to use it.
I also know how to slit my wrists succesfully, but I don't WANT to use that! <
G>
I LOVE to learn new things. Happens every day. But calculating area is
totally unappealing. There are folks who love it. I'm quite happy to please
them and let them show off! <G>
~Kelly
[Non-text portions of this message have been removed]
love-it-here@... writes:
> I don't like to have to depend on other people to know things for me. IBut you can't know everything. Not even a little about everything. There are
> think you can get taken advantage of a lot in life if you count on others
> for those things.
too many "things".
And I can always get a second or third opinion. Or ask someone I trust. I
don't get taken advantage of much, 'cause I ask a lot of questions. If I do,
then it won't happen again! <easy study>
I think it's better for me to focus on what I do well and rely on those who
do what I can't/won't.
CPR's a cool thing to know, no matter what. And hopefully you'll never need
to use it.
I also know how to slit my wrists succesfully, but I don't WANT to use that! <
G>
I LOVE to learn new things. Happens every day. But calculating area is
totally unappealing. There are folks who love it. I'm quite happy to please
them and let them show off! <G>
~Kelly
[Non-text portions of this message have been removed]
[email protected]
On Sun, 12 Jan 2003 12:07:06 EST kbcdlovejo@... writes:
cheaper that way. But, I guess I could just load the excess into the
trunk of my car and shovel it onto his doorstep. Naaaahhh, it's a lot
easier to just find out how much I need! <grin>
Wende
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> And I can return what I don't use---and HE has to restock it! <G>That won't work for me. I have it delivered by dump truck. It is a lot
cheaper that way. But, I guess I could just load the excess into the
trunk of my car and shovel it onto his doorstep. Naaaahhh, it's a lot
easier to just find out how much I need! <grin>
Wende
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In a message dated 1/12/03 10:04:08 AM, love-it-here@... writes:
<< Yep, and also has a vested interest in over-selling to you! >>
You could get a second opinion, or just keep the receipt and bring back
unused overage.
Most people are honest.
Sandra
<< Yep, and also has a vested interest in over-selling to you! >>
You could get a second opinion, or just keep the receipt and bring back
unused overage.
Most people are honest.
Sandra
[email protected]
In a message dated 1/12/03 12:32:29 PM Eastern Standard Time,
SandraDodd@... writes:
year.
Pam G.
[Non-text portions of this message have been removed]
SandraDodd@... writes:
> <<Yep, and also has a vested interest in over-selling to you! >>And they want good word of mouth and happy customers that will come back next
>
> You could get a second opinion, or just keep the receipt and bring back
> unused overage.
>
> Most people are honest.
>
>
year.
Pam G.
[Non-text portions of this message have been removed]
[email protected]
On Sun, 12 Jan 2003 12:20:26 EST SandraDodd@... writes:
effectively encourage my children to live this way. It may just come
naturally to them. It isn't to me. As Ren said in an earlier post, we
have been brainwashed. I am moving on, and look at things differently,
and "start where you're not" is a very good suggestion.
Wende
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> Instead of worrying about overcoming, knowing or using strengths andI am not sure what you mean here.
> weaknesses, how about just encourage childs are?
> This is an odd case of "start where you're not."I have realized that. I have to work on my own unschooling, before I can
> If you start where you are, you'll be blocked.
effectively encourage my children to live this way. It may just come
naturally to them. It isn't to me. As Ren said in an earlier post, we
have been brainwashed. I am moving on, and look at things differently,
and "start where you're not" is a very good suggestion.
Wende
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[email protected]
In a message dated 1/12/03 11:07:38 AM, love-it-here@... writes:
<< > Instead of worrying about overcoming, knowing or using strengths and
and maybe will help fill up that exciting hole
I have no idea what it used to say.
I can't find an outgoing mail copy either to see what it might've been.
It was a more polished (probably) version of...
Instead of worrying about math, let the children live in the math-filled
mathematical world and soak the math in naturally and without the aversion
school puts into people.
School does a lot of damage to kids, and parents can do that same kind of
damage at home if they're not careful NOT to do it.
Sandra
<< > Instead of worrying about overcoming, knowing or using strengths and
> weaknesses, how about just encourage childs are? >>a phrase leaked out into the ozone
and maybe will help fill up that exciting hole
I have no idea what it used to say.
I can't find an outgoing mail copy either to see what it might've been.
It was a more polished (probably) version of...
Instead of worrying about math, let the children live in the math-filled
mathematical world and soak the math in naturally and without the aversion
school puts into people.
School does a lot of damage to kids, and parents can do that same kind of
damage at home if they're not careful NOT to do it.
Sandra
[email protected]
> SandraDodd@... writes:You are a lot more trusting than I am.
> > Most people are honest.
> genant2@... writes:One would think. But it seems like around here there is a definite
> And they want good word of mouth and happy customers that will come
> back next year.
> Pam G.
arrogance in marketing. I'm in a rural area, where there aren't all that
many businesses to choose from: ie: one grocery store, one lumber yard,
one coal supplier, etc. If you are not happy with service, and tell them
so, they pretty much tell you that that is the way it is, and to go
somewhere else if you are not happy (knowing full well that there isn't
any other place to go) They are VERY independent here. Therefor, I like
all business transactions to be straight, and final, at least to the best
of my ability.
I was really only using the mulch thing in my original post as an
example of the kinds of formulas I was searching for. But, as it has been
shown to me in various posts, formulas are not the best way to come up
with end results. Which just reminded me of another story, somewhat off
topic.
I have a good friend who broke away from the Amish community about six
years ago. She is the best darn cook I have ever seen, and I asked her to
share some of her recipes with me. She looked at me blankly, and finally
said that she never used recipes, like that was a given. She said you
just put stuff together till it tastes good. I guess that is a little
like unschooling math. It is more about the end result than how you
actually get there. (I think)
Wende
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Fetteroll
on 1/12/03 11:09 AM, love-it-here@... at love-it-here@... wrote:
it. And then build the problem up a bit to put your theory to the test
before committing it for real.
How would you handle a play yard that was 3'x3'? It's a good place to start
but it turns out too simple to tell us much. What at 4'x4'? 6'x6'? And so on
until you can see what you're doing and why you're doing it.
Joyce
> For instance, using my mulch problem, in my mind's eye I canA good technique is to simplify the problem until you can see how to finish
> visualize the play area broke up into little cubes, let's say 1' square.
> But short of counting out each of the cubes one by one, and then dividing
> this number by 3 to come up with the cubic yard measurement (if that is
> even correct), I have a mental block as to how to finish the equation.
it. And then build the problem up a bit to put your theory to the test
before committing it for real.
How would you handle a play yard that was 3'x3'? It's a good place to start
but it turns out too simple to tell us much. What at 4'x4'? 6'x6'? And so on
until you can see what you're doing and why you're doing it.
Joyce
Fetteroll
on 1/12/03 12:20 PM, SandraDodd@... at SandraDodd@... wrote:
us learn to figure out the pros and cons of available tools for a particular
situation, we can look at a tool and not know what situation it would likely
be used in. And we can look at a situation and not know what tool to use.
Joyce
> They didn't teach you how to create theExactly. Since schools teach us to use tools (formulas) rather than helping
> formula. They showed you the formula and taught you how to plug other
> numbers in and "solve" it.
us learn to figure out the pros and cons of available tools for a particular
situation, we can look at a tool and not know what situation it would likely
be used in. And we can look at a situation and not know what tool to use.
Joyce
elissa kroeger <[email protected]>
I find it very interesting that so many adults who went to school,
college etc. took lots and lots of math classes and still hate/ don't
understand or get headaches from math!!! The point is, do we really
actually learn anything from formal math classes? Maybe those of us
who did learn math did so in spite of the teachers and
textbooks...hmm... I was in AP math all through high school, I kept
telling the guidance counselor that I was going to art school, no
math was required and they only offered math classes as an elective
but I tested well so she pressured me to keep taking math at higher
levels. I never brought the book home, I only did homework at school
and only then when I was in the math mood. I never studied for a test
or made any effort to memorize a formula. It was fun but I thought I
was just wasting my time. Then a couple of years ago my son had an
algebra book and I picked it up and realized just how much of the
thinking patterns I learned from higher math I actually do use in
everyday, non-math situations. It was eye opening!
The point in relation to this conversation is; If people who take
formal math classes don't necessarily learn math and people who learn
math don't necessarily take formal math classes, it would then follow
that the two have very little to do with one another!!! Hmm...I think
that is some corrupted form of mathematical reasoning...isn't it?
-Elissa
college etc. took lots and lots of math classes and still hate/ don't
understand or get headaches from math!!! The point is, do we really
actually learn anything from formal math classes? Maybe those of us
who did learn math did so in spite of the teachers and
textbooks...hmm... I was in AP math all through high school, I kept
telling the guidance counselor that I was going to art school, no
math was required and they only offered math classes as an elective
but I tested well so she pressured me to keep taking math at higher
levels. I never brought the book home, I only did homework at school
and only then when I was in the math mood. I never studied for a test
or made any effort to memorize a formula. It was fun but I thought I
was just wasting my time. Then a couple of years ago my son had an
algebra book and I picked it up and realized just how much of the
thinking patterns I learned from higher math I actually do use in
everyday, non-math situations. It was eye opening!
The point in relation to this conversation is; If people who take
formal math classes don't necessarily learn math and people who learn
math don't necessarily take formal math classes, it would then follow
that the two have very little to do with one another!!! Hmm...I think
that is some corrupted form of mathematical reasoning...isn't it?
-Elissa
Have a Nice Day!
Then a couple of years ago my son had an
algebra book and I picked it up and realized just how much of the
thinking patterns I learned from higher math I actually do use in
everyday, non-math situations. <<<
I would love to hear some examples. I know someone did list a few.
I know I use the process of doing proofs for geometry ALL the time. I guess its related to breaking big things into smaller ones, or being able to relate to things logically (though I don't do as well with logic).
I'm wondering about Trig and Calculus though. I didn't do well in Algebra 2, Trig, and never took Calculus.
I watched that movie October Sky (I think thats what it was called) and understood how calculus factored in, but I'd love to hear more example that maybe I'm missing in every day life.
Kristen
[Non-text portions of this message have been removed]
algebra book and I picked it up and realized just how much of the
thinking patterns I learned from higher math I actually do use in
everyday, non-math situations. <<<
I would love to hear some examples. I know someone did list a few.
I know I use the process of doing proofs for geometry ALL the time. I guess its related to breaking big things into smaller ones, or being able to relate to things logically (though I don't do as well with logic).
I'm wondering about Trig and Calculus though. I didn't do well in Algebra 2, Trig, and never took Calculus.
I watched that movie October Sky (I think thats what it was called) and understood how calculus factored in, but I'd love to hear more example that maybe I'm missing in every day life.
Kristen
[Non-text portions of this message have been removed]
Fetteroll
on 2/28/03 4:19 PM, elissa kroeger <elissa_8@...> at
elissa_8@... wrote:
taught. We're taught to recognize patterns and to apply the appropriate
forumla. ("When you see an equation that looks like this, do this to it.")
The goal is to "do" math not to understand it. If understanding comes, it's
a side effect and generally happens to people who are naturally good at
mathematical thinking. Teachers and textbooks go through the motions of
explaining things, but the exercises and tests are designed to test for
skill memorization, not for understanding.
Joyce
elissa_8@... wrote:
> The point is, do we reallyI think we learn something different than what it's assumed we're being
> actually learn anything from formal math classes?
taught. We're taught to recognize patterns and to apply the appropriate
forumla. ("When you see an equation that looks like this, do this to it.")
The goal is to "do" math not to understand it. If understanding comes, it's
a side effect and generally happens to people who are naturally good at
mathematical thinking. Teachers and textbooks go through the motions of
explaining things, but the exercises and tests are designed to test for
skill memorization, not for understanding.
Joyce
[email protected]
In a message dated 03/01/2003 3:00:14 PM Central Standard Time,
fetteroll@... writes:
there is a huge difference between the theory of mathematics and the
application of that theory. Classes teach theory, not application.
Unschooling teaches real-life application, but it is nearly impossible to
extrapolate theory from that. She suggested that trying to label real-life
application with a label such as *geometry* is irrelevant. Why not just
enjoy laying out your garden?
Laura B.
[Non-text portions of this message have been removed]
fetteroll@... writes:
>Was talking to a friend about this very subject today, and she suggested that
> > The point is, do we really
> > actually learn anything from formal math classes?
>
> I think we learn something different than what it's assumed we're being
> taught. We're taught to recognize patterns and to apply the appropriate
> forumla. ("When you see an equation that looks like this, do this to it.")
> The goal is to "do" math not to understand it. If understanding comes, it's
> a side effect and generally happens to people who are naturally good at
> mathematical thinking. Teachers and textbooks go through the motions of
> explaining things, but the exercises and tests are designed to test for
> skill memorization, not for understanding.
>
>
there is a huge difference between the theory of mathematics and the
application of that theory. Classes teach theory, not application.
Unschooling teaches real-life application, but it is nearly impossible to
extrapolate theory from that. She suggested that trying to label real-life
application with a label such as *geometry* is irrelevant. Why not just
enjoy laying out your garden?
Laura B.
[Non-text portions of this message have been removed]