algebra IRL
[email protected]
I had a few unschooling families over last week. Math came up, as usual.
In the midst of explaining that math is everywhere and a part of daily
life, I came up with a really simple example of how we all use it every
day.
You understand that algebra is simply understanding how variables
change the equation, right? That's all it is: that something that
*varies* changes the situation.
So...
You're driving along. Up ahead you see a traffic light that's red. When
(at what point) do you apply your brakes?
You're driving long. At that light, there's a car stopped in front of
you. *Now* when do you apply your brakes?
You're driving along. At the light, there's a car stopped in front of
you, and it's raining. *Now* when do you apply your brakes?
You're driving along---in a *friend's* new car (one you've never driven
before). There's a car stopped in front of you, and it's raining. *Now*
when do you apply your brakes?
While driving, we solve all sorts of algebraic equations---many in a
split-second. Without pencils and paper and without formulae. I bet
some of you mathies could put the "problems" above iinto equations. We
don't *need* to to solve them that way. We do *that* every day,
naturally, without 'x' and 'y'. We're still solving algebra in our
heads---and often don't even know it!
~Kelly
Kelly Lovejoy
Conference Coordinator
Live and Learn Unschooling Conference
http://www.LiveandLearnConference.org
________________________________________________________________________
Email and AIM finally together. You've gotta check out free AOL Mail! -
http://mail.aol.com
In the midst of explaining that math is everywhere and a part of daily
life, I came up with a really simple example of how we all use it every
day.
You understand that algebra is simply understanding how variables
change the equation, right? That's all it is: that something that
*varies* changes the situation.
So...
You're driving along. Up ahead you see a traffic light that's red. When
(at what point) do you apply your brakes?
You're driving long. At that light, there's a car stopped in front of
you. *Now* when do you apply your brakes?
You're driving along. At the light, there's a car stopped in front of
you, and it's raining. *Now* when do you apply your brakes?
You're driving along---in a *friend's* new car (one you've never driven
before). There's a car stopped in front of you, and it's raining. *Now*
when do you apply your brakes?
While driving, we solve all sorts of algebraic equations---many in a
split-second. Without pencils and paper and without formulae. I bet
some of you mathies could put the "problems" above iinto equations. We
don't *need* to to solve them that way. We do *that* every day,
naturally, without 'x' and 'y'. We're still solving algebra in our
heads---and often don't even know it!
~Kelly
Kelly Lovejoy
Conference Coordinator
Live and Learn Unschooling Conference
http://www.LiveandLearnConference.org
________________________________________________________________________
Email and AIM finally together. You've gotta check out free AOL Mail! -
http://mail.aol.com
[email protected]
Wow...thanks for that. My dd is going to do driver's ed/training soon and I was wondering what subject categores I could use for her records!
Any other ideas for "educationese" for drivers ed/training?
Kathryn
-------------- Original message --------------
From: kbcdlovejo@...
I had a few unschooling families over last week. Math came up, as usual.
In the midst of explaining that math is everywhere and a part of daily
life, I came up with a really simple example of how we all use it every
day.
You understand that algebra is simply understanding how variables
change the equation, right? That's all it is: that something that
*varies* changes the situation.
So...
You're driving along. Up ahead you see a traffic light that's red. When
(at what point) do you apply your brakes?
You're driving long. At that light, there's a car stopped in front of
you. *Now* when do you apply your brakes?
You're driving along. At the light, there's a car stopped in front of
you, and it's raining. *Now* when do you apply your brakes?
You're driving along---in a *friend's* new car (one you've never driven
before). There's a car stopped in front of you, and it's raining. *Now*
when do you apply your brakes?
While driving, we solve all sorts of algebraic equations---many in a
split-second. Without pencils and paper and without formulae. I bet
some of you mathies could put the "problems" above iinto equations. We
don't *need* to to solve them that way. We do *that* every day,
naturally, without 'x' and 'y'. We're still solving algebra in our
heads---and often don't even know it!
~Kelly
Kelly Lovejoy
Conference Coordinator
Live and Learn Unschooling Conference
http://www.LiveandLearnConference.org
__________________________________________________________
Email and AIM finally together. You've gotta check out free AOL Mail! -
http://mail.aol.com
[Non-text portions of this message have been removed]
Any other ideas for "educationese" for drivers ed/training?
Kathryn
-------------- Original message --------------
From: kbcdlovejo@...
I had a few unschooling families over last week. Math came up, as usual.
In the midst of explaining that math is everywhere and a part of daily
life, I came up with a really simple example of how we all use it every
day.
You understand that algebra is simply understanding how variables
change the equation, right? That's all it is: that something that
*varies* changes the situation.
So...
You're driving along. Up ahead you see a traffic light that's red. When
(at what point) do you apply your brakes?
You're driving long. At that light, there's a car stopped in front of
you. *Now* when do you apply your brakes?
You're driving along. At the light, there's a car stopped in front of
you, and it's raining. *Now* when do you apply your brakes?
You're driving along---in a *friend's* new car (one you've never driven
before). There's a car stopped in front of you, and it's raining. *Now*
when do you apply your brakes?
While driving, we solve all sorts of algebraic equations---many in a
split-second. Without pencils and paper and without formulae. I bet
some of you mathies could put the "problems" above iinto equations. We
don't *need* to to solve them that way. We do *that* every day,
naturally, without 'x' and 'y'. We're still solving algebra in our
heads---and often don't even know it!
~Kelly
Kelly Lovejoy
Conference Coordinator
Live and Learn Unschooling Conference
http://www.LiveandLearnConference.org
__________________________________________________________
Email and AIM finally together. You've gotta check out free AOL Mail! -
http://mail.aol.com
[Non-text portions of this message have been removed]
trektheory
Actually, I think that is more of physics. (Though physics is
strongly math-based.) I don't view that as solving an equation,
though - the level of precision isn't there.
However, there ARE real-life reasons for knowing and using algebra,
geometry, trig., etc. Heck, ask your local carpenter how he figures
out odd-angle mitred corners.
Figuring out how to optimize your fenced garden for minimal money?
The length of the edges/area inside for the garden (and if you have
rambunctious dogs, a fence may be critical!) is an algebraic equation.
Not to mention optimal yield in your garden. (Planting fewer plants
with higher yields, vs more plants with lower yields per plant.)
Other physics -- playing with magnets (that is always a blast!),
tossing a ball up in the air and catching it, etc.
And if you play games, well, there you get probability.
Oh, I love math! ;-)
Linda
strongly math-based.) I don't view that as solving an equation,
though - the level of precision isn't there.
However, there ARE real-life reasons for knowing and using algebra,
geometry, trig., etc. Heck, ask your local carpenter how he figures
out odd-angle mitred corners.
Figuring out how to optimize your fenced garden for minimal money?
The length of the edges/area inside for the garden (and if you have
rambunctious dogs, a fence may be critical!) is an algebraic equation.
Not to mention optimal yield in your garden. (Planting fewer plants
with higher yields, vs more plants with lower yields per plant.)
Other physics -- playing with magnets (that is always a blast!),
tossing a ball up in the air and catching it, etc.
And if you play games, well, there you get probability.
Oh, I love math! ;-)
Linda
--- In [email protected], kbcdlovejo@... wrote:
>
> I had a few unschooling families over last week. Math came up, as usual.
>
> In the midst of explaining that math is everywhere and a part of daily
> life, I came up with a really simple example of how we all use it every
> day.
>
> You understand that algebra is simply understanding how variables
> change the equation, right? That's all it is: that something that
> *varies* changes the situation.
>
> So...
>
> You're driving along. Up ahead you see a traffic light that's red. When
> (at what point) do you apply your brakes?
>
> You're driving long. At that light, there's a car stopped in front of
> you. *Now* when do you apply your brakes?
>
> You're driving along. At the light, there's a car stopped in front of
> you, and it's raining. *Now* when do you apply your brakes?
>
> You're driving along---in a *friend's* new car (one you've never driven
> before). There's a car stopped in front of you, and it's raining. *Now*
> when do you apply your brakes?
>
> While driving, we solve all sorts of algebraic equations---many in a
> split-second. Without pencils and paper and without formulae. I bet
> some of you mathies could put the "problems" above iinto equations. We
> don't *need* to to solve them that way. We do *that* every day,
> naturally, without 'x' and 'y'. We're still solving algebra in our
> heads---and often don't even know it!
>
> ~Kelly
>
> Kelly Lovejoy
> Conference Coordinator
> Live and Learn Unschooling Conference
> http://www.LiveandLearnConference.org
> ________________________________________________________________________
> Email and AIM finally together. You've gotta check out free AOL Mail! -
> http://mail.aol.com
>
Meredith
Social situations can also thought of algebraically. Variables can
include the number of people in a situation, their ages, whether they
are introverts or extroverts (heck, the whole MBTI is a way of
describing personality types based on four variables), etc.
I tend to think about the stressors in mine and my kids' lives in terms
of variables that interact with each other. If x=time since protein,
y=amount of sleep and z=days to my period, how do we caluclate the
likelihood that Meredith will meltdown in the grocery store?
---Meredith (not so well rested, but well-fed and not premenstrual, so
its a good day to shop!)
include the number of people in a situation, their ages, whether they
are introverts or extroverts (heck, the whole MBTI is a way of
describing personality types based on four variables), etc.
I tend to think about the stressors in mine and my kids' lives in terms
of variables that interact with each other. If x=time since protein,
y=amount of sleep and z=days to my period, how do we caluclate the
likelihood that Meredith will meltdown in the grocery store?
---Meredith (not so well rested, but well-fed and not premenstrual, so
its a good day to shop!)
[email protected]
-----Original Message-----
From: trektheory <trektheory@...>
Actually, I think that is more of physics. (Though physics is
strongly math-based.)
-=-=-=-
Yeah---but I never saw much difference between the two.
I think I saw physics as "practical algebra." But neither made too much
sense until just a few years ago. I took those subjects waaaay too
young. I got As, but the letter grades didn't translate in
comprehension---just correct answers on the page. (Imagaine that!)
-=-=-=-=-
I don't view that as solving an equation,
though - the level of precision isn't there.
-=-=-=-=-
Precision is in the eye of the rear-ended. <g>
~Kelly
Kelly Lovejoy
Conference Coordinator
Live and Learn Unschooling Conference
http://www.LiveandLearnConference.org
________________________________________________________________________
Email and AIM finally together. You've gotta check out free AOL Mail! -
http://mail.aol.com
From: trektheory <trektheory@...>
Actually, I think that is more of physics. (Though physics is
strongly math-based.)
-=-=-=-
Yeah---but I never saw much difference between the two.
I think I saw physics as "practical algebra." But neither made too much
sense until just a few years ago. I took those subjects waaaay too
young. I got As, but the letter grades didn't translate in
comprehension---just correct answers on the page. (Imagaine that!)
-=-=-=-=-
I don't view that as solving an equation,
though - the level of precision isn't there.
-=-=-=-=-
Precision is in the eye of the rear-ended. <g>
~Kelly
Kelly Lovejoy
Conference Coordinator
Live and Learn Unschooling Conference
http://www.LiveandLearnConference.org
________________________________________________________________________
Email and AIM finally together. You've gotta check out free AOL Mail! -
http://mail.aol.com
Meredith
--- In [email protected], "trektheory"
<trektheory@...> wrote:
algebraically, and pretty precicely, if you wanted to. One of the
skills drivers learn is "eyeballing" those kinds of measurements -
200ft looks different if you're looking at a line on the road vs a
vertical surface, and different at 5mph than at 15mph. That "seems"
imprecise, but I've learned to "eyeball" a quarter of an inch while
sewing, and at one point I could "eyeball" measurements in tenths of
a milimeter under a microscope.
It can also be solved without getting into the physics/calculus,
since the objects in motion are on a (relatively) flat surface -
just as statstical problems can be solved algebraically or via
calculus without necessarily sacrificing precision.
or buys a jig and does a bit of trial-and-error. I'm not trying to
be obnoxious, but it really does help, when thinking about the way
people learn, to step away from the obvious a bit. There's as much
(and sometimes more) conceptual geometry involved in re-arranging
furniture as carpentry - the carpentry just has more numbers.
Mathematics isn't really about numbers, its about relationships. The
relationship between up and down and sideways is so facinating to us
humans that several different kinds of mathematics exist to describe
those relationships - algebra, geometry, trigonometry and calculus
all deal with those relationships in different ways. The math isn't
in memorizing the jargon and formulas, its in thinking about what
all that stuff is designed to express, and that can be done without
a single number.
The trouble that most people run into is having been taught that the
numbers and the jargon *are* the math - that's what makes a
carpenter using a jig "look" more mathematical than a mom trying to
get her kids home from the park before the traffic gets bad, even
though *he's* just doing what Bubbah showed him and *she's* juggling
fourteen different variables in her head.
---Meredith (Mo 6, Ray 14)
<trektheory@...> wrote:
> I don't view that as solving an equation,I'd disagree ;) It's totally possible to represent Kelly's examples
> though - the level of precision isn't there.
algebraically, and pretty precicely, if you wanted to. One of the
skills drivers learn is "eyeballing" those kinds of measurements -
200ft looks different if you're looking at a line on the road vs a
vertical surface, and different at 5mph than at 15mph. That "seems"
imprecise, but I've learned to "eyeball" a quarter of an inch while
sewing, and at one point I could "eyeball" measurements in tenths of
a milimeter under a microscope.
It can also be solved without getting into the physics/calculus,
since the objects in motion are on a (relatively) flat surface -
just as statstical problems can be solved algebraically or via
calculus without necessarily sacrificing precision.
>figures
> However, there ARE real-life reasons for knowing and using algebra,
> geometry, trig., etc. Heck, ask your local carpenter how he
> out odd-angle mitred corners.Since I happen to have a carpenter handy...he uses a tool. He makes
or buys a jig and does a bit of trial-and-error. I'm not trying to
be obnoxious, but it really does help, when thinking about the way
people learn, to step away from the obvious a bit. There's as much
(and sometimes more) conceptual geometry involved in re-arranging
furniture as carpentry - the carpentry just has more numbers.
Mathematics isn't really about numbers, its about relationships. The
relationship between up and down and sideways is so facinating to us
humans that several different kinds of mathematics exist to describe
those relationships - algebra, geometry, trigonometry and calculus
all deal with those relationships in different ways. The math isn't
in memorizing the jargon and formulas, its in thinking about what
all that stuff is designed to express, and that can be done without
a single number.
The trouble that most people run into is having been taught that the
numbers and the jargon *are* the math - that's what makes a
carpenter using a jig "look" more mathematical than a mom trying to
get her kids home from the park before the traffic gets bad, even
though *he's* just doing what Bubbah showed him and *she's* juggling
fourteen different variables in her head.
---Meredith (Mo 6, Ray 14)
[email protected]
I use geometry while flying airplanes. I use known landmarks and draw trajectory lines in space from point to point, combining two or three trajectories to figure out angles where my next landmark should be located so I can then pick up a heading and fly it. I use landmarks off on the horizon, really "big picture" stuff. I was not taught to navigate this way. I made it up because it worked for me, and I struggled in Geometry in High School. I have never been lost in an airplane, either, but I have been lost in a car.
Kathryn
-------------- Original message --------------
From: "Meredith" <meredith@...>
--- In [email protected], "trektheory"
<trektheory@...> wrote:
algebraically, and pretty precicely, if you wanted to. One of the
skills drivers learn is "eyeballing" those kinds of measurements -
200ft looks different if you're looking at a line on the road vs a
vertical surface, and different at 5mph than at 15mph. That "seems"
imprecise, but I've learned to "eyeball" a quarter of an inch while
sewing, and at one point I could "eyeball" measurements in tenths of
a milimeter under a microscope.
It can also be solved without getting into the physics/calculus,
since the objects in motion are on a (relatively) flat surface -
just as statstical problems can be solved algebraically or via
calculus without necessarily sacrificing precision.
or buys a jig and does a bit of trial-and-error. I'm not trying to
be obnoxious, but it really does help, when thinking about the way
people learn, to step away from the obvious a bit. There's as much
(and sometimes more) conceptual geometry involved in re-arranging
furniture as carpentry - the carpentry just has more numbers.
Mathematics isn't really about numbers, its about relationships. The
relationship between up and down and sideways is so facinating to us
humans that several different kinds of mathematics exist to describe
those relationships - algebra, geometry, trigonometry and calculus
all deal with those relationships in different ways. The math isn't
in memorizing the jargon and formulas, its in thinking about what
all that stuff is designed to express, and that can be done without
a single number.
The trouble that most people run into is having been taught that the
numbers and the jargon *are* the math - that's what makes a
carpenter using a jig "look" more mathematical than a mom trying to
get her kids home from the park before the traffic gets bad, even
though *he's* just doing what Bubbah showed him and *she's* juggling
fourteen different variables in her head.
---Meredith (Mo 6, Ray 14)
[Non-text portions of this message have been removed]
Kathryn
-------------- Original message --------------
From: "Meredith" <meredith@...>
--- In [email protected], "trektheory"
<trektheory@...> wrote:
> I don't view that as solving an equation,I'd disagree ;) It's totally possible to represent Kelly's examples
> though - the level of precision isn't there.
algebraically, and pretty precicely, if you wanted to. One of the
skills drivers learn is "eyeballing" those kinds of measurements -
200ft looks different if you're looking at a line on the road vs a
vertical surface, and different at 5mph than at 15mph. That "seems"
imprecise, but I've learned to "eyeball" a quarter of an inch while
sewing, and at one point I could "eyeball" measurements in tenths of
a milimeter under a microscope.
It can also be solved without getting into the physics/calculus,
since the objects in motion are on a (relatively) flat surface -
just as statstical problems can be solved algebraically or via
calculus without necessarily sacrificing precision.
>figures
> However, there ARE real-life reasons for knowing and using algebra,
> geometry, trig., etc. Heck, ask your local carpenter how he
> out odd-angle mitred corners.Since I happen to have a carpenter handy...he uses a tool. He makes
or buys a jig and does a bit of trial-and-error. I'm not trying to
be obnoxious, but it really does help, when thinking about the way
people learn, to step away from the obvious a bit. There's as much
(and sometimes more) conceptual geometry involved in re-arranging
furniture as carpentry - the carpentry just has more numbers.
Mathematics isn't really about numbers, its about relationships. The
relationship between up and down and sideways is so facinating to us
humans that several different kinds of mathematics exist to describe
those relationships - algebra, geometry, trigonometry and calculus
all deal with those relationships in different ways. The math isn't
in memorizing the jargon and formulas, its in thinking about what
all that stuff is designed to express, and that can be done without
a single number.
The trouble that most people run into is having been taught that the
numbers and the jargon *are* the math - that's what makes a
carpenter using a jig "look" more mathematical than a mom trying to
get her kids home from the park before the traffic gets bad, even
though *he's* just doing what Bubbah showed him and *she's* juggling
fourteen different variables in her head.
---Meredith (Mo 6, Ray 14)
[Non-text portions of this message have been removed]
Nance Confer
unschoolingbasicsHeck, ask your local carpenter how he figures
out odd-angle mitred corners.
***
Then ask him where he learned how to do this -- in an algebra class or on the job.
Nance
[Non-text portions of this message have been removed]
out odd-angle mitred corners.
***
Then ask him where he learned how to do this -- in an algebra class or on the job.
Nance
[Non-text portions of this message have been removed]
Ren Allen
--- In [email protected], "Nance Confer"
<marbleface@...> wrote:
mitre? That's too vague."
He learned the geometry formula for figuring out the unknown
measurement of one side of a triangle on the job. What he says about
building is that basic math skills are all you need unless you're
getting into extreme precision work (ie: detailed furniture or other
masterwork type building). Basic geometry is occasionally useful, but
any kind of regular construction can be done with plain-old-vanilla
basic arithmetic.
He worked in construction for almost 20 years and is one of the most
precise, careful and skilled builders I know and he just told me that
precision math is rather useless when working with wood because it
isn't a precision material.
You can have a 2x4 that is 1 1/2 inches thick or one that is 1 9/16ths
thick. Most all the pieces vary slightly, you're dealing with
different grains etc... Carpenters don't become great by sitting in a
math class and learning algebra. They learn to become great builders
by building. They pick up needed tools as they learn to build. If they
need a geometry formula, a more expert builder will show it to them at
the time they need it (as in dh's case).
The best kind of learning comes from doing.
Ren
learninginfreedom.com
<marbleface@...> wrote:
>My carpenter says "what the heck does she mean by an 'odd-angled'
> unschoolingbasicsHeck, ask your local carpenter how he figures
> out odd-angle mitred corners.
>
mitre? That's too vague."
He learned the geometry formula for figuring out the unknown
measurement of one side of a triangle on the job. What he says about
building is that basic math skills are all you need unless you're
getting into extreme precision work (ie: detailed furniture or other
masterwork type building). Basic geometry is occasionally useful, but
any kind of regular construction can be done with plain-old-vanilla
basic arithmetic.
He worked in construction for almost 20 years and is one of the most
precise, careful and skilled builders I know and he just told me that
precision math is rather useless when working with wood because it
isn't a precision material.
You can have a 2x4 that is 1 1/2 inches thick or one that is 1 9/16ths
thick. Most all the pieces vary slightly, you're dealing with
different grains etc... Carpenters don't become great by sitting in a
math class and learning algebra. They learn to become great builders
by building. They pick up needed tools as they learn to build. If they
need a geometry formula, a more expert builder will show it to them at
the time they need it (as in dh's case).
The best kind of learning comes from doing.
Ren
learninginfreedom.com
Elly
ok, maybe i'm the only nerd who feels this way, but there IS a value to formalizing the
math, and not just knowing how to drive, or how to saw trim, or what-have-you. the
value, in my eyes anyways, is in knowing how to quickly solve NEW problems that you
haven't seen before, and in knowing how to solve problems like the driving thing exactly.
driving a car is NOT the same as knowing algebra. driving a car is driving a car. knowing
algebra is being able to figure out any number of other calculations (a real life example
from recently: if my fabric is 4.9 meters long and is likely to shrink to 4.7m after washing,
and i want to cut it, prewashing, into a piece that, post-washing, will end up 3.2m, where
do i cut?) at will. driving a car, no matter how skilled i am at it, will not help me figure out
any other non-driving related problems. yes, you could formulate kelly's examples
algebraically and precisely, but you don't need to to drive and i'd hazard a guess that
99.999 percent of people never do.
so: school may suck in many ways, but numbers and x's and y's are GREAT at versatility; i
hope my kids choose to use and understand them.
elly
math, and not just knowing how to drive, or how to saw trim, or what-have-you. the
value, in my eyes anyways, is in knowing how to quickly solve NEW problems that you
haven't seen before, and in knowing how to solve problems like the driving thing exactly.
driving a car is NOT the same as knowing algebra. driving a car is driving a car. knowing
algebra is being able to figure out any number of other calculations (a real life example
from recently: if my fabric is 4.9 meters long and is likely to shrink to 4.7m after washing,
and i want to cut it, prewashing, into a piece that, post-washing, will end up 3.2m, where
do i cut?) at will. driving a car, no matter how skilled i am at it, will not help me figure out
any other non-driving related problems. yes, you could formulate kelly's examples
algebraically and precisely, but you don't need to to drive and i'd hazard a guess that
99.999 percent of people never do.
so: school may suck in many ways, but numbers and x's and y's are GREAT at versatility; i
hope my kids choose to use and understand them.
elly
--- In [email protected], "Meredith" <meredith@...> wrote:
>
> --- In [email protected], "trektheory"
> <trektheory@> wrote:
> > I don't view that as solving an equation,
> > though - the level of precision isn't there.
>
> I'd disagree ;) It's totally possible to represent Kelly's examples
> algebraically, and pretty precicely, if you wanted to. One of the
> skills drivers learn is "eyeballing" those kinds of measurements -
> 200ft looks different if you're looking at a line on the road vs a
> vertical surface, and different at 5mph than at 15mph. That "seems"
> imprecise, but I've learned to "eyeball" a quarter of an inch while
> sewing, and at one point I could "eyeball" measurements in tenths of
> a milimeter under a microscope.
>
> It can also be solved without getting into the physics/calculus,
> since the objects in motion are on a (relatively) flat surface -
> just as statstical problems can be solved algebraically or via
> calculus without necessarily sacrificing precision.
>
> >
> > However, there ARE real-life reasons for knowing and using algebra,
> > geometry, trig., etc. Heck, ask your local carpenter how he
> figures
> > out odd-angle mitred corners.
>
> Since I happen to have a carpenter handy...he uses a tool. He makes
> or buys a jig and does a bit of trial-and-error. I'm not trying to
> be obnoxious, but it really does help, when thinking about the way
> people learn, to step away from the obvious a bit. There's as much
> (and sometimes more) conceptual geometry involved in re-arranging
> furniture as carpentry - the carpentry just has more numbers.
>
> Mathematics isn't really about numbers, its about relationships. The
> relationship between up and down and sideways is so facinating to us
> humans that several different kinds of mathematics exist to describe
> those relationships - algebra, geometry, trigonometry and calculus
> all deal with those relationships in different ways. The math isn't
> in memorizing the jargon and formulas, its in thinking about what
> all that stuff is designed to express, and that can be done without
> a single number.
>
> The trouble that most people run into is having been taught that the
> numbers and the jargon *are* the math - that's what makes a
> carpenter using a jig "look" more mathematical than a mom trying to
> get her kids home from the park before the traffic gets bad, even
> though *he's* just doing what Bubbah showed him and *she's* juggling
> fourteen different variables in her head.
>
> ---Meredith (Mo 6, Ray 14)
>
Sylvia Toyama
a real life example from recently: if my fabric is 4.9 meters long and is likely to shrink to 4.7m after washing, and i want to cut it, prewashing, into a piece that, post-washing, will end up 3.2m, where do i cut?) at will.
****
Um, if the size will be important to me post-washing, why not just cut it down then? Is there something to be gained by cutting first, and washing second? And if so, this sounds more like a fabric/sewing problem than a math problem. Besides that, I have no faith in the objective measure of how much my washer and dryer (and can I stretch and use a clothesline instead of a dryer?) will shrink it. I feel much safe just chucking the math and washing before I cut.
****
so: school may suck in many ways, but numbers and x's and y's are GREAT at versatility; i hope my kids choose to use and understand them.
*****
I do almost all math in my head (have since I was a kid, as did/do my parents) and have figured out my own formulas for how to answer the math-kinda questions that come up in every day life (or like the fabric I answer them without using algebra, thru other practical methods) but I have no idea how that would look on paper. And yet, it still works for me. However, if my kids choose never to figure out these tricks it won't bother me a bit! I'm sure they'll fill their heads and minds with the life-coping skills they need in their own lives, not those I deem necessary. After all, I don't get to live their lives!
Sylvia
---------------------------------
Building a website is a piece of cake.
Yahoo! Small Business gives you all the tools to get online.
[Non-text portions of this message have been removed]
****
Um, if the size will be important to me post-washing, why not just cut it down then? Is there something to be gained by cutting first, and washing second? And if so, this sounds more like a fabric/sewing problem than a math problem. Besides that, I have no faith in the objective measure of how much my washer and dryer (and can I stretch and use a clothesline instead of a dryer?) will shrink it. I feel much safe just chucking the math and washing before I cut.
****
so: school may suck in many ways, but numbers and x's and y's are GREAT at versatility; i hope my kids choose to use and understand them.
*****
I do almost all math in my head (have since I was a kid, as did/do my parents) and have figured out my own formulas for how to answer the math-kinda questions that come up in every day life (or like the fabric I answer them without using algebra, thru other practical methods) but I have no idea how that would look on paper. And yet, it still works for me. However, if my kids choose never to figure out these tricks it won't bother me a bit! I'm sure they'll fill their heads and minds with the life-coping skills they need in their own lives, not those I deem necessary. After all, I don't get to live their lives!
Sylvia
---------------------------------
Building a website is a piece of cake.
Yahoo! Small Business gives you all the tools to get online.
[Non-text portions of this message have been removed]
Pamela Sorooshian
On Oct 1, 2007, at 9:06 AM, Elly wrote:
formal math. I enjoy helping other people learn it, when they're
interested.
My observation and experience has been that those who have LOTS and
lots and lots of experience of all kinds, but little paper and pencil
(or online, these days) formal structured math, are very capable of
learning the formal math later, if and when they do have an interest
or discover a need for it.
Also, because numbers and equations and geometry and measurement are,
as you said, "GREAT," kids will be drawn to them and will choose to
use and understand them.
But, that doesn't mean that parents need to act like schoolteachers
and provide lessons. It can all happen completely naturally and even
the formal stuff can arise out of genuine interests.
-pam
[Non-text portions of this message have been removed]
> so: school may suck in many ways, but numbers and x's and y's areI'm a statistician and economist, myself, and really enjoyed learning
> GREAT at versatility; i
> hope my kids choose to use and understand them.
formal math. I enjoy helping other people learn it, when they're
interested.
My observation and experience has been that those who have LOTS and
lots and lots of experience of all kinds, but little paper and pencil
(or online, these days) formal structured math, are very capable of
learning the formal math later, if and when they do have an interest
or discover a need for it.
Also, because numbers and equations and geometry and measurement are,
as you said, "GREAT," kids will be drawn to them and will choose to
use and understand them.
But, that doesn't mean that parents need to act like schoolteachers
and provide lessons. It can all happen completely naturally and even
the formal stuff can arise out of genuine interests.
-pam
[Non-text portions of this message have been removed]
Meredith
--- In [email protected], "Elly" <ellyzoe@...> wrote:
The trouble is, that's not what the vast majority of people learn
from algebra. People either know how to solve problems and apply
that knowledge to algebra or don't see a connection between the
formalized math and any real life situations.
lots of customers and co-workers with high-school algebra who never
once realized that was an algebra problem. Most people learn that
sort of thing either by trial and error or asking the lady who is
cutting the fabric "how much will it shrink?"
know. Some people don't solve problems via logic - my stepson is
one. It drives me and his dad batty sometimes because we're both
terribly logical thinkers (me especially). I've found personality
and learning models like the MBTI and Gardner's theory of Multiple
Intelligences very helpful in learning to understand that this isn't
some kind of lack on Ray's part - its a whole different way of
thinking. *I* need those formalized models to help me think about
him, but he doesn't need them to understand himself or his own
learning processes.
From an unschooling perspective, its more important to ask yourself
what will happen if your kids *don't* either understand or choose to
use formalized mathematical notations as a means of problem solving.
Do you push them to do it bc you believe its "good for them"? Do you
drop the matter and hope it never comes up? Do you help your kids
find other, different ways of looking at situations and finding
solutions?
---Meredith (did I deliberately word my answers so as to suggest a
specific result? wink)
>value to formalizing the
> ok, maybe i'm the only nerd who feels this way, but there IS a
> math, and not just knowing how to drive, or how to saw trim, orwhat-have-you. the
> value, in my eyes anyways, is in knowing how to quickly solve NEWproblems that you
> haven't seen before, and in knowing how to solve problems like thedriving thing exactly.
The trouble is, that's not what the vast majority of people learn
from algebra. People either know how to solve problems and apply
that knowledge to algebra or don't see a connection between the
formalized math and any real life situations.
>(a real life exampleshrink to 4.7m after washing,
> from recently: if my fabric is 4.9 meters long and is likely to
> and i want to cut it, prewashing, into a piece that, post-washing,will end up 3.2m, where
> do i cut?)Perfect! I worked in fabric stores for years, talked to lots and
lots of customers and co-workers with high-school algebra who never
once realized that was an algebra problem. Most people learn that
sort of thing either by trial and error or asking the lady who is
cutting the fabric "how much will it shrink?"
> so: school may suck in many ways, but numbers and x's and y's areGREAT at versatility; i
> hope my kids choose to use and understand them.They may not have the option of "choosing to understand them" you
know. Some people don't solve problems via logic - my stepson is
one. It drives me and his dad batty sometimes because we're both
terribly logical thinkers (me especially). I've found personality
and learning models like the MBTI and Gardner's theory of Multiple
Intelligences very helpful in learning to understand that this isn't
some kind of lack on Ray's part - its a whole different way of
thinking. *I* need those formalized models to help me think about
him, but he doesn't need them to understand himself or his own
learning processes.
From an unschooling perspective, its more important to ask yourself
what will happen if your kids *don't* either understand or choose to
use formalized mathematical notations as a means of problem solving.
Do you push them to do it bc you believe its "good for them"? Do you
drop the matter and hope it never comes up? Do you help your kids
find other, different ways of looking at situations and finding
solutions?
---Meredith (did I deliberately word my answers so as to suggest a
specific result? wink)
Elly
--- In [email protected], Sylvia Toyama <sylgt04@...> wrote:
end up 3.2m, where do i cut?) at will.
more like a fabric/sewing problem than a math problem. Besides that, I have no faith in
the objective measure of how much my washer and dryer (and can I stretch and use a
clothesline instead of a dryer?) will shrink it. I feel much safe just chucking the math and
washing before I cut.
ah. it's a lot nicer to work with pre-washing---flat and starched and stretched out from
the loom. washing can tend to warp fabrics. ironing can help, but prewashing is just so
much easier with many fabrics. and i had very good reason to believe it would shrink to a
particular size. i am glad to have the ability to decide to calculate this or not rather than
"having to" wash first, IYKWIM.
elly
>4.7m after washing, and i want to cut it, prewashing, into a piece that, post-washing, will
> a real life example from recently: if my fabric is 4.9 meters long and is likely to shrink to
end up 3.2m, where do i cut?) at will.
>there something to be gained by cutting first, and washing second? And if so, this sounds
> ****
> Um, if the size will be important to me post-washing, why not just cut it down then? Is
more like a fabric/sewing problem than a math problem. Besides that, I have no faith in
the objective measure of how much my washer and dryer (and can I stretch and use a
clothesline instead of a dryer?) will shrink it. I feel much safe just chucking the math and
washing before I cut.
ah. it's a lot nicer to work with pre-washing---flat and starched and stretched out from
the loom. washing can tend to warp fabrics. ironing can help, but prewashing is just so
much easier with many fabrics. and i had very good reason to believe it would shrink to a
particular size. i am glad to have the ability to decide to calculate this or not rather than
"having to" wash first, IYKWIM.
elly
trektheory
--- In [email protected], "Elly" <ellyzoe@...> wrote:
No, you aren't the only one. The point I had been trying to make
earlier (and failed, I think - and I dropped it there) was that when
you make those judgements while driving, you are NOT doing an
equation. I defy anyone judging when to apply the brakes to tell me
what variable they were solving for, what the distance between their
car and the one in front was, etc. Real world estimating, sure, but
not equation solving.
My son is finding math VERY useful -- he wants to be a programmer -
preferably game programner. He is loving the calculus he is taking
this year, and knows that it, along with the physics he has had (and
probably will have in the future at college) will help him with his
goals.
Word problems try to be real-life sort of applications, which is why
they are so important. Some things, yeah, you can jerry-rig them
without precise calculations. Other things, though, you do want to
get right, or you may waste a lot of time and/or money.
(BTW, if anyone has a child who is trying to learn algebra word
problems and is having trouble, the book that was a HUGE help to my
son was How To Solve Algebra Word Problems. Straight forward title,
eh? We borrowed it from the library.)
Linda
>to formalizing the
> ok, maybe i'm the only nerd who feels this way, but there IS a value
> math, and not just knowing how to drive, or how to saw trim, orwhat-have-you.
No, you aren't the only one. The point I had been trying to make
earlier (and failed, I think - and I dropped it there) was that when
you make those judgements while driving, you are NOT doing an
equation. I defy anyone judging when to apply the brakes to tell me
what variable they were solving for, what the distance between their
car and the one in front was, etc. Real world estimating, sure, but
not equation solving.
My son is finding math VERY useful -- he wants to be a programmer -
preferably game programner. He is loving the calculus he is taking
this year, and knows that it, along with the physics he has had (and
probably will have in the future at college) will help him with his
goals.
Word problems try to be real-life sort of applications, which is why
they are so important. Some things, yeah, you can jerry-rig them
without precise calculations. Other things, though, you do want to
get right, or you may waste a lot of time and/or money.
(BTW, if anyone has a child who is trying to learn algebra word
problems and is having trouble, the book that was a HUGE help to my
son was How To Solve Algebra Word Problems. Straight forward title,
eh? We borrowed it from the library.)
Linda
Elly
--- In [email protected], "Meredith" <meredith@...> wrote:
this. it's not that i want my kids to have to sit in a classroom and study algebra in a
vacuum, it's that i think it's a valuable tool to present and demonstrate, and the
abstractions should not be rejected as "schoolish". i guess i think that if a kid wants to
build a slingshot, or a tree house, or likes to watch "mythbusters", that part of the
discussion and part of what the parent would bring to the project would be the math
underlying it. not to press it on the kid, but if i'm helping someone build a slingshot, i
might find it interesting myself to see how heavy of a weight it can lift, or how far it could
conceivably throw something and how i could make it throw farther (Etc).
and something that's always driven me *nuts* about mythbusters is that, while i love many
of hte experiments they do, it sometimes frustrates me that they do all the experiments
and never discuss the math/physics/whatever underlying some of the myths that they're
trying to bust. and so sometimes their experiments work and they either bust or don't
bust the myth, which is fine, and satisfying as a "proof by example" or "disproof by
counterexample" or whatever, but sometimes they neither prove nor disprove with their
experiments and are left basically saying "we dunno"---those situations especially just
BEG for math. they had one on mirrors where they were trying to reflect hte light of the
sun onto a specific point to make a fire. that just BEGGED to me for a physics book and
some formulas---they could've figured out just how many mirrors etc and whether it
would've been physically possible, and THEN tried to build it to demonstrate...
anyways, i think there are so many ways to make math a part of life. and not in a forcing
or "you should learn this" way, just in a providing-paths-for-exploring-your-child's-
interest way, just as we help our kids with anything (including reading). it seems like
there's a little "equation phobia" here (am i misreading?) where it's almost as though since
equations and abstractions are taught in school folks don't believe they should be part of
life or discussed at all. seems to me like they're as much a part of life as letters and books.
not something to be forced, but not something to be avoided either.
it & help with it as it's relevant to our lives, just like with reading or walking or anything
else, and hopefully it will be connected to and relevant to their lives.
my kids *don't* choose to learn to read? i don't think that's possible. i feel like if i raise
them in a text-rich environment in which reading is interesting and essential and relevant,
they simply WILL learn to read. i don't see how math is any different except that so many
parents are afraid of it or ignorant about it or do not use it themselves. obviously, those
kids would not be growing up in a math-enriched environment. do y'all think there's
something fundamentally unnatural about math that isn't so of reading, walking, or
talking?
i guess i feel like it's part of my job as a parent to create a math-enriched environment,
just as it is my job to create a text-enriched environment, with magazines and papers and
mail and books and notes and etc, and just as it is my job to create an environment
enriched with movement, with swings and slides and climbing structures and bikes and
etc. it's part of creating a healthy place in which a complete person can develop, and
trusting them to develop fully. and yes, i'd say being able to formulate and solve basic
algebra problems is part of developing fully. i dunno that i could argue the same about
calculus, though dh thinks he could. ;)
thanks for providing food for thought!
elly
> The trouble is, that's not what the vast majority of people learni guess my goal as an unschooler would be to create a lot of opportunities for exploring
> from algebra. People either know how to solve problems and apply
> that knowledge to algebra or don't see a connection between the
> formalized math and any real life situations.
this. it's not that i want my kids to have to sit in a classroom and study algebra in a
vacuum, it's that i think it's a valuable tool to present and demonstrate, and the
abstractions should not be rejected as "schoolish". i guess i think that if a kid wants to
build a slingshot, or a tree house, or likes to watch "mythbusters", that part of the
discussion and part of what the parent would bring to the project would be the math
underlying it. not to press it on the kid, but if i'm helping someone build a slingshot, i
might find it interesting myself to see how heavy of a weight it can lift, or how far it could
conceivably throw something and how i could make it throw farther (Etc).
and something that's always driven me *nuts* about mythbusters is that, while i love many
of hte experiments they do, it sometimes frustrates me that they do all the experiments
and never discuss the math/physics/whatever underlying some of the myths that they're
trying to bust. and so sometimes their experiments work and they either bust or don't
bust the myth, which is fine, and satisfying as a "proof by example" or "disproof by
counterexample" or whatever, but sometimes they neither prove nor disprove with their
experiments and are left basically saying "we dunno"---those situations especially just
BEG for math. they had one on mirrors where they were trying to reflect hte light of the
sun onto a specific point to make a fire. that just BEGGED to me for a physics book and
some formulas---they could've figured out just how many mirrors etc and whether it
would've been physically possible, and THEN tried to build it to demonstrate...
anyways, i think there are so many ways to make math a part of life. and not in a forcing
or "you should learn this" way, just in a providing-paths-for-exploring-your-child's-
interest way, just as we help our kids with anything (including reading). it seems like
there's a little "equation phobia" here (am i misreading?) where it's almost as though since
equations and abstractions are taught in school folks don't believe they should be part of
life or discussed at all. seems to me like they're as much a part of life as letters and books.
not something to be forced, but not something to be avoided either.
> >(a real life exampleyeah, well obviously that would be my goal in enabling my kids to understand math; to live
> > from recently: if my fabric is 4.9 meters long and is likely to
> shrink to 4.7m after washing,
> > and i want to cut it, prewashing, into a piece that, post-washing,
> will end up 3.2m, where
> > do i cut?)
>
> Perfect! I worked in fabric stores for years, talked to lots and
> lots of customers and co-workers with high-school algebra who never
> once realized that was an algebra problem. Most people learn that
> sort of thing either by trial and error or asking the lady who is
> cutting the fabric "how much will it shrink?"
it & help with it as it's relevant to our lives, just like with reading or walking or anything
else, and hopefully it will be connected to and relevant to their lives.
> From an unschooling perspective, its more important to ask yourselfokay, so i've gotten wrapped up in my comparison of formalized math to reading. what if
> what will happen if your kids *don't* either understand or choose to
> use formalized mathematical notations as a means of problem solving.
> Do you push them to do it bc you believe its "good for them"? Do you
> drop the matter and hope it never comes up? Do you help your kids
> find other, different ways of looking at situations and finding
> solutions?
my kids *don't* choose to learn to read? i don't think that's possible. i feel like if i raise
them in a text-rich environment in which reading is interesting and essential and relevant,
they simply WILL learn to read. i don't see how math is any different except that so many
parents are afraid of it or ignorant about it or do not use it themselves. obviously, those
kids would not be growing up in a math-enriched environment. do y'all think there's
something fundamentally unnatural about math that isn't so of reading, walking, or
talking?
i guess i feel like it's part of my job as a parent to create a math-enriched environment,
just as it is my job to create a text-enriched environment, with magazines and papers and
mail and books and notes and etc, and just as it is my job to create an environment
enriched with movement, with swings and slides and climbing structures and bikes and
etc. it's part of creating a healthy place in which a complete person can develop, and
trusting them to develop fully. and yes, i'd say being able to formulate and solve basic
algebra problems is part of developing fully. i dunno that i could argue the same about
calculus, though dh thinks he could. ;)
thanks for providing food for thought!
elly
Sylvia Toyama
and i had very good reason to believe it would shrink to a particular size. i am glad to have the ability to decide to calculate this or not rather than "having to" wash first, IYKWIM.
elly
*****
I have the ability -- I could do the math my way, and on paper just to keep track of the smaller numbers, but I doubt it would look like any algebra formula anyone ever wrote. The two years I spent in high school algebra was the most frustrating experience of my entire life. Really. The teachers insisted on *showing work* so they could know you understood the formula being taught. No matter how I tried, those formulas made NO sense to me. I could figure out the answer in my head -- and get it right -- but not using their formulas. The just did not make sense to me. My solution -- at my Mom's suggestion, since she had the same difference with math learning -- was to do the work my way, get the right answer, then plug my numbers into the required formula. Math homework took twice as long as it should, and I NEVER learned the formula being taught. Sure, I got a B in Algebra both years and got my credit, but it scared me away from math for many years.
Since then, I've discovered that -- had anyone bothered to ask since no one really expected me to excel at math -- that I like have some degree of discalculia. While I was in high school, tho the answer was math for dumb girls and jocks. <g> The actually made us waste a three- week block on something they called FOIL factoring. I suspect it was a special form of math designed to keep the non-math students busy, because it took me no time at all to find a much faster method for solving those problems -- again leaving me to do the math twice.
I'm sorry to have to say it, but no one can convince me that math -- as it's taught in high school -- is a useful endeavor at all.
Sylvia
---------------------------------
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[Non-text portions of this message have been removed]
elly
*****
I have the ability -- I could do the math my way, and on paper just to keep track of the smaller numbers, but I doubt it would look like any algebra formula anyone ever wrote. The two years I spent in high school algebra was the most frustrating experience of my entire life. Really. The teachers insisted on *showing work* so they could know you understood the formula being taught. No matter how I tried, those formulas made NO sense to me. I could figure out the answer in my head -- and get it right -- but not using their formulas. The just did not make sense to me. My solution -- at my Mom's suggestion, since she had the same difference with math learning -- was to do the work my way, get the right answer, then plug my numbers into the required formula. Math homework took twice as long as it should, and I NEVER learned the formula being taught. Sure, I got a B in Algebra both years and got my credit, but it scared me away from math for many years.
Since then, I've discovered that -- had anyone bothered to ask since no one really expected me to excel at math -- that I like have some degree of discalculia. While I was in high school, tho the answer was math for dumb girls and jocks. <g> The actually made us waste a three- week block on something they called FOIL factoring. I suspect it was a special form of math designed to keep the non-math students busy, because it took me no time at all to find a much faster method for solving those problems -- again leaving me to do the math twice.
I'm sorry to have to say it, but no one can convince me that math -- as it's taught in high school -- is a useful endeavor at all.
Sylvia
---------------------------------
Looking for a deal? Find great prices on flights and hotels with Yahoo! FareChase.
[Non-text portions of this message have been removed]
Sylvia Toyama
My son is finding math VERY useful -- he wants to be a programmer -preferably game programner. He is loving the calculus he is taking this year, and knows that it, along with the physics he has had (andprobably will have in the future at college) will help him with his
goals.
****
And for him, the math will be a very useful thing to know. Not for everyone, tho - some of us need only as much math as it takes to balance the checkbook and prepare our taxes.
*****
Word problems try to be real-life sort of applications, which is why they are so important.
*****
Then why don't they make them real-life? Who gives a fig when Train A will pass Train B on the track between St. Louis and San Francisco?
Here's a math problem any 16yo can solve -- you have $30 in your pocket for your date tonight. The movie costs $8.75 each, popcorn is 4.50 and cokes 2.75 each. It's going to be 20 miles roundtrip to your date's house and the movie and your gas tank is on empty. Gas costs $2.75 a gallon, and you get 25 miles to the gallon. Can you afford movie for two, 2 sodas, shared popcorn and to put enough gas in your car to get back home tonight?
That's when math will get the support of most high school students.
Sylvia
---------------------------------
Boardwalk for $500? In 2007? Ha!
Play Monopoly Here and Now (it's updated for today's economy) at Yahoo! Games.
[Non-text portions of this message have been removed]
goals.
****
And for him, the math will be a very useful thing to know. Not for everyone, tho - some of us need only as much math as it takes to balance the checkbook and prepare our taxes.
*****
Word problems try to be real-life sort of applications, which is why they are so important.
*****
Then why don't they make them real-life? Who gives a fig when Train A will pass Train B on the track between St. Louis and San Francisco?
Here's a math problem any 16yo can solve -- you have $30 in your pocket for your date tonight. The movie costs $8.75 each, popcorn is 4.50 and cokes 2.75 each. It's going to be 20 miles roundtrip to your date's house and the movie and your gas tank is on empty. Gas costs $2.75 a gallon, and you get 25 miles to the gallon. Can you afford movie for two, 2 sodas, shared popcorn and to put enough gas in your car to get back home tonight?
That's when math will get the support of most high school students.
Sylvia
---------------------------------
Boardwalk for $500? In 2007? Ha!
Play Monopoly Here and Now (it's updated for today's economy) at Yahoo! Games.
[Non-text portions of this message have been removed]
Sylvia Toyama
and something that's always driven me *nuts* about mythbusters is that, while i love many
of hte experiments they do, it sometimes frustrates me that they do all the experiments
and never discuss the math/physics/ whatever underlying some of the myths that they're
trying to bust. and so sometimes their experiments work and they either bust or don't
bust the myth, which is fine, and satisfying as a "proof by example" or "disproof by
counterexample" or whatever, but sometimes they neither prove nor disprove with their
experiments and are left basically saying "we dunno"---those situations especially just
BEG for math. they had one on mirrors where they were trying to reflect hte light of the
sun onto a specific point to make a fire. that just BEGGED to me for a physics book and
some formulas---they could've figured out just how many mirrors etc and whether it
would've been physically possible, and THEN tried to build it to demonstrate. ..
*****
Honestly, if they digressed into a physics book, we'd stop watching. I don't care about all the details of every experiment, but many of them have prompted us to explore the science or math behind them. As you said, if a child is watching mythbusters and they want to explore further that's an opportunity for adult and parent to do so -- along the way they'll find a physics book if they need one.
I realize part of what bothers me about this topic is the assumption that math is somehow more important than other topics, for example history (I'm a big history buff and find it very relevant to life in this world). Sadly, history as it's taught in public schools is nothing more than propaganda, and it's taught in such a boring fashion that most people don't care about history by the time they hit college, when the real education on history is available to them.
Sylvia
---------------------------------
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[Non-text portions of this message have been removed]
of hte experiments they do, it sometimes frustrates me that they do all the experiments
and never discuss the math/physics/ whatever underlying some of the myths that they're
trying to bust. and so sometimes their experiments work and they either bust or don't
bust the myth, which is fine, and satisfying as a "proof by example" or "disproof by
counterexample" or whatever, but sometimes they neither prove nor disprove with their
experiments and are left basically saying "we dunno"---those situations especially just
BEG for math. they had one on mirrors where they were trying to reflect hte light of the
sun onto a specific point to make a fire. that just BEGGED to me for a physics book and
some formulas---they could've figured out just how many mirrors etc and whether it
would've been physically possible, and THEN tried to build it to demonstrate. ..
*****
Honestly, if they digressed into a physics book, we'd stop watching. I don't care about all the details of every experiment, but many of them have prompted us to explore the science or math behind them. As you said, if a child is watching mythbusters and they want to explore further that's an opportunity for adult and parent to do so -- along the way they'll find a physics book if they need one.
I realize part of what bothers me about this topic is the assumption that math is somehow more important than other topics, for example history (I'm a big history buff and find it very relevant to life in this world). Sadly, history as it's taught in public schools is nothing more than propaganda, and it's taught in such a boring fashion that most people don't care about history by the time they hit college, when the real education on history is available to them.
Sylvia
---------------------------------
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[Non-text portions of this message have been removed]
Joyce Fetteroll
On Oct 1, 2007, at 12:06 PM, Elly wrote:
But not everyone does. Just as not everyone enjoys a Jackson Pollock
painting.
I have noticed an interesting phenomenon. I went through school
sucking up the algebra process. I enjoyed identifying the type of
problem and finding the type of solution that went with it. It was
like puzzles to me.
But I didn't truly understand the underlying concepts of what the
formulas represented.
Over the years, though, I've come to understand what lays beneath the
math, how the numbers relate to one another. I *conceptually*
understand what's going on even though I've forgotten most of the
formulas. I can *conceptually* figure out the area of a right
triangle in a number of ways because I understand how all the pieces
relate to each other.
My husband teaches college math. He's become an expert at applying
formulas to problems.
Recently, as just one example, he was stuck on an algebra problem and
asked me to help him see where he was stuck. He wanted to hand me the
formula but I didn't want that. I want to see how the parts all
worked together.
I remember what it was and it's a good one for illustration.
There are two inspectors working independently. A part passes
inspection only if both inspectors pass it. If inspector A passes 80%
and inspector B passes 60%, and the percentage of parts that both
pass is 40%, how many parts are passed by only one inspector?
There is a formula to calculate that.
But the formula doesn't help you understand the underlying
relationships. It's a short cut so you don't have to write out all
the possibilities. I simplified the problem to 5 parts being
inspected, drew a chart of possibilities and came up with not only
the answer but the formula. I could see the underlying way things
were working and I could see how the formula represented that.
But my husband was stuck because he's so used to plugging numbers
into a formula (and enjoys that part of math.) He doesn't need to
understand what the formula represents. He just knows this problem
uses this formula because that's how math is taught in school. (He's
a smart guy and *could* figure it out and understood what I showed
him. The point is that for school math he doesn't need to understand.
He just needs to know how to recognize which problem gets which
formula.)
He's an adjunct professor, by the way, not someone with a degree in
math. His love of teaching math comes from a love of school math. I
loved school math too. I got As in it but it's only after being away
from it that I can see the underlying flaws in how it's taught. It
doesn't teach what they hope it teaches.
And *that's* where the argument lies. What people here are trying to
point out is that unschooling is about understanding the underlying
relationships: intuitively seeing how one thing relates to another.
That's what carpenters do. That's what the ladies buying fabric do.
There may be a formula that will give them an answer, but it's just a
*representation* of what's going on underneath. What people are
trying to point out is that once someone has the underlying
understanding, seeing and understanding the representation (formula)
is not that hard.
No one. NO ONE, is saying avoid formulas just because that's what
they do in school. What people are saying is until you can see how
important an underlying understanding of what the formulas represent
is, you're not going to be able to see what math really is. Until you
can forget that huge reliance that schools have on formulas, you
won't understand what their purpose really is. It took me *years* of
letting go of formulas, *years* of seeing real understand of number
relationships being applied without formulas to appreciate formulas
and what their purpose is.
*conceptual* (feel it in the bones) understanding what the formulas
are trying to represent.
Schools hope that the conceptual understanding will come from the
formulas. Mainly because they can't teach -- and more importantly
can't test for -- conceptual understanding.
Mostly it doesn't work. A few people who would have understood anyway
do get it. Lots of people come out with lots of nifty formulas to
solve book problems. (Lots of people come out hating it.) I had
nifty formulas after 4 years of engineering. What I experienced in
real life were messy problems that didn't look like book problems! To
solve the problems required an underlying understanding of what was
going on. I didn't really have that. Once someone set the problem up
I could do it, but setting it up is the real work and setting it up
requires understanding what's really going on beneath the formula and
numbers. A computer can solve it!
Someone in college said that boys got physics (mechanics really)
because they had spent the previous 17 years throwing, catching and
*being* the ball. Their bodies understood the principles and all they
needed was to see how the formula related to what they already
understood. The girls needed to try to understand the underlying
principles through the formula. It didn't work nearly as well for the
girls as the boys!
(Yes, that's a bit sexist but it was 30 years ago ;-) Though I do
think it still tends to fall along testosterone lines: boys are more
likely (though not exclusively!) to be asking "Let's see what happens
when I punch this really hard." ;-)
Joyce
[Non-text portions of this message have been removed]
> ok, maybe i'm the only nerd who feels this way, but there IS aAs a math head I do enjoy a good formula.
> value to formalizing the
> math
But not everyone does. Just as not everyone enjoys a Jackson Pollock
painting.
I have noticed an interesting phenomenon. I went through school
sucking up the algebra process. I enjoyed identifying the type of
problem and finding the type of solution that went with it. It was
like puzzles to me.
But I didn't truly understand the underlying concepts of what the
formulas represented.
Over the years, though, I've come to understand what lays beneath the
math, how the numbers relate to one another. I *conceptually*
understand what's going on even though I've forgotten most of the
formulas. I can *conceptually* figure out the area of a right
triangle in a number of ways because I understand how all the pieces
relate to each other.
My husband teaches college math. He's become an expert at applying
formulas to problems.
Recently, as just one example, he was stuck on an algebra problem and
asked me to help him see where he was stuck. He wanted to hand me the
formula but I didn't want that. I want to see how the parts all
worked together.
I remember what it was and it's a good one for illustration.
There are two inspectors working independently. A part passes
inspection only if both inspectors pass it. If inspector A passes 80%
and inspector B passes 60%, and the percentage of parts that both
pass is 40%, how many parts are passed by only one inspector?
There is a formula to calculate that.
But the formula doesn't help you understand the underlying
relationships. It's a short cut so you don't have to write out all
the possibilities. I simplified the problem to 5 parts being
inspected, drew a chart of possibilities and came up with not only
the answer but the formula. I could see the underlying way things
were working and I could see how the formula represented that.
But my husband was stuck because he's so used to plugging numbers
into a formula (and enjoys that part of math.) He doesn't need to
understand what the formula represents. He just knows this problem
uses this formula because that's how math is taught in school. (He's
a smart guy and *could* figure it out and understood what I showed
him. The point is that for school math he doesn't need to understand.
He just needs to know how to recognize which problem gets which
formula.)
He's an adjunct professor, by the way, not someone with a degree in
math. His love of teaching math comes from a love of school math. I
loved school math too. I got As in it but it's only after being away
from it that I can see the underlying flaws in how it's taught. It
doesn't teach what they hope it teaches.
And *that's* where the argument lies. What people here are trying to
point out is that unschooling is about understanding the underlying
relationships: intuitively seeing how one thing relates to another.
That's what carpenters do. That's what the ladies buying fabric do.
There may be a formula that will give them an answer, but it's just a
*representation* of what's going on underneath. What people are
trying to point out is that once someone has the underlying
understanding, seeing and understanding the representation (formula)
is not that hard.
No one. NO ONE, is saying avoid formulas just because that's what
they do in school. What people are saying is until you can see how
important an underlying understanding of what the formulas represent
is, you're not going to be able to see what math really is. Until you
can forget that huge reliance that schools have on formulas, you
won't understand what their purpose really is. It took me *years* of
letting go of formulas, *years* of seeing real understand of number
relationships being applied without formulas to appreciate formulas
and what their purpose is.
> driving a car is NOT the same as knowing algebra.No it isn't, but experiencing real life is how people build up a
>
*conceptual* (feel it in the bones) understanding what the formulas
are trying to represent.
Schools hope that the conceptual understanding will come from the
formulas. Mainly because they can't teach -- and more importantly
can't test for -- conceptual understanding.
Mostly it doesn't work. A few people who would have understood anyway
do get it. Lots of people come out with lots of nifty formulas to
solve book problems. (Lots of people come out hating it.) I had
nifty formulas after 4 years of engineering. What I experienced in
real life were messy problems that didn't look like book problems! To
solve the problems required an underlying understanding of what was
going on. I didn't really have that. Once someone set the problem up
I could do it, but setting it up is the real work and setting it up
requires understanding what's really going on beneath the formula and
numbers. A computer can solve it!
Someone in college said that boys got physics (mechanics really)
because they had spent the previous 17 years throwing, catching and
*being* the ball. Their bodies understood the principles and all they
needed was to see how the formula related to what they already
understood. The girls needed to try to understand the underlying
principles through the formula. It didn't work nearly as well for the
girls as the boys!
(Yes, that's a bit sexist but it was 30 years ago ;-) Though I do
think it still tends to fall along testosterone lines: boys are more
likely (though not exclusively!) to be asking "Let's see what happens
when I punch this really hard." ;-)
Joyce
[Non-text portions of this message have been removed]
Meredith
--- In [email protected], "Elly" <ellyzoe@...> wrote:
is ulitmately going to look different for kids who get to unschool
from a young age vs kids who leave school after a few years. Its
also going to be different with a kid who is pretty logically
inclined vs one who isn't. On top of that, unschooling math is going
to look different in families where the parents have some math
anxiety. Those are the reasons why I'm doing the whole "you don't
need numbers and equations to learn math" thing.
In my own family I'm saying a lot of "you don't need formalized math
to figure things out" to my stepson, who is pretty scarred by his
school experience *and* not terribly logical by nature - but is
getting interested in woodworking. But otoh, my 6yo dd and I spent
the afternoon playing with the properties of circles in some pretty
formal ways, yesterday, and had a blast - but then she's always been
unschooled and has a very logical approach to problem solving.
is still there, even if mom doesn't see it. Its *not* like learning
to read - its not really necessary to provide a "math rich
environment" for people to learn about math. In order to remove the
math from daily life you'd have to shut someone in a sensory
deprivation tank. Eating and drinking involve mathematical concepts.
Preparing food requires using them. Playing with any toy at all
involves mathematical concepts. Sharing toys with siblings or
friends requires using those concepts. Looking at a car involves
mathematical concepts - and driving one involves using them.
So its not that anyone needs to create a "math rich environment" -
its impossible to have an environment that lacks math. Formalized
math is something else again. Its lovely - but its not something
most people use. If anything, many people learn to actively avoid
anything that looks like formal math in the same way that many
others learn to avoid organized sports (and for the same reasons).
Its possible to go one's whole life without playing American
football, and its equally possible to go without learning a single
theorem.
normal life, but its not necessary in the same way learning to play
baseball isn't necessary. Some kids will find it fun, others
baffling - or utterly dull. Yes, the opportunity *should* be
available, but parents without a lot of math skills need to know
that they don't have to talk about numbers and proofs and equations
for their kids to learn about math *and* parents with kids who
aren't very logical, or who have had an ugly time in school need to
know that their kids really will learn "enough" about math to do
what the want to do in their lives *without* the formal stuff.
I'm not trying to discourage Anyone from sharing their love of
formalized math with their kids! Good grief, that would be like
saying "read to your kids but avoid mentioning sonnets" or "play
with your kids, but don't say anything about soccer". That's not
what I'm trying to say at all.
---Meredith (Mo 6, Ray 14)
>> there's a little "equation phobia" here (am i misreading?) whereit's almost as though since
> equations and abstractions are taught in school folks don'tbelieve they should be part of
> life or discussed at all. seems to me like they're as much a partof life as letters and books.
> not something to be forced, but not something to be avoided either.Well, there are a few different issues intertwined. Unschooling math
is ulitmately going to look different for kids who get to unschool
from a young age vs kids who leave school after a few years. Its
also going to be different with a kid who is pretty logically
inclined vs one who isn't. On top of that, unschooling math is going
to look different in families where the parents have some math
anxiety. Those are the reasons why I'm doing the whole "you don't
need numbers and equations to learn math" thing.
In my own family I'm saying a lot of "you don't need formalized math
to figure things out" to my stepson, who is pretty scarred by his
school experience *and* not terribly logical by nature - but is
getting interested in woodworking. But otoh, my 6yo dd and I spent
the afternoon playing with the properties of circles in some pretty
formal ways, yesterday, and had a blast - but then she's always been
unschooled and has a very logical approach to problem solving.
> okay, so i've gotten wrapped up in my comparison of formalizedmath to reading. what if
> my kids *don't* choose to learn to read? i don't think that'spossible. i feel like if i raise
> them in a text-rich environment in which reading is interestingand essential and relevant,
> they simply WILL learn to read. i don't see how math is anydifferent except that so many
> parents are afraid of it or ignorant about it or do not use itthemselves. obviously, those
> kids would not be growing up in a math-enriched environment.This is the sort of mis-understanding I want to address - the Math
is still there, even if mom doesn't see it. Its *not* like learning
to read - its not really necessary to provide a "math rich
environment" for people to learn about math. In order to remove the
math from daily life you'd have to shut someone in a sensory
deprivation tank. Eating and drinking involve mathematical concepts.
Preparing food requires using them. Playing with any toy at all
involves mathematical concepts. Sharing toys with siblings or
friends requires using those concepts. Looking at a car involves
mathematical concepts - and driving one involves using them.
So its not that anyone needs to create a "math rich environment" -
its impossible to have an environment that lacks math. Formalized
math is something else again. Its lovely - but its not something
most people use. If anything, many people learn to actively avoid
anything that looks like formal math in the same way that many
others learn to avoid organized sports (and for the same reasons).
Its possible to go one's whole life without playing American
football, and its equally possible to go without learning a single
theorem.
> anyways, i think there are so many ways to make math a part oflife. and not in a forcing
> or "you should learn this" way, just in a providing-paths-for-exploring-your-child's-
> interest wayIts totally possible to make formalized math a familiar part of
normal life, but its not necessary in the same way learning to play
baseball isn't necessary. Some kids will find it fun, others
baffling - or utterly dull. Yes, the opportunity *should* be
available, but parents without a lot of math skills need to know
that they don't have to talk about numbers and proofs and equations
for their kids to learn about math *and* parents with kids who
aren't very logical, or who have had an ugly time in school need to
know that their kids really will learn "enough" about math to do
what the want to do in their lives *without* the formal stuff.
I'm not trying to discourage Anyone from sharing their love of
formalized math with their kids! Good grief, that would be like
saying "read to your kids but avoid mentioning sonnets" or "play
with your kids, but don't say anything about soccer". That's not
what I'm trying to say at all.
---Meredith (Mo 6, Ray 14)
[email protected]
-----Original Message-----
From: trektheory <trektheory@...>
No, you aren't the only one. The point I had been trying to make
earlier (and failed, I think - and I dropped it there) was that when
you make those judgements while driving, you are NOT doing an
equation. I defy anyone judging when to apply the brakes to tell me
what variable they were solving for, what the distance between their
car and the one in front was, etc. Real world estimating, sure, but
not equation solving.
-=-=-=
But understanding that variables are at work in that example can evolve
into an equation that would make sense if you were to want to give
values to the variables.
Algebra made sense to me when I was riding race horses. I was learning
how to handicap a race. Algebra seemed worthless during high school but
was crystal clear in racing! <g>
~Kelly
Kelly Lovejoy
Conference Coordinator
Live and Learn Unschooling Conference
http://www.LiveandLearnConference.org
________________________________________________________________________
Email and AIM finally together. You've gotta check out free AOL Mail! -
http://mail.aol.com
From: trektheory <trektheory@...>
No, you aren't the only one. The point I had been trying to make
earlier (and failed, I think - and I dropped it there) was that when
you make those judgements while driving, you are NOT doing an
equation. I defy anyone judging when to apply the brakes to tell me
what variable they were solving for, what the distance between their
car and the one in front was, etc. Real world estimating, sure, but
not equation solving.
-=-=-=
But understanding that variables are at work in that example can evolve
into an equation that would make sense if you were to want to give
values to the variables.
Algebra made sense to me when I was riding race horses. I was learning
how to handicap a race. Algebra seemed worthless during high school but
was crystal clear in racing! <g>
~Kelly
Kelly Lovejoy
Conference Coordinator
Live and Learn Unschooling Conference
http://www.LiveandLearnConference.org
________________________________________________________________________
Email and AIM finally together. You've gotta check out free AOL Mail! -
http://mail.aol.com