teaching algebra? real-world math (and an answer for Pam?)
[email protected]
About teaching algebra, we don't.
About kids learning algebra, they do.
<< > I talked
a puzzle he couldn't figure out.
Once we pre-kids we were talking and I said the only math I ever got was the
the word puzzles, and the laid-out sets of numbers seemed nonsense to me. I
could do it and get a good grade, but the teachers couldn't tell me what it
was good for, so I quit taking math partway through tenth grade.
I took one math-for-non-majors course in college, and the book was WORDS!
Sometimes a little chart of picture, but it told math in words, and I
understood that. But I told myself even then that it was just like "math
appreciation," as non-musical folks will take music appreciation and get a
grade basically for knowing a harpsichord from an organ or knowing full
orchestra from chamber music.
By my husband, who was able to tutor all our friend in calculus and t
rigonometry, said the word problems were the only "problems" there! The rest
were solutions without the calculations having been completed. He said doing
an algebra problem that's already laid out for you isn't algebra, it's just
computations.
So when unschooling came into our lives, what I looked for is "what are the
math problems?" And I looked for what algebra looked like in the real world,
and where division and multiplication came to the surface of the real world,
and I've never worried about my kids as they've grown up. Each has come to a
point of asking what the mathematical symbols meant, usually because of a
computer game like Treasure Math Storm or Outnumbered. For algebra,
though, they have concepts learned from allowances (already at a
rate-per-week, so they add consider other factors in addition to the existing
"problem"), working at a store AND (byproduct) from everyone in the family
having had their discount at said store go up from 5% to 30% for Kirby
working there. The boys can figure both of those in their heads.
Card games with strategies for different amounts on different kinds of plays
(Rummy with aces high for 15 or low for 5 pts, Yahtzee, Five Crowns) have
helped me see them use their mathematical knowledge, and they don't need a
pencil and paper, either. Holly is the quickest of any at mental
manipulation of numbers.
My grandfather (same one who taught me 'to carry') used to call it
"ciphering." That refers literally to the marks on the paper--numbers and
symbols representing other concepts. And that's an interesting point here.
In school, math is on paper, because teachers need proof for their bosses,
and for the parents, that children "DID math." They have the children
"cipher." But when asked "What is this good for in the real world?" many
teachers told me "you need good test scores," or "you need to pass this test
so you can take chemistry" or some other TOTALLY school-based answer. They
weren't teaching me math, the greater language of mathematical thinking and t
heory and the joy of dancing patterns in everyday life. They were teaching
me to cipher quickly and obediently, and so I decided math was stupid, and I
shut that door in me and quit "taking math."
Sandra
About kids learning algebra, they do.
<< > I talked
> her into doing it by calling the math "puzzles to solve." >>My husband is an engineer who has never met a math class he couldn't ace, or
a puzzle he couldn't figure out.
Once we pre-kids we were talking and I said the only math I ever got was the
the word puzzles, and the laid-out sets of numbers seemed nonsense to me. I
could do it and get a good grade, but the teachers couldn't tell me what it
was good for, so I quit taking math partway through tenth grade.
I took one math-for-non-majors course in college, and the book was WORDS!
Sometimes a little chart of picture, but it told math in words, and I
understood that. But I told myself even then that it was just like "math
appreciation," as non-musical folks will take music appreciation and get a
grade basically for knowing a harpsichord from an organ or knowing full
orchestra from chamber music.
By my husband, who was able to tutor all our friend in calculus and t
rigonometry, said the word problems were the only "problems" there! The rest
were solutions without the calculations having been completed. He said doing
an algebra problem that's already laid out for you isn't algebra, it's just
computations.
So when unschooling came into our lives, what I looked for is "what are the
math problems?" And I looked for what algebra looked like in the real world,
and where division and multiplication came to the surface of the real world,
and I've never worried about my kids as they've grown up. Each has come to a
point of asking what the mathematical symbols meant, usually because of a
computer game like Treasure Math Storm or Outnumbered. For algebra,
though, they have concepts learned from allowances (already at a
rate-per-week, so they add consider other factors in addition to the existing
"problem"), working at a store AND (byproduct) from everyone in the family
having had their discount at said store go up from 5% to 30% for Kirby
working there. The boys can figure both of those in their heads.
Card games with strategies for different amounts on different kinds of plays
(Rummy with aces high for 15 or low for 5 pts, Yahtzee, Five Crowns) have
helped me see them use their mathematical knowledge, and they don't need a
pencil and paper, either. Holly is the quickest of any at mental
manipulation of numbers.
My grandfather (same one who taught me 'to carry') used to call it
"ciphering." That refers literally to the marks on the paper--numbers and
symbols representing other concepts. And that's an interesting point here.
In school, math is on paper, because teachers need proof for their bosses,
and for the parents, that children "DID math." They have the children
"cipher." But when asked "What is this good for in the real world?" many
teachers told me "you need good test scores," or "you need to pass this test
so you can take chemistry" or some other TOTALLY school-based answer. They
weren't teaching me math, the greater language of mathematical thinking and t
heory and the joy of dancing patterns in everyday life. They were teaching
me to cipher quickly and obediently, and so I decided math was stupid, and I
shut that door in me and quit "taking math."
Sandra
brr_imcold
<They
weren't teaching me math, the greater language of mathematical
thinking and t
heory and the joy of dancing patterns in everyday life. They were
teaching
me to cipher quickly and obediently, and so I decided math was
stupid, and I
shut that door in me and quit "taking math."
Sandra
You could have learned it yourself, *without* a teacher and an agenda
to follow. :(
weren't teaching me math, the greater language of mathematical
thinking and t
heory and the joy of dancing patterns in everyday life. They were
teaching
me to cipher quickly and obediently, and so I decided math was
stupid, and I
shut that door in me and quit "taking math."
Sandra
>How sad! I wish somebody would have handed you a Harold Jacobs book!
You could have learned it yourself, *without* a teacher and an agenda
to follow. :(
Valerie Cifuentes
Thanks for your insights. I think I understand what you are saying.
The thing I think I see too is that you knew "rate per week" because
your husband is very "math minded" and you have had some exposure.
Sounds to me like he has a very special "gift" in that area and he's
passed it on to your daughter! LOL
Good for them! :O)
I personally struggled in math as a student. Not because of the lack of
understanding the purpose, I was the type that figured, well, If they
are teaching it to me then most likely there IS a purpose for it in the
future I just haven't come across it and when I do, I'll be ready. I
guess I was easy to get a long with! LOL!
I am more "literal" than "mathematical," I can learn math, but it must
be 3D for me. I also had to learn it in a non-threatening environment,
like Math Lab at the college. I had a great tutor, he looked funny too
with dyed orange hair sticking up fuzzy all over his head! Immediately,
broke the ice!
Anyway, what's the difference with playing with cards and playing with a
pencil and paper?
My daughter likes the dry erase board. He do the "smartest kid in the
class." She made it up.
She made a medallion that she would push toward me if I worked a formula
faster than her. She LOVES that.
She is quite fast too! This isn't BIG math, just pre-algebra type stuff.
But it's her game, she made it up, so we do it. :O)
But when we go to Wal-Mart and there is a charge for tax, she understand
the percentage rate, or the surcharge at the commissary and the
different rates for food verses non consumables. But she knows it
because we took the time to investigate it. She can now move on to
something else.
You or your husband must have invited their attention to the "rate per
week" idea. How many times do we spend or day inviting our children to
moral issues? hygiene issues? social issues and news? Maybe we tug their
hearts with "animal rights" and "don't be a litterbug." Most children
tend to throw trash down on the ground. Not because they intend to harm
the earth at all, but because they had not yet been enlightened to the
idea that collectively, throwing down trash is detrimental to the
environment and on goes the teaching to them. We teach them to be
careful when handling the birdie because the bones are so soft and
delicate. My children didn't automatically understand that birdie bones
where so much more fragile than their doggie's.
But I enlightened them to it, I personally told them and went so far as
to discuss other bones with them too, using a Gray's Anatomy book! :O)
My hubby is a Corpsman, we have tons of those things laying around.
What I'm saying in short is that whether we use a pencil and paper or a
game or a video or a book or a natural event, I dont think that it
always matters. We use common sense right? To decide what the best way
to teach math would be. They are acceptable ideas even the pencil and
paper. It too can be acceptable.
I think that making up games or playing games is wonderful. But I also
think that using a pencil and paper or markers and dry erase is equally
wonderful. I think that there are others here that might agree?
Thanks for letting me share and helping me think through. I didn't
proofread this~ Hubby is getting on now!
*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~
.· ´¨¨)) -:¦:-
¸.·´ .·´¨¨))
((¸¸.·´ .·´ -:¦:-Valerie Cifuentes
-:¦:- ((¸¸.·´*
I CAN NO LONGER ACCEPT FORWARDS, CHAIN LETTERS AND PETITIONS. THEY ARE
FILLING UP MY BOX AND TAKING UP MY TIME. THANK YOU FOR UNDERSTANDING!
http://nolen.home.texas.net/valerie/Cifuentes.html
I'm A Navy Brat & Wife of HM2 Cifuentes; Active Duty Navy, & Mother of
Three Young Navy Brats!
*~*PLEASE HAVE PATIENCE AS I CHECK EMAIL ONCE IN THE MORNING & EVENING
AFTER 3:00PM AND NOT ON SUNDAY (THE LORD'S DAY.)*~*
-----Original Message-----
From: SandraDodd@... [mailto:SandraDodd@...]
Sent: Wednesday, April 24, 2002 11:27 AM
To: [email protected]
Subject: [Unschooling-dotcom] teaching algebra? real-world math (and an
answer for Pam?)
About teaching algebra, we don't.
About kids learning algebra, they do.
<< > I talked
ace, or
a puzzle he couldn't figure out.
Once we pre-kids we were talking and I said the only math I ever got was
the
the word puzzles, and the laid-out sets of numbers seemed nonsense to
me. I
could do it and get a good grade, but the teachers couldn't tell me what
it
was good for, so I quit taking math partway through tenth grade.
I took one math-for-non-majors course in college, and the book was
WORDS!
Sometimes a little chart of picture, but it told math in words, and I
understood that. But I told myself even then that it was just like
"math
appreciation," as non-musical folks will take music appreciation and get
a
grade basically for knowing a harpsichord from an organ or knowing full
orchestra from chamber music.
By my husband, who was able to tutor all our friend in calculus and t
rigonometry, said the word problems were the only "problems" there! The
rest
were solutions without the calculations having been completed. He said
doing
an algebra problem that's already laid out for you isn't algebra, it's
just
computations.
So when unschooling came into our lives, what I looked for is "what are
the
math problems?" And I looked for what algebra looked like in the real
world,
and where division and multiplication came to the surface of the real
world,
and I've never worried about my kids as they've grown up. Each has come
to a
point of asking what the mathematical symbols meant, usually because of
a
computer game like Treasure Math Storm or Outnumbered. For algebra,
though, they have concepts learned from allowances (already at a
rate-per-week, so they add consider other factors in addition to the
existing
"problem"), working at a store AND (byproduct) from everyone in the
family
having had their discount at said store go up from 5% to 30% for Kirby
working there. The boys can figure both of those in their heads.
Card games with strategies for different amounts on different kinds of
plays
(Rummy with aces high for 15 or low for 5 pts, Yahtzee, Five Crowns)
have
helped me see them use their mathematical knowledge, and they don't need
a
pencil and paper, either. Holly is the quickest of any at mental
manipulation of numbers.
My grandfather (same one who taught me 'to carry') used to call it
"ciphering." That refers literally to the marks on the paper--numbers
and
symbols representing other concepts. And that's an interesting point
here.
In school, math is on paper, because teachers need proof for their
bosses,
and for the parents, that children "DID math." They have the children
"cipher." But when asked "What is this good for in the real world?"
many
teachers told me "you need good test scores," or "you need to pass this
test
so you can take chemistry" or some other TOTALLY school-based answer.
They
weren't teaching me math, the greater language of mathematical thinking
and t
heory and the joy of dancing patterns in everyday life. They were
teaching
me to cipher quickly and obediently, and so I decided math was stupid,
and I
shut that door in me and quit "taking math."
Sandra
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[Non-text portions of this message have been removed]
The thing I think I see too is that you knew "rate per week" because
your husband is very "math minded" and you have had some exposure.
Sounds to me like he has a very special "gift" in that area and he's
passed it on to your daughter! LOL
Good for them! :O)
I personally struggled in math as a student. Not because of the lack of
understanding the purpose, I was the type that figured, well, If they
are teaching it to me then most likely there IS a purpose for it in the
future I just haven't come across it and when I do, I'll be ready. I
guess I was easy to get a long with! LOL!
I am more "literal" than "mathematical," I can learn math, but it must
be 3D for me. I also had to learn it in a non-threatening environment,
like Math Lab at the college. I had a great tutor, he looked funny too
with dyed orange hair sticking up fuzzy all over his head! Immediately,
broke the ice!
Anyway, what's the difference with playing with cards and playing with a
pencil and paper?
My daughter likes the dry erase board. He do the "smartest kid in the
class." She made it up.
She made a medallion that she would push toward me if I worked a formula
faster than her. She LOVES that.
She is quite fast too! This isn't BIG math, just pre-algebra type stuff.
But it's her game, she made it up, so we do it. :O)
But when we go to Wal-Mart and there is a charge for tax, she understand
the percentage rate, or the surcharge at the commissary and the
different rates for food verses non consumables. But she knows it
because we took the time to investigate it. She can now move on to
something else.
You or your husband must have invited their attention to the "rate per
week" idea. How many times do we spend or day inviting our children to
moral issues? hygiene issues? social issues and news? Maybe we tug their
hearts with "animal rights" and "don't be a litterbug." Most children
tend to throw trash down on the ground. Not because they intend to harm
the earth at all, but because they had not yet been enlightened to the
idea that collectively, throwing down trash is detrimental to the
environment and on goes the teaching to them. We teach them to be
careful when handling the birdie because the bones are so soft and
delicate. My children didn't automatically understand that birdie bones
where so much more fragile than their doggie's.
But I enlightened them to it, I personally told them and went so far as
to discuss other bones with them too, using a Gray's Anatomy book! :O)
My hubby is a Corpsman, we have tons of those things laying around.
What I'm saying in short is that whether we use a pencil and paper or a
game or a video or a book or a natural event, I dont think that it
always matters. We use common sense right? To decide what the best way
to teach math would be. They are acceptable ideas even the pencil and
paper. It too can be acceptable.
I think that making up games or playing games is wonderful. But I also
think that using a pencil and paper or markers and dry erase is equally
wonderful. I think that there are others here that might agree?
Thanks for letting me share and helping me think through. I didn't
proofread this~ Hubby is getting on now!
*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~
.· ´¨¨)) -:¦:-
¸.·´ .·´¨¨))
((¸¸.·´ .·´ -:¦:-Valerie Cifuentes
-:¦:- ((¸¸.·´*
I CAN NO LONGER ACCEPT FORWARDS, CHAIN LETTERS AND PETITIONS. THEY ARE
FILLING UP MY BOX AND TAKING UP MY TIME. THANK YOU FOR UNDERSTANDING!
http://nolen.home.texas.net/valerie/Cifuentes.html
I'm A Navy Brat & Wife of HM2 Cifuentes; Active Duty Navy, & Mother of
Three Young Navy Brats!
*~*PLEASE HAVE PATIENCE AS I CHECK EMAIL ONCE IN THE MORNING & EVENING
AFTER 3:00PM AND NOT ON SUNDAY (THE LORD'S DAY.)*~*
-----Original Message-----
From: SandraDodd@... [mailto:SandraDodd@...]
Sent: Wednesday, April 24, 2002 11:27 AM
To: [email protected]
Subject: [Unschooling-dotcom] teaching algebra? real-world math (and an
answer for Pam?)
About teaching algebra, we don't.
About kids learning algebra, they do.
<< > I talked
> her into doing it by calling the math "puzzles to solve." >>My husband is an engineer who has never met a math class he couldn't
ace, or
a puzzle he couldn't figure out.
Once we pre-kids we were talking and I said the only math I ever got was
the
the word puzzles, and the laid-out sets of numbers seemed nonsense to
me. I
could do it and get a good grade, but the teachers couldn't tell me what
it
was good for, so I quit taking math partway through tenth grade.
I took one math-for-non-majors course in college, and the book was
WORDS!
Sometimes a little chart of picture, but it told math in words, and I
understood that. But I told myself even then that it was just like
"math
appreciation," as non-musical folks will take music appreciation and get
a
grade basically for knowing a harpsichord from an organ or knowing full
orchestra from chamber music.
By my husband, who was able to tutor all our friend in calculus and t
rigonometry, said the word problems were the only "problems" there! The
rest
were solutions without the calculations having been completed. He said
doing
an algebra problem that's already laid out for you isn't algebra, it's
just
computations.
So when unschooling came into our lives, what I looked for is "what are
the
math problems?" And I looked for what algebra looked like in the real
world,
and where division and multiplication came to the surface of the real
world,
and I've never worried about my kids as they've grown up. Each has come
to a
point of asking what the mathematical symbols meant, usually because of
a
computer game like Treasure Math Storm or Outnumbered. For algebra,
though, they have concepts learned from allowances (already at a
rate-per-week, so they add consider other factors in addition to the
existing
"problem"), working at a store AND (byproduct) from everyone in the
family
having had their discount at said store go up from 5% to 30% for Kirby
working there. The boys can figure both of those in their heads.
Card games with strategies for different amounts on different kinds of
plays
(Rummy with aces high for 15 or low for 5 pts, Yahtzee, Five Crowns)
have
helped me see them use their mathematical knowledge, and they don't need
a
pencil and paper, either. Holly is the quickest of any at mental
manipulation of numbers.
My grandfather (same one who taught me 'to carry') used to call it
"ciphering." That refers literally to the marks on the paper--numbers
and
symbols representing other concepts. And that's an interesting point
here.
In school, math is on paper, because teachers need proof for their
bosses,
and for the parents, that children "DID math." They have the children
"cipher." But when asked "What is this good for in the real world?"
many
teachers told me "you need good test scores," or "you need to pass this
test
so you can take chemistry" or some other TOTALLY school-based answer.
They
weren't teaching me math, the greater language of mathematical thinking
and t
heory and the joy of dancing patterns in everyday life. They were
teaching
me to cipher quickly and obediently, and so I decided math was stupid,
and I
shut that door in me and quit "taking math."
Sandra
Yahoo! Groups Sponsor
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[Non-text portions of this message have been removed]
[email protected]
In a message dated 4/24/02 9:59:36 AM, brr_imcold@... writes:
<< How sad! I wish somebody would have handed you a Harold Jacobs book!
You could have learned it yourself, *without* a teacher and an agenda
to follow. :( >>
It's not too late!
I've learned lots since, accidently. And more after I figured out one COULD
learn accidently, when it could be more conscious. And I've learned real
math from interacting with my kids who have learned it without a teacher and
without a book.
If Kirby wants to take SATs or GEDs or something one of these years, we'll
get a preparation book, or go to some websites, and when he sees notations he
doesn't understand, or terminology he doesn't understand, it won't be
learning from scratch, but just a vocabulary moment for him to know what he's
seeing, and what they expect him to do with it.
Sandra
<< How sad! I wish somebody would have handed you a Harold Jacobs book!
You could have learned it yourself, *without* a teacher and an agenda
to follow. :( >>
It's not too late!
I've learned lots since, accidently. And more after I figured out one COULD
learn accidently, when it could be more conscious. And I've learned real
math from interacting with my kids who have learned it without a teacher and
without a book.
If Kirby wants to take SATs or GEDs or something one of these years, we'll
get a preparation book, or go to some websites, and when he sees notations he
doesn't understand, or terminology he doesn't understand, it won't be
learning from scratch, but just a vocabulary moment for him to know what he's
seeing, and what they expect him to do with it.
Sandra
[email protected]
In a message dated 4/24/02 10:52:25 AM, homeschool@... writes:
<< Thanks for your insights. I think I understand what you are saying.
The thing I think I see too is that you knew "rate per week" because
your husband is very "math minded" and you have had some exposure. >>
No.
Don't you have an idea that a paycheck is a certain amount per hour, and so a
40-hour workweek will be a certain amount, but a 50 hour week with overtime
rate will be the base 40xhourly, plus the ten times hourly-and-a-half?
If a child's allowance is $7.50 a week (Holly's is), she gets a good feel for
what four times $7.50 is without knowing ANY terminology. And she knew
what $6.75's "rate of gain" was without knowing the phrase "rate of gain."
<<Anyway, what's the difference with playing with cards and playing with a
pencil and paper?>>
One is playing, and one MIGHT be playing, or might be "doing schoolwork."
<<You or your husband must have invited their attention to the "rate per
week" idea. >>
It's not our idea. I don't use that terminology with the kids--we call it
"allowance," but they have a 75 cents per year of age, per week. So Holly
at 10 gets $7.50. Kirby, at 15, gets $11.25. He knows his hourly wage at
work, too, and about how much they take out of it, so when he turns in his
time sheet, he can estimate what his paycheck will be.
I didn't teach him that. I did help provide him a happy opportunity to
figure it out.
<<How many times do we spend or day inviting our children to
moral issues? hygiene issues? social issues and news?>>
No more than I would with anyone else at the house.
I just asked Holly, "Are you going to need to take a shower before the
rehearsal?"
I honestly don't know when she last took a shower. She said she did want to.
It's more for hair-fixing purposes than anything else. (Come to think of
it, she played in the bathtub a long time yesterday or Monday night... the
Barbies are still in there.)
<<Most children tend to throw trash down on the ground. >>
Not in my experience.
I've honked at school kids and said "Hey, pick that up!" if they were
dropping things.
My kids, since they were little, have helped buss tables in restaurants, and
have helped clean up parks in advance of playgroups. They've never been
around adults who dropped trash, but have been around lots of adults who have
spent time picking up other people's trash. We do a lot of group camping,
and the campgrounds are cleaned up before AND after, by volunteers in the
group (kids and adults, whoever wants to help).
<<What I'm saying in short is that whether we use a pencil and paper or a
game or a video or a book or a natural event, I don’t think that it
always matters. >>
It helps to move away from the school model when people are trying to get the
hang of unschooling.
Sandra
<< Thanks for your insights. I think I understand what you are saying.
The thing I think I see too is that you knew "rate per week" because
your husband is very "math minded" and you have had some exposure. >>
No.
Don't you have an idea that a paycheck is a certain amount per hour, and so a
40-hour workweek will be a certain amount, but a 50 hour week with overtime
rate will be the base 40xhourly, plus the ten times hourly-and-a-half?
If a child's allowance is $7.50 a week (Holly's is), she gets a good feel for
what four times $7.50 is without knowing ANY terminology. And she knew
what $6.75's "rate of gain" was without knowing the phrase "rate of gain."
<<Anyway, what's the difference with playing with cards and playing with a
pencil and paper?>>
One is playing, and one MIGHT be playing, or might be "doing schoolwork."
<<You or your husband must have invited their attention to the "rate per
week" idea. >>
It's not our idea. I don't use that terminology with the kids--we call it
"allowance," but they have a 75 cents per year of age, per week. So Holly
at 10 gets $7.50. Kirby, at 15, gets $11.25. He knows his hourly wage at
work, too, and about how much they take out of it, so when he turns in his
time sheet, he can estimate what his paycheck will be.
I didn't teach him that. I did help provide him a happy opportunity to
figure it out.
<<How many times do we spend or day inviting our children to
moral issues? hygiene issues? social issues and news?>>
No more than I would with anyone else at the house.
I just asked Holly, "Are you going to need to take a shower before the
rehearsal?"
I honestly don't know when she last took a shower. She said she did want to.
It's more for hair-fixing purposes than anything else. (Come to think of
it, she played in the bathtub a long time yesterday or Monday night... the
Barbies are still in there.)
<<Most children tend to throw trash down on the ground. >>
Not in my experience.
I've honked at school kids and said "Hey, pick that up!" if they were
dropping things.
My kids, since they were little, have helped buss tables in restaurants, and
have helped clean up parks in advance of playgroups. They've never been
around adults who dropped trash, but have been around lots of adults who have
spent time picking up other people's trash. We do a lot of group camping,
and the campgrounds are cleaned up before AND after, by volunteers in the
group (kids and adults, whoever wants to help).
<<What I'm saying in short is that whether we use a pencil and paper or a
game or a video or a book or a natural event, I don’t think that it
always matters. >>
It helps to move away from the school model when people are trying to get the
hang of unschooling.
Sandra