math
rick and deborah farrington
lorraine,
i too just got smartie pants and i hate math books. i purchased them.
my son is 15 and was amazed how much math is all around us ans has been
reading the books off and on. my dd is not so interested yet but has
gone back to her old key to.. work booklet on decimalsa few times since
i told them they didnt 'have' to do math anymore. they are slowly coming
around and showing interest. i say give it time let themcool off and get
interested in thier own time. and provide a rich learning
envirnment.~Deborah
i too just got smartie pants and i hate math books. i purchased them.
my son is 15 and was amazed how much math is all around us ans has been
reading the books off and on. my dd is not so interested yet but has
gone back to her old key to.. work booklet on decimalsa few times since
i told them they didnt 'have' to do math anymore. they are slowly coming
around and showing interest. i say give it time let themcool off and get
interested in thier own time. and provide a rich learning
envirnment.~Deborah
[email protected]
In a message dated 10/4/01 6:23:35 AM, rumpleteasermom@... writes:
<< So I would say, look into the colleges (by asking other students there -
not the faculty) and see just what will be needed. You may find that he
needs a lot less than you think in the way of formal math - in fact "none
at all" comes to mind here.
People assume that "math" is 180 days of exercies in geometry, followed by
180 days (minus assemblies and bomb scares and other school pull-outs) of
algebra, optionally followed by algebra II or calculus, minus which children
do NOT know math, and WITH which children DO know math.
For one thing, a year of high school algebra isn't as much as a semester of
college algebra. With math, as with writing or history or science or music
or anything, either a kid sparks and GETS IT, in which case much of his
learning happens in his own head, or goofing with the ideas on his own, or
looking at other sources, or maybe the kid sparks because he already was a
mathematical thinker; or the kid does NOT spark, just sits in a room where
the teacher is trying unsuccessfully to get the spark lit, suffers through
homework he doesn't understand, gets bad grades on tests he's not
understanding, and comes out at the end of the year not knowing any more than
he knew before except that he hates math more (whatever "math" is to him).
Playing, building, puzzle solving, video game playing, are all more real to
mathematical thought and understanding than formulas in a textbook are.
There are 100 level math courses at most colleges and ALL local/jr/commmunity
colleges. There are computer games (algebra blasters) and there are internet
review sites. There are laminated study-guides. There are other humans to
ask questions of.
Nobody, college bound or otherwise, has to take "math classes" in the classic
sense. If you and your kids want to know what kind of math is on the ACT or
SAT, get sample tests, look at websites, buy (USED!) study guides for them.
Much of this worry, pressure and grief comes from the parents not being clear
on where math is in the real world, or not being aware that most kids who do
well in math in jr. high and high school already understood it and had an
interest before they got into the classroom, so for the best students, it's
just naming ideas they already had and putting graphs and charts to things
they had instinctively figured out already without the formalities.
Mathematical notation is like musical notation, or like diagramming
sentences. Someone can be a great speaker and writer, a poet, and not know
what a past participle is (and not NEED to know). Someone can be a great
musician AND compser, a Paul McCartney, and not read music or know "modes"
and "subdominant chords" (not by name). Let your kids do math like
musicians play by ear or like writers write in ideas, not in sentence
structures.
IF they love it and if they're good at seeing it, thinking it, using it, they
might (or might not ever) want to learn the written notation. And if they
understand it FIRST the written notation will never take them 180 days to
learn.
How many people feel sure they are NOT musicians, and won't even pick up an
instrument, because of early failures to understand how to read musical
notation? It's a shame, that so many teachers have taught people to hate
their subject matter.
Sandra
"Everything counts."
http://expage.com/SandraDoddArticles
http://expage.com/SandraDodd
<< So I would say, look into the colleges (by asking other students there -
not the faculty) and see just what will be needed. You may find that he
needs a lot less than you think in the way of formal math - in fact "none
at all" comes to mind here.
>>I agree.
People assume that "math" is 180 days of exercies in geometry, followed by
180 days (minus assemblies and bomb scares and other school pull-outs) of
algebra, optionally followed by algebra II or calculus, minus which children
do NOT know math, and WITH which children DO know math.
For one thing, a year of high school algebra isn't as much as a semester of
college algebra. With math, as with writing or history or science or music
or anything, either a kid sparks and GETS IT, in which case much of his
learning happens in his own head, or goofing with the ideas on his own, or
looking at other sources, or maybe the kid sparks because he already was a
mathematical thinker; or the kid does NOT spark, just sits in a room where
the teacher is trying unsuccessfully to get the spark lit, suffers through
homework he doesn't understand, gets bad grades on tests he's not
understanding, and comes out at the end of the year not knowing any more than
he knew before except that he hates math more (whatever "math" is to him).
Playing, building, puzzle solving, video game playing, are all more real to
mathematical thought and understanding than formulas in a textbook are.
There are 100 level math courses at most colleges and ALL local/jr/commmunity
colleges. There are computer games (algebra blasters) and there are internet
review sites. There are laminated study-guides. There are other humans to
ask questions of.
Nobody, college bound or otherwise, has to take "math classes" in the classic
sense. If you and your kids want to know what kind of math is on the ACT or
SAT, get sample tests, look at websites, buy (USED!) study guides for them.
Much of this worry, pressure and grief comes from the parents not being clear
on where math is in the real world, or not being aware that most kids who do
well in math in jr. high and high school already understood it and had an
interest before they got into the classroom, so for the best students, it's
just naming ideas they already had and putting graphs and charts to things
they had instinctively figured out already without the formalities.
Mathematical notation is like musical notation, or like diagramming
sentences. Someone can be a great speaker and writer, a poet, and not know
what a past participle is (and not NEED to know). Someone can be a great
musician AND compser, a Paul McCartney, and not read music or know "modes"
and "subdominant chords" (not by name). Let your kids do math like
musicians play by ear or like writers write in ideas, not in sentence
structures.
IF they love it and if they're good at seeing it, thinking it, using it, they
might (or might not ever) want to learn the written notation. And if they
understand it FIRST the written notation will never take them 180 days to
learn.
How many people feel sure they are NOT musicians, and won't even pick up an
instrument, because of early failures to understand how to read musical
notation? It's a shame, that so many teachers have taught people to hate
their subject matter.
Sandra
"Everything counts."
http://expage.com/SandraDoddArticles
http://expage.com/SandraDodd
[email protected]
In a message dated 4/15/02 5:10:16 PM, sugarcrafter@... writes:
<< In school I always got all the answers right,,,except the word problems and
I missed them all. I had a 4.0 gpa and I am so lousy at math that now,
years later, I don't even remember the first thing about simple algebra.
They would give a whole page of problems and maybe 4 word problems at the
bottom. If you missed those you could still get a good grade. I never
understood the theories. >>
I always understood the word problems. They were the only part I liked and
"got."
Sometimes I would use the word problems first (often #29 and #30, with the
other 28 being just the same layout of "number problems) and from
understanding the word problem, I got an idea what the heck those little
columns of numbers, or those equations were supposed to represent.
But I often figured out the answers with words and ideas, too, and didn't
"show my work," so I did great on standardized (multiple-guess) tests on
math, but got really frustrated in classes and with math teachers who looked
at me blankly when I'd ask "What is this good for in the real world?" Or
they would say something insipid like "Well you have to pass algebra I so you
can take algebra II."
That was NOT remotely the "real world" about which I was (regularly)
inquiring.
Sandra
<< In school I always got all the answers right,,,except the word problems and
I missed them all. I had a 4.0 gpa and I am so lousy at math that now,
years later, I don't even remember the first thing about simple algebra.
They would give a whole page of problems and maybe 4 word problems at the
bottom. If you missed those you could still get a good grade. I never
understood the theories. >>
I always understood the word problems. They were the only part I liked and
"got."
Sometimes I would use the word problems first (often #29 and #30, with the
other 28 being just the same layout of "number problems) and from
understanding the word problem, I got an idea what the heck those little
columns of numbers, or those equations were supposed to represent.
But I often figured out the answers with words and ideas, too, and didn't
"show my work," so I did great on standardized (multiple-guess) tests on
math, but got really frustrated in classes and with math teachers who looked
at me blankly when I'd ask "What is this good for in the real world?" Or
they would say something insipid like "Well you have to pass algebra I so you
can take algebra II."
That was NOT remotely the "real world" about which I was (regularly)
inquiring.
Sandra
[email protected]
In a message dated 4/25/02 8:15:32 AM Central Daylight Time,
[email protected] writes:
<< Can someone give me some example on involving math and sience in
everday life? I would like to hear stories of children under 8
intergrating math and sience with there lives in a natural course of
learning. >>
Well, I don't "try" to integrate it...it's all around us.
Let's see.
We did go to a science museum today, just for fun. Outside, during lunch,
Jared found a fuzzy seed pod of some kind and brought them home. They played
with sticks, watched boats on the canal behind us, watched birds, played on
the playground equipment etc....
Science was all around us. Just the act of observation is a scientific tool.
Math?
In a typical week you'll find my children budgeting and counting their money,
comparison shopping with same money, measuring while helping me cook or bake,
counting things in the woods, estimating how much money they will save by the
conference.......and so on.
Real life is full of science and math. If you live and give kids access to
their world, they can't get away from it.
Ren
[email protected] writes:
<< Can someone give me some example on involving math and sience in
everday life? I would like to hear stories of children under 8
intergrating math and sience with there lives in a natural course of
learning. >>
Well, I don't "try" to integrate it...it's all around us.
Let's see.
We did go to a science museum today, just for fun. Outside, during lunch,
Jared found a fuzzy seed pod of some kind and brought them home. They played
with sticks, watched boats on the canal behind us, watched birds, played on
the playground equipment etc....
Science was all around us. Just the act of observation is a scientific tool.
Math?
In a typical week you'll find my children budgeting and counting their money,
comparison shopping with same money, measuring while helping me cook or bake,
counting things in the woods, estimating how much money they will save by the
conference.......and so on.
Real life is full of science and math. If you live and give kids access to
their world, they can't get away from it.
Ren
Alan & Brenda Leonard
> her 8 and 6 y/o brothers had asked her to help her play a Family Math gameWhat's family math?
brenda
[email protected]
In a message dated 4/28/2002 7:19:16 PM Pacific Standard Time,
abtleo@... writes:
put out by a university, I think. The copy I'm using now is borrowed from
the library, but I'll probably end up buying it as it only costs about $20.
The original Family Math is for all ages, and then there's also "Family Math:
The Early Years" and "Middle School Family Math".
Sandra
Homeschooling Mom to Five
[Non-text portions of this message have been removed]
abtleo@... writes:
> What's family math?A book of different, really neat math games for all ages that was originally
put out by a university, I think. The copy I'm using now is borrowed from
the library, but I'll probably end up buying it as it only costs about $20.
The original Family Math is for all ages, and then there's also "Family Math:
The Early Years" and "Middle School Family Math".
Sandra
Homeschooling Mom to Five
[Non-text portions of this message have been removed]
[email protected]
In a message dated 5/8/02 12:56:06 AM Central Daylight Time,
[email protected] writes:
<< You associate the word with school and torture? But doing the computations
for a real purpose doesn't have that association? >>
Ah, yes....that sounds right.
I have believed I was genetically not able to be good at math for so long
that it's really exciting to think that's not true.
Ren
[email protected] writes:
<< You associate the word with school and torture? But doing the computations
for a real purpose doesn't have that association? >>
Ah, yes....that sounds right.
I have believed I was genetically not able to be good at math for so long
that it's really exciting to think that's not true.
Ren
[email protected]
In a message dated 5/8/02 10:52:49 AM Central Daylight Time,
[email protected] writes:
<< And lots of people here probably shut down after they saw the first number
;-) The exact process I used wasn't important. The important part is getting
the problem simple enough that I can do it easily in my head. >>
Exactly.
My 8y.o. ds, with not a single math hang up, asked me what 14 X 4 was the
other day. I told him that two fourteens was (and he popped in with 28), and
then I pointed out that 4 14's was just two 28's then.....and he got it.
I hear him manipulating and playing around with numbers all the time. It's so
fascinating to me, watching this child that has never had a math lesson
(other than my showing him place value).
I can actually remember as a child in school, that I could get the right
answer but get my problem marked wrong if I did the PROCESS different than
the one they were trying to teach us.
One time, my Dad (who is very good with math) showed me a really great way to
do division, but it didn't use the process they showed and so I had to re-do
the entire sheet.
If the whole point is getting people to use math proficiently, it shouldn't
matter one whit how they get their. But the whole point of schools isn't to
help people gain proficiency anyway, silly me!!
It's been proven to me time and again, by these sweet children I've been
blessed with, that math is natural. That letting them roll things around and
use it irl makes it fun and they don't need to put it to paper until they
want to!
It works.
That's all I care about.
Ren
[email protected] writes:
<< And lots of people here probably shut down after they saw the first number
;-) The exact process I used wasn't important. The important part is getting
the problem simple enough that I can do it easily in my head. >>
Exactly.
My 8y.o. ds, with not a single math hang up, asked me what 14 X 4 was the
other day. I told him that two fourteens was (and he popped in with 28), and
then I pointed out that 4 14's was just two 28's then.....and he got it.
I hear him manipulating and playing around with numbers all the time. It's so
fascinating to me, watching this child that has never had a math lesson
(other than my showing him place value).
I can actually remember as a child in school, that I could get the right
answer but get my problem marked wrong if I did the PROCESS different than
the one they were trying to teach us.
One time, my Dad (who is very good with math) showed me a really great way to
do division, but it didn't use the process they showed and so I had to re-do
the entire sheet.
If the whole point is getting people to use math proficiently, it shouldn't
matter one whit how they get their. But the whole point of schools isn't to
help people gain proficiency anyway, silly me!!
It's been proven to me time and again, by these sweet children I've been
blessed with, that math is natural. That letting them roll things around and
use it irl makes it fun and they don't need to put it to paper until they
want to!
It works.
That's all I care about.
Ren
Saddle Mountain Academy
quick question regarding that "math" topic.
Just wondering, if you don't "teach" math and your state requires testing, how will they know the material they need to know for the test regarding basic and intro geometry, algebra, or lets say even division if they haven't "learned" it yet? My state doesn't require testing (whew) and I completely hate the idea of teachers "teaching to the test" but I'm just curious how others unschool with math if their state has requirements.
Sue
Saddle Mountain Academy
Snake River Plains
++ ++
+ ++ + +
+ +
[Non-text portions of this message have been removed]
Just wondering, if you don't "teach" math and your state requires testing, how will they know the material they need to know for the test regarding basic and intro geometry, algebra, or lets say even division if they haven't "learned" it yet? My state doesn't require testing (whew) and I completely hate the idea of teachers "teaching to the test" but I'm just curious how others unschool with math if their state has requirements.
Sue
Saddle Mountain Academy
Snake River Plains
++ ++
+ ++ + +
+ +
[Non-text portions of this message have been removed]
[email protected]
Some people don't register with the state.
Some parents teach their kids tricks for guessing well. Standardized tests
are multiple choice, and so it's not REALLY dividing formally and showing all
your work, it's eliminating the wrong answers.
Some states don't care about the resultant scores.
Some states allow home-administered testing.
If a child isn't able to read the questions, they can be read to him. At
home that's easy. In a state with more formal requirements, you might have
to pay a counselor or psychologist to do that if you truly wanted to be
aboveboard.
I have an article I tried to cut and paste into here but it didn't work, but
it's at
http://SandraDodd.com/tests
and I'll try again to get it into another e-mail. But it's a recommendation
on how to invalidate test results for a good purpose.
Sandra
Some parents teach their kids tricks for guessing well. Standardized tests
are multiple choice, and so it's not REALLY dividing formally and showing all
your work, it's eliminating the wrong answers.
Some states don't care about the resultant scores.
Some states allow home-administered testing.
If a child isn't able to read the questions, they can be read to him. At
home that's easy. In a state with more formal requirements, you might have
to pay a counselor or psychologist to do that if you truly wanted to be
aboveboard.
I have an article I tried to cut and paste into here but it didn't work, but
it's at
http://SandraDodd.com/tests
and I'll try again to get it into another e-mail. But it's a recommendation
on how to invalidate test results for a good purpose.
Sandra
Deb
a good long list of math words, Ned, in the article you referneced.
Thanks.
Debbie
Thanks.
Debbie
Alan & Brenda Leonard
So, now that I'm done ranting about music.....
I have a math question. We seem to get into the wildest math concepts here,
just by living. We had fun with irrational numbers last week (they're my
favorite); fractions, decimals, etc. all seem to come up around here
regularly. Tim understands the concept of multiplication, and likes the
cool patterns you get with things like 11's (22,33,44,55, etc.) and 9's
(09,18,27,36,45, etc.). Great, right?
But there's this "schooled" part of me that wonders about the things he's
missing. He vaguely understands they idea of carrying over to the 10's
column in addition (he had to keep money records for a scout project), but
is completely lost at the idea of borrowing when subtracting, and other more
elementary concepts. Of course, these are things way beyond what a 6 year
old needs to know, or would even learn in a nice dutiful school program. I
guess I just get nervous about the wacky order his math learning has been
going. Is this typical? (Not the nervousness, the wacky order. I know
parental nerves are typical!)
brenda
I have a math question. We seem to get into the wildest math concepts here,
just by living. We had fun with irrational numbers last week (they're my
favorite); fractions, decimals, etc. all seem to come up around here
regularly. Tim understands the concept of multiplication, and likes the
cool patterns you get with things like 11's (22,33,44,55, etc.) and 9's
(09,18,27,36,45, etc.). Great, right?
But there's this "schooled" part of me that wonders about the things he's
missing. He vaguely understands they idea of carrying over to the 10's
column in addition (he had to keep money records for a scout project), but
is completely lost at the idea of borrowing when subtracting, and other more
elementary concepts. Of course, these are things way beyond what a 6 year
old needs to know, or would even learn in a nice dutiful school program. I
guess I just get nervous about the wacky order his math learning has been
going. Is this typical? (Not the nervousness, the wacky order. I know
parental nerves are typical!)
brenda
[email protected]
<<So, now that I'm done ranting about music.....
I have a math question. We seem to get into the wildest math concepts
here,
just by living. We had fun with irrational numbers last week (they're my
favorite); fractions, decimals, etc. all seem to come up around here
regularly. Tim understands the concept of multiplication, and likes the
cool patterns you get with things like 11's (22,33,44,55, etc.) and 9's
(09,18,27,36,45, etc.). Great, right?
But there's this "schooled" part of me that wonders about the things he's
missing. He vaguely understands they idea of carrying over to the 10's
column in addition (he had to keep money records for a scout project), but
is completely lost at the idea of borrowing when subtracting, and other
more
elementary concepts. Of course, these are things way beyond what a 6 year
old needs to know, or would even learn in a nice dutiful school program. I
guess I just get nervous about the wacky order his math learning has been
going. Is this typical? (Not the nervousness, the wacky order. I know
parental nerves are typical!)
brenda>>
Just speaking from my own experience, I have found that math is one of
those
subjects that you don't "get" until you "get" it, and there is no real
order that is better than the other. For example, most schools teach
algebra->trig->calculus, with
the implied assumption that you will completely understand one before
moving on to the
next. However, for me, I didn't really "get" trig until I was completely
done with
calculus, and same with algebra. I think it's because the following
subject gives an
applied use of the theoretical concepts presented in the previous one, and
that gave me the tools to play around with and understand the "why".
Hope that makes sense!
Kevin
~~~~ Don't forget! If you change topics, change the subject line! ~~~~
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Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.
[Non-text portions of this message have been removed]
I have a math question. We seem to get into the wildest math concepts
here,
just by living. We had fun with irrational numbers last week (they're my
favorite); fractions, decimals, etc. all seem to come up around here
regularly. Tim understands the concept of multiplication, and likes the
cool patterns you get with things like 11's (22,33,44,55, etc.) and 9's
(09,18,27,36,45, etc.). Great, right?
But there's this "schooled" part of me that wonders about the things he's
missing. He vaguely understands they idea of carrying over to the 10's
column in addition (he had to keep money records for a scout project), but
is completely lost at the idea of borrowing when subtracting, and other
more
elementary concepts. Of course, these are things way beyond what a 6 year
old needs to know, or would even learn in a nice dutiful school program. I
guess I just get nervous about the wacky order his math learning has been
going. Is this typical? (Not the nervousness, the wacky order. I know
parental nerves are typical!)
brenda>>
Just speaking from my own experience, I have found that math is one of
those
subjects that you don't "get" until you "get" it, and there is no real
order that is better than the other. For example, most schools teach
algebra->trig->calculus, with
the implied assumption that you will completely understand one before
moving on to the
next. However, for me, I didn't really "get" trig until I was completely
done with
calculus, and same with algebra. I think it's because the following
subject gives an
applied use of the theoretical concepts presented in the previous one, and
that gave me the tools to play around with and understand the "why".
Hope that makes sense!
Kevin
~~~~ Don't forget! If you change topics, change the subject line! ~~~~
If you have questions, concerns or problems with this list, please email
the moderator, Joyce Fetteroll (fetteroll@...), or the list
owner, Helen Hegener (HEM-Editor@...).
To unsubscribe from this group, click on the following link or address an
email to:
[email protected]
Visit the Unschooling website: http://www.unschooling.com
Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.
[Non-text portions of this message have been removed]
[email protected]
In a message dated 11/14/02 3:23:32 PM, abtleo@... writes:
<< Of course, these are things way beyond what a 6 year
old needs to know, or would even learn in a nice dutiful school program. I
guess I just get nervous about the wacky order his math learning has been
going. Is this typical? >>
YES!! It's fine for a kid to understand percentages before he knows fractions.
And guess what?? I have kids who can do some pretty cool math in their
heads, but Marty is 13 and just lately asked me about some of the symbol keys
on the computer. He didn't know the marks for division or multiplication.
But he can calculate things in his head.
This morning Holly and I were talking about allowances. She's 11 now and so
has gone up to $8.25 from $7.50. She misses being able to sing the
Schoolhouse Rock song about "Seven fifty once a week" and it be true, but
that's fine. We were talking about allowance in general and why we didn't
make it 50 cents or a dollar per year of age, and I said Keith was afraid we
wouldn't be able to afford it when they were all teens. I asked her what the
total was now, thinking she might know offhand. She's that kind of kid.
She started figuring it in her head. I said "I'll race you!" So first she
figured out each kid's allowance. I wrote it down just to help her. She was
still adding in her head, and I wrote down 16, 13, 11 and added them. GOOD!
Even. 40. 75% of 40 is easy; $30. She had 30 too.
$30 a week we pay out in allowance. The average is toward Kirby, until after
Marty's birthday in January. Right now Marty's at $9.75. Each week I give
him a ten, and he gives me a quarter. Sometimes it was my quarter. I never
care. He's generous with money and always brings me change and a receipt
when he goes on an errand.
Sandra
<< Of course, these are things way beyond what a 6 year
old needs to know, or would even learn in a nice dutiful school program. I
guess I just get nervous about the wacky order his math learning has been
going. Is this typical? >>
YES!! It's fine for a kid to understand percentages before he knows fractions.
And guess what?? I have kids who can do some pretty cool math in their
heads, but Marty is 13 and just lately asked me about some of the symbol keys
on the computer. He didn't know the marks for division or multiplication.
But he can calculate things in his head.
This morning Holly and I were talking about allowances. She's 11 now and so
has gone up to $8.25 from $7.50. She misses being able to sing the
Schoolhouse Rock song about "Seven fifty once a week" and it be true, but
that's fine. We were talking about allowance in general and why we didn't
make it 50 cents or a dollar per year of age, and I said Keith was afraid we
wouldn't be able to afford it when they were all teens. I asked her what the
total was now, thinking she might know offhand. She's that kind of kid.
She started figuring it in her head. I said "I'll race you!" So first she
figured out each kid's allowance. I wrote it down just to help her. She was
still adding in her head, and I wrote down 16, 13, 11 and added them. GOOD!
Even. 40. 75% of 40 is easy; $30. She had 30 too.
$30 a week we pay out in allowance. The average is toward Kirby, until after
Marty's birthday in January. Right now Marty's at $9.75. Each week I give
him a ten, and he gives me a quarter. Sometimes it was my quarter. I never
care. He's generous with money and always brings me change and a receipt
when he goes on an errand.
Sandra
Betsy
We do a lot of "head math" in my house. The operator symbols were
definitely the last thing learned.
Betsy
**And guess what?? I have kids who can do some pretty cool math in
their
heads, but Marty is 13 and just lately asked me about some of the symbol
keys
on the computer. He didn't know the marks for division or
multiplication.
But he can calculate things in his head.**
definitely the last thing learned.
Betsy
**And guess what?? I have kids who can do some pretty cool math in
their
heads, but Marty is 13 and just lately asked me about some of the symbol
keys
on the computer. He didn't know the marks for division or
multiplication.
But he can calculate things in his head.**
Tia Leschke
> But there's this "schooled" part of me that wonders about the things he'smore
> missing. He vaguely understands they idea of carrying over to the 10's
> column in addition (he had to keep money records for a scout project), but
> is completely lost at the idea of borrowing when subtracting, and other
> elementary concepts.For borrowing, I found that using money helped Lars get it. If you have to
subtract 6.59 from 8.60, obviously you can't take 9 pennies from nothing.
So you change the 6 dimes to 5 dimes and 10 pennies. Then you can take 9
pennies away from that. If he works a few out with real money, he'll
probably be able to do it on paper as well.
Tia
Pam Sorooshian
>>Of course, these are things way beyond what a 6 yearold needs to know, or would even learn in a nice dutiful school program. I
guess I just get nervous about the wacky order his math learning has been
going. Is this typical? (Not the nervousness, the wacky order. I know
parental nerves are typical!)
<<
It is awesome!!!! Concepts concepts concepts - play with ideas.
Ask him to do this: What happens if you walk halfway to that wall? Do it.
Now walk halfway from where you are now. Then walk halfway from there. If
you keep doing that - will you ever actually reach the wall?
(There is no "out of order" -- there is no "in order" -- let that go, okay?)
--pam
Pam Sorooshian
National Home Education Network
www.NHEN.org
Changing the Way the World Sees Homeschooling
[Non-text portions of this message have been removed]
Mary Bianco
>From: Alan & Brenda Leonard <abtleo@...><<I guess I just get nervous about the wacky order his math learning has
been going. Is this typical? (Not the nervousness, the wacky order. I
know parental nerves are typical!)>>
Yes yes yes!!!!
With unschooling nothing is typical and everything goes. Orders don't count
because there mostly isn't any. It depends on the child and what their
interests are. You stated that you have favorites in math and from the sound
of it, so does your son. It's only natural for him to excel at what he likes
and to save the other stuff for later, if at all. If math continues to be a
point of interest for him, he'll pick up all the other stuff at another
time.
Mary B
_________________________________________________________________
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Alan & Brenda Leonard
11/15/02 07:57:
are harder than others.
My son thought the walking to the door (no open walls in my house!) idea was
fun, and did it about fifty times. He concluded it was "like infinity, but
the small way". Cool!
brenda
> Ask him to do this: What happens if you walk halfway to that wall? Do it.Thanks, Pam. I'm trying to give up the school order ideas, but some places
> Now walk halfway from where you are now. Then walk halfway from there. If
> you keep doing that - will you ever actually reach the wall?
>
> (There is no "out of order" -- there is no "in order" -- let that go, okay?)
>
are harder than others.
My son thought the walking to the door (no open walls in my house!) idea was
fun, and did it about fifty times. He concluded it was "like infinity, but
the small way". Cool!
brenda
Alan & Brenda Leonard
11/16/02 03:35:
I think Tim is getting the concept that numbers can go on forever. He comes
up with these amazing "numbers" (a million trillion bazillion jillian
crillian) and then says, "but I know a bigger one! A million trillion
bazillion jillian crillian and ONE!" and starts laughing hysterically. It
really was funny the first several hundered times.... :P
brenda
> So -- now you've got some "infinity" conversation going -- what you want isThanks for another good idea, Pam.
> for him NOT to get the idea that infinity is some kind of really really big
> number.
>
> You can ask him what happens when you keep dividing something in half, over
> and over, now. Then you can talk about what happens if you divide nothing
> in half <G>.
I think Tim is getting the concept that numbers can go on forever. He comes
up with these amazing "numbers" (a million trillion bazillion jillian
crillian) and then says, "but I know a bigger one! A million trillion
bazillion jillian crillian and ONE!" and starts laughing hysterically. It
really was funny the first several hundered times.... :P
brenda
[email protected]
In a message dated 11/16/02 3:00:56 PM, abtleo@... writes:
<< Then you can talk about what happens if you divide nothing
nothing, I'm SURE.
(Sandra, who does her math in words...)
<< Then you can talk about what happens if you divide nothing
> in half >>It's easier to divide a Big FAT nothing than just any old theoretical
nothing, I'm SURE.
(Sandra, who does her math in words...)
Tia Leschke
> I think Tim is getting the concept that numbers can go on forever. Hecomes
> up with these amazing "numbers" (a million trillion bazillion jillianOne of my first and favourite unschooling stories is about a family we were
> crillian) and then says, "but I know a bigger one! A million trillion
> bazillion jillian crillian and ONE!" and starts laughing hysterically. It
> really was funny the first several hundered times.... :P
visiting. The oldest boy had been really turned off math in his 2 years of
school. Some time after leaving school, he started a project all on his own
of doubling numbers. 1+1+2, 2+2+4, etc. When he finished the trillions, he
had to ask his mother what came next. After the quadrillions, they had to
look up what came next. He got bored with the project during the
quintillions. Can you imagine a schooled kid taking on a project like that?
(No calculator was used.) That boy has grown up to be a fine musician. <g>
Tia
Alan & Brenda Leonard
2/6/03 22:36:
paper, somehow you're missing a piece in your head.
Many people here have talked about how their kids know how to do math
things, but not on paper. They know how to do them in their minds, because
they understand the concept. When shown how to do it on paper, it's a
simple transfer.
I think it's like learning to play piano without music, and then having
someone explain what the silly little black marks on the paper mean. This
black dot here refers to this key on the piano, and we call it C. We could
call it George, or Fudnups, or whatever, but we call it C. It's giving a
name and a symbol to something that any pianist would understand, but didn't
know how to put into writing.
School math is all about memorizing a series of steps to convert fractions,
come up with common denominators, multiply them, etc. If your son memorizes
that series of steps, then he'll "get" it. But only as long as he remembers
the steps. (Hopefully long enough for the test is how I usually figured
it!). But if he truly understand the big picture and understands what
fractions and decimals are, and how they work *in real life*, then doing it
on paper is merely an extension of that.
For him to have success at this, he needs to go find fractions, decimals,
and all that stuff, all over your life. USE them, manipulate them, and live
with them. When you go back to the paper, THEN your son can expect success.
brenda
> He just can't do it on paper, which is what the school will want him to beBut it's a bigger problem than what the school wants. If you can't do it on
> able to do.
paper, somehow you're missing a piece in your head.
Many people here have talked about how their kids know how to do math
things, but not on paper. They know how to do them in their minds, because
they understand the concept. When shown how to do it on paper, it's a
simple transfer.
I think it's like learning to play piano without music, and then having
someone explain what the silly little black marks on the paper mean. This
black dot here refers to this key on the piano, and we call it C. We could
call it George, or Fudnups, or whatever, but we call it C. It's giving a
name and a symbol to something that any pianist would understand, but didn't
know how to put into writing.
School math is all about memorizing a series of steps to convert fractions,
come up with common denominators, multiply them, etc. If your son memorizes
that series of steps, then he'll "get" it. But only as long as he remembers
the steps. (Hopefully long enough for the test is how I usually figured
it!). But if he truly understand the big picture and understands what
fractions and decimals are, and how they work *in real life*, then doing it
on paper is merely an extension of that.
For him to have success at this, he needs to go find fractions, decimals,
and all that stuff, all over your life. USE them, manipulate them, and live
with them. When you go back to the paper, THEN your son can expect success.
brenda
Have a Nice Day!
Brenda,
You make a good point. But I think working with math formulas are much more involved than learning to read music simply because there are so many formulas and all are multi-step and abstract on paper. When reading music, each of the notes always corresponds with a paritcular key.
Though, I would say that learning to read music is kind of ridiculous if you aren't actually playing an instrument. So, its probably equally silly to try to learn arithmetic language without the appropriate concrete application. But I"m not that great at concepts myself.
I have a question for you (or anyone good at math).
Why, when we are dividing fractions, do we flip the second one over and multiply?
And how does that fit in with "real" fractions?
I honestly never "got" that. I memorized everything but I don't get *all* the concepts.
Kristen
You make a good point. But I think working with math formulas are much more involved than learning to read music simply because there are so many formulas and all are multi-step and abstract on paper. When reading music, each of the notes always corresponds with a paritcular key.
Though, I would say that learning to read music is kind of ridiculous if you aren't actually playing an instrument. So, its probably equally silly to try to learn arithmetic language without the appropriate concrete application. But I"m not that great at concepts myself.
I have a question for you (or anyone good at math).
Why, when we are dividing fractions, do we flip the second one over and multiply?
And how does that fit in with "real" fractions?
I honestly never "got" that. I memorized everything but I don't get *all* the concepts.
Kristen
----- Original Message -----
From: Alan & Brenda Leonard
To: [email protected]
Sent: Thursday, February 06, 2003 7:57 PM
Subject: Re: [Unschooling-dotcom] math
2/6/03 22:36:
> He just can't do it on paper, which is what the school will want him to be
> able to do.
But it's a bigger problem than what the school wants. If you can't do it on
paper, somehow you're missing a piece in your head.
Many people here have talked about how their kids know how to do math
things, but not on paper. They know how to do them in their minds, because
they understand the concept. When shown how to do it on paper, it's a
simple transfer.
I think it's like learning to play piano without music, and then having
someone explain what the silly little black marks on the paper mean. This
black dot here refers to this key on the piano, and we call it C. We could
call it George, or Fudnups, or whatever, but we call it C. It's giving a
name and a symbol to something that any pianist would understand, but didn't
know how to put into writing.
School math is all about memorizing a series of steps to convert fractions,
come up with common denominators, multiply them, etc. If your son memorizes
that series of steps, then he'll "get" it. But only as long as he remembers
the steps. (Hopefully long enough for the test is how I usually figured
it!). But if he truly understand the big picture and understands what
fractions and decimals are, and how they work *in real life*, then doing it
on paper is merely an extension of that.
For him to have success at this, he needs to go find fractions, decimals,
and all that stuff, all over your life. USE them, manipulate them, and live
with them. When you go back to the paper, THEN your son can expect success.
brenda
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[Non-text portions of this message have been removed]
[email protected]
In a message dated 2/6/03 7:17:47 PM, litlrooh@... writes:
<< But I think working with math formulas are much more involved than
learning to read music simply because there are so many formulas and all are
multi-step and abstract on paper. When reading music, each of the notes
always corresponds with a paritcular key. >>
It's a set of symbols for a language, same as with music. Reading music
isn't as easy as you seem to think. If you're talking about piano, maybe
it's possible to think of one note corresponding to a particular key, but
once you get to mixed instruments, a "note" might not even be the same for
different instruments. There's a lot of weird transposition.
And that's just thinking of one style of music.
There are lots of kind of music and musical notation.
There are different kinds of mathematical notation too, not all done with
numerals and function symbols.
<<Though, I would say that learning to read music is kind of ridiculous if
you aren't actually playing an instrument. So, its probably equally silly to
try to learn arithmetic language without the appropriate concrete
application. .>
I'm pretty sure that was the point of the musical analogy. There's no sense
in showing your son any notation if he doesn't already understand what
fractions and percentages are and what they do. It would be like trying to
teach someone to read Chinese who doesn't know what any of the Chinese words
mean or even sound like.
Concepts first. Concrete understanding FIRST, and then notation second.
Sandra
<< But I think working with math formulas are much more involved than
learning to read music simply because there are so many formulas and all are
multi-step and abstract on paper. When reading music, each of the notes
always corresponds with a paritcular key. >>
It's a set of symbols for a language, same as with music. Reading music
isn't as easy as you seem to think. If you're talking about piano, maybe
it's possible to think of one note corresponding to a particular key, but
once you get to mixed instruments, a "note" might not even be the same for
different instruments. There's a lot of weird transposition.
And that's just thinking of one style of music.
There are lots of kind of music and musical notation.
There are different kinds of mathematical notation too, not all done with
numerals and function symbols.
<<Though, I would say that learning to read music is kind of ridiculous if
you aren't actually playing an instrument. So, its probably equally silly to
try to learn arithmetic language without the appropriate concrete
application. .>
I'm pretty sure that was the point of the musical analogy. There's no sense
in showing your son any notation if he doesn't already understand what
fractions and percentages are and what they do. It would be like trying to
teach someone to read Chinese who doesn't know what any of the Chinese words
mean or even sound like.
Concepts first. Concrete understanding FIRST, and then notation second.
Sandra
[email protected]
In a message dated 2/6/2003 9:56:10 PM Eastern Standard Time,
SandraDodd@... writes:
Learning English (or any native tongue---or any second language!) is best
learned with hearing first, then UNDERSTANDING, then some spoken words, THEN
reading and writing. Schools have kids reading and writing with NO
understanding.
My husband is still in the "toddler stages" of German. He can understand MOST
of what's spoken. He can speak a bit, but it's broken. He can read a little.
He can write even less (if any).
Look at math that way. After you UNDERSTAND the concept, it's really EASY to
plug in the signs and numbers.
~Kelly
[Non-text portions of this message have been removed]
SandraDodd@... writes:
> I'm pretty sure that was the point of the musical analogy. There's no senseThat's my big problem with how foreign languages are taught in school.
>
> in showing your son any notation if he doesn't already understand what
> fractions and percentages are and what they do. It would be like trying to
>
> teach someone to read Chinese who doesn't know what any of the Chinese
> words
> mean or even sound like.
>
> Concepts first. Concrete understanding FIRST, and then notation second.
Learning English (or any native tongue---or any second language!) is best
learned with hearing first, then UNDERSTANDING, then some spoken words, THEN
reading and writing. Schools have kids reading and writing with NO
understanding.
My husband is still in the "toddler stages" of German. He can understand MOST
of what's spoken. He can speak a bit, but it's broken. He can read a little.
He can write even less (if any).
Look at math that way. After you UNDERSTAND the concept, it's really EASY to
plug in the signs and numbers.
~Kelly
[Non-text portions of this message have been removed]
Have a Nice Day!
There are different kinds of mathematical notation too, not all done with
numerals and function symbols.<<<<
Really, that is fascinating. Can you give me an example?
But to write it in decimals on a piece of paper, it makes zero sense to him. He's not connecting the fact that pennies are "Hundredths" and dimes are "tenths" of dollars.
Why is that? Does that mean he *doesn't* have concrete understanding of money? How much more concrete can it get when he can deal with actual real money on a daily basis?
What is it that he's not getting that would make it easier for him on paper?
Kristen
[Non-text portions of this message have been removed]
numerals and function symbols.<<<<
Really, that is fascinating. Can you give me an example?
>>>Concepts first. Concrete understanding FIRST, and then notation second.<<<Ok here's an example: he understands money. He understands how to add and subtract it in his head. He can make change.
But to write it in decimals on a piece of paper, it makes zero sense to him. He's not connecting the fact that pennies are "Hundredths" and dimes are "tenths" of dollars.
Why is that? Does that mean he *doesn't* have concrete understanding of money? How much more concrete can it get when he can deal with actual real money on a daily basis?
What is it that he's not getting that would make it easier for him on paper?
Kristen
[Non-text portions of this message have been removed]
Fetteroll
on 2/7/03 1:07 AM, Have a Nice Day! at litlrooh@... wrote:
in order for the "rule" (how the numbers get written down) to make sense.
Where else does he encounter decimals? Sports statistics? Video games?
Joyce
> What is it that he's not getting that would make it easier for him on paper?Time to notice decimals used in other ways. He needs a repetoire of examples
in order for the "rule" (how the numbers get written down) to make sense.
Where else does he encounter decimals? Sports statistics? Video games?
Joyce
Fetteroll
on 2/6/03 9:54 PM, SandraDodd@... at SandraDodd@... wrote:
of your non-learning days because it might be something you don't know and
you wouldn't want to take a chance ;-) Unlike English there isn't a
connection between the spoken word and the written word. You could read
Chinese without speaking it. In fact I'm pretty sure the written Chinese can
be read regardless of the language one speaks. Here's something:
understands the concepts and knows how the concepts relate to the notation,
they can read Chinese (or math). But if somene is hazy on the concepts or
doesn't understand the relationship between the concepts and the notation
then the written language isn't going to mean much.
Joyce
> It would be like trying toActually not the best example ;-) (But no one should read this if it's one
> teach someone to read Chinese who doesn't know what any of the Chinese words
> mean or even sound like.
of your non-learning days because it might be something you don't know and
you wouldn't want to take a chance ;-) Unlike English there isn't a
connection between the spoken word and the written word. You could read
Chinese without speaking it. In fact I'm pretty sure the written Chinese can
be read regardless of the language one speaks. Here's something:
> In China there are many different dialects. Dialects usually refer toWhich makes written Chinese like mathematical notation. As long as someone
> "regional forms of a language." However, many of the regional variants which
> are commonly referred to as "dialects" of the Chinese language are more
> different from one another than French is from Spanish or Norwegian is from
> Swedish! Below are some figures for different "dialect groups" in China:
>
> Dialect Group Number of Speakers (approx.)
> Northern(Includes Mandarin) 387,000,000
> Jiangsu-Zhejiang 46,000,000
> Hunan 26,000,000
> Jiangsi 13,000,000
> Hakka 20,000,000
> Northern Min 7,000,000
> Southern Min 15,000,000
> Cantonese 27,000,000
>
> One thing that makes the Chinese dialect situation unique -- that is different
> from the situation confronting speakers of French and Spanish or Norwegian and
> Swedish -- concerns the fact that all speakers who are literate share a common
> written language. Thus, while oral forms vary greatly, written symbols can be
> used to communicate effectively between speakers of different dialects.
understands the concepts and knows how the concepts relate to the notation,
they can read Chinese (or math). But if somene is hazy on the concepts or
doesn't understand the relationship between the concepts and the notation
then the written language isn't going to mean much.
Joyce
Fetteroll
on 2/6/03 9:14 PM, Have a Nice Day! at litlrooh@... wrote:
Educators need to break it down into memorizable steps because kids don't
understand the concepts. And since it's really tough to test for
understanding, the educators rely on testing if someone can recall something
they've memorized.
At the conference I was (not very successfully since I need lots of time to
gather my thoughts!) trying to explain how kids get arithmetic. I was
explaining the steps my daughter might use to add 2 largish numbers. It
would involve changing the numbers around to make them into numbers that are
easy to manipulate in your head. But the man I was explaining it to pointed
out that it was way more complex than learning to borrow and carry.
Well it is if you were teaching it as a formula. But when it's done because
someone understands how numbers work, it's very simple.
memorizing procedures to spit back for a test.
Think about it conceptually. If you take a whole (1) and divide it into
larger and larger numbers of pieces 1/2, 1/3, 1/27. 1/100, you get smaller
and smaller pieces. If you divide a whole into 1 piece, you'll get 1 piece
(1/1). If you divide a whole into smaller and smaller numbers of pieces
(though the normal way of describing division doesn't work so well --
dividing 1 into half a piece, or taking 1 piece out of 1/2 pieces doesn't
make much sense), the pieces should get larger and larger. In other words
they have to get bigger than one. So 1 divided by 1/2 is 2 (or 2/1 which is
1/2 flipped over.) 1 divided by 1/6 should be 6, so 2 divided by 1/6 (
2/(1/6) which is the same as 2x(6/1)) should be twice as much, so 12.
Math needs to describe things that fall outside the realm of physical
objects. So though in some contexts it make sense to divide by numbers
smaller than 1, it doesn't make much sense to divide a plate of cookies by
1/2 a child. ;-) But it might help make the concept clearer if you tried! If
there are 5 cookies to divide by 1/2 a child, how many cookies does a whole
child get? If there are 2 cookies to divide by 1/6 of a child, how many
cookies does a whole child get? How many cookies would 3 children get?
Joyce
> But I think working with math formulas are much more involved than learning toOnly in school math. Math in real life is done much more intuitively.
> read music simply because there are so many formulas and all are multi-step
> and abstract on paper.
Educators need to break it down into memorizable steps because kids don't
understand the concepts. And since it's really tough to test for
understanding, the educators rely on testing if someone can recall something
they've memorized.
At the conference I was (not very successfully since I need lots of time to
gather my thoughts!) trying to explain how kids get arithmetic. I was
explaining the steps my daughter might use to add 2 largish numbers. It
would involve changing the numbers around to make them into numbers that are
easy to manipulate in your head. But the man I was explaining it to pointed
out that it was way more complex than learning to borrow and carry.
Well it is if you were teaching it as a formula. But when it's done because
someone understands how numbers work, it's very simple.
> Why, when we are dividing fractions, do we flip the second one over andIt's convention. It works out that way. ;-) And that's the problem with
> multiply?
memorizing procedures to spit back for a test.
Think about it conceptually. If you take a whole (1) and divide it into
larger and larger numbers of pieces 1/2, 1/3, 1/27. 1/100, you get smaller
and smaller pieces. If you divide a whole into 1 piece, you'll get 1 piece
(1/1). If you divide a whole into smaller and smaller numbers of pieces
(though the normal way of describing division doesn't work so well --
dividing 1 into half a piece, or taking 1 piece out of 1/2 pieces doesn't
make much sense), the pieces should get larger and larger. In other words
they have to get bigger than one. So 1 divided by 1/2 is 2 (or 2/1 which is
1/2 flipped over.) 1 divided by 1/6 should be 6, so 2 divided by 1/6 (
2/(1/6) which is the same as 2x(6/1)) should be twice as much, so 12.
Math needs to describe things that fall outside the realm of physical
objects. So though in some contexts it make sense to divide by numbers
smaller than 1, it doesn't make much sense to divide a plate of cookies by
1/2 a child. ;-) But it might help make the concept clearer if you tried! If
there are 5 cookies to divide by 1/2 a child, how many cookies does a whole
child get? If there are 2 cookies to divide by 1/6 of a child, how many
cookies does a whole child get? How many cookies would 3 children get?
Joyce