Algebra?
Dean and Rhonda Johnson
Dear Unschoolers,
At this point we are pretty relaxed but I know we are definitely not
unschooling. As the daughter of a former public school teacher I think I
have more than the normal amount of hang ups. <grin>
All my kids seem to learn math computation easily from life but I am having
trouble understanding how they are going to learn algebra and other higher
math concepts. My oldest is interested in several career paths that would
require learning advanced math thoroughly.
He has requested an algebra course. Is there a better way to do this?
What are unschooling thoughts on this?
Thanks!
Rhonda
rjohnson@...
home educating Cole, 13; Shelby, 9; and Connor, 7
"When I was younger, I could remember anything, whether it had happened or
not."
- Mark Twain
[Non-text portions of this message have been removed]
At this point we are pretty relaxed but I know we are definitely not
unschooling. As the daughter of a former public school teacher I think I
have more than the normal amount of hang ups. <grin>
All my kids seem to learn math computation easily from life but I am having
trouble understanding how they are going to learn algebra and other higher
math concepts. My oldest is interested in several career paths that would
require learning advanced math thoroughly.
He has requested an algebra course. Is there a better way to do this?
What are unschooling thoughts on this?
Thanks!
Rhonda
rjohnson@...
home educating Cole, 13; Shelby, 9; and Connor, 7
"When I was younger, I could remember anything, whether it had happened or
not."
- Mark Twain
[Non-text portions of this message have been removed]
Shyrley
On 4 Nov 02, at 10:33, Dean and Rhonda Johnson wrote:
my opinion if that is what the child or young person wants.
If your son wants to learn algebra, then workbooks can help.
In my opinion, unschooling is 'child-led' and sometimes children
lead us to textbooks.
Shyrley
"You laugh at me because I'm different. I laugh at you because you are all the same."
> Dear Unschoolers,Unschooling doesn't preclude the use of workbooks and courses in
>
> At this point we are pretty relaxed but I know we are definitely not
> unschooling. As the daughter of a former public school teacher I think
> I have more than the normal amount of hang ups. <grin>
>
> All my kids seem to learn math computation easily from life but I am
> having trouble understanding how they are going to learn algebra and
> other higher math concepts. My oldest is interested in several career
> paths that would require learning advanced math thoroughly.
>
> He has requested an algebra course. Is there a better way to do this?
>
> What are unschooling thoughts on this?
>
> Thanks!
>
> Rhonda
my opinion if that is what the child or young person wants.
If your son wants to learn algebra, then workbooks can help.
In my opinion, unschooling is 'child-led' and sometimes children
lead us to textbooks.
Shyrley
"You laugh at me because I'm different. I laugh at you because you are all the same."
[email protected]
In a message dated 11/4/02 9:35:41 AM, rjohnson@... writes:
<< All my kids seem to learn math computation easily from life but I am
having
trouble understanding how they are going to learn algebra and other higher
math concepts. >>
"Learning algebra" in school is learning how to maniplulate already-set-up
"equations" and to do the computations to complete what someone else already
started.
My kids "do algebra" in their heads. They wouldn't know what it looked like
on paper. Many people who did well in math, made A's in finishing problems,
wouldn't know what it was really good for, because that question wasn't on
the test.
When someone who understands algebra is shown the notation for doing more
difficult forms, they might actually have a chance to understand it, instead
of just following directions to get the solution.
I know I just used this analogy the other day, but algebra is taught in the
same way it would be to teach musical notation to someone who neither sang
nor made music, nor had really heard music.
My husband's a math guy and once wrote some stuff I'll look for.
Sandra
<< All my kids seem to learn math computation easily from life but I am
having
trouble understanding how they are going to learn algebra and other higher
math concepts. >>
"Learning algebra" in school is learning how to maniplulate already-set-up
"equations" and to do the computations to complete what someone else already
started.
My kids "do algebra" in their heads. They wouldn't know what it looked like
on paper. Many people who did well in math, made A's in finishing problems,
wouldn't know what it was really good for, because that question wasn't on
the test.
When someone who understands algebra is shown the notation for doing more
difficult forms, they might actually have a chance to understand it, instead
of just following directions to get the solution.
I know I just used this analogy the other day, but algebra is taught in the
same way it would be to teach musical notation to someone who neither sang
nor made music, nor had really heard music.
My husband's a math guy and once wrote some stuff I'll look for.
Sandra
[email protected]
The following was written last November and was originally private mail
between my husband and someone on this list.
============================
Math is a highly structured abstract modeling tool and requires a strong
sense of discipline, but ...
A true math student must possess a strong passion for discovery in a realm
which has little direct connection to the world of our five senses. My
experience says that the passion will grow in children if they are shown the
myriad of modeling applications in their everyday world (physics, chemistry,
finance, sports, arts, etc). All growth takes time and gentle nurturing.
Unschooling is about educating the parents as much as educating the
children.
Keith Dodd
(husband to Sandra)
------the other parent:=======
Keith, I really appreciate you writing this. Sandra wrote me a few weeks
ago, telling me something you'd said about math that really helped her, and
it helped me too, at least as far as beginning to tell the difference
between real math and computation. But I'm sort of stuck here. I really
don't know how to show my son these applications. You're surely right that
the parents need educating as much as anyone. Not just my husband and his
wishes for structured math, but me and how do I show math around us and how
it applies? I would love for there to be that passion for discovery that you
write about. Much education needed here....
==========Keith:========
I don't know the ages of your children (or yourself or your husband :) but
it doesn't really matter. Think of your everyday actions, then look at how
they can be represented with math. Scaling of cooking ingredients (ratios),
boiling water (physics or chemistry), bouncing a ball (physics), watching
the moon circle the earth (geometry), (as in why does a ball fall to earth
but the moon does not?). Find art with a protractor, compass, straight
edge, (like the Greeks) or just play with graph paper (geometry & trig).
Look for symetry in nature or man made artifacts (ratios again). Look for
applications of fractions (ratios, division, combinatorics). Talk about the
lottery or statistics in elections or sports.
Algebra and calculus are abstractions to be delved into once you see the
need for modeling in the first place. Interest in "the need" I find to be
hinged on a budding interest in some tangible format. Do they like
architecture or engineering (mud pies to model planes)? How about
competitive puzzles (board games, cards, video games)? My son (12) just
finished reassembling a TV. (The picture was cutting out.) He now knows
that the insides are not some kind of magic. We talked a little about
circuits and assembly and troubleshooting. In the process of finding the
broken circuit, we talked about TV signals and waveforms and how both audio
and video came from the same antenna. I didn't try to go into the math of
electronics (really complicated modeling), but he now is a little more
interested in just how that stuff works. It took him 3 days of putzing
around with it, (and a $20 part) and mostly all I did was encourage him to
be careful and take small steps.
I think the greatest thing I have learned from homeschooling, it the fact
that it is ok to say, "I don't know, let's find out." The other side of
that is being able to judge when the child is bored with the subject and you
can let it slide.
=====from the other parent=====
[Child in question] is almost 11, and can manage basic arithmetic computation
(all those
enforced math lessons). Lately he seems to be enjoying fractions, and in the
way you're speaking of. He thinks in fractions a lot of the time: I've
finished making one fifth of my bed, I've read 3/12 of this book's chapters
or 1/ 4 of them. That kind of thing. He seems to be enjoying that and it's
not something I coached him in, he just started figuring them out. So doing
ratios like you mentioned, with cooking, would be a natural to him. I bet
he'd enjoy that. And symetry too. He loved that Donald Duck in Mathemagic
Land video, with its golden rectangles. He thought that was really cool how
the same proportions came up over and over. And lotteries we talked about
the other day. We went over how they worked and did do some math during the
discussion. All the rest of your ideas are things I hadn't touched on, ever,
so that gives me a lot of ideas. What are combinatorics????
=============Keith again=========
Combinatorics:
Consider a lottery drawing of 3 balls from 3 separate pots of 10 balls each.
The odds of picking a specific combination of numbers is:
1/10 * 1/10 * 1/10 = 1/1000 or one in one thousand combinations.
Now consider drawing the 3 balls from a single pot.
1/10 * 1/9 * 1/8 = 1/720 or one in seven hundred twenty combinations.
Combinatorics is the study of ratios.
Computer Programming:
This is more like logic than math, but the same principals apply. My
recommendation would be to buy your son a simple programming environment
(like Visual Basic or even better Microsoft Access) and a couple beginner
books on programming. Even so, it will require a rigorous effort because of
how 'dry' the materiel really is. The artistry of programming is in
conceptualizing just what it is you want to accomplish.
Glad you enjoyed this
Keith
between my husband and someone on this list.
============================
Math is a highly structured abstract modeling tool and requires a strong
sense of discipline, but ...
A true math student must possess a strong passion for discovery in a realm
which has little direct connection to the world of our five senses. My
experience says that the passion will grow in children if they are shown the
myriad of modeling applications in their everyday world (physics, chemistry,
finance, sports, arts, etc). All growth takes time and gentle nurturing.
Unschooling is about educating the parents as much as educating the
children.
Keith Dodd
(husband to Sandra)
------the other parent:=======
Keith, I really appreciate you writing this. Sandra wrote me a few weeks
ago, telling me something you'd said about math that really helped her, and
it helped me too, at least as far as beginning to tell the difference
between real math and computation. But I'm sort of stuck here. I really
don't know how to show my son these applications. You're surely right that
the parents need educating as much as anyone. Not just my husband and his
wishes for structured math, but me and how do I show math around us and how
it applies? I would love for there to be that passion for discovery that you
write about. Much education needed here....
==========Keith:========
I don't know the ages of your children (or yourself or your husband :) but
it doesn't really matter. Think of your everyday actions, then look at how
they can be represented with math. Scaling of cooking ingredients (ratios),
boiling water (physics or chemistry), bouncing a ball (physics), watching
the moon circle the earth (geometry), (as in why does a ball fall to earth
but the moon does not?). Find art with a protractor, compass, straight
edge, (like the Greeks) or just play with graph paper (geometry & trig).
Look for symetry in nature or man made artifacts (ratios again). Look for
applications of fractions (ratios, division, combinatorics). Talk about the
lottery or statistics in elections or sports.
Algebra and calculus are abstractions to be delved into once you see the
need for modeling in the first place. Interest in "the need" I find to be
hinged on a budding interest in some tangible format. Do they like
architecture or engineering (mud pies to model planes)? How about
competitive puzzles (board games, cards, video games)? My son (12) just
finished reassembling a TV. (The picture was cutting out.) He now knows
that the insides are not some kind of magic. We talked a little about
circuits and assembly and troubleshooting. In the process of finding the
broken circuit, we talked about TV signals and waveforms and how both audio
and video came from the same antenna. I didn't try to go into the math of
electronics (really complicated modeling), but he now is a little more
interested in just how that stuff works. It took him 3 days of putzing
around with it, (and a $20 part) and mostly all I did was encourage him to
be careful and take small steps.
I think the greatest thing I have learned from homeschooling, it the fact
that it is ok to say, "I don't know, let's find out." The other side of
that is being able to judge when the child is bored with the subject and you
can let it slide.
=====from the other parent=====
[Child in question] is almost 11, and can manage basic arithmetic computation
(all those
enforced math lessons). Lately he seems to be enjoying fractions, and in the
way you're speaking of. He thinks in fractions a lot of the time: I've
finished making one fifth of my bed, I've read 3/12 of this book's chapters
or 1/ 4 of them. That kind of thing. He seems to be enjoying that and it's
not something I coached him in, he just started figuring them out. So doing
ratios like you mentioned, with cooking, would be a natural to him. I bet
he'd enjoy that. And symetry too. He loved that Donald Duck in Mathemagic
Land video, with its golden rectangles. He thought that was really cool how
the same proportions came up over and over. And lotteries we talked about
the other day. We went over how they worked and did do some math during the
discussion. All the rest of your ideas are things I hadn't touched on, ever,
so that gives me a lot of ideas. What are combinatorics????
=============Keith again=========
Combinatorics:
Consider a lottery drawing of 3 balls from 3 separate pots of 10 balls each.
The odds of picking a specific combination of numbers is:
1/10 * 1/10 * 1/10 = 1/1000 or one in one thousand combinations.
Now consider drawing the 3 balls from a single pot.
1/10 * 1/9 * 1/8 = 1/720 or one in seven hundred twenty combinations.
Combinatorics is the study of ratios.
Computer Programming:
This is more like logic than math, but the same principals apply. My
recommendation would be to buy your son a simple programming environment
(like Visual Basic or even better Microsoft Access) and a couple beginner
books on programming. Even so, it will require a rigorous effort because of
how 'dry' the materiel really is. The artistry of programming is in
conceptualizing just what it is you want to accomplish.
Glad you enjoyed this
Keith
Ingrid Bauer/Jean-Claude Catry
> He has requested an algebra course. Is there a better way to do this?That depends. Is he also asking for a different way than a course or would a course meet his needs right now?
You might want to check into Harold Jacob's text called simply "Algebra" I think (he also wrote Mathematics:a human endeavor). These were texts originally written for college students which I discovered through John Holt's recommendation many years ago in the GWS catalogues. Both my son and I really enjoyed them--he has a way of explaining math that relates to life and is not dry, and doesn't assume you're an idiot who needs busywork. My son was about 11-13yo at the time--we didn't do all the exercises in order, we really love math, though I'm definitely not very experienced in higher math. The books are thick and expensive--might be available used (and if I can find them again, I might consider selling mine.)
Hope that helps,
ingrid
[Non-text portions of this message have been removed]
Karin
"Dean and Rhonda Johnson" <rjohnson@...> wrote:
Hi Rhonda and Welcome.
If my son was interested in algebra, I would find books, games, computer
programs and anything else related to alegebra to introduce him to the
subject, as well as trying to learn about it myself as much as I could.
If he was still interested after going through the various things we had
already looked at and I could no longer meet his needs to help him learn
algebra, I would find a class for him, or a friend or tutor to help him more
personally.
Those are my unschooling thoughts. :-)
Karin
>\
> He has requested an algebra course. Is there a better way to do this?
>
> What are unschooling thoughts on this?
>
> Thanks!
>
> Rhonda
Hi Rhonda and Welcome.
If my son was interested in algebra, I would find books, games, computer
programs and anything else related to alegebra to introduce him to the
subject, as well as trying to learn about it myself as much as I could.
If he was still interested after going through the various things we had
already looked at and I could no longer meet his needs to help him learn
algebra, I would find a class for him, or a friend or tutor to help him more
personally.
Those are my unschooling thoughts. :-)
Karin
[email protected]
In a message dated 11/4/02 11:48:59 AM Central Standard Time,
SandraDodd@... writes:
~Nancy
[Non-text portions of this message have been removed]
SandraDodd@... writes:
> Unschooling is about educating the parents as much as educating theWhere did you find him Sandra?
>
> children.
>
>
> Keith Dodd
>
> (husband to Sandra)
~Nancy
[Non-text portions of this message have been removed]
[email protected]
In a message dated 11/4/02 11:41:57 AM, Dnowens@... writes:
<< Where did you find him Sandra? >>
A madrigal group.
And one of the best costume references I ever came upon was in a cookbook, in
an illustration of the serving of a feast, which showed backs of the servers.
And in a book of hours, I found a picture of baby Jesus in a little walker--a
wooden frame with wheels, 16th century or 15th.
That's how unschooling works. You don't go looking in an algebra book for
algebra. You let a rich life wash over you and everything comes by over and
over.
Sandra
<< Where did you find him Sandra? >>
A madrigal group.
And one of the best costume references I ever came upon was in a cookbook, in
an illustration of the serving of a feast, which showed backs of the servers.
And in a book of hours, I found a picture of baby Jesus in a little walker--a
wooden frame with wheels, 16th century or 15th.
That's how unschooling works. You don't go looking in an algebra book for
algebra. You let a rich life wash over you and everything comes by over and
over.
Sandra
[email protected]
This whole thread is really hitting close to home. I remember, long after
my college algebra and trigonometry classes were over, having an "a-ha"
moment when I realized *why* all those formulas really worked, with "sin2
+ cos2=1" being one of those that never really made sense to me, until I
had time to sit and play with it, and figure it out. Same for all those
other trig identities. I memorized them, and used them when I managed to
remember them, which, unfortunately, wasn't often enough.
Kevin
[Non-text portions of this message have been removed]
my college algebra and trigonometry classes were over, having an "a-ha"
moment when I realized *why* all those formulas really worked, with "sin2
+ cos2=1" being one of those that never really made sense to me, until I
had time to sit and play with it, and figure it out. Same for all those
other trig identities. I memorized them, and used them when I managed to
remember them, which, unfortunately, wasn't often enough.
Kevin
[Non-text portions of this message have been removed]
[email protected]
In a message dated 11/4/02 11:32:03 AM Central Standard Time,
SandraDodd@... writes:
strange pain killer sleep, so I watched it. Cosby had a whole thing about
his geometry teacher and said that he could add, subtract, multiply, divide
and go anything with "If a man..." He LOVED "if a man," (yikes, I hated word
problems) but once he got to geometry he refused to open the book and ended
up reproving all the them. The skit was really funny - Cosby refused to
memorize because the book was too heavy and he didn't want to take it home,
which was meant for play and not homework.
I guess my point is to agree with the above point and use Bill Cosby to do
it. I was a pro at differentiating equations, by the way, but can't remember
and am sure I never knew why I was differentiating them!
Elizabeth (who refused to take any math or science in college because of a
profound disinterest - thankfully Oberlin didn't have required courses)
SandraDodd@... writes:
> Many people who did well in math, made A's in finishing problems,Our PBS station just ran a Bill Cosby thing last night. I'm still having
> wouldn't know what it was really good for, because that question wasn't on
> the test.
strange pain killer sleep, so I watched it. Cosby had a whole thing about
his geometry teacher and said that he could add, subtract, multiply, divide
and go anything with "If a man..." He LOVED "if a man," (yikes, I hated word
problems) but once he got to geometry he refused to open the book and ended
up reproving all the them. The skit was really funny - Cosby refused to
memorize because the book was too heavy and he didn't want to take it home,
which was meant for play and not homework.
I guess my point is to agree with the above point and use Bill Cosby to do
it. I was a pro at differentiating equations, by the way, but can't remember
and am sure I never knew why I was differentiating them!
Elizabeth (who refused to take any math or science in college because of a
profound disinterest - thankfully Oberlin didn't have required courses)