Keith Dodd on math and unschooling
[email protected]
<< Sandra, when I read your response, I realized that I hadn't been clear in
my post (well, I didn't "realize" that, I knew it all along). I was listing
the ways I've heard math described
rather than saying that "music is a tool". >>
I know. It was rhetorical exploration of the idea, not argument with a
particular statement.
Keith found and sent me the rest of his exchange (I'm sending only his end,
because I had his permission):
From here down the first-person pronouns are Keith Dodd:
-----------------------------------------------------------------------------
This is from my archives.
-------------- my response 11/2 ---------------
Sandra sent me your note.
<< ... and my husband still won't loosen the structured math reins ... >>
Math is a highly structured abstract modeling tool and requires a strong
sense of discipline, but ...
A true math student must possess a strong passion for discovery in a realm
which has little direct connection to the world of our five senses. My
experience says that the passion will grow in children if they are shown the
myriad of modeling applications in their everyday world (physics, chemistry,
finance, sports, arts, etc). All growth takes time and gentle nurturing.
Unschooling is about educating the parents as much as educating the
children.
Keith Dodd
(husband to Sandra)
-------------- my response 11/5 -----------------
I don't know the ages of your children (or yourself or your husband :) but
it doesn't really matter. Think of your everyday actions, then look at how
they can be represented with math. Scaling of cooking ingredients (ratios),
boiling water (physics or chemistry), bouncing a ball (physics), watching
the moon circle the earth (geometry), (as in why does a ball fall to earth
but the moon does not?). Find art with a protractor, compass, straight
edge, (like the Greeks) or just play with graph paper (geometry & trig).
Look for symetry in nature or man made artifacts (ratios again). Look for
applications of fractions (ratios, division, combinatorics). Talk about the
lottery or statistics in elections or sports.
Algebra and calculus are abstractions to be delved into once you see the
need for modeling in the first place. Interest in "the need" I find to be
hinged on a budding interest in some tangible format. Do they like
architecture or engineering (mud pies to model planes)? How about
competitive puzzles (board games, cards, video games)? My son (12) just
finished reassembling a TV. (The picture was cutting out.) He now knows
that the insides are not some kind of magic. We talked a little about
circuits and assembly and troubleshooting. In the process of finding the
broken circuit, we talked about TV signals and waveforms and how both audio
and video came from the same antenna. I didn't try to go into the math of
electronics (really complicated modeling), but he now is a little more
interested in just how that stuff works. It took him 3 days of putzing
around with it, (and a $20 part) and mostly all I did was encourage him to
be careful and take small steps.
I think the greatest thing I have learned from homeschooling, it the fact
that it is ok to say, "I don't know, let's find out." The other side of
that is being able to judge when the child is bored with the subject and you
can let it slide.
Good luck,
Keith
------------- and I answered 11/6 --------------------------
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
my post (well, I didn't "realize" that, I knew it all along). I was listing
the ways I've heard math described
rather than saying that "music is a tool". >>
I know. It was rhetorical exploration of the idea, not argument with a
particular statement.
Keith found and sent me the rest of his exchange (I'm sending only his end,
because I had his permission):
From here down the first-person pronouns are Keith Dodd:
-----------------------------------------------------------------------------
This is from my archives.
-------------- my response 11/2 ---------------
Sandra sent me your note.
<< ... and my husband still won't loosen the structured math reins ... >>
Math is a highly structured abstract modeling tool and requires a strong
sense of discipline, but ...
A true math student must possess a strong passion for discovery in a realm
which has little direct connection to the world of our five senses. My
experience says that the passion will grow in children if they are shown the
myriad of modeling applications in their everyday world (physics, chemistry,
finance, sports, arts, etc). All growth takes time and gentle nurturing.
Unschooling is about educating the parents as much as educating the
children.
Keith Dodd
(husband to Sandra)
-------------- my response 11/5 -----------------
I don't know the ages of your children (or yourself or your husband :) but
it doesn't really matter. Think of your everyday actions, then look at how
they can be represented with math. Scaling of cooking ingredients (ratios),
boiling water (physics or chemistry), bouncing a ball (physics), watching
the moon circle the earth (geometry), (as in why does a ball fall to earth
but the moon does not?). Find art with a protractor, compass, straight
edge, (like the Greeks) or just play with graph paper (geometry & trig).
Look for symetry in nature or man made artifacts (ratios again). Look for
applications of fractions (ratios, division, combinatorics). Talk about the
lottery or statistics in elections or sports.
Algebra and calculus are abstractions to be delved into once you see the
need for modeling in the first place. Interest in "the need" I find to be
hinged on a budding interest in some tangible format. Do they like
architecture or engineering (mud pies to model planes)? How about
competitive puzzles (board games, cards, video games)? My son (12) just
finished reassembling a TV. (The picture was cutting out.) He now knows
that the insides are not some kind of magic. We talked a little about
circuits and assembly and troubleshooting. In the process of finding the
broken circuit, we talked about TV signals and waveforms and how both audio
and video came from the same antenna. I didn't try to go into the math of
electronics (really complicated modeling), but he now is a little more
interested in just how that stuff works. It took him 3 days of putzing
around with it, (and a $20 part) and mostly all I did was encourage him to
be careful and take small steps.
I think the greatest thing I have learned from homeschooling, it the fact
that it is ok to say, "I don't know, let's find out." The other side of
that is being able to judge when the child is bored with the subject and you
can let it slide.
Good luck,
Keith
------------- and I answered 11/6 --------------------------
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
Elizabeth Hill
SandraDodd@... wrote:
take a couple steps down stage, face the footlights, and launch a
soliloquy. Part of what makes the list fun!
Betsy
[Non-text portions of this message have been removed]
>Yeah... many of us will pick up a cue from someone else's post and then
>
> I know. It was rhetorical exploration of the idea, not argument with
> a
> particular statement.
take a couple steps down stage, face the footlights, and launch a
soliloquy. Part of what makes the list fun!
Betsy
[Non-text portions of this message have been removed]
[email protected]
In a message dated 12/2/01 12:22:32 PM Mountain Standard Time,
ecsamhill@... writes:
In keeping with the musical theme of my recent posts, it's also like a big
music jam, and one introduced theme can lead to a little spate of solos.
We're creating a "wall of sound" of unschooling ideas.
Sandra
[Non-text portions of this message have been removed]
ecsamhill@... writes:
> Yeah... many of us will pick up a cue from someone else's post and thenGood analogy.
> take a couple steps down stage, face the footlights, and launch a
> soliloquy. Part of what makes the list fun!
>
In keeping with the musical theme of my recent posts, it's also like a big
music jam, and one introduced theme can lead to a little spate of solos.
We're creating a "wall of sound" of unschooling ideas.
Sandra
[Non-text portions of this message have been removed]