Keith Green

Does anyone have advice on how to learn advanced math topics outside of school? I know with earlier math it's usually not too hard to figure stuff out on your own. But what about the kind of stuff that would normally be taught to seniors at university? That's harder to pick up, especially if the parents don't know it and don't have friends who know it.

Would you get a standard school book and do a bunch of the exercises, or would you take a different approach?

There are math lectures online, but they generally are created at schools, and have a school style to them. Would you say it's good to use those, or is there a better way that's more different than school?

Joyce Fetteroll

On Dec 23, 2009, at 2:49 AM, Keith Green wrote:

> But what about the kind of stuff that would normally be taught to
> seniors at university? That's harder to pick up

It's effortless for a child to learn English when English is spoken
at home. It's much harder for someone to learn English when no one
around them is speaking it.

Math is the same. Addition, multiplication, percentages, and so on
get used in everyday life so they get absorbed the same as a native
language.

Higher math is harder to pick up unless you're doing something that
uses it. If you're are, then an understanding gets absorbed because
it's describing something physical you're working with.

What do you want to use math for? Is it for you or are you asking for
someone else? If you're worried about how someone else will acquire
higher math then the answer is different.

> Would you get a standard school book and do a bunch of the
> exercises, or would you take a different approach?
>

Depends on someone's learning style.

Everything and anything that someone finds helpful is fair game for
learning. Unschoolers come across as anti-anything that's found in
school, but that impression comes from helping people turn away from
school and face the real world. Until someone lets go of their
dependence on textbooks, textbooks are a crutch.

Once someone trusts that learning is what we do naturally by living
life, then textbooks are just another resource that some people might
find useful.

> There are math lectures online, but they generally are created at
> schools, and have a school style to them. Would you say it's good
> to use those, or is there a better way that's more different than
> school?
>

Again, depends on someone's style.

Textbooks and lectures are a fairly efficient way to absorb a chunk
of knowledge *if* someone wants that knowledge. The problem is that
quiet often, especially with math, the knowledge is divorced from
use. Math is taken out of context. The purpose of math is to describe
the world. One of math's purposes is to allow people to manipulate a
model of the world so they don't have to, for instance, go shifting a
planet around the solar system to see what effect that has on the
rest of them ;-)

Without the world, math is esoteric and much harder to learn. Unless
someone's love is math! :-) Some people love grammar. Some people
love timelines. Playing with those in isolation may give someone a
structure to hang information on but imploding buildings, English
language and political leaders sending out their troops to suppress
and insurgency are all dynamic entities. Beginning with the rigid
structure will hamper someone's understanding of the real world.

In college I learned how to manipulate nice tidy equations to get an
answer. I had no deep understanding of what the equations could
describe, or why I might want the answer, but I could make the
equations perform for me. The problem is that the real world isn't
neat and tidy. Real world equations can be messy. Unless you have a
good understanding of the real world object the equation is
describing, the equation is just confusing.

So, what do you want to use the math for? If you're fascinated by
math, then any resource: books, DVDs, manipulatives, museum displays,
math geeks that helps you understand is good. In fact using a variety
of resources is better since understanding rarely happens from a
single explanation. (That's why it's so notable when those flashes of
insight happen!) Real learning comes from encountering the same idea
several times in different contexts. Our understanding builds slowly.

If, on the other hand, your goal is astronomy or rocket science,
better to delve into those and learn just enough math as you need it
to get by.

In either case, go to Amazon and your library and Barnes and Noble
and start browsing for things that capture your interest. Two pieces
of damage that schools do is in making people believe 1) that it must
be dry and difficult or it's not good and 2) that if someone doesn't
understand then it's their fault. Not true. You need resources that
match your styles of learning and your interests.

Standard Deviants are good:
http://www.standarddeviants.com/

The Teaching Company is good:
http://www.teach12.com/

If you're not easily offended, even Bikini Calculus looks like an
amusing introduction ;-) (I learned the difference between integral
and differential calculus in less than 5 minutes!)
http://www.howtodogirls.com/episodes/s1e1_intro_to_bikini_calculus.php
(There's a 50 minute DVD at Amazon http://tinyurl.com/y9cdbza)
There's a script beneath the video. One thing you will learn is that
if you want to say differential calculus you shouldn't have a tongue
stud.)

MIT has courses online, available through "iTunes U".
http://ocw.mit.edu/OcwWeb/web/home/home/index.htm

Don't shy away from "dumbed down" books like the Demystified series
and the Manga guides and How To Ace Calculus and so on. They're good
at hand holding and going slow.

If you want a text book, I remember Harold Jacobs had some very good
ones for high school math.
http://tinyurl.com/ylapnwq

Joyce







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Sandra Dodd

-=-But what about the kind of stuff that would normally be taught to
seniors at university? That's harder to pick up, especially if the
parents don't know it and don't have friends who know it.-=-

Why would someone who's not a senior at university need to know that
kind of math?

Sandra

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Keith Green

On Dec 26, 2009, at 6:53 AM, Sandra Dodd wrote:

> -=-But what about the kind of stuff that would normally be taught to
> seniors at university? That's harder to pick up, especially if the
> parents don't know it and don't have friends who know it.-=-
>
> Why would someone who's not a senior at university need to know that
> kind of math?

Math is fun and useful. It can be used to solve various problems. It is also a prerequisite for some careers.

Sandra Dodd

-=-Math is fun and useful. It can be used to solve various problems.
It is also a prerequisite for some careers.-=-

Fun and useful math can be learned as a person goes. Math that is so
esoteric that it's only taught to seniors at universities will
probably be learned at the university where the person is fulfilling
the other prerequisites for his chosen career, though.




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Keith Green

On Dec 26, 2009, at 8:58 AM, Sandra Dodd wrote:

> -=-Math is fun and useful. It can be used to solve various problems.
> It is also a prerequisite for some careers.-=-
>
> Fun and useful math can be learned as a person goes. Math that is so
> esoteric that it's only taught to seniors at universities will
> probably be learned at the university where the person is fulfilling
> the other prerequisites for his chosen career, though.

Do unschoolers advocate that people attend university? What makes it fundamentally different than school? I don't see a lot of difference between them.

Sandra Dodd

-=-Do unschoolers advocate that people attend university? -=-

There is no governing body of unschoolers, and so no one can say what
unschoolers as a group advocate. I can tell you what I think.
I think that anyone who wants to go to college or university should be
assisted to go, and anyone who doesn't want to go shouldn't be
pressured to go.


-=-What makes it fundamentally different than school? -=-

In light of homeschooling, the difference has to do with laws
concerning compulsory attendance. If a child doesn't want to go to
school and the law says he must, the his parents will need to jolly
him up or find an alternative. Homeschooling is an alternative.
Unschooling is a way to handle the situation once homeschooling is
chosen.

-=-I don't see a lot of difference between them.-=-

University isn't required by the law. By the time someone is old
enough to want to go to college and take those math courses only
seniors take, he's probably old enough to do that and maybe old enough
to pay for it or to sign for a loan. Very different from the options
a seven-year-old has.

Just because my children were all unschooled doesn't mean I can give
them a college degree. There comes a point when one's children are
18, 20 and 21 (well, in my case anyway, and that point is now) and
homeschooling doesn't apply to their present situations at all, except
when they're filling out job applications. On a line about whether
they graduated from high school, they write "homeschooled." Where it
asks if they have a bachelor's or master's degree, "homeschooled"
isn't an option.

Sandra

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Joyce Fetteroll

On Dec 26, 2009, at 12:26 PM, Keith Green wrote:

> Do unschoolers advocate that people attend university? What makes
> it fundamentally different than school? I don't see a lot of
> difference between them.

The essence of unschooling is creating an environment where kids can
explore their interests freely and learn naturally. How kids explore
depends on how they enjoy learning so no particular approach is
advocated.

While the format of school and college are very similar, the *huge*
difference is choice. Kids can choose whether or not to go to
college, where they go, whether or not to stay, how they spend their
time. They can also choose their major based on their interests and
strengths, and depending on the college, have greater freedom in what
courses to take.
> Math is fun and useful. It can be used to solve various problems.
>

Which is why kids pick math up by using it! ;-)

> It is also a prerequisite for some careers.


So you weren't asking for yourself?

For natural learning it's far better to help kids feed their passions
and explorations. That way they want to pull more in and are
motivated to plow through something difficult when *they* see a use
for it. Trying to pour in some knowledge someone believes they'll
need for the future is a good way to dampen passion for an interest.

As for college *senior* year math, geez, I think I gave up on math in
my junior year of college. ;-) Partial differential equations and
finite math (maybe it was) had me flummoxed and I can't imagine
anyone needing that kind of math and beyond unless they're pursuing a
field of study at a university. It's pretty esoteric stuff.

Joyce

Alan Marshall

***Math is fun and useful. It can be used to solve various problems. It is also a prerequisite for some careers.***

I could say that about what I think is fun and useful for me:

"Opera singing is fun and useful. It can be used to solve various problems (it really can, by the way). It is also a prerequisite for some careers."

It would be ridiculous for me to start telling anyone of any age that they should learn to sing opera like a college senior voice major. Only those who are passionately interested in opera singing have any reason to do that. I think it is just as ridiculous to expect anyone to learn about math in that way, and for the very same reasons.

Alan




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Hotmail: Free, trusted and rich email service.
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Keith Green

Hi all,

Alan,

Just to clarify, my question was about how to learn advanced math, if one wants to. I wasn't telling anyone that they should learn math and I have nothing against opera.

Sandra and Joyce,

I agree that choice and freedom are very important. Making school compulsory isn't just cruel to the people it makes unhappy, it also makes the school worse at teaching for a variety of reasons. It means there are unhappy or uninterested people around who are distracting. It means the teachers do not find ways to attract students with interesting and fun lessons. And it results in a self-selected group of teachers: the teachers are going to be people who, for whatever reason, don't mind that school is compulsory. These are significant disadvantages compared to a university.


I also take your point that learning things the parents have enough knowledge to teach, and learning things beyond the parents' expertise, are different situations.


I agree that kids, or anyone, can pick up math, or any other knowledge, without a formal curriculum. Learning can be done in a natural or apparently automatic way, and such learning is not inferior. Learning can also be done in a more guided way (the lead guide, with the final say in all decisions, should always be the learner himself).


One thing that no one mentioned is some of the reasons schools are bad places which universities share. For example, schools have grades and tests, and so do universities. Grades and tests are well known to be unpleasant and stressful, and well known to be unwanted by most students. They are, for most people most of the time, bad thing. And they aren't too surprising to find at a compulsory place that doesn't care what the students want. But why are they are universities too? And they aren't optional at universities, they are forced on everyone. Why doesn't the university take care to provide only what its students want, and only things that don't hurt anyone? Why didn't they at least make the grades and test optional, or find some alternative choices to offer people who don't like them? There is something wrong with universities too.


If one makes the choice not to attend a university, for various reasons such as not wanting to be graded and other issues, they may still want to learn some of the things which universities teach. There are a wide variety of options open to them. They are not in a bad situation. There are many ways to learn it which would work out great! But there are also ways to try to learn it that would not work out. Some options are good, some not so good, and one has to figure it out. That takes some thought, and perhaps some advice.

It's difficult to ask most people for advice about a situation like that because their view of education revolves around formal schooling. The only option they know is formal schooling. They've never thought about alternatives much. So they don't have a lot of help to offer. That's why I thought this list might be a good place to discuss it. There may be people here who are familiar with options besides school, and can pass on some of their hard-won wisdom. Or there may be people currently interested in similar issues. Or there may, at least, be people sympathetic to the idea of not attending school, and open minded to discussion of what that may entail.

Robyn L. Coburn

<<<< > It's difficult to ask most people for advice about a situation like
that because their view of education revolves around formal schooling. The
only option they know is formal schooling. They've never thought about
alternatives much. So they don't have a lot of help to offer. That's why I
thought this list might be a good place to discuss it. >>>>

I'm a little confused about what you want to discuss Keith.

You don't have to convince us that school testing is generally bad for kids.
However you do talk about parents teaching within their own expertise which
betrays some misunderstanding of how unschooling works.

This is a good place to discuss the practices, thought process and
principles that help parents to unschool their kids.

Are you wanting to learn some higher math yourself without going to
university to do it and want some ideas or resource recommendations to
accomplish that?

Are you asking on behalf of your kids? If so how old are they and how long
have you been unschooling? Are you making predictions about the future?

You might think these are odd questions, but sometimes people new to
unschooling come here all worried about stuff and asking "How do they learn
calculus?" type questions, with a lot of fear behind them, and their kids
turn out to be 3 years old. The best answer in that type of case is "live in
the moment with your child, play with them, and work on your own
deschooling" - which means purging the school think and shadow schooly
assumptions from your mind.

It is a lot easier to offer advice about real and immediate problems, rather
than hypotheticals, because the answers differ depending on why you want to
know. *Why* is a huge question in unschooling. Why is a question we ask
ourselves a lot.

Keith, it seems like you are already aware of many of the negatives of
school. For me, I avoid and limit my involvement in other people's school
conversations. I found that school conversations sucked me into a negative
mental space - we all know that schools have a lot of problems and
facilitate some pretty awful situations for kids. The only advice I have for
any of my friends who are distressed by their kids' school experiences and
determined to rehash the problems endlessly, is to say that they do have
other choices, of which I am living proof. Unfortunately that answer is not
what most others want to hear. They are more interested in either
commisseration, or strategies to tweak the system as much as is possible, or
strategies to manipulate their kids into compliance and the appearance of
greater happiness. I have little to add to any of those agendas.

When I first went to college directly from school, I was in the wrong place.
Although there were parts of my classes that I truly enjoyed, much of it was
just flat too difficult (including Higher Math) and not relevant to how I
wished to earn my living. When I returned to college some years later to
follow my passion for Theater, it was a much better experience. The
assessment system had few examinations involved, and those were all in the
Freshman year. Later years included mostly project based grading with
similar criteria as one would find in the professional world of Theater, and
some essays for the theory portions. It is possible to find University
studies that do not include exams.

However I think the experience of most unschoolers as they grow up and
participate in various kinds of classes and formal learning opportunities,
is that they are able to assess fairly quickly whether the hoops are worth
it to them. They tend to be willing to put up with the rules, assignments,
tests and grades as just a small part of the price of admission of exploring
this new fun park.

An overweaning desire or intention to avoid grading or tests at all costs,
especially at college level, doesn't sound like the usual thinking or
practice of the grown unschoolers who are attending tertiary education with
great success and enjoyment. It seems a bit like throwing out the baby with
the bathwater.

Perhaps unschoolers are acceptant of tests and grading at college level
*because* they have lived a childhood free of this kind of external
judgment. They haven't been defined and confined by grades all their lives,
so as young adults they don't have any emotional aversion to them .

If being graded or taking tests as an adult is so repugnant to you, Keith,
perhaps that is an area of school damage in your psyche worth winkling out
and exploring for the sake of healing. Personally I would love to develop a
greater sense of self worth released from my concern about how others are
seeing and judging me. I believe I tend to worry about other's opinions
because I had good grades and was a good test taker in school. Letting go of
grades as a measure of my value has been a journey.



Robyn L. Coburn
www.Iggyjingles.etsy.com
www.iggyjingles.blogspot.com
www.allthingsdoll.blogspot.com

Joyce Fetteroll

On Dec 27, 2009, at 1:08 AM, Keith Green wrote:

> Why doesn't the university take care to provide only what its
> students want, and only things that don't hurt anyone?


There are some colleges that don't grade. Many colleges provide
options to take classes for no credit so homework and test scores can
be feedback rather than a refection on the student. MIT offers its
classes online for free so anyone can take them. I believe Harvard's
grades are a mere formality.

But just because college can be a choice, for many it's merely the
next required step after high school. Few are going to college for
personal fulfillment. Most are passing through to get what's promised
at the other end. When the journey itself isn't seen as valuable,
then it's natural for people to find the easiest route. (Whether the
journey colleges offer is actually worth sucking everything from is a
totally different argument and would vary from college to college,
class to class.)

My daughter and I took a comic book writing workshop over the summer
offered for anyone 17 or older. There was no other purpose to be
there other than to suck what one could from it. There were no
carrots at the other end. The journey was it. And people used the
resources and time of that week to travel where they wanted to go.
Obviously there were no grades and people put in a huge amount of
hours outside of the workshop trying to get what they wanted from it

People go to Hampshire College (which uses detailed evaluations
rather than grades) because they want that four years of experience
at Hampshire, not because it's a stepping stone to some vague
American Dream.

At most colleges, most students are there to get a piece of paper at
the end. The colleges who want the piece of paper to mean something
need a way to weed out or at least wake up the sleepers ;-) Grades
for those colleges are pretty much a necessity.

> There are many ways to learn it which would work out great! But
> there are also ways to try to learn it that would not work out.
> Some options are good, some not so good, and one has to figure it
> out. That takes some thought, and perhaps some advice.
>

I would say no one way is universally good or universally bad. What
works great for one might be lousy for another. So the advice for
them would be the same as for unschooled kids: finding what works for
them. If they're unschoolers they already know that classes aren't
the be all and end all of learning. If they're burned out from
school, they probably need time to discover that and own that idea.

> It's difficult to ask most people for advice about a situation like
> that because their view of education revolves around formal
> schooling. ... There may be people here who are familiar with
> options besides school, and can pass on some of their hard-won wisdom.
>

The question is feeling rather strawmanish. Is the question being
asked for a real person with a real need? Or are you just speculating?

Exploring and finding what works for a particular person is the best
advice, but you seem to be wanting more specific advice. Or a big
pile of ideas people could choose from. But who are these people? Do
they actually exist? Or is it you? If it's you, what's your specific
need?

Joyce

Sandra Dodd

-=-It would be ridiculous for me to start telling anyone of any age
that they should learn to sing opera like a college senior voice
major. Only those who are passionately interested in opera singing
have any reason to do that. I think it is just as ridiculous to expect
anyone to learn about math in that way, and for the very same reasons.-
=-

While I think "ridiculous" is too harsh a word to use, I wanted to
throw some other examples on the table.

I *love* the history of English. I don't remember the details of the
great vowel shift, and I lost interest when it comes to the
differences between Jutish and Saxon, or whatever, but when a word has
a story, or a clear origin you can just see by looking, I'm jazzed.

But then other people say if I love it so much why don't I learn other
languages? Some people are sure that bilingualism, trilingualism, is
the condition that leads to clarity of thought and of understanding of
any language, so to them I'm stunted.

For me, I can't imagine the thought processes of anyone who isn't
musical. Music ties everything together for me. When someone
suggests that poetry is dead my head floods full of rock'n'roll lyrics
and I want to defend the living use of rhyme, meter and imagery. That
doesn't mean that I want to "study poetry" and hear what someone's
professor's professor said about some heroin addicted French poet who
died years ago. It means that I think "Until it ends there is no end"
on Cyndi Lauper's "Time After Time" is as beautiful, in its context,
as any line of poetry has ever been. I think "Will I wait a lonely
lifetime?/If you want me to, I will," in the 1960's voice of Paul
McCartney, is plaintiff, perfect, and also evidence of the throes of
biochemical love. I collect things like that. I put them where
people can see them. But higher math eludes me. I married a math
guy, so if one of us needs to whip up a quadratic equation or analyze
some odds or whatever, Keith can do that. When it comes to designing
a specific roll-up bag, or a tent, though, I'm better at that. If
it's simple geometry that can be visualized or done with a ruler, that
(to me) is like harmonizing, or transposing from one key to another.
It's not a big deal. I don't need the numbers, I need the proportions
and the relationships, some chalk and a yardstick. I can figure 45
degree corner-sections plus seam allowance without a formula. I can
figure out how much cloth will be needed for a Viking a-frame, and how
to fasten in ties for the door and loops for stakes that will NOT come
undone. Does everyone need to do that?

Part of civilization, or any team, or any partnership, is knowing who
has what strengths. At work, the people on Keith's engineering teams
know who's good at what. Not every one of them in any group needs to
understand the math or logic or programming or specifications or
interface of every big of each project. They just need to know who
does know.

Sandra

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Sandra Dodd

-=-Just to clarify, my question was about how to learn advanced math,
if one wants to. I wasn't telling anyone that they should learn math
and I have nothing against opera.-=-

That was clear, I think, but the discussion was in response to your
direct questions, asked as they were asked, and the assumptions many
people have about the value of mathematics over and above training
horses or restoring furniture.

-=-I also take your point that learning things the parents have enough
knowledge to teach, and learning things beyond the parents' expertise,
are different situations.-=-

You took that point out of your own head, though, because no one here
said that.

-=-One thing that no one mentioned is some of the reasons schools are
bad places which universities share. For example, schools have grades
and tests, and so do universities. Grades and tests are well known to
be unpleasant and stressful, and well known to be unwanted by most
students. They are, for most people most of the time, bad thing. And
they aren't too surprising to find at a compulsory place that doesn't
care what the students want. But why are they are universities too?
And they aren't optional at universities, they are forced on everyone.
Why doesn't the university take care to provide only what its students
want, and only things that don't hurt anyone? Why didn't they at least
make the grades and test optional, or find some alternative choices to
offer people who don't like them? There is something wrong with
universities too.-=-

There are alternative schools. But this list wasn't created or
maintained for people to discuss why schools are bad places. It's for
the discussion of what a family can do to encourage learning and to
help children grow up whole and strong, so that they won't be hurt by
jobs or universities or joining the circus when they're grown, and so
that they might feel and have real choices about such things, and to
be aware of those choices, and not go to college or join the circus
out of fear or avoidance or escapist reaction to a harsh childhood.

-=-If one makes the choice not to attend a university, for various
reasons such as not wanting to be graded and other issues, they may
still want to learn some of the things which universities teach. There
are a wide variety of options open to them. They are not in a bad
situation-=-

I have three young-adult children who have not gone to college. Kirby
took a couple of classes. Marty intends to. By the time I was
Marty's age I had graduated from college, but I was there from a
combination of fear, escapism, adventure, and the joy of learning.
I needed that because I wanted to be a teacher in the public schools.
Did that, did it quickly, did it young. My husband didn't finish
college until he was 29. No one who knows us now would know that if
we didn't tell them in the course of some discussion about young
adulthood and college and early jobs, or whatever. Kirby has a really
good job. Marty is unemployed and being very picky. (He's been doing
some casual labor for friends and isn't broke, but he's behind on his
jeep payments to his dad.) We're not shaming Marty or suggesting he
be more like his brother. We *know* at a level beyond theory that
people can and do develop at different rates and come to commitments
and decisions in different ways. We know that if any of our kids
decided to pursue formal mathematics with its written and spoken
language that they could do that, and we'd offer support and assistance.

Sandra





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Sandra Dodd

Ah, jeez... I wrote from sounds and not spelling. <G>

is plaintiff PLAINTIVE.... not "plaintiff." Doh!

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Keith Green

On Dec 27, 2009, at 5:15 AM, Sandra Dodd wrote:

> -=-I also take your point that learning things the parents have enough
> knowledge to teach, and learning things beyond the parents' expertise,
> are different situations.-=-
>
> You took that point out of your own head, though, because no one here
> said that.

It was my interpretation of this statement:

"Just because my children were all unschooled doesn't mean I can give them a college degree."

(I took the degree to mean the knowledge behind the degree, rather than a piece of paper.)

Sandra Dodd

"Just because my children were all unschooled doesn't mean I can give
them a college degree."

(I took the degree to mean the knowledge behind the degree, rather
than a piece of paper.)

No, when I say college degree, I really literally mean college
degree. Much of the knowledge I gained in my university studies is
shared here and other places on the internet and with my kids in their
everyday lives. Art history and psychology and child development and
Renaissance music and Chaucer and Shakespeare and anthropology...
those have permeated all my thoughts and actions and have affected my
children's entire lives.

Someone can know all about something, more than some PhD in the field
knows, and still not have a college degree. Nor "a college
education." Seeing knowledge as separate from school, and not as the
opposite of school, either, will help you see everything in the world
and in yourself more clearly.

Sandra

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Pam Sorooshian

On 12/27/2009 10:11 AM, Sandra Dodd wrote:
> Someone can know all about something, more than some PhD in the field
> knows, and still not have a college degree. Nor "a college
> education." Seeing knowledge as separate from school, and not as the
> opposite of school, either, will help you see everything in the world
> and in yourself more clearly.
>
>
This conversation does, yet again, point out the problematic nature of
the term "unschooling," though. When people take it to mean "anti"
schooling, they can get too focused on not schooling rather than
focusing on supporting learning.

-pam

Alan Marshall

***While I think "ridiculous" is too harsh a word to use***



I did not intend to be harsh or even to assert a particularly strong
opinion. I used that word because I think it is easy for most people to
see how pointless it would be to expect someone to learn a highly
specialized skill like opera singing unless they wanted to do exactly
that, even if they were interested in opera or music or other kinds of
singing. It seems like it is less easy for many people to apply the same principle
when it comes to math.



I did not mean to suggest that anyone was currently being ridiculous. I quoted your words when I wrote that, Keith, so I'd like to apologize to you for leaving that impression.



***Just to clarify, my question was about how to learn advanced math, if one wants to. I wasn't telling anyone that they should learn math ***



I know that. The post I responded to, however, spoke specifically about the value of learning math. The crux of the discussion has been the way math is overvalued because it is seen as a core subject that everyone must know, sometimes even by those of us who would never think of forcing someone to learn it. Sometimes unschoolers might be tempted to jump on an interest in math because we are conditioned to think it could lead to a lucrative career or produce impressive credentials.



***and I have nothing against opera.***


I have nothing against math, nor against people who do have something against opera.


I know of people who believe that opera singing is the only kind of singing or music anyone should be interested in. It is what they like and what they do so they believe all singers should do the same. Now that is ridiculous.


Alan





_________________________________________________________________
Hotmail: Powerful Free email with security by Microsoft.
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[Non-text portions of this message have been removed]

Keith Green

On Dec 27, 2009, at 3:56 AM, Robyn L. Coburn wrote:

> You might think these are odd questions, but sometimes people new to
> unschooling come here all worried about stuff and asking "How do they learn
> calculus?" type questions, with a lot of fear behind them, and their kids
> turn out to be 3 years old.

That's pretty funny. Sad too, I guess :/

> It is a lot easier to offer advice about real and immediate problems, rather
> than hypotheticals, because the answers differ depending on why you want to
> know. *Why* is a huge question in unschooling. Why is a question we ask
> ourselves a lot.

Hypothetical situations can include why reasons. For my hypothetical, I gave several. One was that learning math is fun.

Discussing real situations directly has several difficulties. One is privacy. Another is bias. Everyone makes mistakes, but we can reduce them by going about things in ways that make it harder for mistakes and bias to creep in, and keeping things impersonal can do that. It's also common that one thinks irrationally about his own life or the people in his family, but would understand the same issue better if it weren't about him.


> However I think the experience of most unschoolers as they grow up and
> participate in various kinds of classes and formal learning opportunities,
> is that they are able to assess fairly quickly whether the hoops are worth
> it to them. They tend to be willing to put up with the rules, assignments,
> tests and grades as just a small part of the price of admission of exploring
> this new fun park.

>

> An overweaning desire or intention to avoid grading or tests at all costs,
> especially at college level, doesn't sound like the usual thinking or
> practice of the grown unschoolers who are attending tertiary education with
> great success and enjoyment. It seems a bit like throwing out the baby with
> the bathwater.
>

> Perhaps unschoolers are acceptant of tests and grading at college level
> *because* they have lived a childhood free of this kind of external
> judgment. They haven't been defined and confined by grades all their lives,
> so as young adults they don't have any emotional aversion to them .

Thank you for stating this clearly.

I disagree. It seems to me this view does not sufficiently respect human beings. School hurts people and being hurt is bad. It's not a matter of hoops. It's not a negotiable part of life. Being hurt is not something to be weighed against other factors. It's certainly not a "small part of the price of admission" (if anything, it's 99% of the cost, certainly far more important than the price of tuition). And it's not a "new fun park" if one is being hurt. Being hurt is not fun, and it spoils any fun.

I do not think people should go through life accepting suffering. If a life path involves suffering, it's not good enough. To me that indicates a problem to be solved. And problems can be solved. There is never any time to give up on having a fully pleasant life and accept bad things.

I think people are powerful, and they don't need school. They can learn things, and accomplish their goals, without it. There is no external force stopping people from living life on their own terms.

I do not think an aversion to suffering should be deemed emotional in the sense of a bias or prejudice to be discounted. It's rational.

People are sacrosanct and should not by acceptant of their lives containing unpleasantness or or dirty bathwater. People should not put up with things. They should live the life they want.

That's what I think.

Joyce Fetteroll

On Dec 31, 2009, at 8:05 PM, Keith Green wrote:

> Hypothetical situations can include why reasons.

The problem with hypotheticals is that they're logically plausible
but may not exist in the real world.

The other problem is that while some people may share some surface
problem -- eg, someone who doesn't want tests to be a part of their
learning -- the most useful solutions will come from the whys beneath
their stated limitations, not from their limitations.

Maybe for some not wanting tests is a philosophical objection. Or a
fear of being judged. Or flashbacks to the humiliation of school
tests. Or a fear of crowded places. Or a fear of public performances.
Or something else.

Despite sharing a similar exterior, it's likely tackling the
foundation will be most helpful because it will open up a world of
solutions for them.

That's why why is important.

But this list exists for us to help parents help their children
explore the world. Some of what we say could be helpful to people
wanting to explore higher math on their own but that's not our focus.

Our focus is the real live moms and kids that we're happy to make the
time to help. If your passion is these hypothetical people who want
nonclassroom ways of exploring higher math, cool. But you'll need to
draw from a lot of resources and do the grunt work yourself. It isn't
reasonable for us to turn over our time to a project that isn't near
and dear to us the way unschooling is.

> Everyone makes mistakes, but we can reduce them by going about
> things in ways that make it harder for mistakes and bias to creep
> in, and keeping things impersonal can do that. It's also common
> that one thinks irrationally about his own life or the people in
> his family, but would understand the same issue better if it
> weren't about him.
>

No one way covers everything for everyone. Some people are most
helped by the philosophical discussions so they can understand why
and then they can do. Some need practical examples to understand the
philosophy. Some need to actually see it in action. Some need more of
one thing for some parts, some need more of another for other parts.

If you choose to use hypotheticals to draw out information, that has
it's own weaknesses (and strengths). But there's no one best way to
help everyone for all time. That's why it's helpful for our purposes
to have a lot of different voices contributing so different people
can find the way that works best for them to figure out unschooling.

> It seems to me this view does not sufficiently respect human
> beings. School hurts people and being hurt is bad.
>

Which is the weakness of hypotheticals and generalizations. Not
everyone will be damaged the same way. Not everyone at all parts of
their lives will be damaged the same way.

While it's a logical conclusion that testing will in some way damage
even adults, what real life data are you basing that conclusion on?
I'm not dismissing the idea that some people will be damaged. I'm
asking what really happens with real people. (Not for you to report
back. For you to ask yourself.) And is there some difference between
the experiences of schoolers and unschoolers?

What unschoolers and unschooled kids have reported is that because
the kids have felt empowered in their learning, that they can see the
game being played with grades more clearly for what it is. Unlike
schooled kids they're less likely to take grades personally. They're
more likely to be in class because they want the information, not
because they feel it's the only option or because they feel a gap
that only experts can fill.

Not all unschoolers, certainly, but that's the tendency for kids
who've been raised this way.

(Schooled kids, on the other hand, have a huge amount of baggage and
that problem is beyond the scope of the list. They might find
something useful in what we say here, but they can't be the focus of
the list because their needs will keep the list from helping its
intended audience. The list exists to help unschooling parents help
their kids. Your list could focus on the audience you want to reach.
(Though it's useful to figure out who that audience is and what they
want!)

What you're basically saying is that schools are bad and you -- and
you're trying to convince us to make it a we -- need to protect
people from that. We prefer to help parents help kids explore the
world of options, try out various tools, figure out who they are and
what they need. If people are empowered, then they don't need others
protecting them from the world. They become people who explore ways
to meet their needs rather than letting one way squash them.

But that's *our* focus. It needn't be yours. Nor should you try to
make your focus our focus. We have a real live, ever changing
audience with real needs that we've been offering help to for 15+
years. You get to choose your own audience.

> I do not think people should go through life accepting suffering.
> If a life path involves suffering, it's not good enough. To me that
> indicates a problem to be solved.
>

While it's rousing words, you need less vagueness and more real data
in order to be effective. What you're saying is basically that there
are people starving in the world and that's not right and something
should be done.

Who are the people? What are their specific needs? How empowered are
they to help themselves? What resources do they have at their
disposal? Some might need an ox and plow. Some might need cash. Some
might need the dictators removed. Some might need moved to another area.

The factors beneath their surface need are what will dictate the best
solutions, not the surface need itself.

But your vague need to relieve people's suffering is just too
unfocused and beyond the scope of this list. Some have offered some
ideas that might help, but asking us to reform our vision to help you
isn't fair to the audience we're already helping.

Joyce

Sandra Dodd

-=- Everyone makes mistakes, but we can reduce them by going about
> things in ways that make it harder for mistakes and bias to creep
> in, and keeping things impersonal can do that. -=-

I'm living my life, not an impersonal life.
My children grew up in our family. Each was an individual. We didn't
treat them impersonally.When I write about unschooling I'm using a
little principle and theory, but after many years of discussion, some
of what I'm writing about is solid knowledge and experience, not at
all impersonal. I know that kids can learn to read without lessons.
I know, because I can name people who have done it.

-=-It seems to me this view does not sufficiently respect human
beings. School hurts people and being hurt is bad.-=-

Alcohol hurts humans (and their families). Prohibition didn't work
out well at all. (U.S., early 20th century).
Tobacco doesn't sufficiently respect human beings. Smoking tobacco
hurts people and being hurt is bad.
Automobiles have no respect whatsoever for human beings. Cars hurt
people and being hurt is bad.

Except where those things are discussed incidentally in the course of
discussing unschooling, they're off topic, and not at all the stated
business of this list.

Sandra

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Sandra Dodd

-=-I do not think people should go through life accepting suffering.
If a life path involves suffering, it's not good enough. To me that
indicates a problem to be solved.-=-

Maybe Schuyler will be by today to modify or clarify this, but "a
problem to be solved" is a very male kind of response. One way women
have traditionally learned (not just lately, but thousands of years,
maybe more) is to share details of childbirth, for example, or how
someone got hurt or sick, and what helped them get well or better.
And for a long time men have said those discussions are silly and
unimportant. When they're sick or have a wife in labor, they listen
to other women bigtime, but in a sunny season, men tend to belittle
female conversation, or ignore it.

I don't mind men being on this list at all. I occasionally make the
point that the list is about discussing our families and that it's not
intended to be about anything but how people learn and how parenting
can help with that.

This list has solved thousands of problems in individual lives. We
are helping people untangle their problems, and putting a light on the
confusing parts, and helping them think of alternatives.

I'm not out trying to make spanking illegal in the U.S. I'm staying
here and helping individuals see alternatives.
I'm not trying to abolish schools. That would make a huge mess, and
some kids need school more than they need their dangerous or lifeless
home environments. I'm staying here and helping individuals see
alternatives.

Sandra

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Sandra Dodd

-=-> You might think these are odd questions, but sometimes people new
to
> unschooling come here all worried about stuff and asking "How do
they learn
> calculus?" type questions, with a lot of fear behind them, and
their kids
> turn out to be 3 years old.

-=-That's pretty funny. Sad too, I guess :/-=-

-=-Discussing real situations directly has several difficulties. One
is privacy. Another is bias-=-

So in an objective, impersonal way, you're telling us that there could
(in your case) be problems with privacy. Or bias (Ours, I assume
you mean.) But people are asking whether this is about you or a child
or whether you're a parent because in the context of these
discussions, those things do matter.

In a situation in which one is volunteering her time and energy and
knowledge to read what others write and respond thoughtfully, each
respondent's decisions might be based on whether the question is
useful to others on the list, or whether the person asking has an
immediate and pressing need for assistance. We know most of the
people here have a problem of the moment with which they could get
deeply useful help. If another person has a hypothetical, made-up
"what if" problem, and if that puts the damper on those wise moms who
are willing and able to help, and if it makes the list less
interesting and enriching for those who come to read and don't post,
then that hypothetical question becomes a problem for me as the list
owner.

You can have all the privacy you want by reading and not posting.
If you're going to post, you need to be willing to give more
information about what you want to know and why.
If the fear of bias is that if you provided more details we might be
dismissive, then pay attention to those fears. Some topics are less
worthy than others. Some viewpoints are less worthy than others, in
one discussion or another. If I go to a bricklayer's discussion I
need to be really quiet there, because I know very little about it
(though I've done a small mortarless floor and helped with
cinderblock--that's not enough to get me the microphone, as it were).

Sandra




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Ronnie

--- In [email protected], Keith Green <popper256@...> wrote:
>
>
> For my hypothetical, I gave several. One was that
> learning math is fun.

I confess I've lost track of your original question amidst all this philosophy, but this statement has reminded me that I had specific concerns when I read it: Are you asking about learning higher math because you believe you or someone else *should* find it fun? Are you hoping someone will provide a new and creative way of learning higher math that will make it fun for you or someone else?

If so, I would encourage you to let go of all that. People who enjoy math are drawn to it and will not need to be enticed. People who don't enjoy math will be hurt by even benign pressure to do so.

To someone who finds learning about higher math fun, a by-choice math class can BE fun and not damaging. And if this someone who likes the class doesn't like being tested, perhaps he or she can audit the class.

Alternatively, if learning about higher math in a classroom is *not* fun, then reading about it alone might be, or joining a Yahoo! group for math geeks, or starting or joining a math club.

> It seems to me this view does not sufficiently respect human
> beings. School hurts people and being hurt is bad. It's not a
> matter of hoops.

Often, it is, and to deny the existence of situations where jumping through hoops is required is counterproductive and impractical. It is true that unschoolers serendipitously and creatively learn a lot about things that are momentarily or permanently interesting to them. But when unschoolers have specific goals in life, such as careers that can only or most easily be obtained via a degree in mathematics, they find out what they need, explore various ways of getting it, and jump through whatever hoops are necessary.

As a case in point, my 15yo daughter is interested in a career in set design. She did her research and discovered that a theater degree can be very helpful in obtaining the types of jobs she would like to one day have. As a result, my "I'm not going to college" free spirit is now looking at college entrance requirements, considering ways of improving SAT scores, and designing her own curriculum of sorts. There *are* hoops to jump through, and she's quite willing to do so in order to pursue this thing that she wants.

Will any of this cause her pain? Maybe. But so might avoiding the hoops out of fear of pain!

> If a life path involves suffering, it's not good enough. To me
> that indicates a problem to be solved. And problems can be
> solved. There is never any time to give up on having a fully
> pleasant life and accept bad things.

I am not aware of any life path that is free from suffering. Many unschoolers choose joy as a lifestyle, and yet we suffer health issues, unemployment, the loss of loved ones, and, yes, a fair amount of tedium. Be wary of limiting your own life or your child's by seeking to avoid all suffering.

> I think people are powerful, and they don't need school. They
> can learn things, and accomplish their goals, without it.

I agree in theory. But if college is the most expedient path to a goal, I'm not going to encourage my kids to choose a more difficult path merely as a matter of philosophy.

Ronnie
http://sites.google.com/site/dragonflykaizen/

Keith Green

On Jan 1, 2010, at 11:28 AM, Ronnie wrote:

>
>
> --- In [email protected], Keith Green <popper256@...> wrote:
>>
>>
>> For my hypothetical, I gave several. One was that
>> learning math is fun.
>
> I confess I've lost track of your original question amidst all this philosophy, but this statement has reminded me that I had specific concerns when I read it: Are you asking about learning higher math because you believe you or someone else *should* find it fun?

No.

> Are you hoping someone will provide a new and creative way of learning higher math that will make it fun for you or someone else?

No.

> If so, I would encourage you to let go of all that. People who enjoy math are drawn to it and will not need to be enticed.

Yes.

> People who don't enjoy math will be hurt by even benign pressure to do so.

Yes.

> To someone who finds learning about higher math fun, a by-choice math class can BE fun and not damaging.

Maybe, but that's a bizarre reply to a question that specifically asked about how to learn math outside of school on an unschooling list.

> And if this someone who likes the class doesn't like being tested, perhaps he or she can audit the class.

> Alternatively, if learning about higher math in a classroom is *not* fun, then reading about it alone might be, or joining a Yahoo! group for math geeks, or starting or joining a math club.

Yes. Do you, or anyone here, know a good book? I know that for both physics and computer science, Feynman's lectures are very good. I do not know the equivalent for math (or for chemistry, if anyone happens to know that).

Does anyone know an appropriate yahoo group that is active?

Jenny Cyphers

***People are sacrosanct and should not by acceptant of their lives containing unpleasantness or or dirty bathwater. People should not put up with things. They should live the life they want.***
 
In theory that sounds nice, but it's not life at all.  Life is both good and bad all wrapped up together all the time.  I put up with a small house with carpet that I hate.  If I lived the life I wanted in that regard, I'd be living in a bigger house without carpets.  I lived in a bigger house without carpets before now and perhaps I will do so again in the future, but for right now, that is what I have to live with.  I can accept it and move on and find happiness where I'm at, or I can piss and moan about my lack of big house without carpets.
 
Sure, we can make changes, even big ones in life by not accepting the status quo.  This is what I see whith my teen that is different from what I experienced; I felt completely and horribly stuck when I was her age.  There were things I wanted to do that I couldn't because of school and how it consumed my life.  Chamille, my daughter, doesn't have that.  She doesn't have this intense desire to escape that, and even though there are things in life that she would like to change, she is much more able to accept those things that she really can't change than I was at her age.  I really believe it is directly related to unschooling and how that impacts her own control over her own life and choices.  So many people grow up without that and then look externally to change things because they've never learned how to be the master of their own destiny.





[Non-text portions of this message have been removed]

Sandra Dodd

-=-People are sacrosanct and should not by acceptant of their lives
containing unpleasantness or or dirty bathwater. People should not put
up with things. They should live the life they want.

-=-That's what I think.-=-

I think when you get older you'll think differently.

It's easy to be idealistic when one is young, but fury without
substance (even a furious flurry of peace and perfection) shows an
immaturity of thought and a lack of ability to see the world as it
is. Not everyone can "live the life they want." A great thing to
consider doing is to find ways to be satisfied with and grateful for
the life you have.

The only way to live without dirty bathwater is to never, ever take a
bath. <g>



Sandra

Keith Green

On Jan 1, 2010, at 6:13 PM, Sandra Dodd wrote:

> -=-People are sacrosanct and should not by acceptant of their lives
> containing unpleasantness or or dirty bathwater. People should not put
> up with things. They should live the life they want.
>
> -=-That's what I think.-=-
>
> I think when you get older you'll think differently.

It's a common mistake in society in general to be condescending to young people. It's common, when children hold opinions we consider very dumb or bad, to attribute this to their age rather than their mind. It's common to think it's not a real opinion seriously held, and to assume it will be changed to match our own opinion if only it's given more thought.

But that is a temptation we must resist. Young people deserve respect as people with minds and shouldn't be judged based on impersonal demographic information like their socioeconomic status, skin color or age.

Another common phenomenon, on the internet, is to guess a person's age based on how strongly we disagree with him. This is, again, a way of delegitimizing the disagreement. It's not a clash of ideas to be treated rationally and with an open mind; it's just a child being childish and thus his thoughts needn't actually be addressed. Behind this kind of guessing is the same ageism as in the first phenomenon. To confidently guess a low age based on someone holding ideas we think are bad is to assume children are the dominant source of bad ideas.

nellebelle

==Yes. Do you, or anyone here, know a good book? I know that for both
physics and computer science, Feynman's lectures are very good. I do not
know the equivalent for math (or for chemistry, if anyone happens to know
that).==


When I want to learn about something from a book, I often start in the
children's section of my library. Librarians in general are good sources for
book recommendations. Modern bookstores have sections for math and other
topics. You may find something useful browsing there. If the interest is
specific to college-level math, perhaps you could ask a math professor for
ideas, or look on one's shelves to see what they are reading.

You might also check sources such as Scholastic, Publisher's Weekly, etc. An
internet search for "math books" might help.

Mary Ellen