Before I get into my post - please forgive any preconceptions, or myths I might be relying on (but PLEASE correct me!) My mom is a high school principal, and I have only been in traditional education environments. I have been reading about many alternatives, but have tons of questions...

How do you teach or plan to teach mathematics and the more rigorous sciences? It has been my experience that algebra, geometry, and calculus require a ferocious amount of discipline from both the student and teacher - mostly because it can get frustrating and the only way to get a handle on it is frequent repetition & a certain amount structure. Also success in these subjects depends completely on the solidity of the early math skills. (It is great if Jane can intuit that for x + 9 = 30, that x = 21. However, if she can't understand *how* she arrived at the answer, it is pointless to move on, KWIM?)

THE RESPONSES:

• I've heard the suggestion to either find a professor or the like whose speciality is the specific material. As far as setting the foundation, I would assume that most people who are dedicated homeschoolers would have enough knowledge to either teach the basics, or seek the resources necessary to aid in the learning (pre-packaged curriculums, for example). And you wouldn't believe the resources you can obtain through local HSing groups! I'm learning (slowly!) that there are no limits to the possibilities with HSing. The more creative thinking, the better! I have to admit, it's hard breaking out of this 'trained student' shell, though!

• To refine my question: No matter how good a circulum or "content expert" there is - if your child doesn't have any interest or discipline (or are just easily frustrated) - How do they learn the subject? I guess my question is more directed to those planning to unschool or loosely following your child's lead in education. I love the idea for language arts, history, and the social sciences. But I can't figure out how unschooling works with math & science (in mostly older children).

• Acutally, what I've heard is that science is the most popular subject among unschoolers simply because American schools butcher it so badly! My school was terrible in math and science (and it was a nationally recognized, affluent school), and it wasn't till I got well into college that I started reading about science with interest. Frankly, the majority of people don't need higher math. If a child wants to go into a career that requires it, then tbe parent and child work together to find solutions.

  A gifted friend of mine (one of dh's former students) filled in the blanks by starting college quite early (8th grade). He only studied math there, unschooled everything else, and now in his early 20s is doing hush hush cryptography work. But his unschooling has given him such a broader perspective on learning than a typical gifted kid in school. At any given time he will be taking art classes, playing in his band, or going on archeology digs. He has retained his enourmus curiousity, and so many other gifted people I know end up choosing ambition over true education.

  Another unschooled/homeschooled friend of mine never pursued math, did miserably in college, and has her passion in cooking. She is working to open a catering company. She is as much a succes as Jeremy (the young man described above). She lives with joy and curiousity, but she is not academic. Going to school would not have created an academic person out of her. Staying out of school has left her with the confidence and curiousity to pursue what she wants in life unhindered. And she didn't need higher math at all!

  Unschooling would never force a child to do academic exercises to no end. The children need to find the desire to do math, and have a purpose for it (say, wanting to be an engineer). But in truth, I can't believe that math and science require any more discipine than other subjects. For example, someone who wants to be a professional artist or writer has to work just as hard at their craft as a scientist does in the lab. It would be as ridiculous to force a budding teenage writer to spend hours laboring over calculus as it it would be to make junior scientist edit a teen literary magazine. If one has unhindered passion for something, one learns discipline to achieve their goals. School is more of a hinderence to true discipline and vocation than a help. I am passionate about reading and writing, but I got in trouble countless times for reading Tolstoy in algebra or writing poetry during geometry. School worked against my sense of discipline in my art by teaching me that bowing the agenda of others is more important than pursuing my art.

• I TOTALLY agree with this. And let me add that the ONLY place I've ever used my higher math skills was as an artist doing sound sculptures and sculpture in general. And guess what? I only learned how to do the formulas when I had a *need* for them.

  My son's primary interests are in the sciences and he is learning all his math skills in conjunction with his physics experiments, with his chemistry interests. He also knows that we have limited resources at home for a lot of his science interests and he plans on taking classes outside the home when the time comes.

  He's 7 - can do addition, subtraction, multipication and division with manipulatives, can do addition and subtraction in his head, can carry and borrow on paper, can do simple algebra all without me teaching him. He has just started expressing an interest in learning his time tables by rote in song form. Because he is interested in math and loves puzzles he looks for math games on the computer and asks us to play other math games with him - mainly those involving algebra. He has introduced me to venn diagrams; he is constantly looking for mathematical tricks and magic. What good would it do for us to sit him down and teach him math...all I can see it doing is putting out his fire. I can't intuit how his mind is making connections around these concepts, he needs to direct those interests.

  He taught himself to read using a children's physics guide - The Way Things Work...so it goes both ways - he may not like reading fiction but the reading skills followed his scientific interest as well. If you leave most kids alone they will learn what they need and it will cover the basics and then you can continue sitting on your hands and watch them really blossom and follow their interests.

• We have The Way Things Work here too. My boys love it!

• My experience watching my kids has been very much the same. They tackle things that I would never has expected them to have an interest in, or thought of introducing to them had I been following any sort of curriculum. They busy them selves ALL day learning, experimenting, reading and growing. Occasionally I will give them a point in some direction or other...like "why don't you guys go dig out the microscope this afternoon, I bet there would be tons of cool stuff in that pond in the park you could check out." I only do this if something neat sparks MY interest and I'd like to share it, or if they seem a little bored and restless. Sometimes they take me up on the idea, sometimes they are inspired by it to do something different...sometimes they ignore me!

  They have all come to reading and math in their own way and continue to follow their own path. My oldest is a voracious reader. He'll read anything...fiction, non fiction, containers, packages, instruction booklets. He lives for the library! All my kids are good at looking things up and using library systems, but he is the master. He taught himself to read with little help from me at around age 2 and has just kept going. He reads about 2 books of fiction a day, more if they are short books. He likes to have a couple of heavy duty books on the go and a bunch of 'reading snacks' as he calls them. Some Calvin and Hobbes treasuries, a few quick easy books. Math he does only when he has a specific need. He doesn't want to do heavy math...just what he needs. That makes sense to me. IF there is ever a need...no problem learning something new!

  My second child loves math, problem solving, logic puzzles. He's always loved being read to...never liked to read to himself much. Just before Yule, dh introduced them to dungeons and dragons. He has the bug!! HE loves it...he went from struggling to sound out words to reading quite well in about a week. He reads players manuals, dungeon master manuals and online stuff. He practices long and hard so he can plan and DM an adventure for the whole family. Since then he has discovered a couple of series of fiction that he likes and is reading in bed for over an hour each night. He just needed a REASON to get busy and do it. He had to want it!

  We have The Way Things Work book too...got it from a friend who found it at a yard sale for us, gotta love it! We picked up the kit that goes with it for the boys at Borders for a Yule gift. It comes with tons of cool stuff and experiments. We haven't gotten into it much yet, but I'll let you know how it goes once we do.

• Thanks for sharing. However I disagree with this statement: "The children need to find the desire to do math, and have a purpose for it (say, wanting to be an engineer). ... It would be as ridiculous to force a budding teenage writer to spend hours laboring over calculus as it it would be to make junior scientist edit a teen literary magazine."

  I strongly believe advanced math is essential for developing basic reasoning and problem solving skills. My husband was cheated out of a math education - and even in his artisitic world, he is handicapped. You may not have a direct need to solve a differential equation, ever, but the rigorous process you learn when solving it is essential. I guess I see math as not a "extraneous academic persuit," but a real life skill like cooking, cleaning, drawing and minor household repair.

  I personally was cheated out of any creative writing or arts education as a teenager. My passion for mathematics and science was honored by my school to the point where I took nothing else. I had wished my parents and teachers had forced me to take art and humanities - when I got to college, those doors were shut to me. (My pet peeve is schools "typing" kids or allowing kids to think they can only be one way. Even at 15 or 16, kids should not be forced to choose to be an "artsy" person or an "egghead".)

• I disagree. My husband did not take any higher math courses in high school - just sciences - because they had direct applications he could work with. This has not handicapped him at all either in his creative work as a science fiction writer, as an academic, or in his work where he is required to do a lot of stats. He learned the skills he needed on the job. His *interests* in science mean that he knows more than most people he engages in conversation about it.

  The rigorous process required to learn 2-d and 3-d design, colour theory served me well, physics served me well, biology and chemistry served me well...advanced math bored me silly, and wasted my time in school and made me feel like a failure; because I had no interest I did poorly in the classes. I did horribly in high school physics but when I reached university and had a use for it I learned what I needed very quickly.

  I would suggest that having the skills necessary to discern a braque from a picasso require just as much basic reasoning and problem solving skills.

• I agree. Skills to tell a braque from a picasso are equally valuable as being able to figure out a mortgage or find your way in a city. And I think math teaches all three very well. True, you can develop reasoning skills outside of math, but I think it is much harder to do. I don't want to say math is the *only* subject or a *better* subject. I think it is as equaly neccessary as art or writing. KWIM?

  This is kinda getting away from what I was asking. (I know I didn't say it to well.) My question was: Let's say my child wants to figure out how much fuel he would need to put our family car in orbit. Halfway through our findings, he gets frustrated with all the ð/ðx notation. At what point do you as the parent/teacher/facillitator say "Yes, you can do it! And it is important to know. Let's work on it for week." Or "I am sorry - you haven't wanted to learn math until now - if you work real hard you might get to derivatives in a few years."

• Here's my story. I quit school after 8th grade. I HATED any and all math I took up until that point. I could do simple arthmetic, and that was about it. I decided to go to community college as an adult, and when I took the placement test, I WAS ABLE TO DO ALGEBRA. Never ever was I "taught" to do it. In college, I had good teachers, and LOVED to do math, and excelled. I just don't think that any area of subject matter is a "now or never" proposition.

• But the reality is the learning curve when you want to know something is much shorter. You can sit your child down for an hour a day drilling math into their head and they'll slog through it, learn the basics (and promptly forget anything you've taught them that they can't use) learn to resent it completely...or you can wait til they express an interest and show they have a reason to learn it and they'll pick up everything they need to know in a few hours. My sister needed math for her masters program. She had grade 9 general math - she did ALL her high school prerequisites for the university courses she needed in a month - and that wasn't simply learning what she needed to know but actually demonstrating course based knowledge to pass with a mark in each over 75%. She was motivated.

  I don't know ANYONE who wants to learn a math concept that can't - if they have a reason to learn it. Pleasing mom isn't the kind of motivation I want my children to work by.

• I just wanted to add some things. I went to public school.. took Algebra, Geometery, Algebra 2. Don't remember squat except that I got a C barely in Geometery and C's in Algebra. I lucked out in that I didn't need math in college, just took a Philosophy class instead.

  I don't believe that kids need to know everything. I don't need to know upper level math. It is very very rarely that I need anything over multiplication. If I do, I figure it out on a need to know basis, just as most people do not need to know how to fire a kiln.

  I agree with the women who have pointed out that a child will learn what they are interested in and what they need to know to survive. I as an artist don't need math, could definately use more chemistry since I have none, but again have taught myself it as I've gone. Kids do not need to be taught everything they will need in life in the first 18 years of life. I believe strongly that more important is the life-long need to educated yourself. I am constantly learning new skills, reading about solar energy, new cooking techinques, clay recipes and glazes etc.

  So I guess what I am saying is sometimes it is okay if your kids aren't taught everything. Believe me the forced math I received is not with me any more. And its okay with me if my kids want to learn math and could care less about art. As long as it is their passion.

• You wish you had been forced? Really? What would that have looked like? Would you have gladly written sestinas, painted minatures, played the harp? Or would you have seethed about all the time it took away from your beloved numbers? I can't ever think of a time when I wanted people to force me to do something against my will. I can't wrap my head around the idea of wishing someone had forced me to study something I wasn't curious about. I only wish I had been let alone.

  I didn't prosper in school. There used to be monthly "what will we do about A" meetings at my high school. All of my teachers, my principal, my parents, my guidance counselor would get together and compare my standardized test scores to my miserable grades. They would cajole, bribe, and punish me endlessly. I remember little ole teenage me giving them lectures on learning in freedom. Their response -- well, when you grow up you can change things, but you have to do what we say now. I am so proud of that radical teenage girl! I have even saved all of the "progress reports" detailing what a stubborn little shit I was about pursuing my passions. I remember giving my ditzy English teachers lists of books they should read because they seemed so freaking illiterate to me! I was so rude (but in a delightful little way). My mother (a former teacher) now admits that I should have been homeschooled. I was just head over heels in love with language -- not an illness school could cure.

  Sadly, that girl got lost. I started getting the A's (yes, even in college math). In college and grad school I was crazy about rewards, recognition, being a good girl. I'm recovering. I want my children never to have to go through that battle to hang on to their natural ability to learn. If that means my children will be "crippled" by not ever reading Keats, so be it. I am perfectly prepared for them to be little math fiends, never knowing the intellectual satisfaction of writing a series of sonnets, as long as they escape childhood with their passion intact.

  I constantly learn new things now. If the need ever arises for me to get a better grip on trig, I have no fear. If I can teach myself how to knit out of a Martha Stewart magazine, I can do anything!

• Yes, forced, encouraged, told it was an option. I was forced to take math (and believe me, there were years I wanted nothing to do with the subject - I didn't start loving math until I was 15 or so) and English and history despite not wanting to.

  And your conferences brought a back memories - I had them, too. I wonder how many "problem" students get drawn to unschooling. But I would love to be able to see colors (to the point where I can distinguish between them). I would have loved to develop the fine motor control required to paint. I take an art class every year or so - but frankly it is humiliating. I could have been spared that if my teachers and parents had worried about that aspect of my education.

  I do not believe that you do a child any favors by allowing them to do anything to the exclusion of other. To allow them time to concentrate on the things they love best is a very good thing, but to not give them enough background to sustain future interests can be devistating.

• But you can see colours, and, for an "egghead," I'm surprised you don't recognize that colour theory is ALL science. Anything that isn't science can't really be taught - it's instinctive and more importantly, its PERSONAL.

  If you have the fine muscle control to write with a pencil or do up buttons on a babies outfit you do have the small muscle control needed to paint. Your fears about being creative and that somehow you missed a critical window to learn how to be ... there is no window ... what you've been taught is that you are somehow unable to be creative. UNLEARN that response and you can be creative. If you want to paint a certain way I guarantee you, you can figure out how.

• Yes, yes, yes! I believe it's your feeling that you "can't," that is stopping you. Either that, or you're taking dreadful art classes.

• Sexist teaching and school ruined maths for me, which I now regret. At my little country primary school, I was the "big brain" who could do everything effortlessly - except maths. I vividly remember how maths time would come around and the focus suddenly switched to the two "smart" boys in the class. I didn't have a natural aptitude, but I don't remember *anything* being done to encourage me to think differently about maths or work out a way that helped me to learn. For years I thought I just had a humanities-oriented brain. When I went away to boading school (single sex and with excellent academic standards), my teachers were perplexed - I was obviously bright and, (here's the smoking gun) good at science too. But by that point the damage had been done - rigid early teaching based on the assumption that girls weren't as good mathematically as boys had created such a loathing for maths and such an immense mental block that it was insurmountable. I was one of only half a dozen girls in a class of 120 that didn't study maths at all for my Higher School Certificate.

  By contrast, high school science was generally easy (except for physics, where the maths block came in). I was always in the top stream and several times was awarded one of a couple of prizes for topping science in my year. The difference? I had a wonderful, classic "mad scientist" woman teacher who was eccentric and passionate and encouraged me to read and explore the topics beyond the textbooks. She used to lend me her copies of "Scientific American" and her experiments were always original and often funny. She liked me and was wise enough to see that I thrived on imaginative teaching.

  Two things have happened in the past ten years that have made me realise how badly and permanently my maths abilities were botched. One has been simply learning to balance a cheque book and keep a running tally of the grocery bill in my head. The other has been watching my boys learn maths in a much more relaxed, engaging way. They do have a natural aptitude, but they're being taught to think creatively about maths.

  Only in recent years, for example, have I realised the most basic addition tricks - to add 27 and 54, add the tens and then add the single digits and put them together. At high school, I would have laboriously added that up in columns and carried numbers over - but all three boys can do it in their heads with ease. And finally, I realise that I can too. I'm no mathematical genius, but I'm a lot better than I ever thought I was - suddenly, in my thirties, the number patterns are beginning to make sense because I'm thinking creatively rather than by rote.

  To go back to your original question, I think that homeschooling could actually be enormously beneficial in creating the mindset that maths is fun and can be learned creatively. If you already have that capacity and belief, then more complex maths will be enormously easier to approach.

• As a math failure, I'd like to comment. You wrote: "It has been my experience that algebra, geometry, and calculus require a ferocious amount of discipline from both the student and teacher - mostly because it can get frustrating and the only way to get a handle on it is frequent repetition & a certain amount structure. Also success in these subjects depends completely on the solidity of the early math skills."

  The assumption you are making is that THIS will happen in your typical American high school. I went to a "good" school with "excellent" teachers. My experience is that those who were naturally good at math excelled and those who weren't struggled, got left behind, or took Business Math for their math credit.

  I was in an advanced class in seventh grade. They took those of us considered "gifted" and let us skip seventh grade math, stuck us alone in a classroom with the eighth grade math book and wanted us to learn that so we could take Algebra in eighth grade. The entire purpose of taking Algebra in eighth grade was to be able to take Calculus in Senior year of high school without having to double up on Math classes. And if you get calculus out of the way in high school, you can jump right into chemistry and advanced math in college. The only problem was---I had NO desire to EVER take calc, or chem, or anything like that. So what was the point?

  So....I am in this algebra class, miss a few days, and was completely lost, never to regain math skills. I missed the day on square roots, guess what? I never learned them. On to high school...I would hand in BLANK tests, the teacher would mark a failing grade, but would never ask me if I needed help. I simply did not understand the material. And I HAD to take two full years of this college prep math to graduate. The next year I was blessed with a wonderful teacher who MADE me understand, he would not allow anyone in his class to fail. I got an A in Geometry! If he taught ALL of my classes it would have been great, but the next year I dropped out of Math III (Algebra and trig) because of the Math fear. My last chance to take math was my senior year, I took Math III, my teacher passed me with a D as a gift. She knew I wouldn't graduate without it and I didnt give her any trouble in the class. (And I got straight A's in all my other classes that year!) It was horrible. I mean I was in my counselor's office begging not to take math, I was in tears. They said that I WOULD need this knowledge in real life.

  Yknow what....I have NEVER had to use any of it! A little bit of basic algebra has helped. There are some basic math skills I never learned (I don't know how to figure out what 29% of $200 is for example), but it doesnt matter. I function just fine! I really think those people who are good at math will be and those who aren't will figure out a way if they need the knowledge. But what formal math education did for me is to ENSURE I would never even WANT the knowledge. And if your child does not want a career in a field where advanced math knowledge is necessary all they need to take to graduate college is a Statistics class (that's the class all the English majors who hate math take.)

• It is easy to learn math outside of a classroom. First of all you can actually make it INTERESTING (omg.....!!!). We like to use manipulatives like leggos and the montessori rods. My partner is a mechanical engineer so he has plenty of background in math and science so I am not worried at all for our kids when they get older and it is time for all that cool fancy math so they can understand physics and quantum mechanics, etc....but for now they can learn all the magical physics stuff without math which I believe will lead to an interest in learning the equations (ie: how did Newton and Planck and Einstein figure that out! How amazing!). I am able to teach a lot of math through cooking and measurements. It is actually fun! Also just everyday things like money are a great way to talk about mathematics.

• Thanks for sharing all your experiences. I realize I am coming from the opposite world. I had a wonderful intense mathematical and scientific education. For my early adolescent years I was less than thrilled that my math skills set me apart from my peers, but I am glad I was required to continue with classes. (There is a marked phonomenon in American Jr. Highs where girls drop out of advanced math classes in droves due to social pressure.) I see the ability to do math help me in everyday life - from reading a map, to being able to troubleshoot and solve problems, to understanding the one universal language. On the converse, I deal with math & logic "cripples" all day long. You can see (at least in my line of work) who has had formal higher math training and who hasn't.

  My one big fear with educating my child, is that somehow he/she won't be interested in math or science - and I'll have to force them. I feel cruel, because I mostly agree with unschooling. But I would feel the same way about having an illiterate 16 year old as I would one who couldn't do calculus. *sigh* (I don't think so - with layman lectures at the local University, from Scientific American, and my ever present chalkboard - I think my child will accept it as daily life.)

• Do you really think not being able to do calculus is the same as not being able to read? I think you are a great person but frankly I find that *mildly* insulting. When I had engineering students in my comp classes it was clear that most of them were "crippled" (to use your term). I was just glad they didn't have their hearts set on being journalists. I didn't have a desire to make them think like me.

  It would be much the same if I insisted that all of my children learned to write blank verse. Can you imagine if I said that I would feel the same about having a sixteen year old who doesn't know how to write a sonnet as I would one who couldn't add two and two? If my child is interested in what I am interested in, I might be flattered, but I have no expectations that they will follow in my footsteps. One of the thrills of parenting is imagining where the curiousity will lead them, the paths I've never even considered walking. I don't have a bias about what their passion is going to be, I just want to make sure that they have one (or many).

  I think of it this way: I studied Latin. I can see countless ways Latin has helped me in my life. I think Latin is great. I would never ever force a child to learn Latin, nor would I think that one who didn't know how to conjugate a Latin verb was somehow experiencing the world in a crippled way. Who knows, maybe one of my kids will want to study Greek, or coptic, or esperanto, or ASL -- just think of what I can learn if I help facilitate them rather than telling them only to study the languages I have found useful.

  The unschooling philosophy requires a far leap away from traditional modes of thinking about education. It involves loads of *trust* and an abrupt resignation of parental ambition. The good news is that because unschooling parents know enough not to live through their children, they have ample reason to keep our own lives vital and full. Curiousity is contagious, and the differences in interests and abilities help everyone in the family continue learning.

• Yes, I think it is equally important for a child to read *well* as it is important to be able to do math *well.* In my opinion, a child is not well educated if s/he can only write well or do math well. IMO, one should be able to be confident in tackling Shakespear or an integral. Obviously, you can see how "crippled" I am trying to convey my thoughts via the written word. (I was one of the engineer students in your class. ) But I don't see calculus as a specialized class only for engineers. I see it as something I encounter on a daily basis, both in and out of work.

  I do meet many people who are cheated out of doing something they love because of their uncomfort in math. I am a DBA/engineer - I run into miscalculations and costly mistakes because people I work with can't read scientific notation, or do math in base 2. (I run into engineers all the time that are dependent on worksheets and estimate tables - *true* they can apply the science, but they don't know when an answer seems wrong.) These people love the work they do, but are constantly frustrated because they don't have the skill to make it a routine task instead of an ordeal. I do believe they are "crippled" - they have been tricked into thinking they don't need math, yet it would truly help them.

  I guess I was a little extreme in comparing a totally illiterate person to somebody who can't do calculus. (Sorry, how about a makeup hug after I manage to extract my ankle out of my mouth?) I do believe that math (calculus) is a gateway - just as reading and writing and art are. As a parent, I feel our job is to make sure no gateway is closed to our children, rather than allow them to close a gateway prematurely. (I guess that's a risk you take in any environment - and I was hoping unschooling had figured it out.)

• But YOU see calculus in everything and use it often because it is your thing. I don't even know what calculus is, and I think I'm doing just fine. When I was doing advanced algebra...I DID use it all the time....IRL, because I was immersed in it, and loved it. I don't use it as much anymore, because that's just not where my interests lie lately.

  Some people see the world through music. They hear "plain ordinary" sounds and interpret them musically. They compose in their heads, they LOVE it, and their musical skill is one they use every day. I'm sure they can't imagine someone thinking differently. But people DO think differently, and DO use thier own "thing" every day, when other people just don't, and don't ever feel the need.

  I imagine that the math deprived engineers you work with COULD LEARN if they would also stop believing that they "can't", or that they missed some magical "window of opportunity."

• EXACTLY! People use their strengths to interpret the world around them. As long as you see your way as the only right way I don't think you can understand how unschooling just *happens*, or appreciate your children as individuals.

• I'm in the group here who did poorly at math but excelled at languages. I never even took calculus, but what I wonder is what applications it has in daily life for someone who chooses a career in the arts (fine or domestic LOL)? I can honestly say I've never yet in my 27 years run across a situation where I was unable to complete a task due to not knowing calculus.

  In my case, I knew from the time I could read (at age 3) that I wanted to be a writer or language teacher when I "grew up." That is still my passion and likely always will be. I do believe in the value of a well-rounded education, but quite frankly advanced maths are not useful to me. I have used elementary geometry in home improvement projects, but I had to repeat a year of geometry (despite being an A student in every other subject, I just couldn't grasp that math class) and I couldn't remember a postulate or theorem if my life depended on it. But when it came time to use geometry in a practical application, I was able to figure it out. I will say that the primary problem I see with teaching math to language geeks and vice versa is the teaching technique - I believe each type learns differently. I also think that math would be much much more accessible if it were taught more "hands-on" instead of as dry theories in a book and practice math problems. A very simplistic example is fractions - fractions are a lot easier to comprehend when you're using them to bake, or divide a cake into pieces, than to see 1/4 + 2/4 on a worksheet. KWIM?

  If what you're saying is that a well-rounded Renaissance education with exposure to many disciplines is important, I'd agree. I think Americans are pathetic for being so stubbornly monolingual and all kids could benefit from knowing a second language. I think knowing at least basic math functions is very useful. But advanced preparation in an academic subject when the child shows no interest is futile IMO. What finally helped my dh (a former education major) "get" unschooling was this: if a child's main interests are nurtured early, an unschooling family can help prepare the child for the career or role that the child really wants. It helps avoid the problem of kids who may dream of being an astronaut for example, but get burned out after 12 years of learning things that bore them and take energy away from their real interests. If a kid wants to be an astronaut for example they will enjoy the advanced science and math they need to learn for that field IF its taught to them in a way in which they can see the whole picture. Unschooling IMO is really an extremely individualized education plan designed to prepare children to fulfill their real dreams. Teaching kids things they show less than zero interest in is only necessary if those kids will join the workforce having no clue what they want to do and therefore drifting into, say, secretarial work or welding. The current education system of teaching kids things they don't care about dulls ambition and natural curiosity and perfectly sets the stage for menial, mindless jobs to be filled - without that dulling of the mind nobody would be cleaning toilets for minimum wage.

  Additionally, I believe what you're talking about is maybe not forced learning, but exposure to different disciplines? I plan to expose my children to all forms of the arts and as many sciences as I can. I agree that a kid shouldn't grow up completely unaware of literature or art etc. (Though that's yet another point against public school, since few schools offer art education anymore.) But I will not force my kids to learn subjects because I don't believe you CAN force learning. I may have eventually "learned" enough to pass my geometry class, but I counter that I didn't truly learn anything from it because I don't remember any of it today. Forced learning doesn't result in long-term retention.

• Exposure is the key -- not force or externally compelled discipline. I see the parent's role in child led learning as one of provider: we offer an "opportunity rich environment" and let nature take its course.

• Your original question seemed to be, how do unschooling families plan to teach their children higher science/math. I would ask, how would you go about teaching your child about art, if you have no skills in that area? I am no expert in unschooling, but I think alot of people think that it means you aren't "allowed" to have structure or "formal" learning. But I think, in reality, it means if the child WANTS that structure, then they get it. I am no artist (although everyone else in my family is, it seems...I was more into acting)...but I plan on encouraging an art class for my child. If he hated it, I'd probably wait a year and encourage it again, or find ANOTHER way to incorporate art into his life. (Maybe he wouldnt benefit from a sit-down-look-at-the-fruit art class----but he really enjoyed the large puppet shows he has seen, so maybe a make-your-own-puppet experience would be a start....) I also grew up in a family where sports was nonexistent. While I *really* don't want a sport addict for a kid, I noticed an interest in martial arts (well ok, an interest in Power Rangers) and swimming. So I am looking into those types of classes for him.

  I think when it comes to higher level education--high school--of course its no longer about "learning fractions in the kitchen" or whatever. YOU can choose to expose your child to whatever you want, if they truly want to learn it then together both of you can find a way to make that possible. I am not sure why anyone would think sitting in a class for an hour everyday with 20 other people and a teacher who may be great or may be incompetent, is the best way to learn *anything* (not saying YOU are saying this). Also, depending on where you live, there may be study groups or collectives/clubs of homeschooling kids with similar interests.

  Everyone has a different idea of what is basic learning, what constitues a well-rounded education. You think higher math is included in this, some would say speaking another language, others would say knowing how to bake a decent loaf of bread. I find it amazing that I was expected to know trig upon graduation, as if I'd really NEED that someday...but no one bothered to teach me how to change a tire!

  And probably, you will be a better math teacher to your kids than someone at the local public high school.

• I feel this way too. There is much room for traditional methods of instruction within an unschooling framework if the child desires such instruction. I even think child-led learning can happen in schools (like democratic schools based on the Summerhill model -- a rare breed).

• Thinking about this last night, I think I have this finally sorted out. My question *REALLY* is:

  I love the concept of unschooling and your child working at their own pace. In most situations, I think they will learn more and retain it. But as your child gets older, I think everyone has a bare minimum "education level" they want their child to achieve before they are adults. It may be different for each person. But how do unschoolers plan to ensure their child reaches the end goals? My guess is you won't have many children that are behind in all areas, but you will get slanted children - a super duper reader who can't balance a checkbook or an astronomer who can't write a compound sentance.

• My only goals for my child is that he have a foundation of self confidence and a love of learning to really follow his dreams whether they are as an academic, as a craftsperson, as an artist, as a scientist, as an auto mechanic - whatever he chooses. I can't live through my child, I can only make sure I don't block the door to his dreams. I do not have any academic goals in place for him.

• You took the words right out of my mouth.

• IMO the only thing one really needs to make sure their child learns is HOW TO LEARN (a subject woefully missing from public education). If your child has the skills to be able to find information for themselves they will as they need it. Today that means being able to read, generate good search engine queries (when I was a child it was being able to use the card catalog to find books at the library), and enough discrimination to seperate facts from fiction. Once they have the confidence that they can learn to do anything they set their minds to I predict they will have the ability at any point in their lives to add knowledge as they need it. (I have learned and continue to learn much more since school then during it.)

  Put another way, which would you rather have, a child who knew calculus, or a child who knew how to learn calculus or any other subject they wanted? (Harkens back to give a man a fish vs teach a man to fish.) I consider education to be a lifelong activity,and consider the ability to aquire new knowledge to be the most valuable skill of all.