I can see two things in what you wrote. You have expectations of your kids eagerly coming to the dull, boring stuff that schools push on them and are confused at why unschooling isn't making it happen. Second, your kids are asking for help and guidance and you're denying it to them in the name of pushing independence on them.
If they are asking for help, they need help. It's not because they are too lazy. It's because the process doesn't come easily to them yet (nor has it been made something to look forward to) and it's not worth the effort for what they want out of it. By insisting they look things up themselves, you are saying — from their point of view — "Looking things up is for kids"; "Yes, I know the answer but I'm not giving it to you. Go get your own answer"; "Looking things up isn't a fun thing or I would help you do it."
If you asked your husband for something in his area of expertise, what would make you feel better about asking again: "There's the book. You're perfectly capable of looking that up," or him happily explaining the answer to you, perhaps showing you things in books and letting his eagerness infect you?
I started answering all your points one by one, but I think if I point out that you've divided life into work and play, tedious things that need to be done, and extras that are fun, you might be able to see solutions.
Yes, life is full of things we have to do. But do we do them because we have to, or because we don't like the consequences? We do our taxes because we find doing them less onerous than the potential consequences of not doing them. We go grocery shopping because it's less of a pain than not having food in the house or eating out all the time and facing the credit card bill each month.
I think you're still caught up in the schoolish thinking that kids have to write, kids have to have neat handwriting, kids have to read, kids have to learn to learn, kids have to multiply. And you are wondering why the kids aren't just doing these things naturally.
Kids don't usually need to mulitply quickly and easily so they don't sit down and learn the tables. Kids don't usually need to write their thoughts down to communicate, so they don't learn to write. Why make them when they don't need the skills—*yet*. Wait for them to need them, then they'll learn them easily and probably eagerly. Make sure they have access to plenty of opportunities for them to take up if they choose, where those skills are used. (And *you* follow your interests too! If you aren't exploring things on your own, why should your children?)
So stop thinking in terms of the skills they need. Start thinking in terms of fun, intriguing, challenging things they might like to do that just happen to use those skills. The skills are *tools*. They aren't the end product themselves. Unfortunately that's the way schools teach so it's hard to break out of that way of thinking. Math is useless unless you want the answer it can get for you. Writing is useless unless you have something to say and a need to do it through writing.
Another thing school has taught us is to expect to learn a skill or fact through one best method. The Civil War was chapters 6-12 in your 6th grade history text. Multiplication was various chapters throughout your 3rd grade math text with drill provided by end-of-the-chapter homework problems plus additional bonus problems on worksheets.
Unschooling turns all that around. Help kids explore their interests and they'll learn the skills to do that because they'll need them. Use the skills yourself. Train yourself to think through problems out loud. *Not* as quizzes for them, but so kids are immersed in the use of basic skills, just as you immersed them in language (and still are) as they were learning to talk. They will absorb how and when you use fractions and multiplication and percent. They'll get a feel for why one is used and another isn't. They'll absorb the way you think through a "why" question. They'll see the connections you use to arrive at why you think someone in history (or just a character in a tv show) did what they did.
Reading a chapter on the politics of Henry VIII's rule is dull. Watching Anne of a Thousand Days is not. (This is just an example. They're probably too young for that one.) They are not equivalent. One fills the head full of "all" the "important" facts in one tidy package (that eventually fade away.) The second has a few facts mixed in with creative license (and you can't tell which just by watching) plus, quite possibly, leaving them with an interest to know a little bit more about those characters. If that interest is explored — *if* they want, it may take a few more references to Henry VII or related subjects to build up enough intrigue — then some of those creative license "facts" will be exposed which might leave them eager to figure out which other "facts" are real and which are made up. Or it might not. But the seed is planted. They might ignore it now. They might read a little or watch another movie and be satisfied. But undoubtedly, the more intriguing references they happen to stumble across about Henry VIII — and these can be *anything* even (or maybe especially) references in cartoons, jokes, satiric art — and things related to things they find out about him, the more they'll want to know. And the more they want to know, the more likely they'll look into something in more depth. It's not an efficient process, but it's way more likely that they'll remember things about Henry VIII this way than by reading a dull chapter in a history text.
Movies that come right to mind that have prompted my daughter to be interested in related things are Pocahontas, Robin Hood, Sea Hawk. I've refered to Indian Jones when Hitler gets mentioned. Hercules and Xena have met up (anachronistically but she enjoys having it pointed out which parts are real and which made up) with all sorts of characters from history. She's stumbled across a fair number of meaningful references to Julius Ceasar so that she get's that "Aha! I know him!" tone when she comes across him.
Doing math problems is dull. Playing board and dice games isn't. But if you see games (or worksheets or any one thing) as *THE* way of getting math into them, you'll be concerned when they don't want to play games and feel you need to force them to do *something*. But math is all around them. Undoubtedly they use it when they need it. It's really us parents who were taught that real math is in textbooks who are the stumbling point. We need to notice math in it's wild state. Check out nutrition labels. (Not as a way of forcing kids to choose a lower sugar cereal, for instance. Just as interesting points of information.) (I recently pointed out to my husband with my daughter there that the adult cereal he likes has *more* grams of sugar per serving than Captain Crunch. She got a kick out of that ;-) Express things in patterns: "Did you know that the zoo is twice as far as Daddy's work? It's 14 miles to the zoo and seven to Daddy's work. I wonder how far the grocery store is that you guys think is so far in comparison." (It makes no difference if you do this particular example or anything remotely like it. Or if your children show no interest. The point is to get a wealth of stuff out there and available for them to pick up on. Much of it will get filed away unconsciously. But the habit of you seeing patterns will create an environment that encourages the noticing of patterns.) "Your favorite show is on in an hour and a half, three Bill Nyes." "Did you know that you are xxx seconds old? And I am xxx seconds old?" "I need to cut this recipe that calls for 3 cups of flour in half. That's 1 1/2 cups."
Yesterday my daughter came in from watching tv and asked how many feet 48 inches was. (Perhaps one of those fruit roll up commercials?) I said "4 feet. There's 12 inches in each foot. And there's 4 12's in 48." Though it's "important" that she know 48 inches is 4 feet, it's *way* more important that she see the process for figuring it out because the process applies to much more in life than the factoid that 4 ft=48 in. So even if she needs to ask me similar questions numerous times, I'll keep laying it out for her so she has an opportunity to see the patterns for herself when her brain is ready for them.
*Sometimes* when she asks me a question, I'll ask her what does she think it is. It depends on the question, on her mood and on whether I know she knows how to do similar things and is perhaps just not seeing the pattern between this question and something I know she at least knew at one time. Sometimes I'll just tell her. Sometimes, when I don't know, I'll say so and start thinking up possible answers and the reasons why they might be true. She's used to that so plays along and comes up with her own possibilities. Sometimes I'll ask if she wants me to look it up. Sometimes she does. Sometiems she doesn't. Sometimes I want to know when she doesn't so I look it up for me. I invite her along if she does want to know. If she wants to, she comes. If she doesn't, she doesn't and I just bring the answer back. It's the *questions* that are way more important than the answers. Anyone can get the answers. But when they ask questions, it means they are thinking. I never want to discourge my daughter from asking questions by turning the answer process into something she dreads.
[Q: What about children who do not write well, children who use capitals in the middle of a word?]That's normal. It sounds like my 7 yo.
My 7 yo daughter has rarely had a writing implement out of her hand since she picked one up at age two. We've gone through at least two cartons of blank paper for her drawings and writings. Her handwriting is still lousy, but not for want of practice at small motor skills or whatever. She spent 2 months in school and it improved then but slipped back after she left because right now it isn't an important part of writing for her. When she writes, the point is to get the thoughts in her head down on paper. (And don't get the idea she's writing Moby Dick ;-) They are very simple stories, notes, signs, sometimes just a label on a picture.) When she is writing, forming the letters in a standard way just interfers with that process. Writing "properly" is more like art and at the moment, she's more interested in other things. When she's interested in writing so others can read, or in more artistic handwriting, then she will do so. *My* part in the process is to provide opportunities for her to take up when she's ready. I make sure she knows the books on Italic handwriting are there for her, pull out the calligraphy books every once in a while, pull out the Magnadoodle and form letters with her occasionally (this is a *game*, I don't make her do it if she'd rather do something else). I did write out a bunch of fun personal words and names, one or more for each letter of the alphabet. Maybe I should have them laminated so she can play around with them and trace over them. She'll write well when she's ready as long as she has access to materials to help her, a helpful mom and she knows the process will be intriging and the skill useful or pleasing to her.
[Q: They love having penpals, but complain about writing. They want to know what to say, how long does it have to be, etc. All I tell them is to write about what's happened this week, how they feel, etc. and the letter will be as long as it will be. I don't care how long it is, as long as it's more than Hi...bye. I am confused at their interest in things as long as I do all the work.]How about if you do this *with* them rather than as an assignment that they need to do. Do *you* want to write letters? If you don't, why should they? Perhaps get a bunch of stickers and markers and make artisitic letters together. Get some calligraphy or books of fonts and make up some wild fonts or make each word different. Do it on the computer and go wild with fonts, colors and embedded pictures. Perhaps you could all sit down together and brainstorm things that happened that week that might be interesting to tell someone else. Perhaps they could take their trip to the zoo and be reporters writing it for a newspaper. Perhaps they could turn it into a story of an adventurer who went on a safari to see these animals. Or a wildlife tv personality like the Kratts Brothers or The Wild Thornberrys. Perhaps they could write a comic strip or book of what they did that week. Perhaps they could make the letter a rebus with drawings or stickers for some words.
You can't make the skill fun or something they look forward to unless the process is fun.
And don't be worried if they turn all these down. These aren't the only ways of learning to write. There are notes, grocery lists, labels for pictures, posting on message boards, letters to favorite actors or tv shows or authors, letters of complaint. There are plenty of opportunities.
There's plenty more ideas where those came from ;-) if you still have problems seeing how your kids will acquire the skills they need. (In fact I never come up with these ideas unless someone asks. I'll have to see if my daughter is interested in any of the writing things :-)
More on Unschoolers and Writing
including links to Joyce's writing page, and a list to go with it
Ideas about kids being "lazy":
The danger of "Lazy" and other thoughts