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About square_25

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    Hive Mind Queen Bee

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  1. We are pretty much almost entirely out of the box :-). Even when it comes to the basics, we do very little that’s standard. My daughters an accelerated 7 year old, so I’m sure that makes it easier. We don’t follow any curriculum for any of the 3Rs. She gets a ton of input into her writing lessons. Last year, one of our big projects was making our own Mad Libs from scratch. This year, she’s randomly decided to write an extremely long book report on the series “The Sisters Grimm.” She wrote one very disorganized but otherwise surprisingly mature report, and we’re about to start on the second draft. I think finishing it up will pretty much take up our fall semester. So we’re almost entirely interest-led for writing. And for reading as well, because she loves reading. For math, I do the work in the order that seems logically correct to me, which means she’s been multiplying since she was 5 but she just learned how to add and subtract by stacking this year. We’ve also done fun in-depth studies of cool topics like combinatorics (I think I have a thread on that project somewhere on here), binary, primes, and negative numbers. I do make sure that the projects help us progress in arithmetic fluency (for instance, combinatorics was amazing multiplication and division practice), but we do follow a lot of rabbit trails. We used to have more time at home, but given the choice, my daughter picks taking tons of classes out of the house, so our schedule has actually gotten quite demanding. She does get lots of play time, but not a ton of unstructured time. That’s something we need to work on...
  2. As a FYI, the online AoPS precalc class is largely not what people call precalc. It does have trig, but that’s followed by complex numbers and linear algebra. It’s a really fun class (and I did a lot of work on a beta version), but if you’re talking standard precalc, you’ll want Intermediate Algebra first.
  3. I have a natural speller in 2nd grade and we just write and correct mistakes along the way. We might do more official spelling and grammar at some point, but for now, this works.
  4. I wouldn’t use a computer program for kids that little. They need one on one interaction to help make sense of math. It’s really easy for kids to get into pattern matching modes.
  5. We do homeschooling center classes because they are my daughter’s favorite part of homeschooling: she absolutely loves them. And I signed her up for a few external classes so I don’t have to deal with some things (but they are paid for, not a coop.) I’ve also been teaching math at a homeschooling center here... but that’s something I love doing, and again, it’s paid. I have no idea if these count as good reasons, but they make us happy.
  6. Sounds about right to me. Eventually the names do help you organize your knowledge.
  7. Honestly, I prefer the kind of mental regrouping that kids do to using the associative property. Mental rearranging makes sense to kids. However, products of 3 numbers are basically not well-defined until you actually talk about the associative property, and when you calculate something like 8*2*4 you're taking it on faith that it's the same thing whether you do (8*2)*4 or 8*(2*4). Having spent some time talking about the associative property with my AoPS kids, it's not particularly well understood. Lots of kids think it comes from commutativity, for example. So I guess I like the idea of working on this kind of regrouping as pure logic and as the kind of experience that'll later set you up for the associative property :-). I think it gives kids ownership.
  8. Yes, I absolutely expect explanations, and no, I wouldn't expect the explanation to involve multiplying one term by 2 and dividing the other one by 2. I think a good explanation at this age is "We had 16 fours, and I grouped them into pairs of fours, so then I had eight pairs (since 8*2 = 16), and each pair contained 8, so I did 8*8." I'd prompt an explanation along these lines, because I do think hooking up mathematical logic to verbal logic is valuable to most kids. But I wouldn't expect use of the associative property. I think doing this kind of shortcut sets him up for associative property later on :-).
  9. My younger girl (she’s not even 4 yet, but this seems hardwired to me) has way more trouble with these than my older one did. I’ve found that introducing pairs really slowly helps, getting her comfortable with one pair before introducing another confusing one helps, and making sure she’s not guessing by reminding her to look carefully helps. Basically, you’re working on mindful practicing instead of just floating along. In my experience, that’s what you want to do in most areas when there are conceptual issues that don’t just naturally resolve with experience.
  10. I teach my kids early (so far, before 4 for both kids, but they are both at least somewhat accelerated) so that it feels low stress and low stakes :-). That’s been working well for us, anyway. And we read a ton to them while we work on phonics, so at least for us, it’s been unrelated to that joy. As a note, 100 Easy Lessons actually explicitly teaches blending. My favorite thing about that program is how thoroughly thought out and tested it is, and the blending teaching is totally one of the things I would have never thought of myself but works really well. (I’ve actually had to modify it slightly for both kids — my younger girl, in particular, needs more time to master the look of a letter than the program gives her — but I love how thoughtful it is about what kids struggle with.)
  11. Yes, of course the ability to redirect is the beauty of homeschooling :-). And if phonics really isn’t working, I’d try something else. But starting out with approaches with known issues seems like borrowing trouble. Anyway, I’m not sure I have much else to contribute without us actually starting to dig into the data, so I’ll bow out :-).
  12. I think like most things, it's best to just let kids do things the way that make sense to them until they memorize the ideas. If he sees 2^4*2^6, what would he do? Would it help to tell him to rewrite it as a product of a bunch of 2's and see what happens (as opposed to, say, calculating both)? Would practicing this a bunch without requiring memorization for now help? It might just take a while to get down while keeping it logical.
  13. My older daughter was in kindergarten in the US for a year, and it doesn’t sound too different from what you’re describing. I have to say I wasn’t super impressed with the level of fluency after a year of instruction (their curriculum involved making books, and they had to read them out loud to the parents, so I got to hear them read.) So when you say “reading by age 6,” it’s hard for me to know exactly what it means. I assume the level of reading varied quite a bit even in the group who in some sense “got it.” And you’d need to show me data to convince me that this worked better than phonics. I looked into the data at some point before teaching my older girl to read, and whole language instruction is basically unsupported by data.
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