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Everything posted by square_25

  1. Our kids sound similar, actually. My daughter is very mathy but she has very little interest in banging her head against the wall. I sometimes think that AoPS... well, doesn't exactly give the discovery method a bad name, but makes it seem trickier than it is. I do have my daughter discover all the rules of math herself, but we do so without doing more than dabbling in really challenging problems. I like the phrase "expert generalist"! My kiddo is very much like that :-). She's very mathy, but she also loves reading, and learning languages, and learning to play the piano, and gymnastics, and so on, so forth :-).
  2. Got it! Does she get frustrated with having to discover everything? We do a very scaffolded version of the discovery method over here :-). But we do follow a lot of rabbit trails. I think my daughter finally memorized her additions to 20 as we were working on binary...
  3. We live in NYC, and there are absolutely more chances to both meet other homeschoolers and to meet other kids who are as serious about academics here. Of course, the two groups don't seem to intersect all that much....
  4. Out of random curiosity, what didn't work about only doing "fun" math?
  5. Oh, I see. What about them? I don’t follow a curriculum, but I’d think there’s nothing there if you’re fluent with fractions and decimals.
  6. It’s all very interesting. We’re homeschooling because we have a very specific vision for what a good education looks like (which by definition means we’re not using much curriculum except for inspiration), and it’s been surprising to see that this makes us the outlier, not the norm.
  7. What arithmetic topics do you think he could use reinforcement with?
  8. Yep, it really varies geographically. I'm in NYC, and I've been asking $150/hour. I get $45/hour from AoPS, and that's work I can do anywhere, at any time, so I'm obviously going to charge quite a lot more than that for work I have to travel for. Also, I have a PhD and more than a decade of teaching experience...
  9. I really don't know about whether idea generation can be taught, because I can't teach WITHOUT requiring idea generation. I've never been interested in teaching procedures, so for me teaching requires engaging someone's mind. The levels at which I engage them varies, but so far, I've been able to do that for most of the kids I've come in contact with. I would guess that most people can be taught to write what I think of as normal proof. That is, I would assume a majority of people are able to do this, although I wouldn't be able to tell you how large a majority. I don't think the ability to engage in a logical argument is a particularly unusual skill. For most of the college kids I've taught, they could use this skill outside mathematics but not within it, which I thought was a great shame. Math is such a great tool for honing one's logic, if you allow it to be...
  10. I wonder if it's really in order to make things accessible or whether it's to reduce the number of man-hours you need to give feedback. I know that both teaching writing and teaching math have been very teacher-intensive for me, because I don't use programs -- I just have kids write or do math and then I troubleshoot and talk to them about their work. It's all a very interactive, human endeavor. I don't think this approach, while optimal, is possible in a large classroom.
  11. Being a bit less snarky, what I mean by "all math should be proof-based" is that I think it's important to think of everything in math as justified and to expect a student to be able to verbalize the reasons for most of the math facts they use at least once in a while. I think that seriously assists in fluency. I have this expectation of my 7 year old, even though she never actually has to write down a proof. But she's started saying things like "We need to prove that!" if I say "we've noticed a pattern, but we aren't sure it always works."
  12. That IS a traditional proof. The two column proof is a bizarre abomination...
  13. Do you two mean the same book? One of you said Engaging Minds, the other Engaging Ideas.
  14. Hmmm, no, I’m brainstorming in general! But I’m least worried about essays. I’m not sure my older girl is going to be interested in fiction either, frankly. So it might not come up for a while anyway.
  15. Oh, you'd be surprised. Ask a random adult WHY a*b = b*a and you'll realize that most people do not have any kind of definition of multiplication in their head. "But... it... just is.... how could it be different?" More people can tell than 6*9 is 54 than can tell you what it is you're actually calculating when you do 6*9. And I think a focus on what a symbol means serves as immediate word problem practice. If you know that 6*9 means you add up six 9s, then it becomes pretty clear that if you buy six things and each one is worth 9 dollars, then the total is worth 6*9... even if you don't see it right away and do 9 +9 +9 +9+9+9, your teacher can point out to you that we have a different name for that and that maybe we remember it or that we at least have some shortcuts for figuring it out. Eventually, it just makes sense.
  16. See, to me, it sounds like the same issue that I always diagnose: they are taught procedures before they understand WHAT they are actually calculating. It's true that they are taught mental math procedures instead of standard algorithms, but it comes to the same thing: they learn shortcuts before they know what the shortcut is taking them to. Same thing with the equality sign, by the way: we spend no time on what it means and immediately start using it in expressions like 54 + 45 = . We THINK that the kids know what it means, but they don't. It takes quite a lot of experience with a symbol to get it down... which is why I fervently believe in working through things using first principles and whatever comes to mind and ideas you've derived yourself (or maybe were nudged towards by the teacher) using the definition for a good long while first.
  17. Technically, all of math should be proof-based ;-).
  18. I’m glad that has been your experience! Is there supposed to be a don’t before the “need to use writing curriculum”? 🙂
  19. Yeah, I had to figure out this problem with my sister 10-20 times over the last few years. It’s tricky. We used to collaborate on Google docs. Lots of back and forth and lots of comments were involved. I’m sure this is a problem one solves anew with each kid and each new essay.
  20. I’m sure that’s true. It’s been true for me in a number of ways: for example, I have way more trouble with my temper than I wish I did. However, I do think I have a sense of what I’m good at? Even if I’m not as good at teaching essay-writing as I think I am, I’m absolutely sure I have no clue how to teach fiction writing, and I ought to know....
  21. I don’t. I’m super introspective and find teaching of things I understand well easy to do by pulling apart my internal thought processes. I know that this isn’t common, but you’re going to have trust me in that. As I’ve said elsewhere, I helped my sister with her essays for the last few years, both for her IB research papers and for her college applications. I’ve tested my ability to teach essay writing.
  22. I’m good at academic essays :-P. They come easy and I think teaching them will, too. I’m way more worried about the other types of writing. I don’t even like telling stories: I freeze up and can’t think of a plot. As I said, translating fiction helped me think about how I’d write it, but I’m still not a natural.
  23. Can't I just remember struggling? 😉 Actually, seriously, I find that I have no trouble at all understanding mathematical struggles, and the last time I had this issue was in graduate school. But that was recent enough for me to remember what it feels like NOT to understand something.
  24. Gotcha. I'll have to remember that :-). I don't currently have the juice to take on serious essay-writing, I'm afraid... but maybe at some point.
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