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About square_25

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  1. Ah, I see that. I still think there's value in really talking things through and both of you trying to get down to as basic a level as you can together. But you're right, I'm sort of taking for granted that I've thought about how to teach mathematics quite a lot. I think ability to persevere is not entirely gendered, although I see what you're saying! But for example, as a little kid, tricky things just made me more determined, whereas my daughter just gives up. Kids seem to have different tolerance for being stuck. The societal messaging is a huge problem, too, though :-(. I think I mentioned earlier, but in one of our local classes, one of the teachers said something like "don't be one of those girls that's bad at math!" when the girls were acting up or not listening. Way to reinforce the stereotype... luckily, my daughter KNOWS that she's gifted in math. But I don't think the girls that message was directed towards had that confidence.
  2. I like guided discovery, which I don't think is something people do for some reason. I don't like leaving big things to be discovered, since it's super inefficient. On the other hand, I find that facts that are prompted by examples and practice stick way better than things that come "from above": from a teacher or from a workbook or whatever telling you so. But yes, it helps that I feel very comfortable with math. On the other hand, mathematics on this level is not super tricky. And if you don't know exactly the "right way" to do something, that mightn't even be bad for your kids to observe: it's good for them to realize that math is basically just a bunch of observations about abstract quantities that we can all talk about and get wrong and use logic to muddle our way through. I like math to feel alive :-).
  3. Honestly, that sounds like a mental block, since it sounds like she can group tens and group ones and understands place value ;-). It sounds a lot better than it did at first! Just sounds like you need to take a break and go at it from a different angle next time. I'd recommend not doing any of this for a few weeks, then start it up again using mental math, no paper at all. It sounds like her memory is good and she can do this when you talk it out, so that might make it less scary.
  4. Well, that's easier! 😄 By the way, responding to earlier points: I actually don't love and have never had tons of luck showing different strategies to kids. For example, I actually think the number line makes a lot of things less intuitive and obscures the fact that you can move objects around. (I know number lines are popular, I'm just not sold.) What I tend to prefer is to show them the idea, and have them voice their ideas and do things in any way they can. Then I'll gently nudge towards different ways of doing things while validating their methods. For example, when I started with subtraction, I REALLY wanted my daughter to do things like 81 - 79 and 81 - 12 using different strategies. I mean, there are different efficient methods for those! But showing her both of those just confused her. I saw her starting to strain to memorize the different algorithms as she did this. So I gave up. I thought, it makes sense to her to first take away the groups of tens, then the groups of ones, that's fine. She did 81 - 79 inefficiently for a while and we worked on "fact families" using pictures with a boxes for a while. And I encouraged her to "check her answer" using addition. And eventually, I nudged her towards doing these questions differently than 81 - 12. But it turned out to be important for her to have full ownership of the ideas and to do what made sense to her and what clicked. Strategies can wait to be discovered :-). They make way more sense to the kids when they come up with them, anyway.
  5. That totally does happen! That worksheet is rather intimidating, I have to say. First of all, the visuals are too small to really be helpful. So it's not really explaining how to do it in a way that I'd think a little kid would find intuitive. I might really back away from this and definitely back away from the format. I'd work on being able to split up number effectively, on word problems (by the way, I'm not at all a fan of key word underlining: it's one of these shortcuts that short circuits the thing the word problem us supposed to teach you), and on general linguistic engagement with the math: processing math using language as much as processing it visually and symbolically. I'd talk to her about lots of things and about how she knows them and I'd play games. Once this clicks, it'll be trivial. There's nothing here, unless you aren't understanding something or have a block. To get past something not clicking or having a block, you don't just keep pounding at the problem, you kind of go at it from the side ;-).
  6. OK, then I wonder if it's just a habit response as much as anything! Why don't you move her away from the "stacking" format for a bit and do low pressure mental math for a while where the summands are next to each other, and you reason it out in words. Like, 35 + 43, that's 3 tens and 4 tens, how many tens total? Great, how do we write this number down? And how many ones do we have? Great, so we have 7 tens and 8 ones, how do we write that number down? I have to say, clocks, calendars and counting money are nice and all but they are conceptually totally boring ;-). I see what she's saying.
  7. Oh, yeah, they are TOTALLY the same thing! I've seen a couple of ways to introduce binary! One of them is to point out that the reason we use 10 digits is because we have 10 digits... where what I mean is we have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 because we have 10 fingers. Binary is what an alien with just two fingers would come up with ;-). In that case, your only digits are 0 and 1. That means you start out counting 0, 1, and you're kind of... stuck, since you've run out of single digits! So what do you do then?
  8. That's fascinating and I have to admit, I can't figure out exactly what's going on from your description. At this point, I'd probably do quite a lot of detective work about what's going on. It sounds to me like she's struggling with something conceptually, but I'm not sure what it is. If you did the circle diagram thing with the sum in the top circle, say something that was equivalent to 5 + ? = 8, would she be able to explain to you why the right answer is 3? Does she have a flexible understanding of what addition is? Like, if you tell her the same problem in lots of contexts, can she do it in all of them? If you tell her one bowl has 5 apples and the other has 3 apples, does she know that you add? What about if you tell her that we have 5 sixes and another 3 sixes, can she tell you how many sixes that is? That's not key words, by the way, that's just having a really robust sense that addition means putting together. To me, it sounds possible like she's compensating for an incomplete grasp of something using her excellent memory. But from your description, it's a little hard for me to tell what the thing is. It could be place value, it could be addition... it could be what a number actually is. I'm really not sure! All I know is I'd spend a lot of time getting a sense of where she is and where her math intuitions are coming from, at this point. And it sounds like that might be tricky, since she's coming from a rather unexpected place!
  9. If she isn't subitizing well, I'd slow way way down. That's not a skill you can really skip. I also don't think this is too hard for a kid her age by definition, but she just doesn't sound ready for these skills to me. My kiddo is very intuitive about math, so I don't have a ton of experience with this specific issue. But I know that when I see breakdowns of understanding in kids, I tend to lean really heavily into the definitions. I'd work on subitizing with small sums. I'd draw lots of pictures. I'd have her to do whatever visualization helps her do things like 8 + 5 = 8 + 2 + 3 = 10 + 3. What you want from her is an intuitive sense of what a number is and how it breaks up. And for this stage, it's probably better that she count on fingers until she's REALLY getting it than memorizing what to her is meaningless strings of symbols. Having math be meaningless strings of symbols is exactly how I've seen kids get lost. Their mathematical "knowledge" isn't hooked on anything concrete or visual or intuitive in their heads. It's just gibberish. It sounds like right now, she's still working on what addition means and what place value means. And that's a fine place to be! As I said, my kiddo was intuitive about math, but when we started math lessons, she was quite little, so we were at this stage for a while. I remember reading a paper of someone describing their grade 1 class and saying that roughly half the kids weren't yet comfortable with place value, so it sounds like it's honestly pretty common. The lovely thing about homeschooling is that you don't have to move on from the skill she's currently finding challenging. You can just park here until subitizing and place value make intuitive sense :-).
  10. OK, that's interesting. So if she sees a picture that says TEN TEN TEN TEN * * * * and you tell her that each TEN box contains ten *s, then she won't be able to figure out how many things that is? What pictures were you drawing for her?
  11. I don't have a recommendation for a site, but I can probably explain it! 😄 Do you remember whether you were taught anything at all about it, just so I know where I'm starting?
  12. That's a really excellent point. Being rigid about what's a "correct" answer is bad for kids' mathematical confidence. I try to run with an answer as much as I can, while also gently suggesting other angles of approach.
  13. I'd slow down a bit and try to figure out what exactly is going wrong :-). Let her count on her fingers if need be. Where exactly are things going wrong? Will drawing pictures, arduously, for every single problem help? Will sticking with problems with no "carrying" help? What algorithm is she using? Ah-ha, just saw your example. Draw her 10s and 1s (I put my 10s in boxes, usually) and have her just do it visually for a few days. Stop the worksheet problems entirely until she gets confidence that way.
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