Thank you all so much for your suggestions! I'm going to definitely make it more of a point to talk with him about this when he's not upset about stuff. It's definitely a personality thing he has, but it's not as apparent in other areas as it is in piano. My knee-jerk reactions are generally to reassure him, encourage him, etc, because I really do think he's doing great! But he almost gets even more angry, like he thinks I'm trying to patronize him. He only just turned 8... lol. This is definitely something I need to be more intentional about dealing with before it gets completely out of hand, I think! Hmm. I'll ask a pianist friend to watch him and tell me. I had just figured that this song (I know it because I've helped him with it a bit) has his left hand doing more than usual, and particularly his left pinky (which is what he was saying hurt), so some amount of "building up" the muscles in his pinkies might cause discomfort, since those pinky fingers aren't usually asked to do a lot. But I'll definitely make it a point to ask how his form is!

Maybe it's math for your kid or what, but for my kid: it's piano. Few things cause as much frustration as working on a piece and being unable to get it "right." And don't even think about telling him it sounded good when he KNOWS it wasn't "right." And by right, he means perfect. He's currently been at the same song for almost an hour. His fingers hurt. He's been crying for the last half hour. But he won't walk away, and he cries even more when I suggest he come eat lunch and take a little break, because he doesn't want to end his practice session with a "failure." I know he needs to walk away, and we've done this dozens of times in the past, where he SEES that the next day, he does so much better. But he can't remember that in a way that makes this situation any better. I'm going to make him stop now anyway, because sisters need to nap. But I'm wondering for next time. Should I have stopped him long ago? How frustrated should I let him get, so that he works on hard things, but doesn't get obsessed with perfecting them *this very moment*?

I'm amazed and impressed by all these kids who do an hour of math a day. I've tutored math for over 15 years, and I refuse to go longer than 1 hour for most people because I find that right around 50-60 minutes of real work at learning new things, most people's brains start to fry. And that's tutoring adults! lol. :)

Wow! My oldest (8 / 2nd grade) spends 20ish min a day on math (either Singapore or BA - his choice), mostly independently (goes in about 5-10 when we do it together) and he doesn't do any arithmetic or games on top of that.

No, calculus in high school (I didn't actually take a class called "calculus", so I'm speaking of second hand knowledge from high school students I've tutored, college students I've taught, and currently the high school teachers I'm teaching) does not do epsilon-delta proofs of limits. In fact, I went to a smaller college, and didn't see epsilon delta proofs until after I finished calc 3 and was taking Real Analysis. Though I currently teach at a much larger university, and they do teach the concept of an epsilon-delta proof, but they don't require students to actually do it in calculus (it's saved for a later course). Sequences and series are all done very intuitively up until much later. I'm not sure how it used to be, but this is definitely the common experience at this point.

Yes, it is very sad. Though honestly, I was even IN honors courses in high school (IB), and I didn't see induction until college.

With few exceptions, that is correct. Most of my 300 level college students have never seen induction before. And they are math majors who, with few exceptions again, took calc in high school even.

Yes, totally different kind of graphs. In this context, a graph is just a set of dots and a set of lines connecting these dots however you'd like. :) ETA if you imagine the utility problem I referenced above, you can imagine each of the houses and utilities just as dots, and then the problem is really just a question of if a certain "graph" (dots with certain lines between them) exists.

Certainly, Diff Eq has more applications than discrete math. I agree that it would be best to have Calc 3 first, but Diff Eq really was "neater" than Calc 3. Whether or not it's dry really depends on the instructor and the text. I think it can be very dry and boring. But by focusing on techniques of mathematical proof, I assume they mean stuff like learning induction (how if you can show one case is true, and you can show that each case follows from the one before, then it must be true in general), proof by contradiction (if the statement weren't true, life as we know it couldn't exist... lol), and learning how on earth you prove things when all you have to work with are dots and lines (does anyone remember the utilities problem? Three houses, three utility companies - can you connect each house to each utility without overlapping lines? Turns out the answer is no, but how do you KNOW?). Cool proofs for algebraic formulas that don't actually involve algebra - instead you set up a scenario and then count possible outcomes in more than one way (where one way of counting gives you one expression, and another way of counting a different one, but since you're counting the same things, you can conclude that your expressions must actually be equal.) I loved this part, because it really required you to think outside of the box! So there's really a lot of cool content here, and just a very different flavor than proofs in calculus, geometry, or any of the more applied or analytical branches of math.

Well, it may depend on the person. Personally, 210 sounds a lot like my first math class that made me LOVE math. Super fun (and also, super accessible -when taught correctly - even to elementary aged students), and lots of really new, fun ideas where you need creativity and open mind to approach things in new ways. But you have to be willing to veer away from procedural learning in favor of problem-solving. There will be precious few formulas to learn, and far fewer "only one way to do this problem" sort of techniques than in a standard math course up till now. In my experience, something like 222 is mainly going to appeal to someone who enjoyed and excelled at calculus (I, II, and III). It was not a course I enjoyed because it is computation heavy. I enjoyed it far more than I did calc 2 or 3, granted, but that doesn't say very much. I know some folks who loved Diff Eq. I was just not one of them. I'm much more of a discreet sorta gal. :)

Hmm. Thank you for all your thoughts! It's causing me to reconsider what I'll do with the rest of my children. I already own the textbooks for lower levels, and my 6 yo is halfway through 2B. I see a lot of value in having the workbook for the lowest levels, but I wonder if I could switch her to just Textbook and IP once she finishes 2B. Hmmm.... so many good thoughts! I had always thought the IP was for kids who needed MORE practice than the workbook and textbook could provide, and so had steered clear of it!

Can you tell me how the IP is very different from the other stuff? We tried CWP way back (2nd level while he was in the 3rd level of TB/WB), and he could understand and do the problems just fine, but struggled with trying to write out his response in sentences (as was suggested to us prior - "word problems should have word solutions").

Interesting! I never considered forgoing the WB in place of the IP or CWP. Thanks!

Yup, that's exactly what I was wondering! Thanks! I wish the instructions were more clear. "Divide" could mean divide with remainder, divide to get decimal, etc. Thank you very much!

I noticed in the 4th level of Singapore that there are an abundance of exercises available in the textbook. Honestly, we never did any of them, DS just did the workbook, and I was left wondering why we even bought the textbook. I'm considering using the 5th level to transition him from "workbook math" (even though he'll still have his BA workbooks) to "textbook math", so that he can start learning how to put his own work on his own paper, since he'll have to do that with AoPS anyway (I think? I've not actually seen one of their books in person, yet), but he can make this transition with a familiar textbook so it may be easier. It seems to me like it might be a good fit anyway, since he doesn't need all the practice in the textbook and the workbook, and I get to buy one less book, but I'm not sure if maybe that's asking too much of him - especially since I end up scribing things that are heavy on writing for him anyway, still. On the one hand I feel like doing it on your own paper isn't actually much more writing than doing it in a workbook. On the other hand, having a workbook keeps everything nice and contained for just a little while longer. FWIW, he has the 5A workbook already, so we're really only talking about 5B - 6B. I'd love to hear your thoughts!

Thanks! I know they do decimals - it was in the very first lessons of the book, which is why I automatically did it with decimals this time. It just wasn't pretty! lol. We'll keep looking! I can find every single textbook 1A-4B - they're all on the same shelf!! - and not 5A. :P

ETA I figured out in the car that they probably just want you to leave the remainder without turning it into a decimal, but can anyone confirm that for me, please? So I don't refer to the textbook a lot lately and I can't find it at the moment (I'm almost certain that one of my toddlers ran off with it to "read" lol.), so I need to ask a question about the textbook content: My boy just tried Exercise 12 in the workbook (division by a 2-digit number), and it seemed really straightforward for parts (a)-( c.). But then we skipped to part (h) 299 divided by 53, and it went on for a really, really long time, even before we got something that repeated.... We got something like 5.6415094339622 (and then it started repeating again). Now, I have a really hard time believing that this is what they were intending on this problem (especially with such a tiny box to write in?), so somebody please tell me what we were supposed to be doing here!! Was this really it?

Ha ha. I aimed for this for a while, but best laid plans... I have four kids, and - unlike them - I can't spend my entire day reading! lol. They just have lots more opportunity to read than I do, and I can't keep up even though I read more quickly. So I'm always impressed at folks who can keep up with their kids' reading!

Neither, honestly. lol. Since we have long stretches of going without internet, I downloaded all their videos (I checked with them to make sure they were ok with that and they said that that was perfectly legit) and paid for the family license (up to 4 single licenses) of their complete materials for Units 1-6. It was around $150, but we've used it for long enough to feel like it's worth it, even with only two kids currently playing, and even more so if the other two take it up down the road. I know I don't get ALL the goodies that would come with a paid subscription, and I'm ok with that, but I was just reinventing the wheel trying to make my own print materials, and theirs really are very good so I feel it's been a good investment to get their print materials (whether that's via a one time purchase of the complete materials or a monthly subscription would just depend on your circumstances, I think).

I agree it varies by child and activity! I give college students a factor of 10, because I've always been very quick with math - even before I got my PhD in the silly subject - and because I'm asking them to be very rigorous most of the time. :) While other margins make sense for other student groups or in other fields, I just thought that maybe a margin of only 50% extra in every field sounded like it might be a bit much to expect of a 15 yo. Possibly not! But something it made sense to consider. :)

We love it, and my friends who teach piano say the instruction is excellent. They admitted they expected to see a number of problems (e.g., form) when they observed my kids, but the couldn't find a single flaw in their technique or form, and that gave me a lot more confidence using it. I have one child who started 2+ years ago and is in Unit 6, and another child who started 5 months ago and is in unit 5 already. I recommend it highly to everyone who asks me about piano!

I'm curious if the material you're giving him is something you're very familiar with? Because I know that when I teach math, I usually expect my students to take 10 times as long as me on anything. So I know that, if they are to have a reasonable chance at finishing an exam in 50 minutes, I should be able to finish it in just over five. This has held true for me in over ten years of teaching. So, if you're very comfortable with the material, and it takes you 2/3 of his time to do it, then I'd say he's actually working very quickly. Now, if it's just as new to you as him, or there's some other mitigating factor slowing down your own work, then that's another story of course. :) ETA: I use a factor of 10 with undergrad courses, but have taught other courses where I may only use a factor of 5, for instance. I could imagine some fields (like English, where you're writing an essay!) where it might be a much smaller factor! I just thought a factor of 1.5 seemed like it might be fairly challenging for a 15 yo!

Ooh, does your library have those playaways? My kids love listening to a book that's above their reading level (but that they're motivated to read for content) while reading it. The nice thing is that we don't have to spend our own money on it, like if we did Amazon's whispersync, but we just get matching books and audio (often via hoopla) from the library, and they listen to it.

Thanks all. I let him take a break from it for the last week and hope to try it again today with me scribing! :)

I love the Spalding, and you can *usually* buy an older version of the book (the 4th is often recommended) online for < $5. It is systematic and will help with reading and writing.