We went straight from MM5+select topics in Singapore 5 to Jacobs, and it has been a very smooth transition.

Thank you, @mathmarm, that was very comprehensive. And thank you, @daijobu. ETA: To clarify, I wasn't suggesting Feynman's lectures were an introduction to the subject, and I only brought them up because they contain an example of "miles an hour" used by a great scientist in a physics lecture. I had personally studied physics in a different language and only started reading excerpts from Feynman when trying to acquire some fluency in speaking about physics in English.

@EKS, I apologize if I made you feel piled-on. I'm very interested in language and I also learned to talk about physics in English partially by reading Feynman, so that's why I kept posting about this issue. Given that I'm not a native English speaker, I appreciate hearing people's opinions on how to talk about science. If you ever felt like coming back to this subject and explaining why using "miles per hour" is so important in scientific contexts, I will be very curious to read your explanation. And if not, that's fine, too! I will stop pestering you about it now. 🙂

Hmm, so I understand that you believe it, but I'm not sure why. If everyone understands that those two expressions mean the same thing, why does it matter which one you use? Not only that, but both have been used by native speakers of English for a long time, so it's not a matter of one of them being somehow incorrect. Is there an official body that determines what sort of language is appropriate to use in all scientific contexts, during conferences, during physics lectures? And if so, on what grounds? Isn't the most important thing effective communication, and is the effectiveness of communication somehow affected by using "an hour"? Feynman lecturing about physics at a university seems like a sufficiently scientific context, by the way, and he didn't seem to care about using "miles an hour", since he used this expression himself, presumably because it means the exact same thing as "miles per hour" and there was no way his students would misunderstand him. I'll be honest, nitpicking about this seems like unnecessary rigidity to me, but I'm genuinely curious if there is a good argument for being this strict about this issue. In the context of a language program, it is definitely appropriate to use "miles an hour" because it's an accurate representation of how the English language works, and it's important for students to learn about it.

Hmm, I find the strong feelings about "miles an hour" and "miles per hour" very interesting. I was certainly taught both, and I use them interchangeably. I believe "an hour", "a day", etc., is the traditional way of expressing rates in English, which is why it appears in sayings: "an apple a day keeps the doctor a way." I suppose language has evolved towards preferring "per"? Is the concern that it will confuse children? My kids, who are little, understand both without an issue. Feynman uses "miles an hour" in his lectures. Would the ladies who feel strongly about only using "miles per hour" not ever use Feynman? Or is this only a concern when teaching little children for fear they might be confused that there are two ways of expressing the same thing?

Very similar both online and IRL, but I can also definitely see the bolded below, which I guess is a common thread for parents, and especially homeschooling parents, who choose to be diplomatic for the sake of their kids' social life:

That sounds like a fun idea! I have seen a game or two that have timed questions and are somewhat fun (because something fun happens after a question is answered correctly) but they don't allow the player to solve the problems on the screen, so pen and paper would still be required for the actual work. Pretty sure those wouldn't be great for your purposes either, though. (I am actually a bit surprised there aren't better options out there!)

I haven't found anything that I like more than pen & paper, but I'll link a few sites I've seen just in case they are useful to someone. One option for drilling is Khan Academy. (You don't need an account - you can just save the links and open them whenever the child needs to practice.) So, for long division or multiplication with decimals, you could use: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-dividing-decimals/e/dividing_decimals_3 or https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-dividing-decimals/e/dividing_decimals or https://www.khanacademy.org/math/algebra-basics/basic-alg-foundations/alg-basics-operations-with-decimals/e/multiplying_decimals_1 There are more similar quizzes there. If you press the pen icon at the bottom, the whole screen turns into drawing pad, so the child could solve these on, say, a tablet using a stylus. For mental calculations with decimals, here's one option: https://www.thatquiz.org/tq-3/?-j12c-l1i-mpnv600-p0 This one is not for decimals, but it's for long division with two-digit divisors, which might be useful if the child already understands the "decimal" part but needs some practice figuring out how to divide with 2-digit divisors: http://www.thegreatmartinicompany.com/longarithmetic/longdivision.html

That's really nice! Most of the reading DS does in Chinese is the same way, actually: he reads out loud to me, and I make sure he gets the pronunciation and meaning right. One mom I know of did this daily, 20 mins everyday, for 2 years before she decided her daughter was ready to read independently. (Her little girl was very young, though, and they were learning Chinese.) Anyway, it is OK if it takes time, especially if everyone is enjoying the process. One idea that I've seen parents of bilingual kids swear by is listening to audiobooks, perhaps starting with foreign translations of books the children already know well in English. Personally, I do a lot of read-alouds, which your family might enjoy, too. You could start either with very simple books or ones that are translations of books the children already know. What is really nice about doing read-alouds in a foreign language is that you could introduce your children to some really great literature this way, and many authors that are not that popular here in the US. We've been covering a lot of European and Asian children's book authors this way, ones that I would have probably never discovered if we only read in English. There might be some nice bilingual Russian/English kids' groups on facebook, full of ideas for fun books for all levels/ages and also ideas for how and where to best order them. Just beware: if you join those groups, your place might soon start getting buried in beautiful Russian books for your girls while your wallet gets lighter. 🙂

@EKS, thank you for sharing your experience with reading music. I had no idea this could happen! I'm curious, if you closed your eyes and imagined reading an English text on a page in front of you, would you imagine the direction of the text correctly? As in, English is written from left to right, so if you could imagine on which side the text starts, then you'd know that's left. (I'm guessing there is a reason that wouldn't work either?)

Oh gosh, Prodigy. My child played it for a while, and I remember absolutely hating how some of their tutorials explained things. They made literally zero sense to me. It's a great game for review, though. Really motivating if the child gets into it. DS isn't particularly driven to do math problems in his free time, especially if they require writing, but at some point Prodigy had him voluntarily doing multiple very long calculations in his notebook several nights a week, all in his free time. I was amazed. Come to think of it, I need to talk to him to figure out why he stopped playing.

I've recently come across some videos by a guy who learned Polish to a great degree of fluency by very carefully reading and listening to all of the parts of Harry Potter in Polish. (So, not Russian, but a language with similarly complex grammar with its 7 cases, genders, verb aspects, etc.) He acquired the grammar more or less "naturally" through massive exposure to the verb and noun endings. I've also heard of Polish heritage speakers, whose parents used OPOL, but who didn't start using cases properly and consistently until they started reading a great deal in the language. Based on those cases, I do hope my own kids' grammar will improve "naturally" as their exposure (mainly through reading but also through cartoons and audiobooks) to all of the word endings increases. When they are older (later elementary or middle school), I will definitely teach them grammar formally, but I'm hoping most of the work will have been done by then and that we will be starting from a place of a very good natural feel for the language. (We shall see how it goes.) I personally like the idea of books for the purpose of increasing exposure for heritage speakers. (So, for kids who are already conversational and whose comprehension is good enough to handle reading.) This is because, in general, reading is much faster than speaking. Reading a book will expose my kid to many more words per minute than conversation or most other media. I've seen proponents of the comprehensible input method say it takes about 70 exposures to a word in different context for the student to really internalize it. 70 might not be the correct number, but, anyway, the idea is that of providing more exposure to the same word in various contexts. For highly inflected languages, we will ideally want exposures to those words in all of their forms. Not really helpful to you, OP, I know, since you're in a different situation. Just musing.

I'm guessing it's these guys, which is, I believe, how native speakers study cases: https://kartaslov.ru/просклонять-существительное/лингвистика Именительный Кто? Что? Родительный Кого? Чего? Дательный Кому? Чему? Винительный (неод.) Кого? Что? Творительный Кем? Чем? Предложный О ком? О чём? Other than that, maybe you could just go down a list like this one: https://en.wikipedia.org/wiki/Russian_grammar#Nouns to cover the most important use cases for each of the cases?

Yes, they can learn like this. 🙂 I told my kids about simplified and traditional characters, and they haven't been confused. I know a lot of families who learn both simultaneously and it's fine. We use Little Fox in simplified, but when I print out the show transcripts for my older son to read, I do convert them to traditional. The easiest way to get started with doing that is to use a browser add-on that does a pretty good job with conversion like the one I mentioned in a post above. Once you install it, you can just right-click on the page with the transcript and convert!

They have a Learning Guide on their website. It might be helpful to parents who are just getting started with the language. Here's how I use LF with my little kid, who is just beginning to learn. I let him pick which show in Level 1 he wants to watch. (The single stories are great to start with, followed by the Big Green Forest.) We watch an episode and I pause to explain whenever I think they are using language that my son doesn't understand. After the episode, I let him do the quiz, which is a great way of reviewing the material. Sometimes my son asks to watch the episode again, this time without me interrupting. I let him. We go on like this for 20-30 minutes or however long he wants to go. The same words and phrases repeat over and over throughout the shows in Level 1, so there's a lot of built in repetition. But you can use it any way you want, really. You can turn LF into a much more traditional curriculum and make use of the vocabulary lists and PDFs. You can focus on just reading or just listening, if that's where your kid needs the most practice. If I were starting from scratch as a parent not knowing any Chinese, I'd probably read up on Chinese first before using LF with my child (e.g., I'd watch the Fluent Forever pronunciation videos, read about Mandarin phonology, basics of grammar, etc.)