I'm not in any position to say what elementary teachers should do. I don't have any interest in trying to minister to the public school system. None. I've never been into converting other adults to my way of anything. *deleted the rest*

Which definitions are you using? How many definitions is "a bunch"?

Since you have a story already in mind that works for integers and fractions, what is it about your story that you don't like?

In math? YES! The "Math Lies" are kinda a pet-peeve for me! We'd better start a separate thread... As for other subjects, not off the top of my head, no. The natural sciences are not a personal strength of mine so I wouldn't know how to separate the lies from the truths. Of course history is littered with them and we tell a bundle of lies when we do a sloppy half-job of teaching English phonics/spelling....

As blunt as I am, I didn't mean it to be rude. I'm just trying to spare myself time. Great teachers rarely change their tactics on a whim. When you've considered and decided against other approaches on purpose, than you're not about to flip on a whim, abandon a method you've spent months (or years) developing and using successfully. I knew I wasn't going to say anything that would change your mind and I wasn't about to tell you anything about teaching Multiplication in elementary school that you hadn't already considered, discussed and decided against. *shrug* I felt that typing out all that wasn't going to be a great use of my time, and lo and behold it wasn't. You're willfully informed about math pedagogy, not willfully ignorant.

I do not try and teach children (especially outliers) that I haven't met and assessed myself. Experience has taught me it's not a great use of time for anyone involved.

So, with this it brings us back to: Ok, whatever you say.

I'm not sure yet. I know we're not going with an app such as Duolingo or Rosetta Stone. I'm looking to hire a person for X hours of language mentoring each week. I'm planning to pay up some $$$ and get some Native teacher who can do both 1-1 and 1-2 sessions so that each of The Boys can get some individual attention, but still benefit from some shared instruction with his brother. It's not my preference, but at this point language mentor/teacher with private lessons customized to them is just the route I feel that we need to take for Japanese to keep them progressing and prevent their Japanese from getting brittle or decaying. I'm not usually eager to outsource but I'm going to have to do things differently for Japanese because I have no way of effectively coaching or supporting them in Japanese since they're no longer working through finite and sequential resources that I can understand structurally if not linguistically. On the flip side:: How are your families language-treks going? Does your kids approaches to language differ? How is your own endeavor for Spanish going? Feel free to share an update of your own families language treks.

Yes, but the rub is that most young children who are being introduced to multiplication have no idea about positive integers. They aren't being told and they don't typically have the mathematical exposure or experience to know that "Multiplication is repeated addition" is a conditional statement. Any time I've seen a definition in a higher level mathematics that is only valid for a subset, it typically begins with "For all real numbers, n,...." or "Given that k is a whole number,..." or "Yada, yada, yada....provided that n is a rational number. In other words, it's made clear out of the gate that we're making a conditional definition. To be clear, I'm not a professional mathematician, so there could be this practice of giving definitions that are only true conditionally without ever making it clear that it's conditional, but I have never encountered it.

Language Update: Japanese: I've disallowed "deep media immersion" (aka binge-watching Anime) during the COVID quarantine and as a result, Japanese exposure has slowed down. They do watch a couple of episodes each day and they keep a Japanese Journal where they jot down sentences or vocabulary that's new or useful to them. They've continued with Japanese literacy and they're making good progress with the Kanji. They've taken to speaking Japanese here and there so that I don't know what they're saying. I just encourage them to check each others grammar so that they don't reinforce each others mistakes. I'm going to invest in online-language mentor and language-exchange practice for them because we need something to breathe fresh energy into their Japanese trek. It is very hard for me to gauge just how much Japanese they're retaining vs losing because I don't speak Japanese. But it'd really, really, suck for them to lose too much ground. Spanish: Because we're home All.The.Time we've been getting an abundance of Spanish time in. This is when having a home-library of Spanish language media has paid big dividends. It's very easy to spend a lot of time in Spanish each day when their card games, books, video games, music, board games, movies and meal times are all in Spanish. Pal seems to have caught a writing bug. He's started writing a lot of stories and they seem to always be in Spanish. It's a little weird to me that his stories are almost always in Spanish yet his his essays/notes are mix of Spanish, Spanglish and English. (I forbid Spanglish in all academic writing, but when he's writing for himself, he often writes in Spanglish.) I hypothesize that he writes stories mostly in Spanish because for the last 6 or 7 years, Spanish has been the language of imaginative-entertainment. But it's only a theory, and it doesn't stand up well to the fact that Buddy, our resident writer, writes all the time and he writes in English and Spanish. Because he does a lot of fanfiction, he's writing more Spanish these days, but he writes tons in English.

"Multiplication is repeated addition" is a false statement, so that's what's wrong with it. It's a POPULAR statement, but so is that old tale about Santa and we all know that's not true. Obviously, multiplication gives the same result as repeatedly adding a positive integer to itself but that doesn't make the operation of multiplication repeated addition. This is a crude analogy, but I hope it helps illustrate my point. A hammer is a tool to drive nails into, or pry nails out of, wooden structures. Hammers are occasionally used to maim or kill, but that doesn't mean that a hammer is a weapon. Just because a hammer can serve the purpose of a weapon, doesn't mean that we should begin teaching kids hammers are weapons to maim or kill. The truth (for the real numbers) is that the operations of addition and multiplication are not one and the same. To my mind, it's not really sound to teach a known lie for the sake of quick results now only to confuse the kids in a couple of years when you have expose them to the truth, (Also, side rant of mine: Of all the series that teach The Multiplication Lie from 2nd and 3rd grade, I don't think I've ever seen one that goes back and addresses this directly in 4th-5th grade when it's time for kids to begin multiplying fractions. IMO, It's only fair that if you go out of your way to convince your kids that Santa Claus is real, you should at least take the time to clear up the falsehood when you're ready to let them in on the truth. Not just drop the pretense and hope for the best.) Additionally by telling The Multiplication Lie on such a scale, we have to uniformly limit how much of the general truth about numbers they can really access (artificially restricting the "scope and sequence") of elementary school mathematics. By teaching "Multiplication is Repeated Addition" we as a nation don't have to concern ourselves on developing the young childs number-sense and training their quantity awareness early and often. We can instead systematically ignore it. Their number sense only needs to be developed enough to add and subtract, because we're going to screw them on the back-end with The Multiplication Lie. If instead, we taught kids to understand what scaling is, and helped them develop a "feel" for scaling, the way we do for greater/less, or quanties in general, then we could teach them that "Multiplication is a scaling operation" and they can practice multiplication with whole and rational numbers from day 1. Many kids will notice on their own that when I make something half-as-big, it's just cutting it in half, but when I make something twice as big, it's doubling it. And similar for making something a-third as big or triple it's size, etc..." In my experience, helping kids access the forwards and backwards of an operation early and often always off nicely. Then we can prompt 2nd, 3rd and 4th graders with specific exercise sets that enable us to discuss questions such "Do you notice anything about multiplying by whole numbers?" and "When is multiplying not like repeated addition?" But by mis-teaching multiplication as repeated addition on such as massive scale, it restricts the type of numbers we can expect young students to work with. Children are typically taught fractions in only the weakest way in K-3, because we can't have fractions exposing The Multiplication Lie we start dishing out typically sometime in 2nd grade.

Ok, whatever you say.

At this stage in the game, I would explain to them I'm not going to accept half-a$$ed work from them. It sounds like they are old enough and capable enough to write neatly and legibly the first time around, so they need to do it. Sloppy writing literally fulfills none of the purposes of writing as a form of communication. I would have them copy in their best handwriting a paragraph from a book. Then, using that paragraph as their bench-mark, any written work that you deem doesn't meet that standard, tear-up and throw-out. Really. Every time they turn in sloppy work tell them "This isn't acceptable, and I won't even grade it" then tear the page in two and throw it in the trash and make them do it again. Immediately. They will now work by the motto "Do it right, or do it over." This is the fastest way to make them care. This is the fastest way to make them attentive and develop diligence. Of course, they also need to be doing some manual writing every day (note: Saturday is a day, so is Sunday). You can have them copy a paragraph, or quote, convert an outline to sentences, or write a letter to the editor for the local news paper. It doesn't matter what they write, but they need to write each and every day for about 5-10 minutes in the morning and 5-10 minutes in the evening. "Do it right or do it over" was the standard that I used on The Boys when they were younger and to this day, they have some of the best handwriting I've ever seen in children. The same way I don't put up with The Boys walking around grunting and butchering their speech like willful idiots, I don't put up with them going about jotting scrawling randomly on a page and calling it writing either. But "the basics done to the highest standard" was my "Hill to Die On" when my boys were little. Like you, I'd taught them to write properly and they could write neatly but often wouldn't. I finally explained to them one last time that practice makes permanent, so it's too important to cut corners with the fundamental skills. I told them that since they knew how to write, that they had to consistently do high-quality work on their papers or they'd have to do them again. Than I began to tear up their sloppy work and make them do it again. There was no bargaining, no 2nd chance, or opportunity to adjust anything. If it was sloppy, I'd tear it up and throw it away. If it looked half-a$$ed, it was trashed. Period. I had tears initially, but it wasn't something I had to do for months on end, I assure you that. It hurt's in the early days, but it works. Explain to them the new standard. Use a sample of their best handwriting as a model, make them write for a short period of time each day and judge their output against their "best" model. Immediately tear-and-trash all the half-a$$ed work that they turn it. Rinse and repeat.

To understand the multiplication algorithm for fractions you have to be aware of a few things . (1) Multiplication is not repeated addition. Multiplication is more in line with proportionately stretching or shrinking a thing. In other words, it's a scaling operation. Multiplication is not repeated addition. It never was. It never will be. The statement "Multiplication is Repeated Addition" is a lie. (It might be perpetuated in ignorance, or good-intentions or anything else, but it's a lie) (2) Fractions are uniform portions, pieces or parts of something. You never just have 1/3. You will have 1/3 of something. 1/3 of a pancake, 1/3 of a mile, 1/3 of an apple slice, 1/3 of a lb, 1/3 of a unit. This is of course in line with whole numbers. You never just have 6. You have 6 of something. There can be 6 toys, 6 blue markers, 6 spider-man toys, 6 children or 6 chairs. But there is no puddle of "6-ness" just floating around in the world. (3) When you are multiplying fractions you are scaling a quantity up or down appropriately and the result is compared back and framed in-fractional parts of the original thing. This is kind of like regrouping whole-numbers. When you compute 38 + 75 it's true that you get 10-tens and 13-units, but we always frame this result in terms of standard decimal-numbers and call it 1hundred-thirteen 113. When you compute 3/4 x 5/7, we re-frame the result in terms of the original unit and it is 15/28 of the original unit.

You shouldn't be embarrassed. Multiplication and division are uniformly mistaught all over the nation and have been generations. When we combine the Multiplication Lie with a fuzzy, incomplete understanding of Fractions, wait a couple of years and voila! you have an entire nation of educators, the vast majority of whom do not have a good understanding of fractions. When I was in elementary school, I had a teacher explain to the class that fractions were one of the reasons she believed whole-heartedly in god. Because even though fractions make no sense, they do work. She said it was one of the ways we should know god works in mysterious ways. 🙄

They are 13 and 10, so get a piece of paper and pen and all in one room with snacks, have THEM PARTICIPATE in coming up with a long list of Interesting or Constructive Things To Do Around Home/Neighborhood. Can you hit 50 items? What about 100? 150 items. Try and come up with a really long list of SPECIFIC things. Then when the kids display to you that they're bored bring out their list and they pick something to do or assign them something to do. I discourage really vague goals like "learn a skateboard trick" and instead prefer very clear goals "Learn to do an ollie while riding my skateboard" When a goal is clearly defined, you'll know if/when they've hit it.

I try and teach my children manners. Not just the manners that I learned growing up (which weren't many at all) but codes of conduct for situations that aren't apart of our everyday life experiences too. As a family we intentionally learn about and practice situational etiquette--even if it's for something that I don't encounter often, simply because it's important for them to know. To me, it falls on the families AND society to teach children these things. I can't be with them every second of every day, and I can't plan for or catch ever mis-step. If one day Pal or Buddy makes a blunder in public, I suppose he'll feel embarrassed, take his lumps and move on. That's life.

Then there is your answer. If his stamina is "depleted" at 50 minutes, it's depleted. It wouldn't matter too much what you had planned for the 51st minute, would it? If you want to develop his concentration, build his mental stamina or train his ability to focus, then devise a way to do that. But that doesn't mean that he needs to spend more time on math

Plays around like what? Keep in mind that my comment was specifically about the white sheet of paper, where his steps were *perfect* but @mathmarm reported that it took 3 minutes for him to find the quotient. I trust that mm's son has superb number-sense and his math facts rock solid, so I was curious about whatthe hold-up was time-wise. Being distracted out of the math-problem itself makes sense. For a child who is fluent in the prerequisites, and supposed to be fluent in the division itself, that problem should've taken 35-50 seconds, not 180.

Are you 100% sure that he is fully fluent in the multiplication and subtraction algorithms? Since you say he's got a grip on the estimation part, then it really shouldn't take 3 minutes to do this problem with the long-division algorithm.

Since we've been working our way through the home library for over a year now, we are low on untapped secondary language books 😦... Unfortunately, the majority of the books that we own have been read in-depth and repeated. So if this outbreak continues more than a month, I'm not sure what we'll do for reading material.

Oh good lord, my post reads as though it were written by Scrooge McCurmudgeon. That wasn't my intent. There is a huge difference between leading your kids to being independent learners and students, then gradually passing them academic responsibility vs just throwing (cheap) books, (free) apps and (random, inexpensive) trinkets at them and hoping to god that they figure it out and teach themselves because you have your Netflix queued up for a 8-year binge session and heaven help you if you have to put it down and do something akin to TEACH your own children. (Can you tell I know people who have this attitude and approach? I'll give you 3-guesses how I feel about this parenting and educational choice) I made the mistake of getting involved with several local homeschoolers and new homeschools last year and I am annoyed with and appalled by the number of parents coming in to homeschooling asking for ludicrous things like "What apps do you like for teaching reading and letter tracing for 6yos?" "I want a 2nd-grade math that's handsoff for me. My 2nd grader is getting into more addition and subtraction stuff--I'm terrible at math, is there anything that she can do on her own?" "What is a good independent series for science, history, math and English for my dyslexic 7th grader who can't read independently and has never been asked to self-teach? It'll be our first time homeschooling but I don't want to spend a bunch of money, be directly involved or responsible for telling him what to do making him learn anything." "I need an independent phonics program for my K and 1st graders" "What app is best for doing flashcards with my 3rd grader?" "I need a self grading, self-teaching, independent program for K-3, because teaching counting, writing and reading is hard so I don't wanna do it." "Isn't there a website, video series, game system or app that'll teach my kids all the essential PreK-8 skills so that I don't have to do anything to get them ready for highschool or college?" When someone asks me what I recommend and I tell them what I honestly recommend, they look at me like I have 3 heads and talk about how they don't have the energy, interest, discipline, time, motivation, skills, certification, etc... In other words, they want to input MINIMAL TIME AND EFFORT yet have the nerve to express a desire for a HIGH QUALITY output. Or say dumb stuff like "Oh, you must be a genius to do all that." When "all that" is teach a 5-7yo NT kid to read, write and count. *grr* It'd be great to be able to recommend them a book that preaches getting in the mindset of teaching your kids if you want to educate them at home. Like, if your 4yo needs to learn letters and colors, TEACH them their letters and colors. If your 2nd grade is beginning to struggle in math, invest YOUR time and energy into understanding 1st the math that they need to be able to do, then invest YOUR time and energy into helping them understand it. etc. Anyway, I'm ranting at the choir at this point.

For routine, do it quickly and get it right type problems, you can just purchase a textbooks on the same topic and have her do the word problems from each lesson, Mid Chapter reviews and chapter reviews from each chapter, going back to work through the lesson when she's stuck. There are very few workbooks at the high school level of mathematics, but Mark Twain media publishes some. I'm not sure if they're good or not.

Pal wrote a story. In Spanish. Of his own volition. It's a short story, but still a BIG deal. If you'd told me 6 weeks ago that Pal would write a story in his secondary language this year, I'd have told you that you didn't know my kid very well. But I forget that kids can be changing and transforming every week or that sometimes, your child wakes up a completely different person than who they've been for the last several months or years. Sometimes it's like they go to bed and then BAM Update Complete. Please restart the machine. They wake up newly capable of things. So neat. I'll try and write a better update on their language studies soon.

Parents as teachers who are actively teaching. I find materials that teach me how to teach something are more valuable than almost anything else. A guidebook with a strong Just Roll Up Your Sleeves and Do It Your Damn-self vibe to it would be nice to recommend. I find the rampant desire for Independent Subjects for elementary and middle schoolers weird. I think a solid manual for elementary math education is needed. Too many home educators are clueless about math and they are okay remaining clueless and inept at math. Personally, I hate edutainment. I find it gimmicky, and ineffective more often that not. Things that cut out the the teacher/parent as the middle man make me uneasy. I can't lie, it comes across as lazy when parents want an app to teach their young kids how to read, compute, and write. I judge when people outsource math at the 3rd-5th grade level because they're bad at math themselves. Get a book and learn along with your kids. I wish there were more Direct Instruction type products available to homeschoolers, so something with a strong Direct Instruction flavor for math, science and or history at the 4th-8th grade level would be nice.