:grouphug: I see myself in your son. I completely understand the "sincerely promising to do better" - and really, truly meaning it down to the bottom of my heart - and then returning right back to the thoughtless behavior. Over and over and over. For me it was a combination of really wanting to do better but lacking both the skills and the motivation to do better (but at the time I was unaware I lacked the skills - I thought it was just a lack of motivation thing). And I did best for people who had *clear*, *firm*, *straightforward*, *reasonable* expectations - people who made it clear what they expected from me *and* set out a clear path to achieve those expectations *and* provided both encouragement and accountability. I did the absolute worst with people who stood back and accepted whatever I could do on my own. I just didn't have either the motivation or skills to "go above and beyond" in turning things around myself, and I prioritized the people who both made it clear that my actions or lack of actions *mattered*, and who made acting *doable*. (People who made it clear that my actions mattered but didn't make the path for acting doable - them I avoided like the plague once I started failing them. People who never seemed visibly upset with me for my failures were restful to be around but I never did stop failing them - usually I sort of took that as subconscious permission to quit trying to not fail them.) My mom sometimes assumed that my failing to do something she'd asked me to do was because I *refused* to do it *on purpose* in order to hurt her. But honestly it *never* was that, not ever. I don't remember *ever* purposefully refraining from doing something she really wanted me to do in order to hurt her. She always assumed that since what she wanted me to do was simple (generally true) and that she'd made her expectation/desire clear (also true), the only reason I didn't do it was because I didn't *want* to show her love. But that wasn't true at all. It *was* true that my desire to show her love wasn't strong enough to overcome my lack of motivation/skills :( - but my *failing* to act was totally, utterly different than *refusing* to act. I *wanted* to show her love - but wanting it just wasn't enough to be able to make it happen :(. And I hated myself for it - that I was hurting others - and that I wanted to change, but not enough to, you know, actually *change* :(. But I never did it on purpose - I just didn't *not* do it on purpose :(. It felt like I had a zillion things on my plate, and self-centered me did the ones I liked the best and the ones that were the easiest and the ones where the consequences for failure were intolerably high. (Except that my cut-off point for "intolerably high consequences for failure" kept sliding up - I could tolerate more and more serious consequences if it meant I didn't have to do that thing that loomed so high.) And I was a procrastinator - on things I didn't do I rarely intended to not do it from the start, but just kept postponing the starting until the deadline was past. All that to say - he *says* he wants to be with you and do these things with you, and I'd accept that at face value as being sincere. But his actions say that he is unable/unwilling to make that happen on his own, and I'd accept that at face value, too. But when I was in his shoes - wanting to be better but unable/unwilling to make it happen on my own - I avoided the people who made failure too costly (so I didn't have to face the consequences of my failure), and I enjoyed being with people who placed zero expectations on me (can't get easier than that) but that just enabled my self-centered thoughtlessness. But the people I valued the most, who made the most difference - were the ones who were had expectations, but who made *succeeding* at them *doable*. They didn't excuse failure but they didn't make the cost of failure too high, either - and most importantly, they provided not just clear expectations but a clear *path* to achieving those expectations. (In the best cases, walking the path they laid out built in me the skills to be able to later meet those expectations without scaffolding.) I actually *changed* because of them. IDK, that sort of expectation scaffolding is hard work. But I get being that young adult who hates that they are taking the easier, selfish path and desperately wants to be better, yet can't/won't stop taking the easier selfish path when it's available :(. For me, I do the *worst* when there are no overt expectations, when people act like it makes no difference to them whether I do good or just slack off - it's like "permission" to be selfish, because if what I do makes no real difference either way, then why *not* take the easy path? (And this co-existed with my very strong drive for achievement until I could no longer achieve at high levels *while* being on the easy path. My dad, when faced with this choice in college, decided to get off the easy path, work hard and achieve. I decided to avoid choosing, and drove myself into a depression over it, which pretty much killed achievement.) IDK, all that to say, I see some of myself in what you've written of your son. He wants to do better but can't/won't. In some ways, he doesn't do any better than he "needs to", at least when it comes to family life. And the less expectations that are explicitly placed on him, the less he "needs" to do, and so the less he does. It doesn't sound like he likes that reality any more than you do, but he's unable/unwilling to change on his own - not till he *needs* to change. I didn't do well with high-pressure "need to change" situations - because it wasn't *just* a motivation issue with me, but also an executive function issue. (I didn't realize I was mediocre at many EF skills till my 30s, because my general ability and very good memory made up for my so-so organization/planning/execution skills.) But low-but-consistent "needs to change" expectations combined with a clear *path* to meeting those expectations - that's *exactly* what I needed. ETA: Speaking explicitly of Christmas traditions, my mom also gave us a special ornament each year, and every year we'd put them up in order, retelling the stories behind them :). It was so special and wonderful, and it pains me so much that I haven't passed it on with my kids :(. Mom used to give the kids special ornaments, but after one too many years of her coming to visit in June and seeing a pile of un-put-away ornaments in the basement, she figured that giving ornaments caused more trouble than they were worth, and so quit giving them :(. I'm pretty sure she was sad that I didn't value that tradition :(. But that wasn't it at all. I can't *manage* that tradition, but I *love* and value that tradition so much - I have so many fond memories of it, and the kids love remembering with the ornaments they have. And I'd be so *happy* if there were someone who could help me make that tradition happen again.

I've used the tb/wb from 1a-4a and IP from 1a-3b (we run it a semester behind). There is very little repetition between the IP and the WB. The WB follows right along with progression in the text, possibly just a shade easier than the text (or so people say). There's very little explicit teaching in the WB (as that's in the text), but it usually reflects the scaffolding and guidance that's in the text. For example, we're doing fractions in 4a, and they scaffold the process of adding/subtracting unlike denominators by doing some problems where they make the "change to the same denominator" part an explicit, separate step, before giving problems where students have to do that step in their heads, on their own. The point of the WB is to give practice on what you just learned in the text, and IMO it does a good job at that - if my dd understood the text, she generally has little trouble doing the WB independently. OTOH, the IP is meant to go beyond the tb/wb, and there is very little straight review - just about everything is a step up from the wb. The only teaching/guidance is an occasional brief restatement of what the tb said, and the scaffolding can be iffy/insufficient/non-existent. (They threw a three-step problem in 2b without noticeably prepping for it or warning you it was a step up from what you'd seen before; they also threw in one of those "you don't know the starting value but as you work the problem you realize you don't need it" in 2b out of nowhere that really threw my dd. We've seen those problems occasionally since, and she's starting to get more comfortable with them. Somewhere in 3 they threw a "4 ways to get from A to B, 5 ways to get from B to C, so how many ways to get from A to C?" question that was never taught or introduced anywhere. There's a lot of that in IP ime - all-new problem types coming out of the blue with no nothing to help. There's several spots in each book where I work through new problems like that with dd together, kind of use that as her intro to them and teach her how to work them.) You really need to be *solid* on what the text teaches before going to the IP. There is definitely less white space in IP than in CWP. (My dd regularly complains about the lack of space, in fact, and she can get overwhelmed by the number of problems per page. IP went a lot better once I started assigning her a few problems on each page of the chapter each day instead of a few pages each day, and when I provided a graph paper notebook for her to do problems on if there wasn't enough space in the text.) There's a chapter in IP for each chapter in the textbook. Each chapter has 6-8 pages of problems, ten word problems, and 2-4 challenging problems. Usually I divide the chapter into 3-4 days of work. We have CWP, but I haven't been getting to it, b/c between the tb/wb and IP, that's a lot of math that dd is doing each day. Might go through the extra challenging problems in CWP at some point. But two-step problems have become old hat for dd (I think all the IP word problems are at least two step problems), and even most three-step problems are very straightforward for her. And there's a *lot* of mental number manipulation throughout IP. IP stretches dd in ways the tb/wb just don't - it's hard for her, but it's good for her :). (But she does need the wb practice first - going straight to IP does not work for her at all.)

I have, too, but iirc it was usually in the context of people who were 3-4 or more standard deviations from the norm. It's the idea that once the quantitative differences get large enough (how fast you learn, how deep you learn, how abstract you think) it makes for a qualitative difference in how you learn. And, actually, bright kids (call it 115-130 IQ) stuck in a low-performing classroom (targeted to the lowest "typical" IQ range, say 70-85 IQ) are three standard deviations above the targeted instruction level, and that's comparable to a kid with an IQ of 145 being in a classroom where the instructional level is geared for the "normal" child of 100. So I'd think your experience would be a decent comparison. I tend to experience that kind of boredom as there just not being *enough* to think about - not enough material, not enough depth, too much repetition. It's like being at a feast where there's two bites per course and there's five hours between courses - and everyone else seems to eat at a 1 bite/2.5hr pace, like it's the most normal thing in the world. But you are starving and ready to eat the tablecloth. At a certain point, when the differences in speed of learning and amount of material become great enough, it kind of becomes a whole 'nother way of learning. I've heard the same - that a child with an IQ of 130 is as far from the norm (and as equally rare in the general population) as a child with an IQ of 70 (two standard deviations from the norm); a child with an IQ of 145 is as far from the norm as a child with an IQ of 55 (three standard deviations); a child with an IQ of 160 is as far from the norm as a child with an IQ of 40 (four standard deviations); and a child with an IQ of 175 is as far from the norm as a child with an IQ of 25 (five standard deviations).

Short answer, scoring at least 2 standard deviations above the norm on an individual IQ test (usually ~130) seems to be fairly accepted wrt identifying gifted students in the Hoagies' gifted community. And I've seen that means of identification paired with a definition of giftedness as being above the norm in abstract thinking. Generally, I've seen two broad streams of thought in the gifted community - the achievement model (being gifted means producing accomplishments of note, well beyond that of peers) and the developmental advancement model (being gifted means being substantially ahead of peers in some/all areas). With the achievement model, gifted education is about talent development: finding students with the potential to achieve and then supporting and nurturing that achievement. With the developmental advancement model, gifted education is about finding students that are advanced beyond the norm in some areas (and so learn differently than their typical peers) and then supporting and educating them in line with how they learn. The achievement/talent-development model focuses more on what gifted people *do*, while the development advancement model focuses more on who gifted people *are*. There's some overlap in the two models, but sometimes the debate between the two gets contentious. Here's a pro-developmental advancement article contrasting the two: http://www.negifted.org/NAG/Spring_Conference_files/Giftedness%20101.pdf . The author of the article tends to be pro-IQ-test for identification because it can uncover "hidden" giftedness, gifted kids that aren't obviously standing out wrt achievement in their current environment.

Yes, it does make a difference to me when the customer skipped the b&m stores and went straight to online shopping, with all the pros (cheaper, wider selection) and all the cons (can be hard to judge from pictures and brief descriptions, without seeing it in person), or tried the b&m stores first but didn't find anything that worked and so turned to online shopping to find something *different* than what they looked at in person. Because taking advantage of all the pros of b&m shopping (getting to see it in person, try it on, flip through the pages, etc) to overcome the cons of online shopping, but then ultimately purchasing online - you received genuine value from the b&M store (getting to see the items in person), but you didn't value it enough to compensate the b&m store for providing that service to you. If you appreciate the benefit of being able to see an item in person before purchasing, then maybe you ought to be willing to pay for that benefit. Because it's sad when local b&m stores go out of business when they provide a service people just don't want enough to pay for it, but it's rather tragic when b&m stores go out of business when they provide a service people *actually use* yet they still won't pay for it. There are some parallels to theft there - taking offered value without paying for it. I'm *shocked* that people just state outright to the b&m store workers that they are going to buy online - that they see no problem with taking up employees' time and effort and then openly telling them they are going to buy this exact same thing elsewhere. To me that's something you say when the service was so totally abominable that they don't *deserve* getting the sale after what they did. It's a slap in the face - so to do that to people who were genuinely helpful? Exceptionally rude in my book. I knit, and the "see in person, buy online" thing makes things really hard for independent yarn stores. Knitters frequently point out that if you *like* being able to see yarn in person at your local store, then maybe you ought to *buy* it there, too, so the store can stay open and you can continue to have a place to see yarn in person.

I see a difference between "typical" and "typical good" - iow, a typical school might not be that great. Also, I see the GreatSchools rankings as like state tests: scoring well means you are doing well by typical standards, but there's no differentiation in rankings between typically-good and genuinely superior - a high score could mean either. (And in fact state tests form a large part of GreatSchools' rankings - having an above average ranking means you have above-average state test scores - there's quite a ceiling on measured achievement.) So an above-average school on GreatSchools has above average state test scores. And an average scoring school has average state test scores. Average scores mean typical - but are average scores actually *good*? (FWIW, one of our local schools is ranked 4 and I considered it a bad sign, although it's possibly due more to its challenging population than how much teachers are teaching.) Here's an article on GreatSchools about "the murky middle" - what average rankings mean and don't mean about the school: http://www.greatschools.org/gk/articles/what-average-greatschools-ratings-mean/

I got the Alan Lee ones: https://smile.amazon.com/Hobbit-J-R-R-Tolkien/dp/0395873460/ https://smile.amazon.com/Fellowship-Ring-Lord-Rings-Part/dp/061826051X/ https://smile.amazon.com/Two-Towers-Lord-Rings-Part/dp/0618260595/ https://smile.amazon.com/Return-King-Lord-Rings-Part/dp/0618260552/ Our library has them, so I was able to see them in person before buying them.

I really loved Sleeping Murder (the last Miss Marple case), and it came out in 1976.

I loved Pegasus, but I agree with you about Sunshine - eta, no the following rant is about Shadows. It was worth reading once, but not re-reading, and it felt oddly incomplete. She hinted at uncovering a relationship between science and magic, and how the attempts to use science to solve a magical problem were actually making things worse, but then never went further with it - just kind of dropped it and it played no role in the resolution - the whole science/magic conflict/relationship was just left hanging, like she hadn't been dropping hints about it for the first two-thirds of the book. (I'm interested in attempts to reconcile science and the supernatural, so I was intrigued at where she was going to go with it, and was disappointed that the answer was nowhere. Dragonhaven was another book where she was integrating science and magic, and it fell flat for me, too - didn't even finish it.) ETA: Realized I'd smooshed Sunshine and Shadows together. Sunshine was the vampire book (which was mostly meh, although worth reading once), Shadows was a different urbanish fantasy setting. I spent the past 10 minutes trying to tease them apart in my head, and as I'm failing, I'm realizing that they are kind of similar, actually.

Agree with Mary Higgins Clark. I liked her old books, but about 10-15 years ago her books went from having hints of paranormal stuff to being saturated with it - went from being an occasional extra to front-and-center - and with too much of an "it's really-real vibe" for me to have interest in reading them. I liked Lori Wick (a Christian romance author) in my teens, but between me changing and her changing, I didn't appreciate her newer stuff. IDK if her beliefs changed or she just started to get more intentional about including them, but she started putting explicit theological discussions into her later books. While I actually am all about hard-core theology, and completely agree with authors putting their theology heavily into their work, the deeper/more-detailed theological discussions just showed me how I really don't agree with her take on Christianity. I'd always known that, but it highlighted how our respective positions were increasingly diverging, and eventually I couldn't take it any more. (Also her later books didn't have the "magic" of some of her earlier books - idk if that's because of her theological change, or was incidental to the change, but it didn't provide much of a reason for me to put up with the constant awareness that her work was saturated with theology I disagreed with. I haven't re-read her books in years - I'm not sure I would still appreciate her earlier stuff anymore, I've changed so much.) ETA: I binge read the Kay Scarpetta series in college and I burnt out on it and never finished the ones out at the time, let alone seek out new ones. IDK if the later books really did get darker or the cumulative darkness and unhappiness just became too much.

I think there's also an assumption among people who are pro-formal grammar teaching that kids will *naturally* apply their formal grammar knowledge to their writing. (Or, among grammar experts, that teachers will naturally connect formal grammar to writing.). Either way, people expect the promised practical results of formal grammar study to flower naturally, without deliberate effort on anyone's part - and when it too often doesn't, people assume the problem is that formal study is worthless, not that people need *explicit help* applying their formal knowledge to writing. I think part of this is the inherent difficulty in connecting formal knowledge of anything to practical, intuitive knowledge of life (math has long had this problem) and part of this is that we've lost a lot of practical grammar knowledge and knowledge of how to teach grammar.

Pulled out our books and compared. The FAN math books are divided into two parts: the model approach and the heuristic approach, each about half the book. The model approach chapters line up pretty well with the first half of the year (the A books), and you could work through the heuristic part during the B books. FAN math level 2 is pretty good for teaching the models from the ground up. Level 3 has a quick review of the basic models and then jumps into two step problems.

Yes, level 3 of FAN math lines up with Primary Math 3, and so on. The ToC matches up pretty well - you could teach FAN math alongside Primary Math - take a few days to work through FAN math until you catch up to where you are in your main text, and then work FAN math alongside - my plan is to teach the text and then teach the section of FAN math, then do the wb. (Right now we're working through a lower-level FAN book to get dd's confidence up - I expect we'll be skipping up to our tb level soonish as she feels more confident.)

Agree with pp that the HIG and manipulatives and games can help. I think the way SM does, so I haven't gotten the HIGs - my go-to method of teaching is to work out the textbook's pictorial examples with manipulatives (cuisenaire rods, the RightStart abacus, and a "treasure chest" full of "jewels" are my go-to manipulatives). But if that's not enough, sometimes I end up flailing around a bit in my attempts to come up with alternate ways to explain what SM's trying to do - go through several failed tries until I hit something that sticks. If that happened a lot, or I myself didn't quite understand the point of what SM was trying to teach (and why I should care about it instead of skip it), I'd probably get the HIG in order to have some tried and tested teaching helps. Also, since she knows one way of working the problems, it can help to do the problem the way she knows and then do it the new way, explicitly connecting the two together - so she can see how this new way relates to what she already knows. I have the old 3rd edition of 2a, and they teach differently than it sounds like the standards edition does - their approach to the standard algorithm sounds like it might be a good bridge between what Saxon taught and SM's mental math techniques (which is how I think of the "subtract from nearest ten" technique). SM math teaches the mental math techniques *first* (1a and 1b are all about adding and subtracting completely mentally) and uses them as a bridge to the standard algorithm - but there's no reason you can't work the other way. Since you *know* the standard algorithm, you could use it as a bridge to learning the mental math techniques. SM teaches several ways to regroup before applying regrouping to the particular type of regrouping that is carrying and borrowing in the standard addition/subtraction algorithms. You know how to carry and borrow - that's a form of regrouping - and you can apply that understanding of regrouping ones into tens when you carry and tens into ones when you borrow to regroup numbers in other ways, too. IDK how Saxon used manipulatives to illustrate the standard algorithm, but to me (and my Singapore brain) it seems like it would be fairly similar to how 2a illustrates the standard algorithm (let me know if that's not the case). Looking at my part 5 of unit 2, they have the problem illustrated with a hundreds/tens/ones chart and counters. I'm pretty sure I just used base-10 blocks instead (actually I used cuisenaire rods as base-10 blocks). So let's do 62-43. So you have 6 tens and 2 ones (actually set them out with counters or blocks or rods). There's not enough ones, so you exchange 1 ten for 10 ones (and do it for real with your manipulatives), so you have 5 tens and 12 ones. Then you subtract 4 tens and subtract 3 ones (again, actually taking them away physically). That seems like it ought to connect pretty well with what she knows from Saxon. Changing 1 ten into 10 ones when you borrow and changing 10 ones into 1 ten when you carry - having *different* groups that represent the *same* amount - that's just *one* way to regroup numbers. And SM is going to teach you some *other* ways to group and regroup numbers, too. Ok, so now how to connect that to SM's mental math techniques. Probably the easiest "breaking numbers apart" SM technique is "add tens and ones" and "subtract tens and ones" => it's the exact same thing you do when you add/subtract without regrouping (no kidding, as an adult it seems positively trivial as a mental math technique). Only, they teach you to think about it in terms of breaking up the numbers into tens and ones, and first adding/subtracting the *tens* part and then adding/subtracting the *ones* part. For example, for 54+3, you break apart 54 into 50 and 4, and then add the 3 and 4, and then put the 7 back with the 50 to get 57. (When you do this with base-10 manipulatives, it's very natural to see the two parts.) For 54+30, you break apart 54 into 50 and 4, then add the 50 and 30, and then put the 4 back on to the 70 to get 74. And then when 1b does that with subtraction, they integrate the idea of moving a ten over to the ones when needed. So for 57-30, you break the 57 into 50 and 7, subtract 30 from 50, and then put the 20 back together with the 7 to get 27. And for 57-3, you break the 57 into 50 and 7, subtract 3 from 7, and then put the 4 back together with the 50 to get 54. And for 60-3, you break the 60 into 50 and 10, subtract 3 from 10, and then put the 7 back together with the 50 to get 57. For 82-6, you break the 82 into 70 and 12, subtract the 6 from the 12, and put the resulting 6 back together with the 70 to get 76. For 56-14, you break the second number, 14, down to 10 and 4, and first subtract the 10 from 56 to get 46 and then subtract the 4 to get 42. Doing those sorts of problems makes up a *lot* of 1a and 1b - cements place value and practices the idea of breaking up numbers. (You could quickly run your dd through your ds's SM1 textbook, practice working with numbers in those ways.) Another big SM "breaking down numbers" technique is "using number bonds". This is going to extend the idea of regrouping numbers in ways *others* than changing 10 ones to 1 ten and 1 ten to 10 ones. The "add/sub ones and tens" method builds builds off place value to practice breaking numbers into tens and ones, doing something to the tens and ones, and then putting the new amounts back together into one number - it gets you used to seeing numbers as a collection of tens and ones (and carrying/borrowing extends that by *changing* tens to ones and ones to tens - not only are numbers a collection of tens and ones, there are *several* ways to group them as tens and ones). "Using number bonds" builds off math facts to practice breaking numbers down along math fact lines. With 24+6, you'd break the 24 into 20 and 4, group the 4 and 6 together to make 10 (that's your math facts at work), and then put the 20 and 10 back together to make 30. With subtraction, 30-6, you'd break 30 into 20 and 10, group the 10-6 together to get 4 (again, math facts at work), and then put the 20 and 4 back together to get 24. With 39-6, you'd break the 39 into 30 and 9, group the 9-6 together to get 3 (again, math facts at work), and put the 30 and 3 together to get 33. For a more interesting example, with 34-8, you can divide 8 into 4 and 4 (math facts at work), subtract the first 4 to get 30 and the second 4 to get 26. (You can see a large crossover with the previous method.) Another big SM "breaking down numbers" technique combines the previous two: "making tens". This is the one that SM is known for - but the above two build up necessary skills that underlie making tens. In making tens you are using the number bonds that make 10 (1&9, 2&8, 3&7, 4&6, 5&5) to guide you in breaking down the numbers to form one of those adds-to-ten number bonds. So with 15+8, you ask yourself, "how much does 8 need to make 10? => 2" so you then break 15 into 13 and 2, combine the 2 with 8 to make 10, and then put the 10 and 13 together to get 23. You could also ask the opposite question: "how much does 15 need to make 20? => 5" and then break the 8 into 5 and 3, combine the 5 with 15 to get 20 and add back on the 3 to make 23. With subtraction, 34-8, you break the 34 into 24 and 10, subtract the 8 from the 10 to get 2, and then recombine the 24 and 2 to get 26. That last one is the technique that you mentioned in your post. It's probably the most complicated of all the mental math techniques, because it involves *adding* within your *subtraction* problem. It's taken a lot of manipulative work to illustrate this for my oldest, and also it helps to be firm in all the previous add/sub mental math methods. Because all the previous methods work by breaking numbers into groups, doing *something* to one or both groups, and then putting the two groups back together. Once you've got the idea of ending the problem by putting the two groups back together - ending your making tens subtraction problem by putting the remaining two back with the other group is just like what you always do. You can do a lot of manipulative work here - have a number in manipulatives, physically separate it into two groups, do something to one or both groups, and then shove the groups back together. You can illustrate carrying and borrowing this way, too - separate your number into hundreds/tens/ones groups, and then for carrying you'd add to each group, then regroup your ones into a ten, and shove them all together again. For borrowing, you'd separate them by place value, look to see if you can subtract, find there's not enough, so you regroup your ten into 10 ones, and then subtract each group, and shove the groups together at the end. And to show the different ways of regrouping that all get you to the same answer, you could start with the same number, break it into *different* groups and do whatever needs doing to those groups, and put them back together and show how the ending amount is the same. (Also you can show connections between the different groupings and what is done to those groupings - how it's not magic that there's different ways to get the same answer.) IDK, does any of this help it make more sense? There's a lot of practice with number bonds in the SM 1a - practicing seeing 6 as both 2&4 and 3&3 and 1&5 and 6&0. And there's a lot of practice using all those techniques to add/sub within 20 in 1a. Maybe you and your older kid could work through some of them with manipulatives - move things around to help really *see* the different ways to group and regroup - to before going back to 2a and applying those techniques with and without manipulatives to figure out those bigger numbers.

Do you understand how his model works? *Could* it be extended to work for two unknowns? Or is it limited and only works for simple problems but inherently can't be extended to more complicated ones? If his model *could* be extended to work for two unknowns - he just doesn't know how to do it - then I'd probably stick with his model method and teach him how to apply it to the more complicated problems. If his method *can't* be extended to work for the more complicated problems, or if his method would be much more cumbersome and/or prone to error, or you really like bar diagrams, then I'd try to use his method as a base for teaching bar diagrams. Work through several simple problems doing both his method and the bar method and showing how they connect together. (With my dd, it helps a lot to teach bar diagrams with problems she intuitively gets, so the only "new" thing is the diagram itself.) It may or may not help to explicit show him how his method falls apart with two unknowns (if it does indeed fall apart), but if his works but is cumbersome, I've found that working through several problems both ways, till he really *gets* the new method, is sufficient for illustrating how the new method is less work/more elegant. (It's how I got my second dd to acknowledge that multiplication instead of repeated addition might actually be better - doing both together helped her see how they connected and were doing the same thing, and once she understood what was going on, she did kind of tire of writing 4+4+4+4+4+4 instead of 6x4 and saw the point to multiplication ;).)

Is it this "A Dog, a Cat": http://shortvowelphonics.com/phonics/short-vowel-phonics-book-1/ or this, "Max the Cat": http://shortvowelphonics.com/phonics/short-vowel-phonics-book-2-a-i/ Your description reminded me of the Short Vowel Phonics books, and the first two are both about a cat and dog, and the second one has a dark-ish cover.

Bar diagrams don't come easily to my oldest - showing her thinking in general doesn't come easily for her (it took several months before writing the equations and then her answer in a sentence became natural, and even now she still tends to get the answer first and works backward to figure out the equations at least half the time (an improvement from the 100% of the time it was when we started)). Just seeing the examples in the text and CWP and the Singapore Model Method book wasn't enough for her to really understand what was going on and how to use bar diagrams as a problem-solving *tool*. If she had *another* way to visually show her thinking, I'd have let it go, but she struggles at getting what's in her head out in general (whether orally or on paper), and when she can't intuitively see what she's supposed to do, she locks up and has no tools for getting out what she *does* know to aid her in figuring out where she can try to go from there. She needs *some* method of laying it out, and as bar diagrams make sense to *me*, that's what I'm going with for the moment. I bought the Process Skills for Problem Solving books - they build up drawing bar diagrams from the ground up, plus several other methods of problem solving (including other kinds of visual diagrams) - and we're going through that alongside her usual work. As she gets better at diagramming her thinking, I'm going to start requiring bar diagrams along with her equations and answer - I think it's important to be able to show another person *how* and *why* she got the equations she did, as well as have tools for getting your thinking out on paper where you can look at it and mess around with it. Bar diagrams aren't the only way, but as dd currently has *no* way, that's the one I'm going with for the moment - I think it will do her good.

One issue is enough to *break* my vote, but it alone isn't enough to *make* my vote. I have a "litmus test" issue - if a candidate is against it, then that's enough to remove them from consideration for me. But among the candidates that are for it, then I look at other things to decide who to support. (In an ideal world, anyway. Candidates who pass my litmus test are thin on the ground right now - the idea of being able to choose between several seems like an unattainable luxury, and of the few who do, most have a host of other issues that collectively break them. I mostly just don't have a candidate because of it.)

Are you asking why the second is "Stay in the garden often" while the first is "Always frighten bad wolves" - why the different adverb placement in English when the Latin had the adverbs in the same place? English adverbs are pretty movable iirc: "Always frighten bad wolves," "Frighten always bad wolves," and "Frighten bad wolves always." "Often stay in the garden," "Stay often in the garden," and "Stay in the garden often." =>All those would be possibilities. My best guess is that they picked the most "normal" sounding of the possible English choices - the one that sounds the most natural to a native speaker's ear (assuming that the Latin adverb placement was also the most "usual" placement - so if there was no special emphasis in Latin, you are trying to also have no special emphasis in English; if there *is* a special emphasis in the Latin, then you want to try to replicate that special emphasis, as much as possible, in the English translation). "Always frighten bad wolves" is to me the most natural-sounding of the choices for the first sentence, and "Stay in the garden often" does sound more natural to me than "often stay in the garden" - that second wording seems like an awkward sort of command. But I think it's more a matter of style than just grammatical correctness - picking the best of the possible grammatically correct choices. IDK, that help any?

I think they want to be thought of as separate because they believe that: a) there *is* a difference, and b) that difference *matters* and so is worth maintaining. And, yeah, that implies c) that the alternatives are in some way detrimental and sub-optimal, although this could be judged on a spectrum, noting areas of agreement as well as areas of disagreement, instead of making a blanket judgment that everyone-not-us-is-100%-bad. And how you treat people who you somewhat agree with and somewhat disagree with - where the agreement matters but so does the disagreement - that's a related-but-separate issue. I'm not an unschooler, but I have experience with trying to maintain the tension between holding to distinctives-that-matter - and the uphill battle in trying to convince others that they *do* matter - while also trying not to get all insular and cliquish and everyone-who-doesn't-100%-agree-with-us-is-100%-wrong and so has nothing but badness to offer - without then forgetting why the distinctives *do* matter and *are* worth preserving over against similar-ish-but-also-different neighboring groups. A bunch of people who agree with you that your distinctives are good but disagree with you that your distinctives are in fact *better* than other similar-ish groups' different distinctives, or who mostly hold to your distinctives except when they don't - they really mess with your group's ability to hold those distinctives. And, more significantly, a critical mass of conditional instead of unconditional commitment changes *everyone's* ability to understand and live those distinctives, even people who are all-in. IME, the people who yell loudest about how we are all right and they are all wrong are those who have only a very surface understanding of why this matters, and they substitute volume and passion for deep understanding. But people who argue that they agree with us on the topic but don't agree that it matters - they don't have more than a surface understanding either, only they don't think there's any other understanding to be had. And too many people working off just a surface understanding limits the group to only a surface understanding - everyone comes to think that's all there is, loses the knowledge there is more and loses the ability to deepen their understanding - and the only difference is how much you think that surface understanding matters. And then you have lots of yelling with no change :(.

And there's also the difference between someone who's a vegetarian for health reasons and someone who's vegetarian for ethical reasons. If you're a vegetarian for health reasons, then if a strict vegetarian diet isn't leading to the best health results for you, there's every reason to modify it to include some meat if that results in better health. But if you are a vegetarian for ethical reasons, then whatever problems you might have, eating meat is just not an option - because eating meat is *wrong*. Unschooling for educational reasons versus unschooling for ethical reasons - it's a similar thing. Unschooling *so long* as it's the best way (and stopping when it isn't the best way) is just a different kind of commitment than unschooling *because* it's the best way. And as helpful as "unschool as long as it's working" people find the "unschooling or bust" people, it doesn't always work out well in reverse - it would be very frustrating to go to your unschooling support group with your problem and hear a bunch of "unschool as long as it is working" people advise you that it is time to give up instead of helping you find a way to make it work, kwim?

It doesn't help that unschooling can both refer to a way of educating and to a way of life. It's why radical unschoolers coined the term radical unschooling in the first place - to distinguish themselves and their practice of whole-life unschooling from people who just unschool "school" or who unschool the unstructured parts of the day but not school or life in general. Think of it this way, maybe: I say I teach tolerance in history, because how else do I describe emphasizing the contributions of minorities and teaching from several different viewpoints?...I wouldn't call myself an tolerant homeschooler, but I would describe it as teaching them tolerance in that one subject. Someone might say, if you believe tolerance is important, why aren't you teaching it in *all* your subjects, why aren't you living it out in your whole life? Is it possible to genuinely teach tolerance in history while otherwise living an intolerant life? Does a person who is only teaching tolerance in history while otherwise living an intolerant life - is their understanding of what it means to "teach tolerance" have *anything* in common with people who teach tolerance in everything and live tolerance in everything? So someone who lives tolerance in their whole life might quite naturally think that the "teach tolerance in history but otherwise live intolerantly" person fundamentally doesn't understand what tolerance *means*. Living ethically is an all-the-time thing. And radical unschoolers see unschooling as part of living ethically - that the same principles that led them to unschool also impact how they live *all* their life. And so people who see unschooling as basically one method of many for cultivating knowledge, instead of the practice of a certain kind of ethical living applied to education - that's a totally different understanding of what unschooling is. It's borrowing practices developed to support one philosophy, separating them from the beliefs that prompted them and the results those practices were trying to cultivate, and dropping them into a different set of beliefs that are using these practices to attempt to cultivate a different set of results. It's like Christians borrowing from Eastern meditation techniques to enhance their prayer life - you can argue whether or not eastern meditation is compatible with Christian prayer and argue about whether it's even possible (or desirable) to completely divorce the meditation techniques from their original context and plop them down in an entirely new context - but whatever those Christianized meditation practices end up looking like, they mean something very different from what they meant in the original Eastern religious practice, no matter what the surface similarity. Clear as mud? ;)

WRT reading good literature is enough to pick up proper sentence structure and do well on standardized tests - not in my experience. I got very little grammar as a kid - basically the eight parts of speech in elementary and that's it. I read a ton and did pick up a lot of intuitive knowledge of grammar, and generally wrote well enough by the "does it sound right?" method. And that was fine for the state tests, and mostly good enough for AP essays (although I did feel hampered being limited to intuitive guess-and-check to fix iffy sentences, and it seriously limited my ability to do the language analysis on the AP English Language and Composition exam - multiple choice was fine, but my analysis in my essays was mediocre at best - brought my score down to a 4 and I was happy to get it). But what it *wasn't* good enough for was the PSAT. My year was the first year they had a writing portion, chock-full of grammar usage questions, and my "does it sound right?" intuitive-only knowledge was simply not at the same level as my math and verbal knowledge, and that brought my score down. I missed making National Merit Semi-Finalist over it (one bloody point!). But more important than scoring low on the PSAT is *why* I scored low on the PSAT - my intuitive-only grammar skills were much weaker than my formal-and-intuitive math skills and I knew it and disliked how that limited me. Because if I didn't intuitively see the answer, there wasn't anything else I could do - I was stuck. And even when I knew the answer, I didn't know *why* it was correct - only that it was. It's extremely frustrating to stare at an iffy sentence, going back and forth between all the choices I could think of to fix it and have them all sound wrong - to be forced to re-phrase the sentence entirely because my intuitive knowledge of that grammatical structure is lacking and I have no way to correct it, because I don't even know how to describe what it is I'm not getting. I just don't have the language or concepts to go with my intuitive knowledge. The way I look at it, formal grammar knowledge and being able to diagram sentences - that's equivalent to knowing how to add/subtract/multiply/divide and what it means - procedural and conceptual knowledge. Give me 2300/54, give me (a^3+a^2 +3a +6)*(a+4) - I know just what to do and why. Being able to apply that formal knowledge to word problems and math problems in daily life - that's like using your grammar knowledge to analyze and explain what a sentence means and to construct sentences that say just what you want and you know just how you did it. It combines intuitive and formal knowledge, so that you both *feel* the rightness or wrongness, and also are able to formally analyze and explain what goes into that rightness or wrongness. Trying to analyze what makes this sentence good and that sentence mediocre - and what to do to turn the mediocre sentence into a good one - when all you have is intuitive knowledge? It's like trying to do word problems with a basic knowledge of what the add/sub/mult/div signs mean combined with an intuitive knowledge of the addition and multiplication tables - if you see 4 and 6, you know it's probably 10 or 24, and you can usually figure out which it is in a given problem. But sometimes the answer is 2 or 1.5 - and while you know it's not 10 or 24 (and you could rewrite the problem into one that *does* have an answer of 10 or 24), you have no tools to figure out what the answer actually *is*.

I wonder if it has to do with whether generic you is unschooling in service of a different higher good (the higher good is the higher priority and you fit your unschooling into that), or whether the goals of unschooling *are* your higher good, your unschooling convictions are your *core* convictions and underlay everything else you do in life.

WRT "unschooling for everything but math isn't possible" - it's part of "part-time unschooling isn't possible". And ime, that's because unschooling is often seen as a lifestyle, a way of living out particular convictions about the nature of kids and humanity and the right way to treat each other in light of those inherently moral convictions. And so unschooling "part-time" is comparable to following the Golden Rule "part-time" or being kind and generous "part-time" or not stealing "part-time". Unschooling when you can but giving up on unschooling when it's hard or seems impossible or when unschooling prevents you from accomplishing something else - that's making your unschooling convictions secondary. (And generally when people set aside their moral convictions when it's hard or inconvenient or their morals prevent them from accomplishing something "more important" - it says something about how much - or little - they truly value those convictions.) Saying you are a part-time unschooler is like saying you are a Christian on the weekends (but not during the week) or you are a Buddhist after school (but not during school) or you are a Muslim during everything but math class. And incorporating some unschooling practices into your otherwise not-unschooling life is more like borrowing a practice or two from a religious tradition than it is actually being part of that religious tradition. Radical unschooling, ime, is much more like a secular way of moral living than it is a schooling method.