Both of my girls were that way - OG-style spell-your-way-into-reading was great for learning to read, but didn't transfer over to spelling beyond CVC words. Like PeterPan, I did a *lot* of different things with them: *Did another go-around through our OG-style phonogram-based program, but in cursive, using it as both cursive practice and spelling practice. (Was great for learning cursive, for cementing phonics, and for developing the ability to read/write by syllables, but by itself didn't do overmuch for spelling - more helped with precursor skills.) *Did Spelling You See: its visual marking system was just the addition to studied dictation that we needed. (My oldest especially needed it - it taught her to pay attention to the insides of words.) I use SYS's marking system for all our studied dictation (doing Dictation Day by Day with middle now); I also converted WWE's cold dictation into studied dictation for my oldest (because her spelling wasn't good enough to write it without practice), and had both girls use the marking system on WWE's copywork. I do SYS in cursive instead of the print they strongly recommend, because I've got kids who have excellent visual memories but who struggle with spelling by ear, so the way the different fonts interrupt visual memory and require them to work through it more by ear is a feature instead of a bug for us. Dictation in general has been a big help in spelling. *Did Rewards Reading: hit the reading side of working through multisyllabic words by morphographs, but many of the skills it worked on are needed for spelling words by morphographs as well (lots of practice with breaking words into morphographs and putting morphographs together into words). *Did Spelling through Morphographs: this has been *huge* in developing their spelling ability. *Did Touch, Type, Read, and Spell: an OG approach to spelling, so it gives us a third time through OG (and to a higher level) In general, I've combined reading-based instruction, spelling-based instruction, and dictation (studied first, and studied and cold, once they are able to spell well enough). They've needed the targeted instruction to learn *how* to spell, and the extensive dictation work to give them enough practice applying their fledgling spelling skills so that they can learn to spell "in the wild".

Two of my kids are lefties. I don't really remember noticing till age 3 or so. We haven't had too many difficulties. I can write a bit with my left hand, so when I was teaching them to write I'd just pick up the pencil in my left hand and see how I did it, which was a big help. The right-handed mouse issue didn't even occur to me until last year; neither of my lefties had any problem using a right-handed mouse - my oldest even games that way. I tried to teach my lefties to crochet right-handed (so they'd not have to flip patterns around), but my oldest had problems and my youngest automatically switched to using his left hand; I'll probably see if my oldest does better crocheting left-handed. I taught my oldest right-handed knitting (ditto pattern reasons), but she's never persisted enough to know whether handedness is an issue or not. I can crochet left-handed, a bit, but I don't even know where to start wrt knitting left-handed, so that will be fun if dd13 wants to try it. ETA: Because of this thread, all my kids have spent the past 10 minutes trying to write and draw with their off hands, lol. They are all actually pretty decent - they can all produce legible print (albeit a bit wobbly and slanting down the page), and those who've learned cursive can produce legible cursive. My lefties actually did better at drawing with their right hands than my righty did with her left hand - not as good as with their left, but plenty serviceable.

Here's a more elegant way of solving the soda problem than I did before, one that takes better advantage of 1/20 cans as your common unit: Having found your LCM=20, you draw your diagram, dividing your bar into 20 equal units: |-----*****-----*****| Then mark the parts on your bar (2/5 of 20 is 8 units of cherry; 1/4 of 20 is 5 units of root beer; the remaining 7 units are the 28 cans of fruit juice): |-----***|**---|--*****| 1 unit = 28 cans / 7 units = 4 cans 8 units (of cherry) - 5 units (of root beer) = 3 units difference 3 units * 4 cans/unit = 12 cans difference

I will say, if you understand the problem and can solve it another way, it *is* a fun puzzle to then try to figure out how you'd do the bar diagram. Pretty much all bar diagrams fall into two categories: part-whole and comparison. Part-whole is usually one bar subdivided into parts (like the above soda problem), while comparison usually has each part gets its own bar (and you figure out how each bar relates to each other and the total). (And problems can combine elements of both: individual comparison bars being subdivided into parts, or comparing parts of a whole (like the end of the soda problem).) Figuring out which one to draw is the first decision you make with bar diagrams. Some problems can be drawn effectively either way, but some definitely prefer one or the other - if you choose wrong you'll run into trouble at some point. Once you get past the four operations and into fractions, ratios, and percentages, then another element comes into play: that of a unit. Generally speaking, in diagramming a fraction/ratio/percentage problem, you want to define some quantity as your base unit and draw everything in relation to it. Really, it's very comparable to choosing a variable. (Although if you bring algebraic thinking to figuring out your diagram, sometimes you'll end up with a less elegant unit than if you were thinking in diagrams - the diagram becomes more of an appendage or visual showing of your algebra than a genuine tool for solving the problem.) So, in the soda problem, the first bit of work you do is to find your LCM for your unlike fractions, and that's your unit - 1/20 of the total number of cans - and everything sorts out very nicely from there. So, in terms of trying to puzzle out bar diagrams, it helps to think in terms of part/whole versus comparison, and (in fractions/etc.) to seek a common unit to subdivide your bars into.

It's a basic part-whole diagram, but what makes it hard is dealing with the fractions of differing denominators - figuring out how to draw it without basically solving it first to be able to accurately draw it. You can first find your LCM and make 2/5 and 1/4 into equivalent fractions (8/20 and 5/20), and then you'd know just how to draw everything. But you don't have to. The way I deal with the practical issue of drawing unlike fractions accurately but without making equivalent fractions first is to: *draw my bar, *draw lines for fifths on the top and mark the 2/5 cherry soda on one end, *draw lines for fourths on the bottom and mark the 1/4 root beer on the other end, and *mark what's left in the middle as the 28 cans. It would look like this: Then the equation set-up is pretty straightforward: 1 - 2/5 - 1/4 = 7/20 (fraction that are juice cans); 7/20 of the total cans = 28 cans, so total cans = 80 cans; 2/5 of the total cans = 32 cans (of cherry soda); 1/4 of the total cans = 20 cans (of root beer); 32 cans (cherry soda) - 20 cans (root beer) = 12 more cherry sodas ~*~ That said, if she is capable of reliably setting up and solving problems with variables and equations, and you both otherwise like SM7 - is there any reason she can't just do the SM problems that way instead of doing bar diagrams? I mean, I do like bar diagrams for helping to see what's going on, but they are just one tool among many. ~*~ FWIW, I'm finishing up Dolciani Pre-Alg with my oldest and I do like it.

I like to follow up WWE with SWI B. I do make sure to explain that the mandatory dress-ups and banned words and such are exercises, not universal rules for good writing, though. Their point is to shake you out of ruts, to force you to think of alternatives, to help you become comfortable with a range of constructions, not to be a prescription for all writing "in the wild". I do stick with short passages. Just as an adult, I find summarizing a whole book at once to be a difficult task, at least to do it *well* - shorter is easier for me, too. (When I'm summarizing on my own, I summarize in the largest chunks I can easily handle, then start grouping my summaries and summarizing them, until I've worked my way up to one overarching summary.) Honestly, I never really consciously understood the process of summarization until I was on my second go-through of WWE with my middle. I think there's a lot to be said to getting *plenty* of practice making genuinely good summaries of short passages before moving to increasing the length, as it's so easy to do bad or less-than summaries, especially as things get longer than your ability to handle them well. Also, I think making good summaries of longer works starts to require more logical skills and the ability to see more abstract relationships, which tend to be stronger once you hit middle school. A lot of what WWE is doing is developing a good intuitive feel for summaries, and it's easier to grasp the essence of shorter passages than longer ones, especially when you don't have formal tools for working through longer material.

I compared the two forever ago - here's a linky: https://forums.welltrainedmind.com/topic/83103-comparison-of-the-us-and-italian-editions-of-athenaze/ The short answer is that the Italian version is designed to be as much like Lingua Latina as possible wrt providing a reading immersion experience. It has a ton more readings, plus tries as much as possible to use sidebar pictures and diagrams (instead of glosses) to define words (and illustrate grammar concepts).

In addition to what's been said above, I think there's a difference between taking notes and outlining, especially from an oral source. For me, taking notes from a lecture/sermon/oral-source means jotting down things that seem pertinent and/or interesting as you go - where the only order is temporal, the order in which things were mentioned. Whereas outlining is arranging all the points into a *logical* hierarchy - figuring out the main point, the subpoints, and the supporting details, and arranging them into a logical framework. I don't think you can effectively outline as you go, because how can you know how a given point fits into the whole until you've gone through the whole thing? Rather, I think it's a two-step process: take notes as you go, and then, afterward, go back through your notes and arrange them into an outline. But you can do the same thing orally: listen as you go (pausing as needed to discuss), and afterwards discuss it together, everyone telling what stood out to them (or give a summary if they are capable of it) and collectively figuring out what were the important bits and how interesting details fit in. There's a lot of precursor skills to being able to take notes and outline from oral sources, as well as from sources of length (sermon being medium length, maybe the equivalent of chapter length or essay length). Notetaking requires fluent handwriting and summarizing ability, as well as the ability to hold a thought in your head long enough to write it down (dictation is a big help with the latter). Outlining likewise requires fluent summarizing, as well as the ability to see logical connections between ideas (which is why outlining is more of a middle school skill). SWB's Writing With Ease series, for grades 1-4 (I use it for grades 3-5), does a great job breaking down skills involved in narration (retelling) and summarizing ~2 page passages, as well as the skills involved in holding a thought in your head long enough to to write it down. And her Writing With Skill series, for grades 6-9 or thereabouts, extends summarizing to longer passages as well as introducing outlining and writing from an outline. Going through WWE with my kids has taught *me* a lot about summarizing. ~*~ In any case, before starting any outline work with him, I'd recommend you trying out whatever method you are thinking of on yourself, first. It will give you a chance to figure out trouble spots, give you some experience with what the task is like, make sure the task is practical and doable. But I agree with the above posters about saving physical note-taking and outlining till middle school, and instead do oral narrations and discussions. (Or make it a joint experience: come up with what should go into the notes/outline together and you write it down on a big whiteboard or piece of paper.) At eight, I'd start with the simplest form of narration, which is just him telling you whatever he remembers or found interesting, in whatever order he chooses. You could maybe ask him a few questions about what *you've* determined the main point to be, to help guide his attention to the important bits. In WWE, SWB starts out with easy comprehension questions about the main parts of the passage, to guide the student's thinking and prime the pump about which bits are worth noticing. And then she has them narrate. In Year 1, she just has them tell a few things they liked about the passage for their narration. Then in Year 2, after the comprehension questions, she asks very specific, targeted questions whose answers form the summary, and then has them give a summary using that guide/priming. By Year 3, she's phased out the questions - students narrate after the comprehension questions with no initial help; if they falter, then you prime with directed questions. So instead of pausing the feed to have him identify and write down a key point, maybe instead pause and ask him a few questions that help him see and understand that point. And at the end he can retell what he remembers or found interesting, and you (and your spouse) can do the same - have an informal discussion. At age eight, with an adult sermon, you might want to prime him with a few specific, concrete things to listen for. I know my eight year old (and 11yo) gets more out of the sermon when their Sunday school teachers primed them with a few things to listen for. (But fwiw, I don't really expect my kids to listen to the sermon till middle school, when they are doing sermon notes for confirmation. And those notes aren't the logical, hierarchical I. A. II. A. B., etc., kinds, but instead are thematic. There are three categories of things to listen for: proclamations of Law, proclamations of Gospel, and how the passage relates to Christ, and at the end they come up with the main point. So basically, they jot down things that fit each category as they are said, and then at the end figure out the main point, instead of coming up with a complete logical outline of how the sermon fits together. It took a bit for dd13 (then 12yo) to get comfortable with it; I started by basically telling her whenever something fit one of the categories, and she'd write down what I told her, but eventually she started being able to recognize them herself. Depending on how your pastor structures his sermons, you might want to match your eventual note-taking, or your personal note-taking, to his structure.)

Logic of English has a book with all the rules and morphographs in one easy spot: Uncovering The Logic of English (LoE site, amazon). It's OG based, like AAS, so it's the same basic rules/phonograms as AAS. One thing I do with Dictation Day by Day is to use Spelling You See's visual marking system to mark AAS/OG phonograms and prefixes/suffixes (yellow for vowel digraphs, purple for r-controlled vowels, green for y-as-a-vowel, blue for consonant digraphs, orange for silent letters, pink for prefixes, red for suffixes). I do studied dictation with Day by Day: I print out the pages, have dd mark the passage SYS-style and copy the passage, and then later in the day she does it from dictation.

Fwiw, as I understand it, the protest was supposed to be a drive-in protest; aka, protesting while maintaining social distancing. You could argue that what they want - an easing of the restrictions - would put lives in danger, but the protest itself shouldn't be adding to the danger.

What kerfuffle? (Although I always want to say kerfluffle, with an extra 'l'.) ETA: Although I'm not 100% sure I'm up on the "shenanigans with CC" either. Is it that Circe's somehow entangled with CC's MLM-ish business practices, since CC uses LToW? Or am I behind the door here, too?

I'm a big fan of Spelling through Morphographs with my undx dyslexic (as well as my maybe-dyslexic middle). My oldest went from only being able to spell phonetically-regular one syllable words to only making about one mistake per page spelling "in the wild". There's a placement test, so you can see if they are too far beyond it. I bought the necessary components used: teacher presentation book 1, teacher presentation book 2, and the student workbook. Alternately, you could do Touch, Type, Read, and Spell - teaches typing through an O-G progression and so reinforces spelling as well. I've been doing that with both my oldest and middle girls the past two years. I'm pretty impressed at what my oldest can spell now.

My thought is to go back to the beginning - all the way back to "3 apples to 5 apples is how many apples?" - and move quickly forward till you get to a place where he can't do them entirely on his own, to figure out what he does and doesn't understand. (If you still have your elementary math curriculum, you can use it for problems; else, Ray's Arithmetic is free and has a lot of straightforward ones.) With the way he's had problems all the way through, and always needed you to explain them, it might be that he never really internalized how to do even the easier word problems on his own - that he doesn't have the foundation for the harder ones he faces now.

Objective complement, I think. A predicate complement renames or describes the subject; likewise, an objective complement renames or describes the object. So, here, "Tom" renames the DO, "the child".

Most things can be written out in a notebook or on notepaper, even if there was space for it in the workbook; the dd I did it with has dyslexic tendencies, so a lot of times I would help her format the page (if it was potentially tricksy) instead of leaving her to figure it out by herself. There's some places where you are supposed to underline and double-underline things (subjects and predicates iirc), and box and circle things. I wasn't able to come up with a great way to modify this; I ended up letting her write in the workbook, under the theory I'd be able to erase it for the next ones. You could probably do it orally, instead (but my dd was fairly resistant to that).

Sort of. I flipped through it this weekend, and it has a little bit of everything. It has straight thematic vocabulary lessons, it has special spelling lessons, it has special word-building lessons (which are more implicit than explicit morphics), plus a few more odds and ends. It's meant for middle grades, and I think it will be a nice follow-up to Spelling through Morphographs for my middle girl. Word Wealth, for high school, does thematic vocab for the first half of the book and word roots for the second half (again, more implicit than explicit morphics, but more systematic than WWJ), and will be a good follow-up to StM for my oldest (who is beyond WWJ). Both WWJ and WW are very much focused on *vocabulary* in general, as opposed to any specific approach to vocabulary. Another program that combines spelling and morphic-centric vocab is Megawords (gr 4-12).

Oh, also, I got Kwame Alexander's Crossover from the library - got the rec from the thread Lori linked on narrative poetry. I'm 30 or so pages in. I really like the ones that are giving a visceral sense of the basketball experience - lots of good language (reminds me of hip-hop a bit) and they are really effective at getting you to feel it. And I like the little thematic poems that spin off from the main narrative, both the poems themselves and how they spin off from the narrative. But the poems that are carrying the narrative - they are nice enough, but I don't really understand what makes them poems as such, other than having stanzas #poetryphilistine.

Thanks so much for all your responses :). I have the Koch and MCT books, and started reading the Koch one today. The Runyan one looks interesting - I remember looking it up when you'd rec'd it on another thread, Lori; I re-read the Billy Collins poem - I do like that one, the image of torturing a poem to get at its meaning rings all too true. I'm not a huge podcast/audiobook person - I like to see things in print - but I can see the advantage to hearing poems read well. We listen to audiobooks of familiar books, and a good reader's worth their weight in gold. Might look up poems before listening, so I can follow along. Interestingly, 8, I saw another reference to the poetry reading in Anne Gables today :); it's a neat idea, looking up all the poems. Thanks for all the poetry recs - I'm looking forward to looking them all up. I read the bio of Tennyson at the Poetry Foundation today and they talked about his focus on sounds - sounds ;) right up my alley. Re-read Charge of the Light Brigade - don't think I'd noticed before that he's actually positive about the charge being worth something despite it all. Wrt hymns and psalms (and metrical psalms), I think I ought to prioritize them more. I do love hymns, but somehow when I'm singing them I treat them entirely differently than I do poetry; somehow I can't sing something and think about it at the same time - it's like mutually exclusive brain pathways or something. (And usually singing a hymn is more pleasant than thinking through a poem.) But I've got several memorized, and could write them out and then take a bit to think about them. And it nice to take the time to think about them, because it makes singing them a richer experience, in a way that wouldn't happen if I only sung them. Actually, I think I'd be well-served to make a habit of memorizing some poems. Something about having all the words already in my head gives me a head start in thinking about it, plus you can think about a poem whenever you have a bit of spare time, without needing to have the text with you. Plus all the repetition involved in memorizing is helpful - gives a lot of opportunity to have thoughts and for things to click. Also, sheer familiarity tends to promote liking for me - I have happy thoughts when I meet a poem I've met before, just because it's familiar. Likewise, a poem-a-day habit would be a good one, too - just making a habit of seeing a bit of poetry a day - it adds up. Quarter Note, thanks for all your enthusiasm and recs and analysis - I particularly enjoyed your post :).

I've gone from no appreciation whatsoever to a kind of fledgling, neophyte, still-mostly-aspirational-but-occasionally-concrete starter-level appreciation. But I feel like I've stalled out in my progress and I'm not sure how or where to get going. My one real achievement is learning to hear and genuinely enjoy the sound elements of poetry - the rhythm and rhymes and word play and such. I started out firmly in the camp of "why bother putting things into poetry when prose is so much better anyway", but now I can at least appreciate how good sound is worth aiming for. (I still appreciate the stronger and more obvious sounds, though - not sure I'm up for catching the more subtle rhythms.) But I'm still pretty much at square one when it comes to appreciating the visual images; it's still way too much like deciphering the images instead of *feeling* the images; it still feels like the images are getting in the way of the meaning instead of being the substance of the meaning. Actually, I'm not sure I actually grasp all that much about how the rhythms and rhymes and such embody meaning, either, but I enjoy them for their own sake; and for my own sanity, I'm subscribing to the “appreciating poetry for being lovely is at least half of the point of poetry appreciation” school of thought. (I also subscribe to the “the sound of poetry is at least half the point” and “only analyze poems you already love” schools, too.) But I'd like to learn to appreciate the imagery side of poetry, too: to appreciate the lovely images of a poem as much as the lovely sound of it. And to generally increase my poetry reading ability and stamina. As far as it goes, I genuinely *like* nursery rhymes and humorous children's poetry (Lewis Carroll, Edward Lear, Shel Silverstein, Jack Prelutsky, T.S. Eliot's “Book of Practical Cats”, A.A. Milne in Winnie-the-Pooh). And I intellectually appreciate and mildly like non-humorous children's poetry (Robert Lewis Stevenson and the ones in children's anthologies). AKA I enjoy poems with lots of fun rhythms and sounds and wordplay, coupled with straightforward images; plus humor provides excellent motivation. But I haven't really progressed beyond that. There's been the occasional poems I've struggled with on and off because I was motivated to understand them (Tolkien's “Mythopoeia”, Kipling's “The Gods of the Copybook Headings”, some of Dante's “Inferno”), plus I try hard not to just skip poetry excerpts when they are quoted in prose stuff I'm reading (although sometimes I fail when the excerpts are on the longer side). (Interestingly, I just realized that on the “harder” poems I was motivated to understand despite the inherent detriment of their being poetry – I almost entirely ignored the sound. Whereas on the poems I'm reading *because* they are poetry, I pay far more attention to the sound than the images.) Anyway, I've thought about trying narrative poetry, because I like stories (and things with a point), and it might help improve my poetry stamina. But unless the language is really good (while the images are not-too-hard to comprehend), it's going to suffer from “this story would be so much better in prose” syndrome. Any recs for good narrative poems, especially those with a great sound to them? I've also thought about trying short poems of increasing difficulty, hopefully some that have a great sound and are in areas of interest. Any recs for good humorous or religious poems (esp sacramental Christianity; hymn recs welcome)? Or, really, any poems you absolutely love and want to sell me on? Other people's enthusiasm carries me pretty far (esp if the poem is short <shifty>). ~*~ Also, any thoughts or links or recs wrt “why poetry” are welcome. I have only the most fledgling intuitive sense of “why poetry.” It's enough to inspire me to press on, to take it on faith that poetry can convey things that are impossible to convey in prose, and that those things are worth the trouble of conveying - but I still have no idea what those things actually are. I've read a lot of “why poetry” stuff, and while I'm inspired by their writers' obvious passion for poetry, their reasons never resonate. It's like they have the worldview of a poetry-lover and I don't, and until I can somehow manage the paradigm shift, I'll never be able to understand their reasons. Especially since half the time they resort to poetry to try to explain their love of poetry ;). Understandable, given that poetry is apparently the best way to try to say the unsayable, but not as helpful as it could be to the aspires-to-understand-poetry set, lol. (It has occurred to me that my attempts to try to understand poetry apart from actually, you know, actually reading poetry, might amount to me seeking a royal road to poetry <shifty>.) I know I suffer from needing to know *why* I'm doing something, and my reasons for "why tackle poetry" are still a little too "because it's good for you (somehow, in general)". About all I have for intuitive, felt reasons is the inherent pleasure of strong, singsongy rhythms; this one, brief shining moment of poetry appreciation in high school where I had to answer a multiple choice question about the meaning of a line and it just struck me so hard how the line itself was so much fuller and more beautiful and made the test answer seem so ugly in comparison; and when I was filling out a response form for a religious retreat I was on and I didn't have the words to describe what the services were like - I had to resort to "It was really great", and that was just so *inadequate* that it made me wish I'd memorized poetry, so I'd have had the words to do justice to the experience. Those are enough to keep me plugging in an on-and-off sort of way, but not enough to persist in a disciplined sort of way.

Go to where your username is displayed in the upper right corner of the screen, next to the notifications and messages icons. Click on the down arrow to the right of your username, and it should show a menu. Toward the bottom of the menu, under settings, is "Account Settings" - click on it. That takes you to the settings page, and there's a list of options on the left - one of them is Signature (sixth down, I think). Click on Signature and it takes you to the signature editing page. HTH

This is what I use - right now I'm taking my second child through it. I bought it used on Amazon: teacher presentation book 1, teacher presentation book 2, and the student workbook. At the time I bought it (6-7 years ago), I paid ~$30 for the first presentation book, ~$55 for the second presentation book, and ~$5 for the student workbook. Since I've seen prices both lower and way higher for the presentation books - it fluctuates a lot, so it helps to start looking early - but right now it looks pretty good, around $30ish for the first presentation book and around $45-50ish for the second presentation book. I've also seen a steady creep upward in the student workbook prices; I think I paid nearly $10 for the last ones I bought, which looks to be in line with the current prices. I really love it. It's been wonderful for my struggling spellers. I'd say it is heavier on spelling than it is on vocabulary; I'm thinking of following it up with something more purely vocab-focused (I have Word Wealth and Word Wealth Jr on my shelf, from a rec on a thread here, but haven't done anything with them yet). It's a year-long program, teacher-centric, but completely open-and-go. (My oldest and I did the lackadaisical 2.5yr approach, which nevertheless had very good results; my middle and I are doing it at the suggested 1yr rate.) I feel like going through it has helped me learn how to teach spelling. ~*~ Also, Words, by Marcia Henry, has a lot of good info and an interesting approach (albeit not open and go, which is why it is languishing on my shelf).

https://www.soundfoundations.co.uk/en_US/product-category/apples-pears-en_us/ I believe that you can view full previews of the books by clicking on the individual books and then clicking the "look inside" link.

Yep, scam.

That, and also dd13 not caring about what AoPS cared about (and thus having zero motivation to work past the issues making it (extra) hard). I picked AoPS because dd13 has good math intuition and has always cared so very very much about understanding *why* something is the way it is in math (and in general). However, turns out all she cares about is *intuitively* understanding what's going on, not formally understanding what's going on. And she hates having to explicitly *explain* why things are the way they are in general, and super hated having to do it formally. In addition to those "philosophical differences", AoPS expected students to already know or to automatically pick up a lot of "variable manipulation skills" (for lack of a better term), and to be able to follow the steps of a proof as it was worked out. While dd understood the idea of a variable standing in for an unknown number and could solve standard arithmetic equations with variables with ease (all the pre-test asked for), what she did *not* get was the idea of a variable standing in for *any* number. (She's still shaky on that - every time we do functions, she has to be reminded/retaught about how f(n) relates to f(1), etc.) And so while she could follow any individual step in a proof, she had no idea how anything about the proof related to any part of her intuitive understanding of math. Also, while I could coach her through understanding the steps of the proof as I worked it out, she froze at the whole idea of doing math on variables that didn't have to do with finding a specific value for the variable; she also had a hard time seeing how the "doing things to both sides of the equation" way of solving connected to the "write and solve the equation, use what you found to write and solve the next equation" method she used in arithmetic. I think all of that was solvable (I had similar issues connecting her intuitive understanding of math to writing out equations to show her work in word problems, and we managed that) - and working through her problems as they came up was the most informative diagnostic on her underlying conceptual weaknesses I've ever done - but it was a ridiculous amount of work having to stop all the time and explicitly teach her things AoPS assumed she'd naturally intuit, especially since it turned out she actively disliked the whole idea of proofs in the first place.

FWIW, I did a trial of AoPS Pre-A with my oldest (after finishing SM), which conclusively showed that AoPS wasn't a good fit for her. I had Dolciani as a back-up. When I'd flipped through Dolciani prior to trialling AoPS Pre-A, it had seemed dry and kinda uninspiring. But after the trial, when I opened it and started teaching from it, the straightforward logic of it all was a sight for sore eyes, lol. We're 2/3 of the way through it now, and I just keep liking it more and more, to the point making Dolciani my top Alg choice.