Cake and Pi
-
Posts
834 -
Joined
-
Last visited
Content Type
Profiles
Forums
Events
Blogs
Classifieds
Store
Posts posted by Cake and Pi
-
-
I think it's pretty flexible and can just be tossed in where ever, lol. We did the exercises verbally and then picked a couple to use as copywork each day.
My DS 8 did a part of Killgallons Elementary Sentence Composing after MCT Island but before W&R Fable. He did most of the rest near the end of MCT Town and after W&R Narrative I. He's doing MCT Voyage and part-way through W&R Narrative II now and I'd be totally comfortable adding in the last little bit of Killgallons if I felt he needed more copywork. However, at this point it feels unnecessary.
My DS 11 used the same Killgallons book in one solid go after MCT Island and 3.5 years of public school (2nd through half of 5th), just before beginning W&R Narrative I.
-
BA is a complete curriculum and mostly has enough practice for a not-too-typical certain kind of kid... but almost every kid will need more practice than BA has built in at some point or another, some kids more or less than others. I think BA works best when each chapter is used to mastery and supplemented as necessary.
I have some pretty mathy kids, and every one of them used some other program either before or in tandem with BA (Right Start, MEP, Algebra Lab Gear, etc.). Even my radically accelerated DS 8 (the kid who did BA 4 and 5 each in 10-11 weeks and completed AoPS Prealgebra at 6yo) needed more practice with the basic operations than was offered in BA. We drilled multiplication and division facts well beyond what was in BA and did one long division or big multiplication per day as a warm-up all the way into the beginnings of Prealgebra.
And I'll add my grievances to the pot, too. I was deeply disappointed with the way BA covered the multiplication facts. Here's my summary of BA 3B Ch.4: You can skip count to fill in a multiplication table. Look, the multiplication table is redundant and you already know some of it. Great, now MEMORIZE the rest of it! Here are 30 practice pages. I was relieved that my kids had already developed a deep conceptual understanding of multiplication before any of them began BA 3.
Not to bash on BA. We really loved it. It significantly contributed to my kids' problem solving abilities. But, honestly, we didn't use it as a stand-alone.
-
2
-
-
What about tracing instead of copying? At 7yo my dyslexic+dysgraphic DS 10 was dictating his responses and tracing what someone else carefully scribed for him (he was in public school). If he'd been homeschooling I would have let him trace his copywork.
And I second drawing, if that's something your kids are interested in. It might be early for the 7yo, but you could still try. If either has perfectionist tendencies and are likely to get upset if they can't draw what they have in their mind, you might try to guide them toward more abstract or cartoony drawings or even an adult coloring book (not adult themed, just the kind with lots of tiny details).
My dysgraphic (no dyslexia) DS 12 would still cry if you asked him to draw a simple triangle at age 9. Around 10-11yo he discovered political cartoons and was motivated to create his own, and later short comics. He's made simply amazing progress in the fine-motor department over the last two-ish years between his drawing and origami folding. We're still solidly on step #3 of your list, but if he had to write something (short) by hand, he could now, with messy but readable handwriting and no crying.
-
2
-
-
This looks very cool. I wish they were a bit more transparent about pricing, though.
-
Here's a link to a demo of a self-paced class.
https://artofproblemsolving.com/school/handbook/prospective/selfpaceddemo?fbclid=IwAR3IF2LjE4xqS2-nF4GFWRZ43go1PxsX1P5ujE7R7LXL1Un2JmzVXDEVuKAWhen you do an AoPS Online class, you use the book and do Alcumus just like you would without the class, so the class is just *more*.
My boys do the live classes, so no direct experience with self-paced classes, but one of the main advantages for my kids has been the writing/proof problems and the feedback given on those, which you get in either variety of AoPS Online class. Communicating mathematically is something I want to emphasize. Also, in our experience, the classes are more challenging than just working from the textbook.
-
1
-
-
My DS 10 recently came home from PS as well. I pulled him in January and we've been trying to figure out what to do since then. He's 2e with low motivation.
History:
This coming year I'm planning to go through History Quest Early Times (maybe also the beginning of Middle Times) with my DS 10 and DS 8, beefed up with a middle-school literature list, Crash Course world history and world mythology videos, and maybe/probably/possibly Human Odyssey Vol. 1 readings. HQ Early Times is supposed to be for grades 1-4, but it doesn't feel any different than reusing SOTW for a second run through in 5th-8th as recommended in TWTM. It's just the truly secular version of SOTW anyway. Human Odyssey has interesting pictures and a lot more details, but it really doesn't seem secular to me now that I've been reading through it. It's more in the "Christian-friendly-but-not-overtly-Christian" zone. I'm not sure we'll keep up with it. We might end up with just HQ + literature + Crash Course.
There's also a Horrible History class set from Online G3 that would totally add enough to your Horrible History books to count as full history curriculum. DS 12 and DS 8 took the Horrible Romans and Egyptians class last year. I was impressed with the way G3 handled history in general and recommend them.Science:
For science DS 10 is just doing fun picks from Athena's. That really seems fine for this age. If he was more motivated/interested we might to RSO level 2 Biology.DS 8 and DS 12 did Bio 2 a couple of years ago and it was seriously fun. It was a perfect mix of reading, microscope labs, hands-on activities, and research, and we were easily able to accommodate for DS 12's dysgraphia.
-
1
-
-
4 hours ago, Jentrovert said:
I've thought about this possibility too. Sometimes it seems like this might be a piece of it, and then other times not.
Anxiety in kids on the spectrum can look different than what you probably associate with anxiety, and it's extremely common.
I originally took my DS 8 in to his pediatric psychiatrist begging for ADHD meds, but we walked out of that first appointment with an Rx for an SSRI instead. I filled out the anxiety/mood questionnaires and was like, "No. No. Nope. Sometimes. No..." and thought he for sure didn't have anxiety just looking at my own responses. The psychiatrist looked at the questionnaire and noticed patterns instead of degrees, interviewed me and DS 8, considered our family history, and came to the conclusion that anxiety was a major factor in behaviors we were seeing. And he was right! Meltdowns decreased dramatically after a couple of weeks on an SSRI. We eventually also added something for ADHD because his inattentive symptoms were still in full force.
My DS 10 started with ADHD meds but we weren't seeing improvement in impulsivity or hyperactivity. After trialing many different meds and combos, his psychiatrist eventually suggested that perhaps it wasn't ADHD but anxiety, so we added an SSRI. It was MAGIC! We thought it might only be anxiety and tried removing ADHD meds, which removed all doubts about his ADHD diagnosis, lol.
So, our particular nurodivergent family's experience has been that ADHD meds help with attention and some impulsivity while anxiety meds help with hyperactivity, impulsivity, aggression, and sensory meltdowns. Not saying this will necessarily apply to your situation, but it's something to consider.
-
1
-
-
5 hours ago, Jentrovert said:
Is it common for counseling to be required along with adhd meds?
Dunno, but all my kids on meds are in therapy. That said, they all have anxiety in addition to ADHD (and two are on the spectrum). And, side note, getting anxiety under control had a huge impact on behaviors we thought were just ADHD in one kid.
-
1
-
-
Just wanted to jump in and offer some encouragement. ADHD and mood medications have had a profoundly positive impact on the quality of our lives. It's great that you'll be working with a pediatric psychiatrist. They're the experts, after all, and kids on the spectrum often require more expertise than kids who "just" have ADHD.
Also wanted to throw out there that you needn't favor or rule out a particular medication based on the experiences of others. Each kid responds individually. Just in my three older kids, we have one thriving with a first-line stimulant and one who trialed just about every variety of stimulant available and was a raging bull on all of them. We have one who had a rare side effect with guanfacine and one who is doing great with a high dose of guanfacine, and we have and one who had to discontinue Strattera because of headaches while another loves it and has been on it for years.
-
2
-
1
-
-
My older kids (8, 10, and 12) want to "do art" this year. This is a subject I would normally outsource, but because of Covid we'll need to figure it out at home. I have zero talent, experience, or knowledge about this subject, and aside from some pottery classes, we've done close to nothing as far as arts and crafts so far. I need a curriculum to hold my hand!
I'd like something secular / religiously neutral. It'd be cool if it included some art history, but that shouldn't be the main focus since it's the "doing" that my boys are interested in. Any suggestions?
-
My DS#3 will be a third grader this fall. He's an outlier, but since I shared on the grade level threads for all my other kids, I'd feel pretty weird excluding him.
Math: AoPS Online class
Science: Davidson Explore class
ELA: Royal Fireworks Online MCT class
Social Studies/History: Tagging along with DS 10 studying prehistory & ancients, probably using a mix of History Quest, Human Odyssey, and Big History Project, plus a side focus on world religions using the Usborne Encyclopedia of World Religions
Other: KiwiCo Tinker Crate subscription, Code Combat, mindfulness and social/emotional games and books with DS 6 -
My littlest has been in public school all along, but we've recently made the decision to homeschool him next year. He has special needs. Honestly, I'm pretty nervous about cutting him loose from the experts and learning specialists in PS. He'd technically be a rising 2nd grader by age, except that he was retained a year in PS and we're probably going to keep his grade aligned with that.
I'm probably going to have to do a lot of adjusting along the way, but this is what I've got so far:
-- Picture book read-aloud schedule and topically coordinated activities from Five Senses Literature Lessons: Wonderful World
-- Basic number sense, addition within 10, place value to 100, etc. using Ronit Bird alongside MUS Primer, ST Math K, and/or RS games and activities. I figure if I approach it from every possible angle, something's bound to click.
-- Phonological awareness through toys, games, Kilpatrick Equipped for Reading Success, Hearbuilder, etc.
-- Phonics instruction...? I think we may use Barton eventually, but he doesn't pass the screening yet. We'll continue with learning letter sounds and cycle continuous review so he doesn't loose what he's learned so for. I'm tempted to not wait on Barton readiness and try some version of SRA Direct Instruction/DISTAR . He might make some progress, and the worst case scenario it doesn't work and we just have to wait until he's ready for Barton.
-- Private speech and Language therapy
-- HWOT K and then... tracing? Copywork? Spelling You See A to practice handwriting, spelling, and dictation all in one go? We'll have to see where he's at in the spring.
-- Keyboarding Without Tears K
-- Mindfulness and social/emotional games and read-alouds
-- KiwiCo Koala Crate, might move into Kiwi Crate second semester depending on his developmental readiness. -
If your kiddo is a strong reader and loves language, I think it's worth trying. Island is cute and whimsical, definitely a cuddle-together-on-the-couch curriculum. If he doesn't respond well, shelve it and try again in a few months or a year. The Mud Trilogy was/is well loved by all of my kids. It's worth including that literature trilogy whenever you do Island level.
We've only used the first three levels of MCT, so I can only speak to those. I'm curious about the upper levels, too.
My oldest DS started Island as a third grader and it was really too easy for him by that point. We worked on it for ~15 minutes per day and finished the entire level in about 3 months. He did Town in 4th (a perfect fit), Voyage in 5th (bit of a stretch when he got to the writing book), and then moved onto other ELA in 6th.
I started my next kid with Island as a 6.75yo 2nd grader. He worked on it on the side while in public school, and it lasted most of the year for him and was a good fit at the time. He took a gap year in 3rd (Town was going to be too much), and then started Town in 4th but never finished because the homework for PS didn't really leave enough time for much afterschooling. He's now a rising 6th grader and just not that interested in language arts anymore, or really anything academic for that matter, so he probably won't go back to MCT.
DS#3 started Island level about half way through kinder, two weeks after he turned 6yo, and that was perfect timing for him. He did Town spread out over what would have been 1st and 2nd grade, and he's all set to do the Voyage class through RFWP Online this fall in 3rd grade. Admittedly, however, he's a bit of an outlier.
Still, I really think an elementary kid at a 3rd/4th+ grade reading level who shows interest and responds well can be successful with Island. The second level, Town, is a pretty big jump up from Island. If you start Island early, you may need a gap year between Island and Town -- but maybe not. It depends on the kid.
-
2
-
-
14 hours ago, PeterPan said:
How is this affecting his phonological processing? Now it makes sense why you're wanting the Hearbuilder. Is he still getting speech?
The audiologists seem to think his hearing loss shouldn't cause any problems. They say it's mild enough that it shouldn't impact speech development at all. He gets yearly follow ups because a form of progressive, juvenile-onset HL runs in my DH's family, but so far he seems not to have inherited that. The HL is most likely stable and related to his birth history.
I'm sure that he still wouldn't pass the Barton screening because he's still struggling with segmenting sentences into separate words and words into syllables in Hearbuilder. He can't get past the very first exercise where it gives him three choices and he's supposed to find the one that has either one or two words. He's super frustrated about it and has reduced to tears the last couple of times I tried it with him. He doesn't seem to understand what a word is, and no explanation from me has helped. Add in syllables and he gets extra confused.
He had speech at school, but he will loose that now that we're going to officially homeschool. In our state, any child who is not full time is considered to have relinquished their right to FAPE. He will loose his IEP and all related services. I've reached out to our Children's Hospital and I'm working on getting him on a wait list to resume speech with them. We stopped private speech about two years ago because he was getting so many minutes (and summer school) through our district that it seemed like an easy thing to drop so streamline our therapy- and medically-packed schedule. We'll get it going again here asap, but it's going to take at least 3-6 months to get through that wait list.
15 hours ago, PeterPan said:That's interesting that you don't pass the tutor screening. Do you know why?
I'm probably just dyslexic. Despite being highly gifted, I didn't begin reading until half-way through 4th grade, around 10yo. I might have read earlier if my mom would have let the PS do any testing beyond IQ or provide any interventions. She got my IQ back and basically said, "See? She's really smart. She's just being lazy. She could read if she wanted to."
17 hours ago, PeterPan said:Did we already mention Braidy to you from Story Grammar Marker? They are doing tons of free workshops right now, and of course they always have lots of free info on their website and blog. They load up significant videos showing how the approach works. They have a new workshop coming up tomorrow
No, you didn't. It looks interesting. I signed up for the online workshop. Thanks!
17 hours ago, PeterPan said:I'm not sure there's really a replacement for LIPS if he needs it.
I'm not sure I'm qualified to teach him with LIPS? I didn't pass the Barton screening. I also don't honestly have a ton of time. I can probably reasonably spend about an hour to an hour and a half with him one-on-on in a typical day. The three other boys are all very high needs as well (between the three of them we've got ADHD x3, anxiety x3, ASD x2, dysgraphia x2, dyslexia x1, ODD x1, and probably more that I'm forgetting).
Is there no other program that is likely to do the job without being super hard for me to pull off?
17 hours ago, PeterPan said:For some kids the checking out is language overload. It's attention, but it's connected to how they're processing. That's going to take time to sort out and become more obvious.
Yes, I'm interested to see how this progresses over the next couple of years. He's able to do nothing or the same repetitive something for ridiculously long stretches of time. I can call everyone to our home classroom in the morning and he'll sit at his desk quietly basically forever. I've discovered that if I get busy busy with the other kids, he will really just sit there moaning, humming, making sound effects, etc. for a couple of hours. If I don't give him a task he won't do anything. If I do give him a task he'll either do it non stop until I take the supplies away, or he'll ignore it and continue just siting there making noises. It's like he's got his own little world in his head. This is probably how he got so lost at school. The teachers did report at his IEP meeting that he needed an adult to initiate tasks.
-
5 hours ago, PeterPan said:
A kid with dyscalculia doesn't need more computation.
We don't know yet if he has dyscalculia, but I suspect not. His neuropsych eval said he was at risk for SLD in reading, writing, and math (and ADHD) based on his achievement testing being that much farther below his (low-average) IQ. HOWEVER, *I* believe that his math ability may actually be pretty close to average and that his math learning so far has just been severely impeded by his language difficulties. He has excellent spatial skills, and when he plays with our c-rods I get the impression that he's got an innate grasp of quantity as long as no language is involved. You add words like "eight" and "middle" and "more" and it all goes out the window. Point being that I think it's too early to really tell if he actually has dyscalculia or if he has language-limited math achievement.
5 hours ago, PeterPan said:I'm also seriously in love with ANYTHING from Lakeshore Learning
Yes! I love Lakeshore! And Didax. ITA. Just about anything from either of them is awesome.
5 hours ago, PeterPan said:What is ST math?
It looks really promising and claims to be a math program that doesn't use language. "Spatial-Temporal Math." I've read some maybe not-so-positive reviews online, but none are from parents with language disabilities like my DS has, so it still seems worth looking into.
5 hours ago, PeterPan said:MUS is about the same level of instruction as RS
Really? It looks so much more streamlined and simplified to me, like all the bells and whistles were removed. At least that's my impression of Primer. I haven't looked through Alpha and beyond. Did you try MUS with your DS? I met the program author, Steve Demme, at a homeschool conference a couple of years ago. I wish I would have paid more attention. I think I remember him saying he wrote the program largely to meet the needs of his son with Down Syndrome, and, incidentally, my DS 6 has a learning profile very similar to a child with milder Down Syndrome.
5 hours ago, PeterPan said:Ok, you have RB's Toolkit. Have you seen her ebooks? Her Dots ebook is superb. We spent 1-3 weeks on a two page spread. The ebooks are inexpensive and rearrange the instruction into a logical order and include videos. HIGHLY recommend even when you have the print books. Do what you want, but just saying.
I don't have any Apple devices, so I can't get any of her ebooks. 😞
5 hours ago, PeterPan said:Oh my, you want to use SSRW?
Well, I already own SSRW, so...maybe? I only used the SSRW readers with some my older kids. Two needed very minimal instruction and one taught himself before I got around to it, so I just never needed the complete program.
5 hours ago, PeterPan said:I missed it, does he have dyslexia?
He is at high risk for dyslexia. I probably have dyslexia. My brother is diagnosed with dyslexia. DS 10 has a dyslexia diagnosis. It would not be surprising at all if DS 6 were dyslexic, and it's probably safest to proceed as though he were dyslexic.
5 hours ago, PeterPan said:Why the IEP? What are his diagnoses?
His main diagnoses are neurodevelopmental disorder associated with his birth history (IUGR preemie) and moderate-severe language disorder. He also has moderate-severe articulation disorder, sensory processing disorder, mild (sub-speech) hearing loss, and a *very* long list of minor physical diagnoses/differences that probably don't make much difference individually but altogether might impact his ability to learn and achieve. He also almost certainly has ADHD-inattentive (no hyperactivity). He would have been diagnosed at his last eval except that the questionnaire I filled out did not endorse inattentiveness. Now that I've been trying to work with him at home for a few months, I can see that he absolutely does have issues with inattention. He is very much off in la-la land a lot of the time.
5 hours ago, PeterPan said:Here's the Barton screening tool
Did it a couple months ago and he did not pass any part of it. This is how we came to the conclusion that he needed a lot of focused attention on phonological awareness, hence the Kilpatrick book. That said, *I* didn't pass the Barton tutor screening and I still learned to read, so I'm inclined to run phonological awareness and reading instruction in parallel. He may spend a veeeeeeery long time on phonological awareness before he can pass that Barton screening. I figure it's okay to keep moving forward at least learning the letter sounds and beginning some digraphs and blends as he's able to, regardless of his passing the Barton screening. Eventually all the pieces will be present and then we can work on clicking them into place together. Or this was my theory, anyway.
5 hours ago, PeterPan said:http://www.helpinschool.net/home/reading/reading-and-dyslexia-overview/reading-and-dyslexia Here's an article on SSRW for dyslexia.
So SSRW will absolutely go too fast. Since we just spent 11+ weeks on 7 lessons of RS, I'm thinking just about everything will go too fast.
This site is *very* interesting. It recommends DISTAR/ Reading Mastery. TYCTR in 100EZ Lessons is also DISTAR. Does that mean that 100EZ might work? Okay, there wouldn't be enough practice in 100EZ. Maybe I should look at getting some Reading Mastery materials. I actually used 100EZ with two of my boys (plus SSRW readers and Primary Phonics readers) and am very comfortable with the system.
-
1
-
-
Stanford Pre-Collegiate, maybe? Expensive, but still cheaper than Stanford Online High School. Beyond multivariable calculus and linear algebra, they have modern algebra, real analysis, complex analysis, diff equ, and partial diff equ. They also have several physics courses for after AP Physics C. Applications for the fall semester don't close until mid-August.
-
Update with more questions!
UPDATE:
We had DS 6's annual PS review recently and came out with an excellent IEP. He's got goals for articulation (make the "s" sound), auditory memory (follow 2-3 step directions), language (use correct syntax), reading (read at least 8 cvc words), writing (write "at grade level" by writing words that contain correct beginning, middle, and ending sounds), and math (understand numbers 11-19 as 10 and 1s). They increased his speech minutes and kept PT on consult. We also decided to move him to a different school with a higher sped population.
If this were a normal year, I'd be feeling pretty dang good. But it's not. Not only do we have COVID going on, but unemployment dropped state revenue so significantly that our already underfunded district is facing budget cuts of 12% or more. In response, school will only be held 4 days per week going forward. Our district is encouraging families to do fully remote learning in the fall, though we do have the option of choosing a hybrid model where students come to school once a week and do remote learning the other three days. This is not going to work for DS 6, so we're making the leap. We're going to homeschool him officially next year!
I found an in-state but out-of-district homeschool charter that we can use for funding (I'll have $1,500 to use on educational materials!) with very few strings attached. So now I can order pretty much whatever is going to work for him. It's all in the budget, lol.
Learning-wise, we're now heading into week 12 of me teaching DS 6 at home. He's still in lesson 7 of RS A, so it's probably safe to say that RS is not going to work for him. He's not a fan of the abacus, but he loves our Nooms (home-made c-rods) and playing with pattern blocks. He still knows 21 letter sounds, so he hasn't learned any new sounds, but he also hasn't lost any. We're making a sound book, focusing on 1-2 letter sounds each week. He gets a page with the upper and lower case forms of a letter at the top, and then we go on a sound hunt finding things that begin with that sound, which he draws on his page. We review the entire book every day, saying the sounds and words. He's really enjoying it.
I bought Ronit Bird's Dyscalculia Toolkit book and Kilpatrick's Equipped for Reading Success. I'm going to spend the summer reading those and then working through what I can with him. I also plan on experimenting with a bunch of other resources I've got temporarily.
QUESTIONS:
I'd love feedback on the following programs (I've got free trials/borrowed copies now):
ST Math
MUS Primer
HearbuilderREADING: In addition to continuing with Kilpatrick, I'm leaning toward at least trying Sing, Spell, Read & Write with him this coming fall. I already own it and he seems to learn more quickly and retain better with songs than with straight spoken language, plus he saw me going through the box and is now super excited about it and wants to use it. I've never used SSRR though. I just scored a free kit years ago and held onto it just in case. I have no experience with the program itself. Thoughts???
MATH: I understand Ronit Bird is just supplemental, so we'll need a main math curriculum. All I know is that it's not going to be RightStart. 😭 I think I'll still incorporate what I can from RS, card games and such, since it's the program I used with my other three and I'm so familiar with it. However, I need something as a spine for DS 6. I borrowed a copy of MUS Primer and it looks like a good fit for where he is now. I worry about the levels beyond Primer though. I'm a bit nervous about using a mastery based program with him. He needs to keep reviewing or he'll forget what he learned. Do the review pages incorporate skills from earlier levels as you move through MUS?
TIA!
-
2
-
-
So, first I'd just say don't even worry about the 4yo. If she's interested she can tag along as she's able, but there's really no point in putting a ton of effort into trying to include her in content subjects at this age. That simplifies things a bit because you'll have a smaller age range to accommodate if you want to combine the rest of them for science and history/ social studies.
What levels are the middle two kids working at? Can they read above grade level? What about maturity, interest, and motivation?
Are you looking for Christian, neutral, or secular materials?
Have you thought about using a literature based curriculum at all? Doing so would probably make grouping for those content subjects pretty easy.
-
1
-
-
Oh, nope. I didn't fix the link after all. *facepalm* So the first one I linked to is not shorter. It's more workbook style though, whereas the second one is very much a very detailed coloring book with lots of information.
-
1
-
-
If you were planning to make anatomy something you do for just a week or two, this short anatomy coloring book aimed at younger audiences would be good. We also have the Squishy Human Body, which is meh for details, but is great from a sensory perspective and kid-approved in my house.
If you're looking to dive really deep in a particular body system or want something that can last all year, my current 2nd-grader-by-age loves, loves, LOVES this anatomy coloring book. He went through REAL Science Odyssey Biology level 2 a couple of years ago. It was just the right mix of reading, doing, and writing for him at the time. I think that laid a pretty solid foundation, and I highly recommend it, particularly for the hands-on and microscope labs. It is a year-long course, though.
-
1
-
-
On 4/18/2020 at 9:12 PM, mathmarm said:
If you're comfortable, please do! I think it's utterly precious to see kids stuff.
On 4/18/2020 at 9:26 PM, square_25 said:If you don't mind sharing, I'd love to see!
Here ya go! For fun and because it's so cute, there's a page from BA that he did at 5y8m old... and I saved it so it was one of his nicer-looking pages. He turned those workbooks into "art," lol. I like it though because you can sort of see his thinking in his work.
There's a page of pre-algebra challenge problems I coped out for him at 6y6m as a makeshift worksheet during the transition from BA to AoPS. It looks like he lost his minus sign in one of the problems, but it was there in the original. It just didn't come through in the picture.
The next one is his handwritten work for a writing problem in Algebra A at 7y2m. This was significantly better organized than his work for a regular problem because he knew he'd need to reference this work when he typed out his full solution afterward.
The pdf is a picture of a regular short-response challenge problem he did last week in Intro to Geometry. Probably should have saved it as a photo instead of a pdf. It came out very light, sorry!
-
1
-
-
1 hour ago, square_25 said:
Well, you can visualize it, but you still tend to visualize it with "sample numbers," right? You can't actually visualize an x or a y. I know sometimes you visualize sort of... a fuzzy version of a number? But still, there has to be SOMETHING to visualize, even if in some sense you're visualizing something general.
My kiddo doesn't like manipulatives and is mixed on visuals. She definitely thinks of SOME things visually -- if you get her to explain why ab = ba, she does it visually. But she didn't want to use visuals for fractions at all. I don't know why. She's strong with fractions, though: it took her a bit of time, but she figured out formulas for
a/b + c/d, a/b - c/d, a/b*c/d, a/b/(c/d)
from first principles. And she can do most fraction calculations very quickly.
We've done a bunch of mental math, which may be why she does some things verbally: we started fractions verbally, and it may be that it lingered. And we're overall a very verbal as well as a very mathy family. So that may be part of it.
When I visualize it, it looks a great deal like the Algebra Lab Gear blocks, possibly because that's how I originally learned way back in the day. So no, no sample numbers in my head, unless you consider visualizing something like c-rods to be visualizing sample numbers. I asked DS 8 to explain his thinking on (x+y)^2 and he quickly traced out boxes in the air. He said he could "see" them in the air as a table of boxes with letters inside them. I asked him if he imagined the letters as numbers and he said they weren't any particular number but letters that acted like numbers and were sort of like all numbers at once.
He did a lot of self-discovery of properties, too, but he did it mostly with manipulatives and drawings. For example, he figured out the basics of exponents by playing with 1" plastic tiles and wood cubes. It didn't even occur to me that I should provide vocabulary like distributive property or associative property back then. He got all of the terminology through AoPS. (More proof that I'd suck at teaching without curricula to follow!)
I love how you and mathmarm focus so much on naming the properties and proving work with appropriate vocabulary. I feel like it must add an extra layer of understanding for kids with that balanced ability profile. My DS 8 is exceptionally lopsided... I guess "specialized" would be the more positive way to spin it, lol.
Anyway, I find it super interesting to see the different ways these mathematically precious kiddos unfold. I should share some of DS 8's messy, all-over-the-place, step-skipping work from when he was 6-7. It makes the handwritten stuff both of you guys shared look like works of art!
-
1
-
-
10 hours ago, mathmarm said:
How do you proceed, when the kid in question doesn't like manipulatives, and/or seems to be going through an anti-visualizations phase?
Erm, I don't really know. 🤷♀️ My one AL who resists using manipulatives is the weakest in these kinds of concepts, and my one who used manipulatives most extensively is strongest in all things math. You can approach math from a verbal standpoint, but I'm not sure its the most efficient way. I'm coming from an engineering (not real math) background, though. Language was always more of a frilly decoration to be added to math in my mind, but I may be limited by my own visually-based thought processes.
I haven't figured out how to help my one kid who doesn't like manipulatives or visualizing, but instead have found it most effective to let him explore concepts in his own way, which takes significantly longer and seems to result in less robust conceptual understanding. Consequently, he'll be getting to algebra at 10-11 vs. my heavy-manipulatives, super-visual kid who did basic algebraic concepts like (x+y)^2 at 5 and AoPS algebra at 7. The two boys have the same cognitive abilities, so I tend to think the difference is largely due to personality factors and learning habits/preferences.
3 hours ago, square_25 said:She knows the why, she just stopped keeping it in the back of her head when she used the pattern. I think it’s important to learn the difference between “I learned the pattern” and “I can backtrack the pattern to properties I can easily understand.” The former approach is considerably more fragile.
See, and I don't think my DS 8 uses the pattern at all for things that can be visualized. The way he talks when he explains his work, it sounds like commentary on visuals, and he uses his hands to shape ideas in the air.
-
We've never used the online version precisely because I'd read that the voice was terrible. We've gone through several levels of the books, though, and like them. The teacher manual is very thin. There are just a few pages of instructions and then the rest of the book is devoted to daily lists of words with some brief explanations or notes about homophones at the bottoms of the pages. The student book is thick but very simple. On each right-hand page there are 25 numbered blanks to write in the daily words. On the backs of each of these pages there are optional extra practice exercises, things like word searches and unscrambling words. That's it. One of my kids doesn't even use the student workbooks anymore. He just writes on a white board as I dictate the list to him.
How to get to algebra?
in Accelerated Learner Board
Posted
You can absolutely continue through the curriculum, condensing and accelerating as appropriate, while introducing algebra concepts.
I big puffy heart Algebra Lab Gear. One of my kids went through the ALG Basic Algebra book when he was still otherwise working on 3rd grade math.
Hands on Equations is frequently recommended, but it never moves beyond single-variable linear equations, so I'm not really a fan. Seems a bit boring and repetitious to me, but go with whatever works for your kid.
You could also let your kiddo try out DragonBox Algebra 12+ if you haven't already. Once they beat the game there's a whole other side B or something with really algebra-y algebra puzzles.
And, if you think Jacobs would be a big hit, go for it. You can run two math curricula in parallel, letting him practice those foundational arithmetic skills in between playing with variables and such. Sounds like fun to me!