early radical acceleration questions

[MomatHWTK]

I don't think the two are connected at all.  My 13 y.o. is watching college lectures, but I'm certainly not enrolling him in a univesity any time soon.  Just let the child learn what he wants to learn when he wants to learn it. 

[regentrude]

So, I'm kidding myself if I think unchecked accelerated learning can lead to anything besides early college? I guess I just kept reading here that it's okay to accelerate without planning for early college because there's so much stuff available to learn, there's always something else to study.

 

There is no one-size-fits-all answer. And also, it depends on your definition of "early college" : are you talking about an early entrance program at a residential campus? Dual enrollment? Online college in high school? College materials as curriculum for high school? Graduating three years early and entering university as a regular freshman?

 

Some children find plenty of stuff to learn, have no desire to move away from home, and are happy to use the extra time they have due to being accelerated to study according to their interests with whatever resources available. Others are chomping at the bit, very mature, crave the academic environment of a residential campus and can not wait to go away to college. Some children would be able to handle the academics, but not the time management and organization aspects of college. It depends completely on the child!

 

[regentrude]

In the education world, words such as acceleration have a different meaning. Here, acceleration occurs when a student takes a course ahead of the gen ed schedule. 8th grade Algebra is officially an accelerated course -per state law the middle school has to offer at least one accelerated course - but it is not an honors course. An honors course would have more units offered, and more depth to all units, giving it a faster pace than the nonhonors version.

 

But that is again with respect to a time line: the student takes the course earlier than his cohort and is thus progressing faster through the course sequence - maybe the coursework in the individual class itself is not faster, but because he is doing it earlier, he will be done earlier moving through the sequence. So total amount of courses will be completed in less time , i.e. faster.

 

[La Texican]

Ok, doing the first page of a book does not mean you're ready to study the whole thing. The Dolciani '75 arrived in the mail today. It's an unschool day (we school 7 days on, 7 days off). He took a chunk of his free time, at his own insistance, and did a page of the book, using a calculator, deciding if the statements about equalities or inequalities were true or false. I'm not trying to say he could finish the book if I gave him 2 or 3 years and made it a daily assignment, or that he's close to ready for the whole book. I wouldn't let him use a calculator if it was an assignment anyway, and that would have stopped him wanting to do it right there.

 

I was asking about radical acceleration, with a plan, a plan for assessment, a plan for instruction, because I thought the book reccomendation was a suggestion was to tell me I should be doing something different than what I'm doing. The two things that I could see that the book reccomended for me to change was better assessment and placement, and not scaffolding or handholding.

 

One suggestion I took from this thread is wapti saying maybe I should compact his assignments now to make them more interesting. I might take that "more interesting" part of the suggestion and assign Beast Academy every day next week. I've been using BA sparringly as a treat only on the days when his other assignments are heavier than other days.

[snowbeltmom]

So, I'm kidding myself if I think unchecked accelerated learning can lead to anything besides early college? I guess I just kept reading here that it's okay to accelerate without planning for early college because there's so much stuff available to learn, there's always something else to study.

I don't understand what you mean by the term "unchecked" acceleration.  Imo, the beauty of homeschooling is that kids get to learn at their own pace. 

 

Some kids complete the typical high school subjects before the traditional college age.  This does not mean that the child in this situation has to go to college early to continue learning.  There are many ways a student can continue to further his education that don't involve early college. Just as one example, my son has devoted a lot of time the past 1.5 years to research.  He will go to college with his age peers because for a variety of reasons, that is the best choice for him.  For other kids, early college will be the best fit.  You don't have to make that decision now.  For now, let your son move at the pace he desires.

[regentrude]

Agree. I am trying to make the distinction that a faster and deeper paced course is not considered accelerated at all, it is considered honors level. So there can be an honors 8th alg and a reg ed 8th algebra. Both accelerated with respect to cohort sequence, but only one is faster paced and containing deeper content.

 

Which makes perfect sense and has a home schooling equivalent:

1. one can have a student complete an average program one (or several) grade(s) earlier

2. one can have a student complete a deeper and broader and more challenging program, also one (or several) year(s) earlier.

Both can lead to chronological acceleration  - or not, if the more challenging course takes longer so that the student ends chronologically on par with his cohort.

And

3.one can have a student work "on timetable", but with a broader/deeper/challenging program, in which case no actual acceleration happens, but the student simply learns a lot more during the same time :-)

[quark]

One suggestion I took from this thread is wapti saying maybe I should compact his assignments now to make them more interesting. I might take that "more interesting" part of the suggestion and assign Beast Academy every day next week. I've been using BA sparringly as a treat only on the days when his other assignments are heavier than other days.

 

Yes, try flipping your current model! Give him the enjoyable stuff and see where it goes. Get his buy-in first. then follow that lead.

 

He might finish it in a day or two. That's fine. It's challenging to get out of the "one book must last 36 weeks or 12 weeks etc" mindset but that's what happens when a child is learning at his true pace. Just go on to the next thing in the progression. Or throw something else his way. Challenge him sideways. Or give him pure thinking time so he can observe and follow patterns in his head. I didn't have to ask other homeschoolers "should I?" questions about using AoPS counting and probability with an 8yo because DS was already thinking about those concepts in his head and asking us about them constantly. So I googled and found out about AoPS. I bought the book for him to read. I learned about the online class and someone we know locally suggested DS might like it and that we could drop after the first 2 sessions if it wasn't a good fit. DS loved the class so sticking to it felt like the natural next step.

 

That was what he was ready for conceptually and he liked the text chat with the very funny teacher. Physically he was 8 years old and not willing to do every single problem in the book or as assigned online or even read ahead some days. I wrote to Richard R explaining the situation and he said to not worry about. Just do what felt best for DS to keep his interest alive. He also said my DS wasn't the only young one doing it that way. It was a relief but I still worried about it for a while, then let it go. By the time he gets to intermediate counting and probability he will have matured some more and will be able to spend more time working on the book and homework problems. Anything half done is not going to be considered as one high school credit. But I do consider it as a lovely way for him to challenge himself within his ability. Not everything has to be done for credits or as part of school. It can be purely interest-based. He will have a number of math classes not listed on his transcript or listed as ungraded to indicate that they were done purely for interest (it's a bridge I will have to cross when the time comes, not going to worry myself sick about it now).

 

For the homeschooling part where you might feel he needs consistent instruction...you could gradually show how some dedicated daily SM work (or the algebra book or any other material you think he needs to do) will help enhance the learning he receives from the enjoyable materials. And sorry to be a parrot about this...or split it into strands. 10 minutes of SM/ stuff he doesn't usually like to do + 10 mins of math he loves to do + 10 mins of a documentary or video or logic puzzle (or just unschool the time spent on the latter if he likes that sort of thing). Or do SM one day, BA one day and keep alternating. Kids need to see there's joy in learning. You won't need post testing etc because they will naturally talk about it all the time if they are excited!

 

BTW, I hope you know I am trying to be supportive. I was curious about all this too at that stage of our homeschooling. How do we learn if we don't ask ya? Good luck!

 

ETA: sorry, DS was 8 when he started AoPS Intro to C&P, not 7. He was 7 when the concepts first started to interest him.

[lewelma]

I was asking about radical acceleration, with a plan, a plan for assessment, a plan for instruction, because I thought the book reccomendation was a suggestion was to tell me I should be doing something different than what I'm doing. The two things that I could see that the book reccomended for me to change was better assessment and placement, and not scaffolding or handholding.

 

 

Ok, I finally get what you are asking.  A plan for teaching.  All I can tell you is the specifics of what I did with my older (which is different from what I did with my younger by the way). 

 

This is tidied up from what it felt like while I was doing it, but this is the general approach that we fell into:

 

1. Start new chapter in SM. Sit with him for 15 minutes and teach the new concept in the entire chapter for 5 minutes, and then have him do 1 or 2 from each section in the chapter with me either orally or with me a scribe. Finish entire workbook chapter in 15 minutes (with heaps of blanks for problems we skipped).  Or 30 minutes or 45 minutes or however long it took.  If he got one wrong, he did 2 more of that style.  If he got one right in each section quickly and without having to think, we just moved to the next type of question.  This approach allowed him to speed through the easier material with me making sure that he knew it.  The key was that he did not have to write.

 

2. Assign all of the word problems and challengers in the IP.  Have him work on them independently and require full documentation of steps (I taught him how to write stuff down in an organized way).  The IP would take between 3 and 6 days, just depending. 

 

3. Review.  every week I had him do a set of "10 in 10" -- 10 review problems in 10 minutes to make sure he remembered the basics and began to increase his speed.  We typically used the review sections in the WB or textbook. 

 

4. Card drill: add, subtract, multiple, divide, then percents/decimals/fractions.  5 minutes per day. 

 

So from in edu-speak terms: I pretested each chapter orally, and had him do more *on the spot* for anything he missed.  Then he did his independent work which was more difficult and went deeper.

 

He hated any written tests, because he had to write down a bunch of easy answers and it just took so long.  All he wanted to do was get to the hard stuff.  So no written tests or pretests.

 

This is what we did until he refused to let me teach him anymore - at about 8.  But at that point, he knew 'the system' for how to learn and just managed it himself.  At that point he dropped the workbooks and textbook, and just used the IP.

 

Hope that helps,

 

Ruth in NZ

 

[wapiti]

So, I'm kidding myself if I think unchecked accelerated learning can lead to anything besides early college? I guess I just kept reading here that it's okay to accelerate without planning for early college because there's so much stuff available to learn, there's always something else to study.

 

You may find that, as a practical matter, acceleration might not go unchecked.  Rather than thinking of it as a linear path, think of it as a sort of exponential one, getting deeper and wider the further along your student gets.

 

As your student gets further along in math, not only are the concepts more challenging, but the problem solving gets much, much more challenging.  What I was trying to explain in the other thread is that I don't think of problem solving as "enrichment" because it isn't an extra but rather (ought to be?) a core element of a rigorous math education for such a talented kid.  That angle is likely to slow a student way down.  It may be hard to imagine right now, and of course every kid is different (it's impossible to guess what someone else's kid might be capable of or what might be the "right" path for them), but the amount of challenging problem solving available for middle and high school math is tremendous.  And, then there are extra topics off the standard sequence that may be useful and interesting to study, all before one even gets to calc.

 

A year or two ago I skimmed through the book and sent it back to the library.  From what I recall, it indeed was about school, where students have to fit into one box or another.

 

FWIW, if I were in your shoes (as best I can tell what the situation is at the moment), what I would do would look nothing like radical acceleration as I understand the term.  I'd keep adding in the fun and interesting resources that you've been using.  Rather than doing every problem in every SM book, I'd have him do enough problems to master the material (whatever that turns out to be), and then move on, also incorporating review in whatever amount and manner fits him best and incorporating more problem solving stuff as he becomes more able.  Sitting alongside him, you will be able to figure out when to do what, one day at a time.  In doing so, you are able to offer him a much richer and more appropriately-matched math education than what some test-result-driven school-system-oriented radical acceleration plan could.  Should it happen that he leads you by the nose pell-mell ahead or off into tangents, all the better, but I have a hard time imagining radical acceleration without that sort of self-driven aspect.

 

By the way, upthread (or maybe the other thread?) I think HOE was mentioned - that's one way to get him started with the algebra he asked for; i.e., "algebra" doesn't have to mean "algebra 1," especially when he doesn't have the prerequisite skills for alg 1 just yet.

 

eta, quark and Ruth posted while I was writing this - so i will second what they said!!  Spend some time over on the aops website, reading the articles, playing on Alcumus (yourself), etc. and you will see what I am trying to say.

[wapiti]

One suggestion I took from this thread is wapti saying maybe I should compact his assignments now to make them more interesting. I might take that "more interesting" part of the suggestion and assign Beast Academy every day next week. I've been using BA sparringly as a treat only on the days when his other assignments are heavier than other days.

 

To be more specific, when I talked about compacting, I don't envision there being a whole lot of compacting to do by the time you get toward the end of elementary math.  The beginning, however, can be kinda boring - and potentially too easy, to boot - without enough other concepts under his belt to make it more complex and/or interesting.

 

I would feel free to use BA liberally, as far as he is able to go.  Then only use the SM sparingly for more practice or making sure he has all the prerequisite skills for BA or for review.  You're in charge of the curriculum - use it as you think best.

 

Quark and Ruth gave you lots of good advice on specifics.

[Laura Corin]

So, I'm kidding myself if I think unchecked accelerated learning can lead to anything besides early college? I guess I just kept reading here that it's okay to accelerate without planning for early college because there's so much stuff available to learn, there's always something else to study.

 

Calvin is going to university at 17 - within the normal range for Scotland.  I agree that there's always so much more to learn.  He loves English and Classics, and there is no limit to the amount he can read and write without leaving home.  Some children do need to go to university early - that hasn't been the case with him.  Just for comparison: he was tested PG.

 

I think it has helped the English is my thing too.  Yes, he's been in school for the last four years, and has had excellent teachers as he has worked towards the demanding IB.  But I was still able to point him towards books, discuss other aspects to consider, etc.  And he has been working on his poetry over this time: reading up on prosody and practising the art.

 

L

[La Texican]

I think the radical acceleration model spoke more of developing a childs talent than about age or timeline. The timeline was a sidenote to the developing talent part in the radically accelerated model as I read it. It wasn't a schedule to plan "we'll get this done at this time if we do this". That's not what the model was about. The model called for a lot more sequential planning for what to do next, and what to do for each outcome of the last step. If that model was better then I would be wrong to continue mishmashing math in from everywhere and needed to get with the plan. Dmmettler cleared that up when she said the author said her book wasn't the best plan for homeschoolers.

 

Here's how we ended up looking at things outside of the sequence anyway. I see stuff that's beyond his grasp and show it to him and tell him that he won't understand it, but I want him to tell me one or two things he did understand from it. This is to get him listening to things he does not understand and to teach him to try to learn something from it. He's getting a good sense of "knowing what you know, and knowing what you don't know" and listening to someone explain topics you don't know. Plus he's learning the stuff after all because he's watching and learning. Meanwhile he's doing plain math for homeschool, output, and math facts. I hear some folks in this thread saying I need to add in more problem solving work. Heard, accepted, and appreciated.

[kiana]

I really think you're worrying too much about making your program just exactly right. There is no perfect, there is only 'good enough' -- and there are a lot of ways to be 'good enough'.

 

With respect to early college -- there just isn't anywhere near as much enrichment and interesting math that can be done having only partially finished enrichment. But once early parts of the sequence are completed, the potential pathways broaden a lot. For example, after algebra 1, you could do the AOPS counting and probability/number theory textbooks. I'd be surprised if mathematical logic weren't accessible about the same time to an interested child. After geometry, there's some really challenging geometry texts such as Coxeter's which would continue to be challenging for some time. After algebra 2, a college-level discrete mathematics textbook would be one place to go, as would statistics, as would the AOPS intermediate c and p class. After completing precalculus, AOPS has a group theory class -- quite honestly, group theory has very little in the way of formal mathematical prerequisites, although mathematical maturity and proof ability is very much a prerequisite. Topology with a classic yet elementary text such as Mendelson's would be another option. And then there's calculus, and after all this enrichment, the student should be able to handle a genuinely challenging calculus textbook, or perhaps even work through the AOPS and another proof-based classic such as Spivak's or Apostol's.

 

There is so much math to learn, and the more you learn, the more you're able to learn.

[La Texican]

Ok.. so, I only own the textbooks. I'll also take the advice to get the IP and compact a little bit of stuff. Anyone have an old set of IP they want to sell me? I'll go look on the swapboard, but may as well ask while I'm here.

[lewelma]

Ok.. so, I only own the textbooks. I'll also take the advice to get the IP and compact a little bit of stuff. Anyone have an old set of IP they want to sell me? I'll go look on the swapboard, but may as well ask while I'm here.

 

Definitely the IP.  The textbook is really easy in comparison.  I have lots of very heavily written in IPs that will cost you more than the books to ship. :tongue_smilie:  

 

Ruth in NZ

[La Texican]

I already told the hubby, "you're never going to believe this, but you know how I told you I've had a thread lately where I'm getting some good personal advice from respected experienced homeschooler, expert advice.... you'll never believe it, they said I should buy more books."

[quark]

Use library card for living math books.

 

Free stuff. No need to buy:

http://www.cimt.plymouth.ac.uk/

http://www.artofproblemsolving.com/liz/Alcumus/index.php

http://www.artofproblemsolving.com/Videos/index.php

http://www.numberphile.com

http://mathlearnnc.sharpschool.com/cms/One.aspx?portalId=4507283&pageId=5048438 (scroll down for weekly grade level resources K-2)

http://mathlearnnc.sharpschool.com/cms/One.aspx?portalId=4507283&pageId=5051238 (scroll down for weekly grade level resources 3-5)

http://mathlearnnc.sharpschool.com/cms/One.aspx?portalId=4507283&pageId=5149151 (scroll down for weekly grade level resources 6-8)

http://www.numbernut.com/

 

Tons more resources online if you have time to google them.

 

In the future near or otherwise,

https://www.exeter.edu/documents/math2all.pdf

http://forums.welltrainedmind.com/topic/465228-math-olympiad-questions-solutions-links-compilation/

Search for mathwonk's posts on free online books plus his epsilon notes (used with gifted 8-11yos)

http://www.geometer.org/mathcircles/

http://www.cimt.plymouth.ac.uk/resources/codes/default.htm

Some more links in my siggy if that helps.

 

Good luck.

 

[La Texican]

Eek! I was trying to be funny with that last statement. I tend to buy books any chance I get a good reason to. I do try to wait until I have a good reason, or a book I can't pass up. I was happy to pass the blame for why I was buying more books again. Actually, I explained exactly why, but first I made sure to blame it on the board.

[regentrude]

I can't agree..options 2 and 3 w/no chron. accel. w/respect to peers only appear to exist because the honors student hasn't labeled his coursework to include the additional units he did.  This did happen when I was a high school student, due to seatwork rules...kids would complete two courses in one year via enrichment or independent study, but only get credit for one on the transcript; the other one would be noted in the letter of recommendation.  Now the add'l coursework is labeled as 'seminar' or 'independent study' or 'honors' on the transcript to flag that it's more than gen ed and the students are accelerated with respect to their age mates in the similarly titled gen ed, remedial, and sped. coursework.  which are taken at the same grade level.  The label 'accel' is still reserved for those who take the official Regent's (gen ed) course a year ahead of time, and the label 'honors' for those who accelerate by going deeper and doing more units. Sure the nonhonors student can end up in the same class as the honors student at some point....but in those classes the additional background is not a pre-req., or it's a work hard situation for the nonhonors student to accelerate and catch up.

 

I do not understand what you are saying. How a course is labeled is a completely different issue from what the student learns.

My DD's "Algebra 1" credit encompassed the entire AoPS Intro to Algebra text, i.e. a lot more material and in more depth than a typical algebra 1 course; she also did it earlier, so option 2. My DS did the same, but took a lot longer and would not be terribly accelerated.

We also used option 3 by her taking a physics course, but instead of regular high school physics completing a  college course, but I gave her regular high school credit - no chronological acceleration, but a lot more depth and challenge.

 

How records reflect the acceleration/extra challenge is an entirely different issue.

[La Texican]

It's not that bad. Borac has 3 levels, 4 books a level, A hundred dllrs. Singapore IP has two books per grade, five grades of elementary left, another hundred bucks. I am definately using white-out on these answers so my daughter can use these books next. I guess I thought math was math and you really only needed one book per grade. It's actually a good thing that I learned this is not the case. I'll give compacting and enrichment a try. Thanks for the responses in this thread.

 

At least now I know what to do now.

[sunnyday]

It's not that bad. Borac has 3 levels, 4 books a level, A hundred dllrs. Singapore IP has two books per grade, five grades of elementary left, another hundred bucks. I am definately using white-out on these answers so my daughter can use these books next. I guess I thought math was math and you really only needed one book per grade. It's actually a good thing that I learned this is not the case. I'll give compacting and enrichment a try. Thanks for the responses in this thread.

 

At least now I know what to do now.

 

The Borac supplements should really last until your student is 11 or 12, even if he's one of the hugely gifted mathematicians like we see here on the boards sometimes. So that $100 can be amortized over a few years. :)

 

Let me just drop a few resources here that helped me, personally, clarify our direction and purpose for doing math with a talented kiddo.

 

http://www.artofproblemsolving.com/Resources/articles.php?page=calculustrap& (why a standard curriculum is inadequate for mathy kids)

http://mathprize.atfoundation.org/archive/2009/Rusczyk_Problem_Solving_Presentation_at_Math_Prize_for_Girls_2009.pdf (longer document on a similar subject)

http://spark-public.s3.amazonaws.com/maththink/readings/Background_Reading.pdf (how "school math" does not prepare students for university mathematics, because it's hundreds of years out of date)

http://www.amazon.com/Knowing-Teaching-Elementary-Mathematics-Understanding/dp/0415873843/ (how a solid curriculum and an engaged teacher make huge differences for a student's foundational math -- why math is not math, even at the elementary level)

[janabe]

 am glad he isn't any further ahead than he is. I just asked ds's his perspective, and he also says he is glad he isn't further ahead. I asked him why and he said.....his ability to deal with pressure for the classes and workload, ability to relate to peers in class (he is currently physics 367 and 303 and the kids in his classes range in age from 19 - 28 and he also has multiple math credits) and it impacts the way his age peers relate to him. He says it puts you in no man's land with a difficulty for anyone to relate to you. If he were younger, he feels like socially it would be harder. He thinks being older and more mature has made him be able to adapt to the situations where he wouldn't have been able to when he was younger. He says he is really glad we spent more time spreading wide, 

Age and maturity is child dependent  My 19 yo is taking 600 level physics classes and is fitting in great in college.  He is tutoring and an RA.  He was always more mature than his peers, friends with kids older than him.  

[Halcyon]

I haven't read every post here. 

 

How old is your child? My younger is 8, and began doing Zaccaro Real World Algebra about a month ago, after asking for something harder. He hates Math Mammoth, but I "make" him to it so he doesn't have gaps--we do test out of sections. He has no problems conceptually with Zaccaro (I get it's sort of "light" algebra) but if he did, we would step back and revisit it in a week.  He adores word problems, so we have fun with those. We really try and mix it up--that's critical. 

 

Anyway, not sure how old your child is, but like others, I would only accelerate if he asked for it. That said, with my older, he didn't "ask" for it, he just naturally moved more quickly than other kids, so he's doing Algebra in 6th--not radically accelerated by any means, but it was the pace that worked well for him. 

[8filltheheart]

Age and maturity is child dependent My 19 yo is taking 600 level physics classes and is fitting in great in college. He is tutoring and an RA. He was always more mature than his peers, friends with kids older than him.

I'm not suggesting otherwise. There are lots of families that do graduate their kids early. Jenny in FL's dd started her Bachelors at 12 and graduated at 16. She often posts about her dd's experience.

[EndOfOrdinary]

As a previous math teacher and a person who was once considered a young math genius (whatever that means), I think you need to throw out the tests and just let the kid go (unless you are in a situation that requires documentation). Give him resources. If he is going to be accelerated, he will eat resources faster than you can provide them. No one taught me math. I snuck resources out of the reference section at the library, because I chose to do three times the normal amount of homework each night. I skipped my normal math class and sat in the back of AP calculus. I convinced the math team teacher to let me audit the math team because I knew my parents wouldn't let me compete. I was grounded from my math books until I made friends because my father was so worried about it. It meant that I radically accelerated myself. There were holes - I didn't learn long division until polynomials or cross multiplying until I was accepted to college early. Everyone was stunned that I didn't have all these tricks, or some logical progression. However, it means I think about math differently as well. It meant that the math was mine, not the regurgitation of some book. Kids who need or even want radical acceleration do this. Their parents don't force it. It is terrifying as a parent sometimes and downright exhausting at others.

 

If it is going to happen, it will happen. You cannot force it; you can only guide your kid. If he is just starting to play with BA then you have awhile before you are at the point you need tests to assess if he is learning. A test can only show you an answer. It can't tell you what he knows or if he is learning. Talk to him. Can he tell you why something works? Not a process, but a why. Can he give you four other ways to do the problem? Can he create a generalized equation? That means he knows. That is radical acceleration. If he can do that, he will be unstoppable because he gets it. There aren't many curriculums which can teach that and they definitely don't involve tests.

 

I think you are getting a slightly bewildered response from some because it seems like you are wanting some process of how to get your child engaged in a way that will have him going through the curriculum faster. That doesn't normally need to happen with a kid who actually needs the acceleration. The accelerated kid could care less about grade level; they are too busy learning. The parent just holds on while the kid takes off.

[La Texican]

I think you are getting a slightly bewildered response from some because it seems like you are wanting some process of how to get your child engaged in a way that will have him going through the curriculum faster. That doesn't normally need to happen with a kid who actually needs the acceleration. The accelerated kid could care less about grade level; they are too busy learning. The parent just holds on while the kid takes off. 

 

 

 

I do have thick skin and I understand that this is your observation, but I wonder how you got this from this thread? Was it the op or title, which clearly came from processing the information from a book which was recommended to me. In this thread I have gladly accepted the advice to throw in more problem solving, which is the opposite of getting them through the curriculum faster. I have made another too long post this morning, clarifying goals and seeking more advice. I should resist responding in defense on a forum. This is not the first post in this thread that has expressed this sentiment. But this thread has produced for me a gem in the form of a teaching plan for math.

[La Texican]

I know he's not prepared to do all of the Dolciani algebra all at once, but on the first couple of pages he got literally giddy (not silly, really giddy). He's six. I was assigning the singapore textbook, and giving BA and a Great Courses videos occassionally for what I thought was enrichment. I now have a plan, which is compacting Singapore textbook with IP until he finds a tricky spot, using BA and Borac enrichment as regular assignments, as often as I assign Singapore. I learned that enrichment should be the main course, not a rare treat.

[La Texican]

I don't really think about college. It hasn't sunk in. As far as I know advanced homeschooling doesn't mean they have to leave home early, but that they will have the option. I was talking to a friend about it and she asked, "aren't you worried?" I answered I'm going to have to let them make their own decisions eventually anyway. It might just happen a little bit sooner. But it hasn't really sunk that I might have to deal with something when they're 14 or 15. I still see little kids. That's why I started hanging out on this board because on another forum the advice I saw for accelerated kids was either dealing with working with the school system or issues with young kids and college. Here's where I found discussions about educating children.

[La Texican]

My book budget is spent for a little while because I just bought $200 of math books. Here's where I'm at in teaching other areas. I'm open to suggestions. He's not reading Harry Potter, he's reading Bobby vs. Girls. My grandmother is going to send me either a Nancy Drew or Hardy Boys series. Yesterday we swapped pages on Fenyman's easy and not so easy pieces on atoms and molecules in water, ice, and steam. Once we swapped pages on Sophie's World because he started asking religious questions. I have read aloud Peter Pan, A Little Princess, The Whipping Boy, a few like that. Right now I read aloud from the colored fairy series while they draw and color. I bought and printed Scholastic's 3rd grade collection of school plays. We have stuffed animals read the different charachters parts.

[La Texican]

For science, he has an empty chemistry set for colored water, a microscope, bfsu, snapcircuits, a logo programing game, a kids electronics course, and a garden. He keeps a notebook. He has that children's "my body encyclopedia". He has (and reads) the Nat Geo set of life science pocket guides.

[La Texican]

For composition, he's doing The Complete Writer, HWT 5, book reports using Cornell notes, and MCT grammer sentence, and practice island. For spelling I have an old phonetically controlled spelling list which he copies the words from his list 3x each. I just bought and introduced a dictionary. I plan to include definitions and "write a sentence with the word soon." He's taking dictation sometimes in the complete writer and he told me when he's assigned copywork he tries to hold the sentence in his head instead of copying. So, that skill's emerging. I'm definitely going to use WWS. I'm looking at Analytical Grammer or composition 101. Right now I'm using book reports because SWB said to teach composition first based on retelling someone else's ideas

[La Texican]

Right now, history's weak. We're notebooking Usborne World History and tracing State maps from Imagene Forte's one Nation 50 States. My dad thinks I should have at least had him memorize the presidents. We haven't done any memory work yet, but I was going with the idea of expose the big picture first. The thing I'm kind of doing for memory work is playing a game called "periodic quest" which, after so many games will naturally teach you the periodic table. Even with math he's memorizing facts by using them, not by memorizing lists. I own "The Constitution Translated for Kids" to teach citizenship. It will also teach reading unfamiliar English.

I'm looking for a secular history. K-12 is the only reccomendation I've seen there. I don't know exactly what I'm looking for yet. Since I'm looking at higher grades for writing and arithmatic I might end up looking in the higher grades for history too. I haven't seen anything in the younger grades that I'm looking for. I'm going to use blobbing for geography when he's done tracing the maps.

[La Texican]

For art he uses pencil, paper, crayons, canvas, paint, watercolor paper, tube water colors, and how to draw books. His sense of proportion and fine motor skills have always been great. I think I need to show him perspective drawing soon. I thought about using that flatland movie on youtube. I downloaded sculpteris on the computer and he was surprised after he sculpted a guy I showed him it rotated and it showed him the other views were not sculpted on his charachter. He just started Skyppe piano lessons with grandpa. We have ukeleles that I'm trying to learn with the kids.

Everything in this list should take a while because we don't do them and every day and school short days, year round.

[La Texican]

The title to this thread is still good. What I'm asking is about teaching a solid foundation at the front end of an accelerated childs education. Most advice on acceleration is either on identifying an accelerated child, accelerating an education, dealing with effects of acceleration when they're older, or saying a child should do it all by themselves. I feel like it's valid to ask about how to provide a solid foundation for someone who is a great learner right now.

I get it, acceleration is not usually linear and at a consistent pace. There's something to consider early in the education besides getting them through school quickly or expecting a child to educate themselves. I plan to educate my own children in their early years with the goal of letting go. The questions I have are about providing a solid foundation for a rapid learner, in the early years. I've found some answers on my own. Most conversations that try to discuss this solid foundation for an accelerated child at a young age do include these mostly bewildered responses and are kind of weird. I decided it was worth continuing because of the gem of a math plan I was given for trying.

[La Texican]

ETA: the part that made him giddy was not algebra, it was that it was a more interesting problem. True or false: 2+8 =/= 8+2, etc. I feel good about this acceleration and enrichment plan I was given, and the IP and Borac books I bought.

[EndOfOrdinary]

I do have thick skin and I understand that this is your observation, but I wonder how you got this from this thread? Was it the op or title, which clearly came from processing the information from a book which was recommended to me. In this thread I have gladly accepted the advice to throw in more problem solving, which is the opposite of getting them through the curriculum faster. I have made another too long post this morning, clarifying goals and seeking more advice. I should resist responding in defense on a forum. This is not the first post in this thread that has expressed this sentiment. But this thread has produced for me a gem in the form of a teaching plan for math.

My reply wasn't meant as attack - I am sorry if it came off that way. Sometimes writing with the correct tone still baffles me and doesn't come off correctly.

 

As unfortunate as it is, some people want to shove their kids really quickly through grades so that they can be radically accelerated. I think that term "radically accelerated" has gotten a bad rap from parents trying to put their 12 year old in college. (This does not include the other mom on the forum who honestly had a 12 year old going to college, because the kid was truly exceptional.) It is that speeding-through-mediocre-curriculum, Calculus Trap scenerio. So much is this happening, that when radical and acceleration are used together, it is assumed the parent is the one pushing and the content is an inch thick and four miles wide with basic regurgitation rather than true learning. Thus my response as well as a few others who were questioning with more of a cynical tone.

 

My comment is similar, however, with the idea that you do not need to set the foundation. It flat out cannot come from you. The foundation comes from the student immersing themselves in the study because they enjoy it. As the student grows up, and you can isolate what area of math they are interested in, then systematic learning can take place. I realize this is a very "unschoolish" approach, but it is the most honest one I can give you. If your son is looking like he is accelerated in math, give him interesting math and he will get a foundation. YouTube videos, biographies, stacks of books, a Rubik's cube, workbooks, basically anything because he is still incredibly young (it appears). At this point he most likely doesn't know what it is about math that he enjoys. By narrowing that down through exposure, you can see what he is strong in and what he isn't.

 

My son could care less about algebra, math history, or great thinkers. He wants geometry, spatial positioning, artistic mathematics. So we went there first. He hit a wall when it came down to computation and so we spread into PreAlgebra and simple linear equations. At this point, we are focusing a lot on terminology and how to learn what he wants to know because he can begin really tackling his own interests now that he can do the computations and knows the InterLibrary Loan system. (That was an insane run on sentence)

 

I am different. Give me linear algebra, great thinkers, and historic mathematics. My route was much more philosophical math. It looked nothing like my son's, though it was no less intense. Had you smushed me into geometry, there would have been a real issue. When I tried to smush my son into a traditional curriculum, there were issues.

 

Right now, just find what he loves. It will most likely be very apparent and cultivating that enjoyment is by far the most important factor in the acceleration.

 

Again, I am sorry if I seemed aggressive before. It was not my intention. I ws more wanting to caution you against killing your son's desire to learn by trying to take an non-traditional kid and forcing him into some mold of what is "supposed" to happen.

[La Texican]

My comment is similar, however, with the idea that you do not need to set the foundation. It flat out cannot come from you. The foundation comes from the student immersing themselves in the study because they enjoy it. As the student grows up, and you can isolate what area of math they are interested in, then systematic learning can take place. I realize this is a very "unschoolish" approach, but it is the most honest one I can give you. If your son is looking like he is accelerated in math, give him interesting math and he will get a foundation. YouTube videos, biographies, stacks of books, a Rubik's cube, workbooks, basically anything because he is still incredibly young (it appears). At this point he most likely doesn't know what it is about math that he enjoys. By narrowing that down through exposure, you can see what he is strong in and what he isn't.

I'm not sure that I can't lay a foundation for it, because that's what I was just advised how to do.

 

You know what's weird about this conversation?  It usually boils down to asking the parent if it's student driven or parent driven.  I know the draw to that question, it has an easy answer.  If it's student driven, hands-off, if it's parent-driven, stop.  

 

I think I just put my finger on why these conversations are so weird.  From the parents side it doesn't have such an easy answer.  He is looking at math he does not have the prequisites for.  I am working on math from the other end, (now radically accelerated and enriched).  The only way to know if it is student driven is if he continues to figure out this math he's curious about.  It's not going to be linear and paced.  If he drops it completely, it was not student-driven, it was because he was curious about something he was exposed to.  Even then, a driven student may drop something for a while and come back to it later.  Even if this is a fluke for now, the math he is looking at is highschool level.  He will get back to it before he graduates highschool.   

 

 

I would not call it child-led because I assigned watching "mastering the fundementals of math", which told him there was algebra, and other math to learn.  It wasn't until this thread, when I typed it out, it hit me- he's the one who is looking at algebra and trigonometry online.  It's new to him, and he doesn't have the prequisites mastered.  I think Quarks separate math strands explains what's happening here.  If he was getting nothing from it he would say outloud, "this is nonsense" and watch something else.  

 

 

He used to pick division and addition to watch online.  I told my sister and my husband he was doing hoe, which is more than algebraic thinking, but less than a real algebra book.  Then he asked for a real algebra book.  I think it's kind of the unsolvable nature vs. nurture debate.  It's both.  He's not growing up in a vacuum, his parents are right here raising him.  We're not raising a blank slate.  He's definately got his own nature, his own mind about things.  That last sentence sounded artificially tamed and refined for what I'm describing.  He's a rambunctious six year old boy.  There, that's better.

 

 

Sorry, but if I addressed your concern that's great.  If not, please try to ask again.  (Although) I do understand that the time and effort it takes to make a thoughtful post.  If you're talking about unschooling elementary, even in areas of strength (which imo is not just math),  we are definitely talking about different things.   Maybe the it you're talking about and the it I'm talking about are two different things.  If he's looking at what he's asking for, and I'm teaching the foundation, then I think this produces radical acceleration. He's looking like he's accelerated in a few things.  I've only gotten advice on the math so far.  

 

 

End of Ordinary, I'm not picking on you by answering your post, just trying to answer thoughtfully what was written thoughtfully in your post.  I'm also trying to see if there's something I need to understand that I'm not seeing. I just think we're talking about two different things.

[La Texican]

I'm sorry if I made you feel like you were aggressive. Sometimes I wonder if I'm too agressive or defensive. Sometimes, I'm sure.

[sunnyday]

I'm not sure that I can't lay a foundation for it, because that's what I was just advised how to do.

I think this is a distinction of what is meant by "foundation". Do you mean the "grammar" of mathematics? (If so, consider listening to the audio lecture of that name here: https://www.societyforclassicallearning.org/index.php/resources-guest/media-guest )

 

For me, the k-2 "foundation" of mathematical advancement is creating an expectation in the student of engagement, enjoyment, ownership, motivation. And I agree with EoO that these things don't come from the parent. When you show him a video lecture on ratios and fractions and require that he takes notes, but then you crack open an algebra book only to see that he is delighted to explore the concept of commutativity in addition, then that kind of thing is where I am seeing a disconnect between what is imposed upon the student and what's coming from him. "Learning is not a product of teaching. Learning is a product of the activity of learners."

 

 

[La Texican]

Yeah, I think "early radical acceleration foundation" and "grammer stage for an advanced learner" might be two ways of speaking about the same thing. No, I don't think the commutative property was what excited him. He's already "discovered" that before. I say "discovered" because he's asked about it when no one has spelled it out for him, but you know how these math books are. How many pages do you need to see where 9 + 5, and 5+9, or 3x8, and 8x3 are both somewhere on the same page before you "discover" it? I'm not sure what the giddyness was. It might have been the double negative. It used to tickle me to throw four or five negatives in a sentence when I was young. He hasn't heard the double negative (grammer) rule before. That's not enough to cause (very rare) giddyness by itself. Whatevs.

I'm sorry, I tried it, I did not get anything out of it.  The first half hour was super basic, and he's going on about the memory palace which is not helpful to me at this point in time.  I shortened this post, but we already do everything listed in the first 30 minutes.  

I wonder why I'm not understanding the advice I'm not understanding.  Hasn't everybody done what the first half of the lecture says?  Now I'm sure I sound harsh and defensive.  ((Cringes a little)) 

 

 

I told him to take notes on the math lectures because I have him write notes across the contents as part of (my interpretation) of wws and twtm which says to have little children practice writing by first learning to work with other people's ideas.

[sunnyday]

 

 

 

Yeah, I think "early radical acceleration foundation" and "grammer stage for an advanced learner" might be two ways of speaking about the same thing. No, I don't think the commutative property was what excited him. He's already "discovered" that before. I say "discovered" because he's asked about it when no one has spelled it out for him, but you know how these math books are. How many pages do you need to see where 9 + 5, and 5+9, or 3x8, and 8x3 are both somewhere on the same page before you "discover" it? I'm not sure what the giddyness was. It might have been the double negative. It used to tickle me to throw four or five negatives in a sentence when I was young. He hasn't heard the double negative (grammer) rule before. That's not enough to cause (very rare) giddyness by itself. Whatevs.

I'm sorry, I tried it, I did not get anything out of it.  The first half hour was super basic, and he's going on about the memory palace which is not helpful to me at this point in time.  I shortened this post, but we already do everything listed in the first 30 minutes.  

I wonder why I'm not understanding the advice I'm not understanding.  Hasn't everybody done what the first half of the lecture says?  Now I'm sure I sound harsh and defensive.  ((Cringes a little)) 

 

 

I told him to take notes on the math lectures because I have him write notes across the contents as part of (my interpretation) of wws and twtm which says to have little children practice writing by first learning to work with other people's ideas.

 

I think in a lot of cases all of us end up talking at cross purposes because we've got different kids with different needs and we will never convey the whole big picture of living our life with our kids just by writing at each other. ;)

 

I suggested the lecture not because of the "let kids play with manipulatives" (I agree, duh! I zoned out through a lot of that part...I was listening while on a long walk) but because of the overarching "you don't get a foundation for math by teaching arithmetic facts explicitly, you get a foundation for math by exploring mathematical concepts like counting and measuring; even an average child will start extrapolating from there to start developing a conceptual understanding of arithmetic." I'm seeing you say a lot of variations on "he won't know what I don't teach him," and I just feel like this isn't an accurate portrayal of what I believe the whole field of mathematics is about. I thought a Classical educator might be a good voice to hear that even rigorous mathematics can be kind of touchy-feely at the beginning. :)

[La Texican]

:) Thanks for the smilies. I worried a little about being too defensive or abrasive with my last few posts. Really, I worried more that I was being dense and really not understanding a few comments. It might explain some of the cross-purpose if I explain that I live in a small town with no library. They're working on getting a small library annex from the next town over, but when they do (when they had one before) it will be a few shelves with some childrens books and some chapter books and audio books. Really, I could see going to the library every day and unschooling, reading whatever, if that was an option. It's not so much that if I don't teach him, he'll never, ever learn. It's that if I don't buy it we don't have it around.

We do have the internet, and a few shelves of books. He's been watching the khan videos on youtube. He used to choose the simple ones with the rows and columns of circles. Lately, he's been choosing ones he doesn't have the prerequisite math for. I think the great courses "mastering the fundementals of math" showed him that the complex ones are learnable. Since he's looking at the more complex ones, I showed him the aops youtube videos. I asked an AOPS tutor on a forum if I'm sure he's not completely understanding the AOPS videos, but is watching them, is it okay to let him. The answer was that maybe he's understanding more or less some of it, but it's okay as long as he wants to. I'm more interested that he learn all the first math, that's why I was assigning from Singapore. I was building a library to grow into. That's why I have a few great courses math (I thought the ancient history was too Bible heavy, but which one wouldn't be?), the Alice in Quantumland series, the anthology of english lit, I have kids books too. I just know if I don't buy it, it won't be here. Right now he plays in the mud a lot, swings, bikes, plays sports, watches cartoons. I really spend a lot more time finding and buying the books than he spends reading them. I just can't buy an actual library full of books so I spend a lot of time, I'm super picky about what I buy. I almost didn't buy the (kindle) book this thread is based on, but it was recommended to me by a familiar poster whose posts I like.

Eta: the reason I gave him the mastering the fundementals of math video was that I watched it to see when to introduce it and the material in the first whole disc is stuff he knows from khan. The video is clear and the examples are hand selected for clarity. I have no regrets for assigning the video. It's definately writen to an older elementary school class, maybe as a review. And the assignment was an attempt to offer something different some days than copying and answering Singapore math problems. Until now, I was sparing with the "extras". Now I have a stack of extras he can't go through any time soon. I still might have to pay $100 each for the next few years of BA, but now I have more than just one set of Singapore textbooks and a single year of BA.

[lewelma]

You know what's weird about this conversation?  It usually boils down to asking the parent if it's student driven or parent driven.  I know the draw to that question, it has an easy answer.  If it's student driven, hands-off, if it's parent-driven, stop.

 

Not quite.

 

I've finally figured out my confusion to your OP.  I just would never use radically accelerated to describe my son unless backed into a corner, because he is not radically accelerated *for him.* He is only radically accelerated compared to an average child, and that is not how I educate.  Put simply, in every subject for each of my boys, I ramp it up until he is challenged.  I can tell he is challenged by our conversations, his questions, his excitement, etc.  I don't even look at what is typically taught at a public school because I don't really care.  As long as he is 1) doing a certain number of hours of study 2) in a broad range of topics and 3) working at an appropriate level of challenge, he can't go faster or learn more.  Does that make sense?

 

Radical acceleration to my ears sounds proactive, and I am definitely reactive -- up the level to appropriately challenge him, lower the level to appropriately challenge him. And of course it is a moving target for each subject.  Sometimes you over do it and have to pull back, sometimes to underestimate and have to push forward.  But a student working at the appropriate level will have a very efficient education. Never lost, never bored. What more could you ask for?

 

The biggest problem is that you can't plan it. 

 

As to your observation of the advice "if it's student driven, hands-off, if it's parent-driven, stop."  I disagree.  *I* choose to ramp it up to a level appropriate to their skill/talent -- to where they are challenged in the same way that an average student is challenged by an average curriculum.  My kids aren't begging for more material or harder material in all subjects. But if I don't give them material that makes them think, then what are they learning? They are learning that they do not have to work hard to succeed, and that is a *terrible* lesson.

 

So I would suggest that you drop the 'radical acceleration' term. I think that it has different meanings to different people.

 

Ruth in NZ

[sunnyday]

FWIW, even small libraries can be terrific. I live in a town of 1700 people but my library has great librarians and a thriving friends of the library support group (which fundraises for things like our new building and our new books), and it is part of a large county system. Because our library's collection is well-curated, I can find tons of stuff just browsing the one wall of picture books and juvenile novels, and the 4-5 shelves of adult stacks. And what I can't find I can reserve online from another branch and have within days. That said, my educational choices don't really revolve around the library per se. I've bought all my math programs (a little at a time over a year), I'm starting to buy used copies of classic literature, I've bought a few history spines and downloaded some public domain books (including instructional books) on Kindle and Google Play.

 

My kids and I were talking over bath time tonight about ways to jazz up our learning. We decided that it's high time we built a fort and carried our writing supplies into it so that we can tell each other stories and write some of them down or draw pictures. And that is what we will do tomorrow (after DS gets home from school, where he has a substitute and so won't get almost any of his usual differentiated accommodations, sigh). Later in the week we will have a real poetry teatime, but "with juice or milk or water instead of tea", and we will read poems to each other and talk about what, exactly, is a poem (with the understanding that we are just exploring ideas in advance of our poetics lessons coming up soon) and consider choosing one to memorize. Today my son sat next to me and dictated over two pages of summary about castles, all in his own words. He needs to add a paragraph about knights and armor, and draw an illustration, he tells me. Saturday night he spent about an hour balancing weights with BA. Tomorrow I thought I'd pull up the Borac practice on "using negative integers and parentheses" because the last time we had a long drive we spent almost the whole trip talking about negative numbers and number lines.

 

I'm certainly no unschooler, I don't think I have the resources, but so far for k-2 my philosophy is decidedly relaxed. There is so much educational wealth out there, that to me, learning with accelerated kids is like sampling from a buffet of awesome! :)

[EndOfOrdinary]

We do not unschool. We tried it and my son was a nervous wreck. It was my first realization that it is his education, not mine. I do not know if you have come to see that yet. I think that is the disconnect occurring here. Initially everyone goes into homeschooling wanting to create the ideal schooling to maximize their child. Somewhere along the line the lightbulb dawns that that is not what you need to do as either a parent or an educator. Your job is to create an environment for them to maximize themselves.

 

There is a phrase used commonly in teaching, "you can't care more than they do." It refers to the idea of filling a vessel versus nurturing a fire. It sounds as though you are not trying to nurture you child's talent. You are asking for a plan to build his talent. Much as Ruth was speaking about challenge versus acceleration. The distinction is very important.

 

Nurturing means the student has the power. Challenging puts the onus on the student. Build, plan, accelerate all use the idea of you having the power. The student becomes an object being acted upon, not co-operated with. When someone is nurtured they are still the nominative, when the student is challenged he is still the nominative. That is the scariest part of working with gifted kids, you have NO power.

 

I cannot force my son to learn. I can grade skip him, test him, workbook him, condense curriculum so he flies through, but he won't learn. I have no power there. He has to utilize his future with a very undeveloped judgment center and virtually no experience. Seriously scary. You cannot change that. If you try to take the power, it kills everything that makes him awesome.

 

You are talking about academic contests, competitive colleges, grade skipping, AP exams, credit by examination, and slew of things that are light years from where your child is now. If you son is personally talking about going to Yale right now that is another matter. But, it sure sounds like you are talking about him going to Yale. If he wants to take AP chem next year, great. But you wanting to plan his school education is completely not okay. He isn't in middle school. He sounds like he is barely in elementary.

 

I have a vague plan for my child's high school years. Vague is the operative word. My son is currently in somewhere around a high 7th grade across the board. It makes sense to consider everything HE has said he wants in the coming years. He is openly old enough to begin having those discussions mainly due to being at about 7th grade level across the board. Until your child can say, "Mom, can we discuss my math curriculum?" you need to back off. Find out where he is at through testing and then let go. If he wants to learn algebra ask about conceptual algebra, not a 12 year schooling plan or some modus of operation to fulfill his greatest potential as though either of those things are yours to decide.

 

I am not talking about unschooling. I am talking about your child being his own person, not a video game character to level up.

[regentrude]

 .  *I* choose to ramp it up to a level appropriate to their skill/talent -- to where they are challenged in the same way that an average student is challenged by an average curriculum.  My kids aren't begging for more material or harder material in all subjects. But if I don't give them material that makes them think, then what are they learning? They are learning that they do not have to work hard to succeed, and that is a *terrible* lesson.

 

 

This, exactly!

[Uff Da!]

nm

[8filltheheart]

My personal experience is that the child needs his emotional needs met and he needs to reason a bit on his personal philosophy.

This single sentence articulates why I shared ds's experience and his POV. It is the personal ownership over where this path is going to take them and how it is going to impact their life. It is more than just an intellectual path. It is personal as well.

[La Texican]

You are talking about academic contests, competitive colleges, grade skipping, AP exams, credit by examination, and slew of things that are light years from where your child is now. If you son is personally talking about going to Yale right now that is another matter. But, it sure sounds like you are talking about him going to Yale. If he wants to take AP chem next year, great. But you wanting to plan his school education is completely not okay. He isn't in middle school. He sounds like he is barely in elementary. 

 

 

.

I never said Yale. I want both kids to go to college. I never said AP exams, that's another thread and someone else. I did mention competition math, maybe next year. Kangaroo math competition which starts in kindergarten, is supposed to be fun, is close, and they give you a plushie and t T-shirt. (Not lightyears away). I did ask something about credit by examination, but my question was, if it was useful as a testing tool (answer: it is not in homeschooling), the question was if that test would automatically skip him, if I just wanted to use it to check for gaps, but not for a grade skip.

We are truly not talking about the same thing at all. I can stop trying to figure out the advice I don't understand now and listen to the advice that makes sense to me. No hard feelings. We have many years of homeschool ahead of us, I'm sure we'll have plenty of discussions left, you and I. :)

[wapiti]

 *I* choose to ramp it up to a level appropriate to their skill/talent -- to where they are challenged in the same way that an average student is challenged by an average curriculum.  My kids aren't begging for more material or harder material in all subjects. But if I don't give them material that makes them think, then what are they learning? They are learning that they do not have to work hard to succeed, and that is a *terrible* lesson.

 

This may be off-topic here, but thank you for putting this so succinctly.  I feel like I'm constantly battling perceptions from certain individuals at my kids' school that their math acceleration is somehow unnecessary or too much pushing and it helps me *so much* to be reminded why I'm doing this in the first place.  I'm having a tough morning and your words on this point are very encouraging.