(As background context, I'm a mathematician, and I've taught gifted children math over a span of ~10 years.)

Something that I've noticed lately is a widespread implicit acceptance of the norm for gifted children to learn math at grade level, or just 1 year above grade level. My experience has been that even moderately gifted children (IQ ~130) can learn algebra in at age ~11, and that highly gifted children (IQ ~145) can learn algebra at age ~8. Moreover, I think that there are strong arguments in favor of this.

Developmental capacity

• It's not uncommon for moderately gifted children to be 2+ years ahead in reading and for highly gifted children to be 5+ years ahead in reading, so one might expect them to have mathematical potential that's 2+ or 5+ years ahead of grade level (respectively).
• IQ was for a time believed to be "mental age divided by chronological age" multiplied by 100. This notion has (rightly) fallen out of favor, but it's sufficiently close to the truth for people to have believed it. Under this assumption, a 10 year old with IQ 130 has mental age 13 and a 10 year old with IQ 145 has mental age 14.5, and these 10 year olds are correspondingly cognitively ready for curricula aimed at people of their mental age.
• I know of people of IQ ~160 who have learned calculus at age 7: this suggests that in some respects IQ understates "mental age."

Desirability

Some people have suggested that it's better for gifted children to learn a broad range of things rather than accelerating, because if they accelerate then they'll be out of sync with their peers. I think that this is true in some contexts. But I don't think that the benefits of being better in sync with one's peers outweigh the benefits of accelerating through the K-12 math curriculum specifically.

• Grade school math is key to understanding the natural sciences, statistics and economics. Remaining at grade level in math substantially delays a gifted child's ability to understand these things.
• Learning math well builds general reasoning ability, which has benefits across domains.
• Many gifted children find math especially enjoyable once they become deeply involved in it.
• Being far ahead in math can build confidence on account of being an unambiguous signal of intellectual ability.

In The Calculus Trap Richard Rusczyk at Art of Problem Solving argued that rushing through the standard curriculum is not the best answer for mathematically talented young people, suggesting that students should instead focus on learning how to solve complex problems. I agree with him that learning how to solve complex problems is more important than acceleration through the standard curriculum. But the two things aren't mutually exclusive: gifted children can both learn how to solve complex problems and accelerate through the standard curriculum.

Learning precalculus and calculus was a transformative experience: it allowed me to understand physics, it gave me a thrill, and it made me better understand myself on account of tapping into my latent mathematical ability. It was when my intellectual development really accelerated. I was 16 at the time. I wish somebody had encouraged me to start earlier. A sizable minority of the most intellectually impressive people who I know I know had similar experiences.

There are large potential returns to gifted children learning more math earlier on.

I completely agree that depth and breadth can be achieved in tandem through child led acceleration. Children have an innate number sense, and for HG+ children, this can mean that a 2 year old intuitively grasps grade 1 or 2 math implicitly through free play, without any instruction. How keeping that child at grade level--effectively sentencing him/her to a 4-5 year brake on learning--could be construed by educators as being in the best interest of the child is beyond me. Innate interest merits, IMO, a supportive approach to foster those latent abilities.

We do a great disservice to anyone when we predetermine an achievement ceiling based on stereotypes, such as age.

I agree, but would only add: while in principle accelerating and doing hard problems aren't mutually exclusive, in practice very few children, including those who are accelerated, seem to get anything like enough experience with hard problems. If I were going to encourage one cultural change, it would be "more hard problems" not "more acceleration".

DH teaches graduate students statistics and often comments that the foreign students (who are mostly from China) are generally much better at math (and harder-working) than U.S. students. I wonder if that's because math is taught differently in China--I did hear something on NPR a little while ago about how students (maybe in Japan??) were taught to keep working on a problem even if it seemed unsolvable, while U.S. students were quicker to give up. But I wonder if that's all of it, or if compared to our math curriculum the schools in other countries are 'accelerated,' and if so how is it different. Too bad there aren't "Chinese Math" schools or something like that in the U.S.--it might prompt other schools to allow more acceleration, too.

Does this fill that quota? http://www.prismsus.org/ I don't know much about it, but seems pretty neat. Princeton, NJ is full of really excellent (albeit expensive) schools.

Having a little math head myself, I certainly have evidence that math can be learned at a young age - DS3 has become a little mental calculator of late, multi-digit addition/subtraction, and even (to a less extent) mult/div IN HIS HEAD. So clearly on paper it's pretty darn easy for him. I swear the kid can mentally calculate faster than I can. The concept of algebra just seems to make sense to him (at least, the beginning stuff. he blew through dragonbox months ago). honestly, all of it just seems to make sense to him. it's eerie really. His brain is clearly hard-wired for calculations. We discovered he could skip-count pretty much every number to 100 so early on...2.5ish maybe? and we still don't know how he 'learned' that. So, for at least some kids, the ability is in there. Honestly, I think if we sat with him and did legitimate math, every day ...I can't even imagine what the little brain could do. (normally we just follow his lead, whenever he WANTS to sit and do math, we will, but otherwise, it's mostly via conservations....especially in the car)

The concepts are just there, as is the interest. It's pretty awesome to watch.

I'd go so far as to say (at least in my own experience with myself, my DH, and our DD-- all of us HG+)-- that such children rarely learn math in any other way.

Without challenge, there is no real engagement, mentally speaking. It's like trying to "learn" from standing in line at the department of motor vehicles otherwise.

I estimate that, had we followed her natural arc developmentally, that she would probably have been well-prepared and intrigued by algebra and geometry at about age 8-9. Instead, school ruined her. Well. I say "ruined" but I have watched this process in action, let's just say, and the results have been striking.

We've joked that we gave her school a curious, engaged 6yo with a two hour attention span and they gave us a 14yo with a twenty second attention span and cynical, perfectionistic, avoidant outlook on life(gallows humor, obviously).

She's "learned" that the "right" answer isn't about a process, and that if at first you don't succeed, it's because there is something Very Wrong and that it is Probably With You, But Could Be With The Problem-- best to give up.


So I do think that this is partly to blame on how schools think that all children MUST learn mathematics. We should have intervened when they forced her to spend 3 y 'learning' stuff that she knew before she was even four years old. She was at one time like Marnie's DS.

Yes, this. I have a nine-year-old daughter in the same position. She and her older brother (11) have suffered significantly under a math teacher who ranks as bad among bad teachers. I'll be spending time this summer fixing what she's done to them.

Jonah, have you ever seen Hung-Hsi Wu's stuff on the Common Core? He's an emeritus professor of mathematics from UC Berkeley who was an author of the standards. He went beyond the call of duty in that regard and has created a lot of materials for teaching mathematics. IMO, his stuff is very well-suited to gifted kids. IMO, there's also a need to create learning materials based on it (the large textbook manufacturers seem to be failing in that regard).

Here are some links that may interest you and others here:

Teaching fractions according to the Common Core standards

Teaching Geometry according to the Common Core standards

Article about the philosophy behind the Common Core


More stuff here

But there are, lot of private 'Chinese' tutoring centers around where I live to choose from. I'm not convinced that the 'Chinese Math' is inherently "better" there system seems to include a lot of drill.

@ ColinsMum — Thanks for sharing your observations. The gifted children who I've worked with are unrepresentative in various ways (I teach for Art of Problem Solving) and it's good to hear what you think the situation is more broadly.

@ HowlerKarma — Thanks for sharing your experience. I'm very sorry to hear this. I think that this sort of thing is very common. Fortunately, it's not too late (even if it would have been better had things gone differently).

@ Val —  I think that broadly, school is best conceptualized as a constraint that one has to work within (assuming that homeschooling isn't an option, etc.) rather than a place to learn, and to think about time outside of school as the time for learning. Accepting this can be liberating. I was familiar with Hung-Hsi Wu, but these PDFs are new to me: thanks for pointing me to them, they'll be helpful.

@ bluemagic — I think that elementary Chinese math instruction is better than American math instruction on average in that the students actually develop computational fluency, but I certainly wouldn't recommend it as a good way for gifted children to learn math.

I gave the school maths loving advanced kid (not hugely maybe 1 to 2 years), they taught him to add using his fingers and haven't challenged him in two years. Worse than that they haven't improved his weaker subjects either. I would homes hook if I could.

@ puffin — Is the problem that he doesn't have access to good learning resources, or just that school takes up a lot of time unproductively?

It's interesting to watch my eight year old's approach to accumulating math. He's getting above level math problems, particulalry complex word problems, at school which is helping with his attention to detail and general problem solving acumen.

At home, purely self-directed, he watches a wide range of math videos from algebra to statistics to calculus. He has a couple of random algebra books and a geometry book he's reading, and he likes to do timed multiplication and such in various (various here to include excessive) iPad apps. It's interesting that he gets derivitives and integration, but hasn't picked up quadratic equations.

I think his approach points out that there is a conceptual layer different than processes and such. There should be a place in school for gifted kids to get a survey/tour of the range of mathematics.

@ Zen Scanner — It sounds like he's doing great! For calculus, he might like the Center of Math videos http://centerofmath.org/videos/index.html.

Thanks, I'll point him that way. One of his favorites was one from MIT in 1968. http://ocw.mit.edu/resources/res-18...-calculus-fall-2010/course-introduction/ though I think he only went through the first few videos for now. The approach was so engaing, I ended up watching it with him.

I'm homeschooling a six yr old.  I bought the singapore textbooks set, not the workbook.  This year he went through a couple of them (I assigned 1-3 pgs. day).   I put in "the great courses, mastering the fundementals of math".  He understood the first 2 discs.  He has been introduced to a lot of elementary school math outside of the assigned singapore textbook pages, from the great courses and from youtube videos like "turtlehead multiplication."
I just got some advice on enrichment and acceleration by compacting.  Instead of making him do a couple of pages of the textbook each school day I will go over the next item.  If he understands it I won't assign anything from the textbook, but half of the ip, and all of the ip word problems.   I have read that AOPS uses a discovery method, so I'm asking to make sure previewing these lessons a little won't take anything away from that method for later.


I learned that enrichment is not just giving him any old thing on top of his textbook.  Enrichment needs to be problem solving.  I bought the Borac series.  He has Beast Academy 3.  I was letting him use BA as a treat, about once a month for school.  I was informed that enrichment should be the main course.  He should do as much Borac and BA as he wants as an assignment, and compact singapore using ip until it gets to a challenging level.

I just started browsing aops youtube videos to show him. He liked the counting one where a guy used a cube and tried to get to point from point a in seven moves and couldn't, only in six moves it was possible. I guess my question is, it won't hurt anything to show him these videos if he's not completely understanding them, right? Instead of following the logic presented by the math tree, he spent a long time trying to do the block in seven moves, even though the guy just showed him mathmatically why it couldn't be done.

@ La Texican —

I agree that enrichment should be a main course.

As long as he's not frustrated, it won't hurt him to show him videos that he's not able to fully understand. Ideally you could find materials that are just at the right level, but it can be very hard with a gifted child because of the asynchronous development: in general, parts will be too easy, and/or parts will be too hard.

You probably have additional relevant context, and it's likely that he didn't fully understand, but it's worth remarking that just because he was trying to do it in 7 moves doesn't mean that he didn't understand. In math sometimes you can follow a proof of something without developing a visceral sense that it's true. He may have been deepening his intuition.

I wish I'd read this a year ago LOL

This struck a chord with me. Personally the question about math acceleration boils down to what is the end state of the process? Getting through the calculus sequence more quickly than what is possible in school doesn't seem to be worth the effort unless at the end of the road, my son wants to go farther that that in math. But at 7, its really hard right now gauging intensity and interest. While he has an aptitude and we've been doing 15 minutes before school because I have the time and he he seems to enjoy the challenge I can't tell yet if we're in for the long haul or if I should let him fall back to his in school sequence which is already accelerated.

Ben

@ madeinuk — Yeah, I wish there was better dissemination of information. What would you have done differently had you read it a year ago?

@ Ben Ieis — I'm unclear on whether you mean (a) accelerating would be tiring/unpleasant or (b) there are other things that it's more important to learn.

On point (a), probably the most important thing right now is that he enjoy learning, and I wouldn't suggest accelerating him if he wouldn't enjoy it (though it can be hard to judge ahead of time).

On point (b), the fraction of gifted people who go into something that involves math is fairly large, so learning more math at a younger age often turns out to be useful. In many cases this is algorithms (in the context of computer programming), so learning programming and discrete math early is a contender for something more valuable than learning calculus early.

I wouldn't have stopped the out of school Maths after she tore through SM5 a year ago for a start. I had her doing Lure of the Labyrinth through the Autumn/Winter until she finished it plus Zaccaro and the challenging word problems so all was not completely lost. (I hope)

DS6 was offered to be subject accelerated in math by 1 year in his private school. Although we were glad they were open and understanding he needed more, we gently let them know it wouldn't be enough. Seems they are stuck on the fear of "gaps", which to me makes no sense what so ever. I explained to them that there is no way holding back a child because of a few potential gaps that can be easily filled in later.

They agreed to let him skip the school curriculum and do EPGY math instead. So, he could have been sitting in the 2nd grade class right now drilling stuff he already knows. Instead he is working at his own pace, going through 6 years of math since this school year started.

WHY hold back a young child's mind if it is ready for more?

Ugh. I have guilt about this. I strongly suspect DD is ready for more, but her school only works 1 year ahead. She never has any issue learning any of it, ever, and got every problem correct on a state standardized test last year, but expresses no interest in doing additional math. I don't like math and am weak in it, and DH is good at it but also does not like it. I don't think this is her main gift, but I know she could do more. She has too much homework and too many other activities regardless. Someone needs to light her mind up to math and I am not that person.

@ ultramarina,

A few thoughts:

(1) The math that's taught in grade school is analogous to piano scales and chords. A child whose exposure to music consisted exclusively of learning scales and chords might have no interest in doing more even if s/he had a strong musical inclination: learning scales and chords is unrepresentative of the experience of playing and listening to music. So your daughter could be mathematically inclined despite her lack of interest in doing more math.

(2) Even if you don't like math and are weak at it now, these things may change in the future. As above, your exposure to math was likely unrepresentative of the subject. I know that you might have sufficiently strong negative associations so as to not want to revisit it, but I would guess that if you read Arithmetic for Parents: A book for Grownups about Children's Mathematics you'd enjoy it and find it illuminating.

(3) Some math fun books for elementary school aged students are "Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians" Volume 1, Volume 2, and The Man Who Counted: A Collection of Mathematical Adventures and The Number Devil: A Mathematical Adventure. You could offer her one and see if she's interested.

I know we're very guilty of neglecting DD3.5's math talent, relatively speaking.

I go way out of my way to support her literacy development. I spend hours and hours hunting for just the right books.

Math is a different story. Her intense interest in it scared me. I was starting to think John Nash, not that I assumed she's be a great mathematician one day but the level of intensity was a bit pathological. My guess is that her preferred mode for thinking is visual/spatial/numbers and it gave her comfort to be thinking in numbers and it probably still does.

Her other talent that stands out is music (not surprising given her love of patterns - not normal patterns but she seems to find orders in chaos) and we were thrilled to get her started with music lessons. We bought her instruments and hired a private teacher.

Math? Ah, we're leaving it up to her to figure things out on her own. She's doing a pretty good job and why fix things when they aren't broken, right?

I've been asking myself if I'd be this anti-math instruction/curriculum if we had a boy instead. I'd like to believe that nothing would change but maybe I'm in denial about my own gender bias.

Thanks, Jonah. I got her the Number Devil book once, but she was heavily into some other reading at the time and didn't really look at it. She has actually always been rather interested in math "tricks" and larger math ideas, (the number of conversations I've had about infinity--good grief) but would blanch at doing more "math math." That's what I mean...someone who was exciting about math would open her mind. She does like Vi Hart...I need to show her more of those (only watched two so far).

She is actually fairly closely related to a very famous mathematician. I got none of the genes!--but they might be in there somewhere in my kids.

1111, you are fortunate that your child is allowed acceleration by a Year. My older son AP who is currently in 5th grade- Perfect score in Math ERB, ISEE , SCAT & Perfect Score LATIN SCHOOL math competition, not to mention he gets 99% ( yes a few marks taken off due to not reducing fraction like the teachers wanted etc...).

YET his school not only doesn't put him in the Top 5th grade math section but refuses to acknowledge that he may be gifted in Math. He computes numbers and finds a way to solve the problem so fast that it baffles me..He says the school way of doing math is slowing him down ( as he says he doesn't want to loose his math intuition ) . We have gone through many nights of telling him - Hang in there buddy it gets better . But it doesn't :-(
He gets A+ in writing and and science too....( chess, art- ahead many many years than his peers)

We are hoping he does qualify for Davidson Academy Explore test scores ( due March 20th) and we can end his current School misery ! Yes I could home school him..But we like the projects he does in school with his buddies !The recess....yet I know he has no real friends to channel his intellect in school.

His IQ is 145 -so he qualifies to be in gifted category . I strongly feel he should be allowed to accelerate in math...but alas his school doesn't even acknowledge he is gifted in Math. The principal outright told me they are the EXPERTS and I should look for another school if I am not happy ! This a gifted private school he goes to and these are the educators who have made this a personal ego issue- how can we let the bright minds progress at this rate ?

I am not expert in education - but I see a child who wants to learn more, is SUPER well behaved, has shown consistently he excels in math - WHY DENY him ?

He has started learning Trigonometry and he is barely 11 years old ! He can go faster , but my hands are tied ! I keep telling him use the extra time on Fine Arts etc...

What is going on with the teachers at his school??

Schools are typically not influenced by parental feelings but rather by research and evidence, well-presented.
Here is a brief roundup of information at links on the Davidson Database, which may be of interest...
1- Advocacy - Working with your child's school http://www.davidsongifted.org/db/Articles_id_10558.aspx
2- Choosing the right school for your gifted child http://www.davidsongifted.org/db/Articles_id_10511.aspx
3- Basic educational options for gifted children http://www.davidsongifted.org/db/Articles_id_10270.aspx
4- Guidebook - Advocating for Exceptionally Gifted Young People, plus lists of other resources http://www.davidsongifted.org/db/browse_resources_165.aspx

Other discussion threads have explored the possibility of a child taking the school's end-of-term test to demonstrate mastery.

Does your child like school? Friends? Teachers? Curriculum placement and pacing?

If your child's school is resistant to positive, well-prepared, unemotional advocacy, is not open to discussing well-presented evidence, and does not seem like a good fit, you may wish to visit other schools, have your child shadow, and work toward choosing the learning environment with the best (or least-worst) "fit".

Regardless of the school your son attends, you may wish to read up on advocacy as those skills may be needed again.

Another thought: Many students enjoy math activities outside of school to satisfy their voracious math appetite.

indigo. How kind of you to take the time to write to my post. I will absolutely go through all the link you have posted and learn.

1) My son enjoys school and doesn't have any social emotional issues. There are always incidences when he tell me - the kids in his class just don't understand what he is talking about. This frustrates him as he has to talk just for the sake of talk and not truly engage in an in depth conversation.

2) My son loves his English teacher ( wishes he could take her to the next school we hope to land in ) and is channeling his extra energies - left over from math - into English writing.

3) Curriculum and placement - 100% out of synch. It is pvt school and they just don't want my opinion.

4) This year we simply HAD IT and yes we have applied to 2 other schools. They may not be that far advanced in math but a change may be refreshing.

5) Yes we absolutely have a parallel home schooling going on for our son in Math and in Eng Language ( writing).... He can not have survived his school years with it,without falling off the wagon and succumbing to dumbing down effect! We had a math online tutor ( for enrichment ) and he refuses to teach my son any moe math , as he says that my son will get bored all the way till high school ! Surely my son can do better with acquiring more knowledge and more practice - I say ! Mt son beat all the kids in higher math grades and beat all the kids in the region to take home a perfect score 5th grade regional Math competition . But again school is not impressed enough to move him to a higher math section.

6) possibility of a child taking the school's end-of-term test to demonstrate mastery.--> Our pvt school will eject us out of the school immediately if I even dare to ask for this :-( !!!!

Thank you indigo. I will post for which shcool my son lands up next year and how it seems like a better fit :-)

Thank you again for your reply.

Some may say it sounds like the tutor knows the educational system is broken as evidenced by schools being unresponsive to a child's readiness and ability... often not accelerating when indicated.

Agreed! Here is an analogy: If a child liked broccoli (and broccoli is known to be healthy), would one withhold broccoli from a child who wanted more? [If one would not withhold broccoli, why withhold math?]

Some may wonder whether public, private, independent, and parochial schools may be struggling to appease their largest donors who may become offended if one child is openly acknowledged to be ahead in one or more academic areas?

Ultimately, knowing that gifted children could learn math much earlier, but are being dissuaded... in favor of one-size-fits-all education... may be a wide-spread case of appeasement of a variety of powers-that-be.

Luvedu, we are dealing with a great school and feel fortunate. It took all of his K year suffering though. It wasn't until his highly respected 1st grade teacher told the administration she had never seen a child like this before. Seems it doesn't matter what kind of school, it is just a matter of finding this one person that "gets it".

We played with the thought of sending DS to a gifted school but heard a lot of comments about those schools feeling they ARE doing what is right for the gifted and no other accommodations are necessary.

Sounds to me a school switch is in order. One where your child is allowed to flourish!

indigo, again your analysis is right on. Some points that I didn't automatically think about, you rightly pointed them to me! Luv your Broccoli analogy :-) !

I have a mild problem with enriching(takes 4-8 hours) the child at home after school, as it takes away the time of having casual middle of the week unhurried dinners - the ones that open and give way to play/ talk/ discussions. Doing after school enrichment activities the child is already bogged down with million things on his mind!Agreed try to strive a balance- but with a gifted child there is no balance- HE wishes to go all the way deeper and deeper. But without the essential out of school enrichment, my son will "fall off the curious / wants to learn more brain" that is brimming with firing neurons. I feel learning is like LOVE - why withhold it?
It is a "damned if I do damned if I don't"-situation ! I just can't bring myself to let him " go with the flow and sail away where ever the wind takes him!"

We donate a sizable amount to the school too. I am unable to understand the ego behind not allowing a child to learn at his fast pace. Agreed the heavy donors and Board members do not have children who fit this mold. I suspect this makes the school look bad , as not all the children are racing to learn and excel!

** 1111. Only our son's Art Teacher " gets it " :-) . My son is also not challenged with the Art department as they are not giving him challenging meaningful art projects ! I engage him in fine art at home - but 24 hours a day are NEVER enough , alas ! I am seriously considering taking a year off after highschool and sending him to France for a year to continue his love and talent for Art ( will this happen- I don't know ! ), he is willing. He can speak french !

I am grateful for you all giving me feedback and making my decision to switch school , seem appropriate !

Will continue to keep you guys posted.

luvedu, your son's story closely parallels my son's. My son is younger at 6, but your post bought a sense of deja vu to me. I too have problems with "afterschooling" for hours upon hours in my son's areas of strengths. I find it counter intuitive and counter productive. But, I live in an area where it is the norm rather than the exception.

Some strategies that might help:
1. Use online programs (EPGY online is an example) and the Great Courses DVDs as enrichment tools. Your son can learn at his convenience.
2. Try to get your son a mentor or a tutor in advanced math - I have a strong math background and teach my son now, but, I would like him to have a mentor to guide him later on.
3. Enter your son in a Math olympiad or Math Kangaroo like competition - if your son wins a significant prize, the school has to acknowledge that he is gifted in math, right???
4. Please consider enrolling your son into your local Math Circle. The advantage is that your son can interact with like minded peers, advance significantly in math and will have a mentor to guide him.
In addition to these, I have a curriculum that is good that I use to teach my son at home.
I am sorry that your son's gifted school thinks that they are "experts" in teaching your son. If they say that you should look for another school, then, maybe you should ... because in addition to fee, you are paying them a donation too!
Good luck with the DYS application. Maybe they will help you find a solution.

ashley. Great to hear from you.
Isn't it true " I too have problems with "afterschooling" for hours upon hours in my son's areas of strengths. I find it counter intuitive and counter productive ! "

Loved your suggestions.

1. He and my younger son (8) are both in CTY English program. They Luv it. They are in "Where the wild things are ( gr 3) and the older one is in " The process of writing"( gr 5). Can't say enough good things about CTY

2. Finding a mentor in Gifted Math is very very hard. I teach my kids math , just like you do . But I would like some one who can teach him , while drawing on his strengths ! I don't want a repeat of the school teaching ...
3. Ashley he did enter a regional Math competition, got a perfect score , came first - School is not impressed enough to acknowledge he may be gifted.
4. Enrolling in local math circle- I will look into it, but I am suspecting may end up with time constraints.
5. Can you PM me about the curriculum that you are following at home ?
6. I am considering Art Of problem Solving for Spring 2014. Summers at CTD ( northwestern university are great - but this year we will be travelling and can not attend CTD :-( . ) I will consider EPGY ( standford...He is ready to enrol in Algebra -1 honors but can't be sure if that is the correct progression. I find EPGY website very very confusing). How do I find out what is the correct course for my son. I can definitely not follow their age or grade guideline , as my son is beyond it.

7. At 6yrs I was so sure my was gifted but the school dampnen my spirits and at 10 - I just couldn't hold him back anymore..He started complaining if there is anything more to learn in math ever !

8. I have the Great courses DVD and I am sure to wipe the dust off them and put it on for my kids :-)

Please stay in touch and good luck.

ashley do you have any experience with EXPLORE test ?

If winning a regional math competition is not proof enough for your son's school then they really may be trying to hide the fact that they do not have the expertise to teach him. I am using AOPS (Beast Academy right now and hope to use AOPS prealgebra later on). The best places to find mentors are through your local universities and colleges. Math Circles are sponsored by the math departments of acclaimed universities and colleges. They encourage kids to learn math and problem solving at a high level. The professors involved in these circles can and most often do act as mentors for the kids who are interested in learning advanced math.
I am not familiar with EXPLORE - it is a little too early for us to take the EXPLORE. But, there are several in this forum who have experience with it - you can start a separate thread about it. I also suggest that you check out the WellTrainedMind forums (The Accelerated Learners sub-forum in particular) for a lot of valuable resources.

I think this is a very good point, and one that may not be made enough on this board (although one cannot create such a person out of thin air). My DD10 had no such advocate at her first school, and despite copious evidence that she was spinning her wheels, nothing was done for her. DD5 happened to get a K teacher with extensive gifted training, and doors have opened for him and everyone has been accommodating.

This is definitely not limited to the USA - here in South Africa there is a definite copy of the trend there.

I hated maths in high school and have therefore determined to NOT squash my boys' natural affinity for numeracy. I go out of my way to enthuse them and give them the opportunities to keep them engaged in maths. Right now we use Dreambox and Soroban (Japanese abacus) classes. I have recently discovered Life of Fred and am totally in love with them (I am a literary type person so they appeal well!)

I remember when Aiden was 3 and then 4 and in pre school (gifted school - only one in the country!) and he asked about negative numbers (aged 3) and was told he was too young to worry about that now, and then when asking to learn multiplication facts (age 4) was told that counting in 1's is the 1 times table. yes i kid you not.

Suffice it to say, we homeschool now and my boys are flourishing!

Maths (all learning really) should be freely available to any child (person) who wants it when they want it in a way that makes sense to them to understand what they are trying to figure out.

How do I find the Accelerated Sub Forum ?

The book developing math talent" by Assouline has some good suggestions on advocacy and enrichment.

ITA that a good teacher has no problems both compacting/accelerating and enriching all in one class. There are a lot of really cool things which aren't in the standard curriculum.

Lovedu,

I have been through exactly the same resentment tinged ennui that you are experiencing. To some extent it doesn't go away but you become better able to cope with it. What helped us to get the school to come round was a combination of the Iowa Scale and walking them through material on the dangers of not accelerating.

In our case DD's teachers accepted that she was quick to learn and ahead of her age peers but they had reservations due to 2 main areas of concern:-

What I will call the 'we have to look at the whole child fallacy' this allows administrators to effectively ignore academics and protest that removing a child from their age peers will do irreparable harm. Showing the school the literature showing that evidence overwhelmingly supports the opposite conclusion helped us.

The other objection is based on an apparent fear of an absolute torrent of 'our special snowflake too!' Requests for other parents. Here we introduced the Iowa Scale to the school and persuaded them that in it the have an objective bar that most 'me too' requests will fail to clear while making the point that anyone clearing the bar should be accelerated .

Our DD was accelerated a full year and she is still not learning enough really but her over excitabilities have calmed right down.

My conclusion is that it is unlikely that any school will ever go at the pace that my DD can learn at but the skip has relieved some of the pressure that my DD was feeling for the time being at least.

We are trying AoPS now which she seems to like. It is an after school program but it has rekindled her enjoyment in Maths so it is like play to her - weird as it sounds. Not sure what the future holds...

Forget the EXPLORE test. It has been withdrawn by ACT and the jury is still out on a suitable replacement.

In my experience, schools seem to be asking "what's the benefit of having kids race ahead?" when what they should be asking is "what's the harm of holding them back?"

We're in a situation similar to some others here where DD is struggling with basic math concepts that we were playing with at home for fun in Kindergarten (negative numbers, percents, fractions). Yes, she's allowed to work ahead of grade now and basic algebra concepts aren't hard for her, but her early experiences being held back seem to have given her this idea that math is hard and annoying and not at all fun (and I love math).

"Slow down" is inaccurate. It's actually "repeat ad nauseam until you hate everything about it."

An earlier post, Tallulah, mentioned the author Susan Assouline. A couple of publications by her are most appropriate on this topic. 'Developing Math Talent' and 'A Nation Deceived'. The first is available through most on-line book retailers. It is an excellent book, and through it you will also learn that she is the person probably most responsible for the concept of the modern day Talent Search for 4th, 5th and 6th grade students. She is also part of the group that first utilized the ACT Explore test (BTW, the 'death' of that exam has been delayed by at least one year) A very interesting description of the concept of above grade level testing that makes up the Talent Search concept. The second book is available either as a PDF download or as apparently a free copy at the following web site http://www.accelerationinstitute.org/nation_deceived/get_report.aspx

'A Nation Deceived' is a very profound book that addresses exactly the subject being discussed here. I highly recommend both publications...BTW, Dr Assouline was recently made Director of the Belin-Blank Center(University of Iowa), a leading advocate for academic acceleration. Three areas she lists as research interests are Mathematically Gifted Elementary Students, Twice Exceptionality and Academic Acceleration. I think she was also responsible for the development of the Iowa Acceleration Scale. Check out the Belin-Blank site online.

Some comments:

OP mentions IQ, but while IQ is obviously strongly correlated to math ability, they are not the same, so it's better to use math ability tests than IQ tests for math acceleration decisions.

That said, I think similarly to the OP, that a kid (say 8yo) who is at least 2SD above average in math (2.5%=100,000 out of 4,000,000 8yos in the US) should be able to handle a 2 year acceleration in math, and a kid (say 8yo) who is at least 3SD above average in math (0.1%=4,000/4,000,000) should be able to handle a 5 year acceleration in math.

(These numbers seem instinctively right to me, but of course it would be better to have it properly studied.) In any case, large numbers (though small percentages) of students should probably be accelerated a lot, and probably a lot more than is happening now.

What I do know is that students just 1SD above average in math, can achieve 2 or more years of progress more than average students over their K-12 years, simply by going about 20% faster, in an ability grouping setting (without grade skipping) which was the situation when I was at school. The top group, which was about the top one sixth, or 84th percentile and above (standard score 115 and above) reached calculus by about 9th or 10th grade.

(I've got more to say, but I'll submit this so far.)

We are also dealing with this, and the more I read these posts, the more upset and guilty I feel. My girls used to do math problems for fun in the car, and now my younger (HG) says that math is boring, that she hates it...We just had what looked like a promising meeting with the principal, but today I spoke with a woman whose job it is to advocate for kids in the schools, and she stated that our principal always says the right things, but then never follows through. We are doing our best to get our DD accelerated so this is discouraging.
I wrote down every math suggestion on this thread - I hope that some of them pull a good response from younger DD. I want to see that "spark" come back.

Continuing my comments. The question is, what would education look like if everyone could learn at the pace appropriate for them (subject to practical constraints). More able students should not only be at a higher level at any given age, but they should also be able to learn faster, so that "achievement gaps" should widen with increasing age. (For example a 25th %ile student may reach the same level at the end of "college" that a 75th %ile student reaches at the end of high school.)

So not only should gifted+ elementary school kids be learning 2 to several years ahead of the norm, but also kids at the 80th %ile could learn at least 20% faster than kids at the 50th %ile, and so be 2 or more years ahead by the end of high school. [Caveat: I'm guessing these numbers based on my experience. They may not be quantitatively quite right, more study would be needed, but they paint the right picture qualitatively.] Ability grouping, all the way from 0th to 100th %ile, is what is needed to educate people to their level (not just gifted education for the top few percent).

Also different people will reach different plateaus depending on ability (assuming equal opportunities to learn according to ability level) where they really can't progress further because the material has become too difficult for them. And there are many reasons for people to not reach even that potential. One upshot is the "age-equivalents", based on the 50th %ile of a given age, are rather low for an academically oriented kid. If your 7yo kid gets an age-equivalent of 23 or 13 on the topic of fractions, then they are certainly very smart, but more, it says that most adults or teenagers aren't that adept in this topic, and a kid doesn't have to be a prodigy to reach the median for that older age. Another thing to watch out for is when your kid is finding it easy to work several years ahead in math, the course might be pretty easy, aimed at the 50th %ile or even much lower, so the material is not so "advanced" after all.

It's important that a gifted kid can move freely through higher grade material. But when that material is aimed at typical (or struggling) students, the kid will need something else. Two things are (1) tough challenging problems, (2) material not normally covered in the standard school sequence.

(I've got more to say again, but I'll submit this so far.)

So the question is, how should (1) and (2) be done. There are some things you don't want. You don't want, extra busyworksheets, or so-called "gifted pull-outs" or "enhanced/supplemental coursework" if they are not being done really well, especially when they are just some extra fluff on the side for the highly able student who is nevertheless locked into the standard slow-paced gen-ed track. When needed acceleration is denied, you can't make up for it (much) with extra stuff on the side.

One should be very skeptical of a school saying they don't need to accelerate because we've got this "super duper stuff on the side" instead.

That said, as pointed out in "The Calculus Trap" www.artofproblemsolving.com/Resources/articles.php?page=calculustrap
there is a lot of mathematics outside of the standard K-12 sequence. Then it does make sense to learn about these other topics. And I think it even makes sense to then do the standard K-12 sequence at a less accelerated pace while learning about these other topics, than you would if you were just doing the standard sequence.

However, these extra topics mainly start being accessible after one reaches about the pre-algebra or algebra I level (in US courses). For elementary school level standard courses and up to pre-algebra, I really think the sufficiently able student should just get through these courses as quickly as they are truly able, even though there may be other worthwile stuff to do during this time (hard problems and recreational math). This can put them several years ahead of their age cohort, but that's exactly what should happen.