Typically, how far ahead in elementary math are moderately, gifted and highly gifted math kids?

(Humor me...I know there are a lot of factors involved but let's just keep it as simple as possible! :))

I don't think our situation is typical as math is DS7's thing. He has always been at least 1+ year ahead of his grade in math even after early entry to first grade. To make matters worse, during the summer he'd typically make huge leaps in math because it was one of his favorite topics to read about. Now he's at least 3 years ahead of his class, but we have him accelerated only 3 years. All that being said, I do think he's atypical when it comes to math giftedness so I'd probably put him in the "high" category for that subject.

JB

DD7 is in 3rd Grade and was grade skipped in Kindergarten. The first six weeks of school as a 3rd Grader, she tested past the middle of 5th Grade in math and now the school wants to try to accelerate another grade or at least telescope into the next math grade. I was told by the gifted teacher at the school that this was pretty rare. At 6, she tested as moderately gifted.

Do you think our kids are really that gifted in math or that the curriculum is just too easy? Maybe we should moved to Taiwan!

My partner is Taiwanese, and was in school there until she was 11. She says Taiwanese school isn't hard, either. The average kids spend hours on homework and tutoring, but the really smart kids still don't have to work at it.

The kids who are gifted and interested in math can learn the material in a few hours/days whereas the math material is broken down to be taught for 3 weeks!

Some kids are very fast after they learn the material and able to calculate, I would guess these may be the PG and HG kids.

Some kids understand the math but are slow in calculating the answer but given the time, they can come up with the correct answers. I would guess these may be the MG and HG kids.

Depending on the child, some MG - HG kids can probably be accelerated 1-2 years to get some challenge. The HG-PG kids can probably be accelerated 2+ years and I wouldn't be surprised at 3-5 years. Not just skipping but more that the pace of delivery can be increased.

1st Grade to 5th Grade Math is pretty basic.

I can't speak yet about DD since she's not there yet but I know in third grade (I was a young at the time) the school had an algebra tutor that was suppose to come in once a week to work with me (but didn't always show up). I do remember learning some algebra through that but they made me do the normal math homework too. As for testing, I'm not sure of my exact IQ score but other tests would probably put right between MG/HG.

My twin DD6's are both MG/HG and I would say easily 1 yr ahead in math possibly 2. They have tried some typical tests for material 3 years ahead and get about 50% correct

I think it's important to distinguish "learning the material" - learning new concepts and how to do routine things with them - from real mathematical ability, the ability to solve hard mathematical problems in which it isn't obvious what the steps to be taken are. Trouble is, such a vast majority of school time is spent on the former that it's quite hard to focus a comparison on the latter which is really more important and more interesting.

We don't have IQ test data so can't help with the MG/HG/PG stuff, but there is certainly a kind of child for whom there's just no friction with learning the material in this early maths. It isn't that it takes less time to learn - it takes no time at all to learn. All you have to do is explain what the words mean, and then they can do it. DS7 is still like this whether learning concepts intended for 16yos or for 20yo undergraduates.

So, when people only look at material knowledge, it looks as though DS is 9 or 13 or whatever years ahead of his age. Generally, I think how far ahead a mathematical child is with learning the material depends a lot more on exposure than talent. You can't demonstrate mastery of things you've never seen.

However, when you look at the stuff that matters, DS isn't "really" that far ahead - he can't solve the same mathematical puzzles as a good 20yo mathematics undergraduate (choosing words carefully here!) So how far is he ahead in what he can do with puzzle-type mathematical problems? Of course for this you have to compare him with older children who are mathematically interested and being stretched, since most childen, sadly, never get any significant exposure to this kind of challenge. He now finds things (e.g. national competition questions) aimed at mathematically-strong 11yos a bit too easy but I don't think we'd have to go that much further to find things that would be too hard (although this reminds me it is time to look for that boundary again, since it has moved). Say he's 5-7 years ahead for problem-solving, when compared with mathematically-inclined children.

*But* even this over-simplifies, because it's not that ability in problem-solving is independent of exposure, either. I don't know how to estimate or talk about phenomena like children who are intrinsically very mathematical but simply don't get encouragement to tackle hard problems. How fast do they catch up when they do get the exposure, how far is "intrinsic" mathematical ability really intrinsic and how far is it altered by exposure to hard problems? My guess is that it's unstable enough that if you took a bunch of children with little exposure to problem solving and tested them for 2 hours on problem solving, they'd probably be a lot better at problem solving at the end of the 2 hours than they were at the beginning! But then again, how far is my guess affected by having an unusual DS? I'm wittering, I'll stop.

I agree with Colinsmum. Students who are in a problem solving type math class have a different experience. My daughter was so lucky to have a teacher, who was gifted, for third grade math. They were ability grouped. They would go through the lesson in about two seconds and then apply it in a unique way - such as determining how much are the school took up and building runways. This extended her so far into engineering thought processes and gave her a real love of math.

Regular students would not have been interested in this as much as these gifted kids. They spent their time enjoying the calculations. Their teacher was def on their wave lengths.

My oldest is HG, but math is her weakest personal area. She was younger for grade with an early fall/late summer bd and she has skipped one grade. She is about 1 grade up for math achievement right now (performs in the top 10% of her current grade and is in accelerated math), so I'd say, overall, she's about 2 yrs ahead of her chronological age in math. I'd expect that most HG kids for whom math is a strength, not a weakness, would perform higher than her in that area, though.

I also expect that there are plenty of bright, but not gifted kids who are performing 1-2 grades above grade level in math. Dd10 scores slightly above the average 8th grader in math on the EXPLORE (8th grade test) at age 9 (4th grade). She doesn't consistently perform superbly in math (she is subject accelerated one year currently), but she grasps abstract math concepts quite well. I'd say that she does better with much higher level math and not as well with grade level or one grade level accelerated math due to the more concrete nature of 5th-6th grade math. She's maybe MG, maybe HG+ and I do think that math is somewhat of a strength of hers.

Has anyone else read Developing math talent? I am partway through, and it talks a lot about the lag in computation skills compared to conceptual understanding. It is such an interesting and helpful book, I highly recommend it. There is a new edition, released a couple of weeks ago.

I think there is something to be said for that. In the homeschool GT community kids doing "easier" curriculum certainly move faster than kids doing "harder" curriculum like they might use in Taiwan from what I've seen. My 4th grader is at algebra level doing "rigorous" curriculum and that is challenging. It's not the concepts to him that are challenging. It's the multi-faceted way math is presented and advanced problem solving. He's still not the best with keeping long calculations all in order either. So I'd say he is conceptually beyond where he is in the curriculum. Which I don't think is unusual.

You don't want to move to Taiwan, it's a crazy pressured school system with a lot of tutoring and parental pressure. We use Singapore math, which is marketed as great because Singapore has great standards. But I think it's mostly that Singaporean kids are highly pressured and tutored.
My DD's excellent K teacher had something interesting to say recently. The PTB had found her a book with some word problems. My DD can't read, so the teacher sat down with her during free play to take her through a few problems. (I know, we are lucky)

The teacher said "I sat down with her and read through the problem, but she didn't seem to really understand it. I went home and thought no, she's just not ready for it. But the next day I thought I'd give it another try, and she had them figured out". Yes, because you taught her how the day before!

It's so interesting that her gut feeling was that if you need to be taught something you're not ready for it. I'm sure she doesn't have that thought when she's teaching kids to read or count. But it definitely illustrates how these kids are expected to be perfect and computational errors are taken to be signs that they're not ready for the work. Does every child need to get 100% every time before they are allowed to move to the next grade?

We're also figuring out how to politely tell the school that the test they're planning on is one or two grade levels too low.

I agree that the depth of math, at least in our DS8's public school district is lacking. Its mostly operational math, with litlle thinking skills. We supliment using MOEMS, and may look at the AMC8 next year. DS8 is math skipped 3 grades to 6th, he may need one more skip, as the work still seems to repetative and not challanging. Even the 6th grade math is mostly operational math. MOEMS was challanging last year and again this year DS is not doing better then 4 out of 5 correct, so it still seems to be a good fit. I think in the age of NCLB the focus is mostly just getting them to reach a certian test level rather then teach problem solving.

DS7.5 is on that track: 6th grade/pre-algebra. It's material he knows, but it is relatively formulaic. On his own he's read through to Algebra 1 in Life of Fred. However our current acceleration is already pretty radical (going to the middle school for period 1 in the morning, then back to his 3rd grade homeroom for the rest of the day). He's only been doing it for a month but similarly he gets 4 out of 5 correct give or take. Typically they're dumb mistakes like forgetting to include the minus sign or something.

We really wished there was more teaching like the LoF books because those included great word problems.

JB

I read it a while back, and didn't really find it helpful at all; not wrong, just obvious, as I recall. But I have background in both maths and education; I suppose I didn't really need it, I was just curious about what it would say!

For me without an education background, it's nice to get case studies and the right language to talk to teachers. And the list of curriculum areas to cover is nice for me, and the reinforcement of my thoughts that they need a curriculum, not a collection of enrichment activities.

I am actually asking about a home schooled child who is working through 2 of the more advanced math programs (Singapore and Horizons) at least 3 years ahead of her chronological age compared to our local public school. Math and science are her strengths. They are NOT my strengths and I'm having a very hard time coping (if that's the correct word) with her ease and speed in math.

Thanks for everyone's helpful responses! What prompted this post was basically this: I thought she was about 2 years ahead of her age in math. Then recently I looked on the local school district's math curriculum map and discovered that she is THREE years ahead of what I thought - according to our local ps. I guess I didn't take into account how advanced Singapore and Horizons are. But it was just a little bit of a shocker. And she has been asking for harder math. Sorry, but my heads spins sometimes!

I thought maybe there was something that I couldn't find (on Hoagies, from Ruf or Webb) that kind of tells you if your kiddo is about x amount of years ahead, then they are gifted and if they are xx amount of years ahead then they are HG, and so on. I guess it's kind of a dumb thing to ask but I really do appreciate this discussion.

This is your 4.5yo, is it, MamaJA? That's a tricky age for asking for harder maths if it isn't your thing, since (I suppose?) she's not likely to be up for being handed a book yet. Do look at the Sir Cumference books and that kind of thing, though; encourage her to play with numbers and look for patterns in what happens when you add this to that (evens, odd) or multiply this by that... Get her to see what shapes she can make that tessellate, i.e. that fit together and cover as much floor as you like with no gaps... Explore arithmetic in different bases (where instead of bags of 10 you have bags of something else, e.g. "17" in base 8 means 1 bag of 8 plus 7 units = 15 in base 10". Etc... If you want ideas for exploring particular directions that interest her, just ask - there are plenty of people who like to talk about maths here!

Yes, we were surprised as well.

Not sure if you gave an age for your child. Our DS7.5 really, really enjoys the Life of Fred books. (Now he's a voracious reader and very autodidactic when it comes to learning math...) They're a good mix of funny story telling and doing real-world math.

JB

Very recently I helped another homeschooling family find math curriculum for their GT 2nd grader. They were using very a very straight forward curriculum that most people would use as extra practice. They had to come down 3 grade levels from where they were before to start their child in Singapore. Singapore is a very dense, deep curriculum IMHO. I have a math/science background and spent quite a bit of time looking at math options for us.

I think math is one of those things that is harder for kids to leap on without exposure and encouragement compared to language arts. My own child conceptually gets so much, but can still be intimidated by notation. So I think there are kids that are very gifted in math that might not be able to demonstrate all their conceptual knowledge on a particular test. Some computationally saavy kids may not have as deep of knowledge conceptually. I'm not sure it can be as simple as testing X years ahead = some particular level of giftedness.

Needless to say, your child is extremely gifted! My child was working 3 years ahead in Singapore last year and tested 5-6 years ahead in math.

Yes, my dd just turned 4.5! I know she is young and when I started home schooling her, I had no idea she would excel so quickly.

Thank you for all of the positive feedback and advice.

I have a bunch of things that keeps her busy...
She sat and completed a MightyMind set very quickly in one sitting - all the cards, one after another. She promptly asked for the harder one. She likes the Patternables book. She even likes me to read Penrose the Mathematical Cat to her. I have a bunch of Marilyn Burns mathy story books too. Math cubes, scales, c-rods and other manipulatives. All the good stuff.

She does love patterns and even found some interesting patterns in the bathroom of the Chili's Restaurant! LOL

Wow! That thought (5-6 years ahead) really makes me a bit ! LOL

Technically, IQ x chronological age is mental age. Average IQ of 100 at 5 years old starts at K level but with Gifted student with IQ of 140 already is 2nd grade level and IQ of 160 would be in 3rd grade level at 5 years of age.(Granted that the kids are being challenged/stimulated).

The research has shown that IQ correlate better with Math than reading level. Some kids with above grade reading level may have average IQ.

Good point.

My own observations lead me to suspect that it is the rate of acquisition that probably points to the underlying ability of the learner. Otherwise, it's probably a matter of exposure alone.

So it isn't reading level that matters really, so much as how rapidly they PROGRESS. Well, those differences more or less vanish entirely for a PG child by about age four to six, since they are reading at an adult level. How does one "progress" at that point in terms of reading level? The options are limited.

With mathematics, there is a much clearer way of measuring progress for much longer, since advanced mathematics continues quite a steady learning curve through early adulthood.

It's hard to point to "adult level" mathematics, if that makes sense. Is that basic algebra? Calculus? It depends, but even most PG children don't get there until they are 4-10 years old.

What is "adult level" reading? A newspaper? A best-selling novel? Many PG children are already there by the time they are chronologically kindergarteners.

I guess I'm framing this as an assessment ceiling issue as much as anything else. An assessment with a low ceiling (like literacy, in this context) is not going to be very useful as a differentiator. Mathematics has a much higher natural ceiling, so it is probably a better tool for correlation to IQ.

It also seems to be that literacy acquisition is something which is difficult to truly assess well, which might be why it doesn't correlate with IQ as cleanly as mathematics does. It's harder to break out the individual skills and differentiate them with objective criteria, which leads to a lot of noise in the data when children are assessed.

A child can "read" (meaning decode and pronounce) text that s/he can't really "process" yet, too. That really isn't possible in mathematics, so inflation in scores isn't possible from that kind of artifact.

That may have been true of the old IQ tests, where IQ was calculated as a ratio of "mental age" to actual age, but these days IQ scores are based on how many standard deviations from the mean the scores are. And I think the norms are done for every age, but I'm sure we have people who know how testing really works who can explain better.

I believe this formula of figuring the IQ doesn't apply anymore. The way you explain it looks simple, but in reality, it isn't. My Dds8 is technically a second grader, and he is doing intermediate Algebra right now, so that places him about seven grades above grade level. So that would make his IQ about 178? Then his younger brother, who is six, technically in kindergarten, is doing seventh grade math, and pre algebra. So that would place his IQ about 200. In reality, there's almost no comparison between the two. The amount of information ds8 knows, his comprehension, vocabulary, etc., is much more advanced than ds6, and it was even when he was 6. I think that gifted children learn more advanced work when they are exposed to it. If they are ready to learn it, then they do so, but that shows the child is gifted, but not necessarily how gifted they are.

As a side note, my niece was doing third grade math when she began kindergarten, and she did not score high enough in an IQ to be accepted into the gifted program in PS.

I agree with learning other bases. I remember going to a summer gifted program (in the 1970s, but can't remember how old I was). We learned different numbering systems and I was so excited about the different systems.

When I grew up, I became a programmer and was in hexadecimal more than I was in decimal. I think that you don't really know the decimal system until you try a different one.

DS6 is a PG kid who will complete the 5th grade curriculum this year at school (so +4 in math including one full skip and 3 additional for subject acceleration). He is a very mathy kid who is still way ahead of the 5th grade curriculum, that is just the pace they are taking which is going well. He still does his own math stuff on the side like algebra and other stuff. He also is doing lots of interesting enrichment and things on the side like math olympiads and learned hexidecimal this year and now loves to take numbers and convert to binary and hexidecimal for kicks. I do know of many other HG/PG kids that are not quite so mathy and have other areas that they excel in. There are such varying degrees it is hard to say.

There are several things going on here. First of all, achievement test scores, even from individual achievement tests like the WJ-III, don't indicate the level at which a child is truly working. When my son was 9, he scored well beyond the "adult" level in math calculation on the WJ-III. He had just finished 6th grade math and knew how to do simple "solve for x" type problems. This shows a whole lot more about the math ability of the average adult than it does about my son's ability. At the time, my son was working at a prealgebra level in math.

As for how far ahead gifted kids are in math, my older son (who has dyslexia) started out behind by about two years in 2nd grade. By the end of 2nd grade he was ahead a year. By the end of 3rd grade he was ahead two years and he continued to the two years ahead at the end of 4th grade (when he tested at an adult level). In 5th grade he moved into algebra I at half pace, making him (sort of) three years ahead. He finished algebra I at the end of 6th grade, so he was back to two years ahead. He did some "fun math" for about six months and then we messed around a bit trying to find a geometry program that worked for us, so he ended up finishing geometry in the middle of 8th grade, making him about 1.5 years ahead. Then again we messed around finding an algebra II book that worked for us. He is now on track to finish algebra II at the end of 9th grade, making him 1 year ahead.

My younger son, now 9, started out doing 1st grade math in K. He didn't seem particularly gifted in math and he moved ahead at a typical one level per year rate in K and 1st, so that at the end of 1st he had finished 2nd grade math (his WJ-III scores indicated that his math achievement was at a 5th grade level at that time). Then he started speeding up. He was two years ahead at the end of 2nd grade, and now in the middle of 3rd grade, he is doing a prealgebra program and is on track to start algebra in 4th grade, making him 4 years ahead. I anticipate that we will move more slowly through upper level math as I intend to heavily supplement the standard curriculum.

I just realized that I didn't offer any particulars for my own child in my post.

DD (now 11) is taking honors geometry, which is (I guess) considered the "10th grade" course in the 'regular' progression. Now, she's an 8th grader, so that means she's 2 yrs ahead, but that's artificial as well since it doesn't account for her chronological age. She should (chronologically) be in 5th grade, maybe 6th. So I guess that means she's four grades above her chronological placement in mathematics. But this, too, is somewhat artificial since the school has set the pace for her for the last three years, and there is NO doubt that it's slower than ideal for her personally. She worked through Prentice-Hall's math series starting with course 1 when she was eight, and has since done Course 2, Pre-algebra, and Algebra 1.

I definitely do not think of her as being particularly mathy-- she has a leaning toward applied mathematics but really doesn't care much for theoretical math for its own sake. She was not a kid that seemed to figured out a lot of things early and on-her-own. At least not obviously so. She just seemed to only need one repetition to learn almost anything. Long-division excepted. She was definitely able to handle simple algebraic manipulations and symbolic thinking well before age 5, however. She worked through Singapore's curriculum (supplemented with the CWP workbooks, which she loved) levels 1-4 in about two years at ages four(ish) to six.

In contrast, her rate of acquiring literacy was a lot faster-- she went from phonetically controlled readers and easy readers at age 4, to reading Harry Potter on the sly under the covers with a flashlight about 8 months later, and reading college level materials less than six months after THAT. She has never been challenged in terms of literacy by anything that school/curriculum has thrown at her. She read her first Shakespeare play at age seven.

She is EG/PG.