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Carol Bainbridge

Advanced Math Abilities of Gifted Children

By October 24, 2010

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I've written before about the advanced language abilities of gifted kids, but haven't written much about advanced math abilities. There are reasons for that.  For one thing, I'm a linguist and so language is interesting to me and I know something about it.

For another thing, my son was one of those verbally gifted kids, so I am personally familiar with advanced language abilities. And finally, advanced verbal skills are so common among gifted children that it is essentially a defining characteristic. That is not true of advanced math skills. While we do have many mathematically gifted children, advanced math skills aren't a defining characteristic of giftedness.

Those advanced math skills can actually be a problem for mathematically gifted children. They might have been multiplying double digits in their heads before they started first grade and yet be asked to complete endless numbers of single digit math problems. They may know the right answers to math problems intuitively, but fail math tests because they don't "show their work" or don't show the "correct" work that indicates how their arrived at their answer.  How do you show intuition on paper?  

Does (or did) your child have an math skill? Share some stories with us by clicking on the "comments" link below. Tell us about something your child did that you think showed an advanced math development and be sure to tell us how old your child was at the time that sign showed up. Don't worry about anyone thinking you're bragging either! You can share your stories here and know that people will understand.
October 27, 2010 at 10:44 pm
(1) Barb says:

When my son was 18 months old, he made a multi-dimensional bar chart of his Duplos, sorting them by color and size. He noticed a discrepancy: there was no green 4-stud brick, but there were 4-studs of all his other colors. Too bad he was too young to say “discrepancy”.

When he was 2 he fell in love with triangles, knew every triangle (gable, sign, brickwork) between our house and preschool.

At 3 he beat his 3rd-grade brother at flash cards, so we instituted a rule: Big Brother does the card as shown, Little Brother changes the operator.

When he was 4, he figured out that 8 bananas costing $1.97 come out to 24 cents each, while I was trying to figure out how to prevent a tantrum right there in the produce department if he COULDN’T find the solution. He explained to me how he did it, but I couldn’t quite understand him.

And yet the school insists “we really can’t identify giftedness until 3rd grade.”

October 29, 2010 at 10:54 am
(2) den says:

my son is 5 yrs. old he is kinder, he can do 3 digits addition and subtraction with regrouping, master multiplication, division, he is advance in mathematics, and also in reading, he can read books on his own, he is a fast learner.
when he was 3 yrs. old he can memories the plate number easily.sometimes im amaze when he solve the problems easily.

October 31, 2010 at 2:19 am
(3) Shubhangi says:

My grandson is could recite numbers upto 200 backwords,jumping and whatever way when he was 20 months old.He could recognise all shapes at 18 months, point out similarites in different and disparate objects.But hates learning by heart the times tables. He can, of course remember them easily.

November 1, 2010 at 11:33 pm
(4) anon says:

My daughter is 2.5 . She does the adult version of tangrams with no help… clicked through all the puzzles on the iPad. She also spells words phonetically ( she knew the entire alphabet– caps and lowercase — before age 2 ). We are really having issues challenging her.

January 14, 2011 at 5:12 pm
(5) Cindy says:

As the parent of a pre-schooler who loves numbers and any type of game involving numbers I have found the website below useful for free resources:


February 13, 2011 at 11:25 pm
(6) Chris says:

Hum..that’s long story for me, it took me more than a year to confirm that my son is mathematically gifted(I think he is HG+)
child. Even I was very good at math when I was young, won lot of math competetions,but..my son is way advanced than what I can image.

Here is the meilstone of his math ability development

* Know all the numbers at 18 months
* Count to hundreds at 2
* Do 3 digit addtion/substraction at 3,skip counting etc..
* Know times table at 3 1/2
* Know Division at 3 3/4
* Tell time at 3/12 and complete understand time at 4
* Tell date and count money at 4
* Matsered 2-3 digits multiplication and long division,
squre, squre root, decimal operation ,some fraction and percentage, and easy algebra before 5

He always keen to numbers and had endless questions about math, he has amazing memories about anythings comes to anything related with numbers like birthday, date, times, books pages, all songs’ tracks on the CD,friend’s house numbers…He has unique way to fix math problem that I don’t know where it comes from?
like 11+22+33..+88+99…he told me is 495 because 11+99 is 110,22+88 also 110..therefore 4 times 110 plus 55 is 495
(he did that in his head) ,before he turn 5!

He is in kindy now, the school got him tested and promised us give him individual math work, but we don’t know if it will work.

By time way, I heard math and music connected, yes for my son, he self taught himself to read notes and play piano at 4yrs and 2 months, all his music/piano teacher commented that they never taught any kids like him.

August 29, 2011 at 7:29 pm
(7) Valerie says:

My son absolutely loves math (and science). His math skills did not show up as being gifted until he came home from school with a letter to be retested and a drive to understand all math (algebra, calculus, trig, and even differential equations).

In your article above it states that gifted childen usually have a defining characteristic in language. When he was just 2 years of age, a teacher was stunned by his ability to speak so well at such a young age. He nows reads on a high school level and writes much more advanced for his age than other kids in his classes (per the teachers).

He is now in 4th grade, and as of last year he was testing on an 8th grade level in math. Several months ago he talked with a college math professor, who was quite blown away. They ended up having a 1/2 hour conversation about math (mostly calculus). The professor stated that he is on the right course and should continue his studies in advanced math…but reminded him that with everything in life you must learn the basics…he really wants to skip all of the “easy” stuff in school and go straight for calculus.

I have been told that math and music go hand-in-hand also…this is due to the “counting” involved in both. He has a great ear and is able to pick up on tunes from movies (Harry Potter, Church music, etc). He plays the piano also. His recital (the original score) of “Fur Elise” by Beethoven was so beautiful. He has a real talent, his teacher is now doing theory with him…if only he would practice without arguing (he just wants to write music…)

His goal in life currently is to be a the next Albert Einstein!

February 22, 2012 at 6:55 pm
(8) Freddy says:

More important than how fast they learn are the kind of questions they ask. in third grade I was explaining him how to find the area of the rectangle and explaining to him of the importance. He ask me how to find the area of the circunference. I told him that the area of the circunference was = 2 * PI * r. (I told him that PI = 3.1415..) easy right?
not so fast, he wanted to know what was PI and how it was calculated? I always use the formula and never asked myself that question?

February 27, 2012 at 8:42 pm
(9) Hineata says:

Hi! Enjoyed reading this. However I was wondering why verbal gifts are a defining characteristic of giftedness and mathematical skills are not? Am not sure that that makes a lot of sense. I agree with you though about higher mathematical abilities sometimes causing problems. My daughter was adding/ subtracting multiple digits in her head by 5 and a half, and the teacher would carry on telling me how wonderful she was in that she could answer double digit equations. Refused to believe she could do much more than that, and kept her working on’baby’ sums
(to DD, anyway) for years.

April 5, 2012 at 3:24 pm
(10) Julie says:

My almost 7 year old son will ask, out of the blue, does ‘you need to handle it’ have 17 letters. I’ve sometimes thought that he thinks this out and counts it in his head before asking, but there have been more times than not, that wasn’t possible. Has anyone heard of this? He’s been doing this ‘trick’ for months now

May 7, 2012 at 6:17 am
(11) compound interest says:

Thank you for sharing your info. I really appreciate your efforts
and I will be waiting for your further write ups thank you
once again.

July 10, 2012 at 2:50 am
(12) myintterestcalculator says:

Outstanding quest there. What happened after?
Good luck!

November 23, 2012 at 8:30 pm
(13) JD says:

We adopted my 9 year old niece 3 years ago. I taught her multiplication and division facts at age 7. She has just mastered systems of linear equations. She is also writing linear equations for perpendicular and parallel lines through a given point.

March 1, 2013 at 6:42 pm
(14) Mohit says:

@Chris, my son is exact copy of yours.
So whats going on now days and how did you guide him further?

Please contact me if possible mohitbansal02@gmail.com

March 3, 2013 at 3:47 pm
(15) Donna says:

My son is also exactly the same as Chris’. I am lucky that he is also excelled in the verbal area. It has been incredibly hard getting my son’s teachers to extend his work, let alone grade skipping. Get an IQ test done for your gifted children, and fight for your kids! Do not give up until your children have the same rights, as all the other kids, to a proper education.

March 14, 2013 at 2:00 pm
(16) Sharon says:

My 6 1/2 year old son is finishing up pre-algebra, and will be starting algebra soon (we homeschool).

March 20, 2013 at 7:05 am
(17) craig says:

My son is 6 and is pushing the teacher at school and after a very good parents evening the teacher suggested a gifted register but dont know what to do i have given him a year 6 age 10 maths test and he scored 10 out of 10 please help

March 21, 2013 at 5:16 pm
(18) Fritz says:

Gifted might not be the proper word. Frustrating fits much better. My son has always loved numbers and shapes. By second grade he knew the multiplication table as well as division. By 4th grade, 5th grade math was so boring that his teacher let him play games on the computer in class while he taught. During 5th grade he was bullied so much from others (beat up, spit on) because he was in a 6th grade class and getting the top grades. My wife and I pulled him out of school and home schooled him. He flew through pre-algebra and algebra by the end of 6th grade. I asked the school district to allow him to take high school entrance exam in math and they said no. He now has passed geometry and algebra 11 and he isn’t even done with 7th grade. He has no problems showing teachers why the book is in error and why his answers are correct. So far he has been correct 100% of the time. He cannot only tell you what is going on in math but do hands on problems with ease. He just turned 13 and we are trying to get him into a college class for pre-calculas but so far not luck. He would love to have a teacher to ask questions too but school district won’t put him into a high school classroom with bigger kids. What does a parent do with a kid like this??? No one seems to have an answer. If he was slow in math there would be teachers with lots of answers but with my son, none. So for this dad, the word is frustrated.


April 18, 2013 at 12:04 pm
(19) Sharon says:

When my son was 3 he enjoyed adding and subtracting (numbers up to 10) using his Hot Wheels cars. At the time, we had no idea this was unusual. At 4 he was able to multiply and divide and do multi-digit adding and subtracting with borrowing/carrying. That’s when we started to realize he was advanced. At 5 he was doing long division, multi-digit multiplication and adding/subtracting simple fractions (with like denominators). At 6 he’s doing pre-algebra work, and I suspect that he’ll be ready for algebra within the next 6 months. He isn’t the kind of kid that sits around doing math in his head for fun, but he learns concepts very quickly and gets bored with repetition. Once he has learned a concept, he wants to move on to something new.

July 4, 2013 at 12:07 am
(20) Ed says:

My son turned 4 two months ago. He can add and subtract 1 through 20, as well as many 2 digit numbers in his head, and can multiply and divide 1-12 (as well as the related factors of 10) in his head as also. Can add and subtract larger numbers with borrowing/carrying the ones on paper if I help him draw the numbers (still working on writing letters/numbers). Can skip count by 2′s 3′s 4′s 5′s etc forward and backward indefinitely. Knows the value of pi out to 10 digits and what it’s used for. Constantly wants to be quizzed on math and play math games on the iPad. Can also solve math word problems fairly well (has been reading for over a year now). We plan to do IQ and gifted testing in a few months.

While I’m very proud of him, I’m already concerned about keeping him interested and engaged, and getting him the enrichment he needs, when he starts kindergarten.

August 26, 2013 at 10:55 am
(21) Rachel says:

I don’t agree with your comment that being gifted verbally is a defining characteristic of giftedness. Verbal giftedness just makes it easy for persons to “display” to others how gifted they are- It makes a teachers job easy. They may or may not be gifted in other areas but being able to communicate effectively certainly will increase their probability of success in the learning environment.

How do you show tuition on a maths paper? Easy- by getting the right answer quickly. Bright kids will get the right answer and show all the workings but truly gifted children will not and why should they? Why should you teach the abc to someone who can already read Dickens?

September 10, 2013 at 3:54 pm
(22) Amy says:

My son, age 6, recently tested for a gifted program. He had to have a cumulative IQ score of 132 in order to order to be accepted (which he passed).

My frustration is that the gifted program seems to be aimed at verbally gifted children. They explore things like history, social studies, and language development. However, my son’s highest scores on his IQ test, and the area in which he shows preference, is problem solving related to math.

There is a Lego League that he has been begging to join – but they will not allow him until he turns 7, 10 months away. In the meantime, he is outdoing his 8-year-old sister (who is also gifted) in math. I have to tell him to stop saying the answers before she does!

At an early age, he:
Wanted to count everything
Although he knew both numbers and letters before he was 2, it was numbers that he would notice. “Look! There is a 6!”
Loved to measure things at an early age – with his ruler, or a scale, etc.
Loved puzzles and could do advanced puzzles.
Loved games involving counting or math, like Monopoly.
Interested in knowing “how much” of something, and interested in knowing “what would happen” if the amounts or numbers were changed.
Could count by 2s, 3s, 5s, 7s, etc, without effort, at an early age.
Understood the concepts of math without anyone explaining them.
Never had to “memorize” math facts; he seems to know them intuitively.
Interested in shapes and how things fit together.

I hope this helps, and I hope that there will be more written about children who are mathematically gifted. Thanks!

September 21, 2013 at 11:31 pm
(23) LaDonna Palmer says:

My child just turned 7. She started talking very well at a very young age. She seems to have a way with understanding language, and a wild memory. I have a youtube video of her doing her state puzzle at age two and she knew about 25% of them and some information about family in the video. At that time in her life we would test her by doing things like having her line up 30 plus toy animals, ask her to walk away, take 5 out, push the rest in, get her to return and she would tell us each one missing. At age two or three she watched an episode for the first time ever of Garfield. She and I were lying around the next morning and she started telling me a story, character by character acting it out. I quickly realized she was saying every word of each character and playing out the episode from that show the night before. These kinds of things happen often. Now she has finished her K year of school and did not have one point off her report card. Her year in first grade has started and she is going strong and has missed not a thing on a test yet. She seems to have some gifts that I did not have growing up, and I am more than proud of her. I have worked with her over the years in all areas of learning. I love to find knew things to teach her. My only fear is that she will not get the challenge in our education system and that the work we do at home will seem unfair to her at some point when others are just doing the little school work and getting by. I do not make her do everyday extra or go crazy over having to teach teach teach….have the smart perfect child…..No! that isn’t me at all. Pretty easy going and simply believe my place in her life is to parent to the best I can and part of that is to teach her what I can.

October 8, 2013 at 1:14 pm
(24) Siva says:

My son exhibits all characterestics of Chris’ / Mohit’s son.

He is now 6 years old.

Apart from mathematical abilities (, which is the most prominent in him), he has been showing incredible curiosity in Physics, especially Cosmology. He learnt quite a bit of the solar system when he was just 2.5 and now explores The Universe, Big bang, Dark Matter/Energy, Quantum mechanics, etc, etc.

How did Chris and Mohit help their children out? I am really eager to know and do something to help my son. Can you suggest.

My email id: siva1857@gmail.com

October 18, 2013 at 10:45 pm
(25) Lisa says:

My daughter is two months shy of turning six and has been identified as gifted. Tonight she was joking around about the length of time it would take to do her homework. She said it would take “twenty half hours” then she said “you know that’s ten hours, right mom?” She did the math in her head in a nanosecond. Her brain amazes me. And she’s my oldest so I have no idea what’s “normal” mental math computation.

December 17, 2013 at 11:52 pm
(26) Brandie says:

I am trying to find help with my 7 year old. I found this thread and was curious to ask your thoughts. My daughter has been recognized as gifted. I mean she repaired my mother’s computer at the age of 5 for goodness sakes. Where I am having a complete melt down is the fact she doesn’t not have a memory recall for math facts-at all. If you give her the hardest word problem in math, she will get it correct. But from day to day, you have to reteach math facts as simple as 7+7. I can’t find the disconnect or any solution to our problem.

December 21, 2013 at 9:29 pm
(27) R. Nickel says:

I was just wondering what kind of testing they are doing in your children’s schools, and what the scores are especially if any take the NWEA test. Thanks.

January 1, 2014 at 2:44 am
(28) Tricia says:

I am a language person so when my son was young I never stressed numbers at all. I didn’t even try to teach him to count and since he was home with me and didn’t watch a ton of TV it didn’t come up until last year. He has been reading since he was 2 1/2 but since he needed to start school in the fall (early entry cause he wasn’t quite 5) I thought it would be good if he could at least count to 20 before that. I started number order in May and he is now multiplying, adding, subtracting, dividing, both word and written problems. He was distracting himself on a long car ride by counting by 5s, when he got to 200 I said “you know that is 40 5s you just counted” He said yeah and when I get to 300 it will be 60. Every day he wants to know more, he will be beyond me long before JR high. Thank goodness daddy is a math wiz. I am concerned about the gifted programs in general. Here they pull the kids out of normal classes once a week and give them extra work. We have had other boys in the program and they hated it. Both his dad and I had similar programs in school and we both hated it too. Gifted kids need to be around kids that are like them so that they don’t feel so strange. Putting them in a normal class does not make them feel normal it just reminds them they are different and makes it harder to find friends with common interest. There is this trend in public education that demands they teach to the lowest common denominator and doesn’t allow those that excel to move at a faster pace. We fail as a country to educate because we fail to separate kids by their skill levels. Both the faster and the slower would benefit more from educations tailored to their needs instead of the one size fits all but we are too PC to ever separate them

January 6, 2014 at 1:55 pm
(29) Ellen says:

I’m not understanding the comment that advanced math abilities are not a defining characteristic of giftedness. I would say the same about advanced verbal characteristics. There seem to be a LOT of verbally precocious children and not near as many gifted math children. I personally know 4 kids (3 girls) in K that can read middle school words. However, by their lack of mathematical reasoning, or general problem solving capabilities, I do not see them as gifted at all. Unfortunately most of the profs. and educational researchers are mostly from the linguistics/literary field and place way too much importance on verbal precociousness. Gifted mathematicians don’t get degrees in education or educational research to call their research ridiculous. Einstein didn’t talk until he was 4, doesn’t everyone know that?

January 23, 2014 at 4:43 am
(30) Louise says:

It’s weird to say this on my own but when I was 4 I was already able to do 2 digits multiplication and was really fond of dictionaries. English is not my mother tongue but by the age of 5 I was in junior high school english class. My parents wasn’t really paying attention to my math skill but I was tested by kumon branch manager against his son which was a record holder in memorizing numbers, manage to beat him in 4 digits multiplication. My IQ was 147 when I was tested as a child. I didn’t enter any gifted programs as there are none back then in my area. Though I’m partly glad I didn’t.
I’ve never had any problem in learning through out junior high school, I read a lot of encyclopedia and history book as a kid which most of the content I still remember until today.
There’s one thing I’m really interested in since I was 3, it was art. My parents never worry even though all I did was drawing and painting most of the time since my score is continuously high and they also support me learning what I like.
Now I’m 18 years old and currently learning fashion design in one of the famous art school in Asia. All 12 years of my education is gone with the wind. I’m still able to learn and memorize a lot of things but now I use it in different ways.
Though, I have some regret not having gifted children education and going to art school in the end instead. I’m worrying whether I’m able to return all the support my parents gave me all these years through art. Always wondering if I’m in medic school or law or business wouldn’t it make them happier and more assured?
To the parents out there I suggest not to put so much pressure on your children, provide what they need to learn but let them choose what to learn. I’ve seen a lot of genius children that are pressured by their parents really lacks in social ability and even being very dependent to parents. In my case, I learned a bit of everything on my own with my parents as guide and I lived a very happy life.

January 30, 2014 at 1:13 pm
(31) Louis-Paul says:

My kid is gifted in math.

At 18 month, he could count 0 to 10 and count down 10 to 0. The was a clock at a restaurant running backward (countdown to the next game) and he said look Dad, there is a countdown. He was singing the alphabet song and I ask him can you do it backward like a countdown… he did strait from z to a without blinking.

On his second birthday, you could answer question like how many duck in the picture ? He knew number to 100 soon after.

Before his 3rd birthday, he could do single addition and substraction. At 3 he picked up negative number instinctivly (we were playing big brain academy on the wii where you have to blow up ballon in the right order… on the highest difficulty there negative number, he asked what they why there was a – before the number. I gave him 2 min explaination on negative and he understood right away…. he could answer something like 22 – 27 right after the explaination.

At 4 he started multiplying. When went go shopping he loved to play… if you by 7 of these and 5 of these how much will that cost.

At 5 he started division

He’s 6 now and starting to pick up power, roots and algebra .

He’s one year advanced in school (early entry), He’s acing math while doing above average on the other subjects. At first he had trouble because he didn’t show his work but eventually picked up what the teacher wanted to see.

February 20, 2014 at 5:31 pm
(32) Hineata says:

Hmm, not sure where you get the idea that verbal skills are a defining characteristic of giftedness and mathematical abilities are not. I personally, as a G & T teacher in a school with many ESOL learners, encounter many more students with math ability as a defining characteristic. Many of my students are not terribly forward in their verbal abilities in their home languages either – their skill areas are math and logic.

March 9, 2014 at 9:35 am
(33) ed says:

Our son now 16, always excelled at math but rarely showed his work. Grade school teachers let him do “his own thing” . He did cyberspace school from 5th to 8th grade where he didn’t have to show his work. Started traditional high school and freshman year the advanced algebra teacher thought he was cheating because he’d know the answer before the teacher finished finished writing out the problem. For a few weeks made him show work which just slowed him down. The teacher finally relented and told him he could go back to the way without showing the work. He considered him his math genius. Sophomore year is here and he takes geometry and Honor’s algebra. Started the year not showing work and the Honor’s teacher told him “no work. no grade”. He said it only gets harderfrom here and if he doesn’t show work he wont get a passing grade. That was his policy. No exceptions. Fast forward to January and once again he doesn’t have to show work. As teachers through now have concluded some people are more talented in some things and not in others.

March 28, 2014 at 12:59 am
(34) Devyn says:

My 5 year old son can memorize a 14 digit number in a matter of seconds AND retain it. In addition he is capable of doing 3rd grade math such like knowing all the division and multiplication tables, adding ect. He is also fond of roman numerals and fractions. His pre school teachers seem unfazed by this and when I mention my interest in having him tested they just roll their eyes as if to say we have heard this before….all parents think their child is gifted. It is very frustrating ….perhaps I should wait until he begins Kindergarten and then ask for him to be tested? Any feedback or advice would be appreciated. I should also mention that he is athletically gifted and many people have noticed and commented on his athleticism. We have been approached by coaches who want to train him for a traveling soccer team!!! although he lives to play sports I think his age is a tad young to be trained. Why is it that his athleticism is noticed, commented on, lauded and people have expressed a desire to help us nurture it whereas his mathematic gifts have not been identified!?

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