Gifted Issues Discussion homepage Forums General Discussion Gifted children could learn math much earlier

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 It has been withdrawn by ACT and the jury is still out on a suitable replacement.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