David Cox and I were having a discussion about gifted kids over at Classroom 2.0, he sent me a message and wanted my to elaborate--it turns out my response was WAY TOO LONG for CR 2.0 messaging system so I decided to post it here in case anyone else was interested.
At the elementary level we explore all kinds of things; you can see all we've done in the last few years here.
In the Center our kids with math goals focus on problem solving--we have probably have 50 different types of activities which include all kinds of logic--matrix, grid perplexors, Venn Diagrams, etc. We also have Sudoku, Karoku, Crossmatics, Pentominos, tangrams, etc and 3D stuff like like 3-D Pentominos, Shapes and Solids, Google Sketchup, etc. We also have problem solving software and simulations.
The only math "curriculum" we ever teach is Hands On Equations--we've done that with as young as second grade. I like it.
Our district provides PreAlgebra for our more precocious math students in 6th grade, but it comes at a price. It's at 7:00 AM!! Not the best time for many bright kids who stay up too late. If they take PA at 6th, they take Alg 1 at 7th and go to the high school for Honors Geometry in 8th and so on.
Here's my observation about gifted mathematicians--they just get it. No matter what it is, if it deals with numbers, they just intuit how to do it, there is no "thinking". Many gifted kids are not gifted mathematicians (and of course you would see them in a gifted magnet school), the pleasers will work hard and learn quickly but they just don't "get it" like a gifted mathematician does. I've had many gifted kids who IQ is really lopsided 145 Verbal, 120 performance--these kinds of kids look pretty normal in a math class but excel in writing, language, reading, vocab etc. Scoring at the 99% on achievement test doesn't necessarily show this, the hard-worker-bees can score high but not have the "gift".
My observation about gifted kids in general--their skills, work ethics, and personalities vary as widely as the general population. Example---I've had kids who have been grandfathered into my program with 120 IQ, they are in the same class as the kid with an IQ of 160. The range (and ability) between the two is wider than the lowest and highest kid in a regular classroom. Depending on the criteria for your school, you may not have to have an IQ in the gifted range (135+). I have kids who are very hard workers and some who don't work at all, I have kids who are leaders in their schools and communities and kids who couldn't lead their heads out of a paper bag. I have kids who play 4 sports and kids who play 4 instruments. I have kids who are "most popular" and kids who have no friends. The more you know about gifted kids they better teacher of them you will be. Read Tamara Fisher's blog, Unwrapping The Gift, she's written some very insightful articles about gifted kids.
My observation about highly gifted kids---many of them have concomitant problems related to being just TOO smart, TOO outlying, TOO different. They are a poor fit for the way we teach them today, underachievement is entrenched by 3rd grade.
Here is something to think about---the average kid spends 80% of the time thinking and working in the lower levels knowledge, comprehension, and application. You can see this when you teach them something---they learn it (with 17 repetitions), then they understand it and they can use it. A kid with an IQ of 130+ spends 80% of the time thinking in the higher levels synthesis, analysis, and evaluation. You teach them something (with 1-3 repetitions) and they are already thinking of every other thing they know about that topic and how what you taught them applies to what they already know. (It’s why they don’t seem to be paying attention—they have long passed you!) They just THINK DIFFERENTLY. The more you know about them the easier they are to teach.
Here's a challenge to you---maybe you need to teach differently. Like Dr Phil says, "the best predictor of future performance is past performance". Maybe you need to ask different questions to get different answers. Maybe you need to shake things up!! Go read Dan Meyer's blog , he's a young math teacher that is asking some hard questions. Read his latest entry (and all the other stuff) on "The Math Text Book I Would Buy". He's suggesting a whole different way to engage kids with a focus on thinking!! Read the comments and look at Problem Pictures and what Hot Chalk has done with using Motocross to teach Algebra (suggestions from commenter). Amazing stuff.
I remember hearing a presenter respond to the question "How do we keep kids from plagiarizing?" with "Give them assignments they can't plagiarize." There is some connection to your comments here---if the question your kids are asking is "Is this the right answer?" then maybe you need to change the question!! Whew, did any of that make sense!! Keep in touch, N.
3 days ago