Friday, January 02, 2009

Thoughts on Gifted Math Kids

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.


Doug Noon said...

This reminds me about several kids I've worked with who qualified as gifted, and were really not good at school.

One kid would ONLY read, and insisted on doing all of his math "in his head" which actually worked sometimes. He couldn't have cared less about getting it all done. For him, the challenge was doing it without writing it down. Any time he had to pick up a pencil, he was miserable.

We had a rough time, he and I, mostly because his mother wanted him to get good grades. Thanks to him, I learned that a kid doesn't need to write anything on the state benchmark assessment to get a passing score. He filled in all of the bubbles in the grammar and usage section, but refused to write anything in the essay portion of the test. And he passed!

Another young man, many years ago when I taught second grade, wasn't quite sure how old he was. "I don't really keep track of that stuff," he told me. I referred him for testing the next day.

I've always looked at the gifted program as an intervention rather than a club for smart kids, as so many people seem to want it to be.

nbosch said...

Underachieving gifted kids are the bane of most teachers' existence. There is noting more frustrating that a smart kid who "doesn't use it". Did you read my previous blog on Connor?

One of my funniest interactions with a kid occurred about 4 years ago. I'd been called to one of my schools to interview Frank, a fifth grader. I'd heard about Frank for several years but since he was failing all of his subjects, his teachers weren't seein' gifted services in his future.

He and I chatted for an hour or so ad then I said "Hey, I hear your not too wild about school." Here's what Frank said, "You know, Mrs. Bosch--here's how I see it. My classroom hangs in my brain like a black and white pencil drawing. When someone interesting come into the classroom they are in color. If something happens that is boring or I don't like, I ERASE it!!" No wonder Frank wasn't into writing his spelling words 5X each! His brain was already full.

We tested Frank and he had an IQ of 156--and failing grades in all fifth grade subjects. He started recieivng services in my classroom.

That semester we did a great project on Leonardo DaVinci (I wrote the curriculum and if I do say so myself is was brilliant!) The final project was a multimedia slide show/renaissance play where 30 kids had speaking parts. There was big Frank dressed in tights and a Seinfeld ruffled shirt, beret cocked on head saying his part as well as any Shakespearean actor....but Frank also knew ALL the lines from all 30 other kids. He's in high school now, haven't heard how he is doing--I'll have to check.

My advice to teachers about these kids is don't get into a power struggle with them---you will lose. The best teachers will figure out how to work with the kid and make accomodations--sounds like you make a great teacher for all kids.

David said...

Thanks for the link to Dan Meyer's blog. It sounds like he is doing some amazing things. I agree with you completely about having to "shake things up." I have always been a "question" guy. I am convinced that education isn't about finding the right answers, it is about asking the right questions. I spend a lot of time helping my students learn how to ask good questions. Sometimes the questions need to be procedural and other times they are conceptual.

Leaving the high school and working with the advanced kids has changed the way I view a good way. I am amazed at how many teachers just do what we have always done without really questioning why we do what we do. An example of this led has led to the homework discussion over at classroom 2.0.

I don't have too difficult of a time engaging the truly gifted student. I just know that at some point in their math career, they will need to actually write something down. Maybe showing work is something they will learn when the time is right. One of the things that has helped is having them create mathcasts using voicethread. This way if they don't write it, they at least have to say it ("it" being the process by which they would solve a problem.)

I just started using a wiki this year and the results have been pretty good. Having students create resources has been pretty successful. (

I think that the thing that I struggle with is the fact that, as Doug stated, many people want the gifted class to be a club for smart kids. Parents want their kids in the class as some sort of status symbol.

All of my 7th graders take pre algebra/Algebra and then as 8th graders we do algebra/geometry. It ends up being three courses over the two year period. Some are ready for algebra 2 as freshmen and the rest will have a head start for their high school geometry class.

So what do we do with the kid who is truly advanced, but won't show the work? Do we say, "alright, show me how you do this a few times" and then allow them to move on to something different? I agree that there are a lot of really engaging "non curriculur" things to do with math like sudoku and things like this, but aren't your kids expected to take "the test" just like the other kids? If so, how do you ensure that you have covered the material that is mandated by your state and/or local standards?

nbosch said...

Dave, Thanks for the nice reply, it sounds like you are doing a great job with your new population.

In my special ed program I don't "have" to teach anything that is going to be tested, they do that in the regular classroom. Thank Goodness! Teaching gifted in my district is the best job in the world, I think that is why I am having a hard time retiring.

OK, brainstorming about the kids that don't show their work--- some suppositions

They need to pass the assessments--are they passing?

Their grade will be lowered if they don't show their work--will it? Do they care?

Problems will become so complicated that they won't be able to solve them if they don't write down the steps-- a given.

OK what to do? One credo is gifted ed is "it is not your job to teach the curriculum, it's your job to make sure they know it." With that in mind it doesn't really matter how they "know it" as long as they know it and assessment prove they know it. So many teachers think they are the only ones who can impart knowledge and try to control these kiddos--which usually doesn't work. I'd try to make a deal with the hardheaded ones--"you don't have to show your work as long as it's correct, once you start missing problems you have to show your work." Probably won't work but just an idea.

Another thought--if any of these kids are going into math related college courses they will eventually reach the point where they have to conform--or fail.

With three gifted sons of my own and a 25 year career of teaching gifted kids I've learned a few things. Kids (adults, too) don't embrace skills until they need them--many gifted kids go years without a stitch of organization, eventually the work load gets to be so heavy that they have to find a way to organize---or fail. It is impossible to teach a kid organizational skills, "things have been OK up to now", until the natural consequences force them to. You'd be amazed at how easy (K-6) coursework is for gifted kids and how little is expected of them, many fall into some really bad habits early on.

Good luck with your teaching and enjoy Dan's blog.

Kevin said...

"Kids (adults, too) don't embrace skills until they need them--many gifted kids go years without a stitch of organization, eventually the work load gets to be so heavy that they have to find a way to organize---or fail."

I agree with this completely. My son got in trouble in 6th grade for refusing to write down homework assignments. The principal mediated a compromise: as long as he turned in all his homework on time, he didn't have to write it down. If he once missed an assignment (without a note of explanation from a parent), he would have to comply with the rules about writing down homework. He never missed turning in an assignment. (He did, surreptitiously, write down homework that he was not sure he would remember.)

For math classes,he writes down the absolute minimum required by the teacher. This is usually more than he needs to solve the problem. He is finding the proofs in geometry class a bit tedious (too many obvious steps that are required to be written down).

David said...

Man and I thought I had the best job. Sounds like you have me beat. So do you have a "pull out" program? Our district is completely different. We have an elementary school that has been tagged the "GATE" school and my middle school is the extension of that "GATE" program. So the GATE 6th grade teacher has all the "gifted" kids. Problem is, like you said, not all kids are gifted in all subject areas. Do you have specific times in the day when you have your gifted math, lang arts, etc?

Our program at the middle school has built in intervention. We run a 7 (45 minute) period day but math and language arts are run in two period blocks. So technically, I do the grade level stuff as well as the advanced work. My version of intervention is simply taking them beyond the grade level. This works out nicely as the kids end up getting a double dose of algebra. If they truly get the algebra in 8th grade, then we just spend more time on the geometry. This is cool because there are a lot of applications with things like GeoGebra that we have been working with. I actually had a student create an applet demonstrating that the sum of the angles in a triangle is 180. You can check it out here if you like:

I like your idea on not trying to "control" all the knowledge that is imparted. I am learning that I am more effective if I just get out of the way sometimes.

nbosch said...

David, Our elementary program is based in seven centers throughout the district (30,000 kids), serving all the elementary gifted kids. The middle schools have a class where they do things like Debate, Future Cities, MathCounts and work on their personal goals (from IEP). The high schools of course have Honors, AP and two of our high schools have IB. There is a class they can take--freshman year it allows for compacting Health and Computer Apps. Junior year they focus on careers and college applications. The high school gifted kids also participate in Academic Decathalon.

We have a strong program throughout the district but the elementary service model is hampered by a "one program for all" approach--even though the state mandates a continumn of services---they get what we have no matter what they need. I'm guessing this will change over the next few years as we identify more and more 2e kids---Aspergers, Autism, OHI, etc.

We have the same kids every year so we write different curriculum. Part of the time the kids work on a huge project, part of the time they work on their personal goals (from IEP). We've introduced literature into our program and will do online book discussions once or twice a year.

I team teach with another gifted ed certified teacher and we have a full time para to help with office work, production, work with kids etc. Right now our para has a Masters in Computer Science-- highly over qualified. See, it is a great job!!

You can see all our projects here

We just finished The Inventive Process with 5th and 6th, moving on to Robotics. We'll end the year with Sports Math and Science. Our little kids wrote and illustrated ooks using, we had author's teas before break. Let me know if there is anything else you need.

nbosch said...

Kevin, You are lucky to have a school that will work with you and your son. I've read about some of your trials over at GE 2.0.

meep said...

My problem as a gifted youngster was I didn't always know how I got to the answer. I just knew what the right answer was. My teachers in many cases just thought I was being difficult. But it was like the train of thought disappeared as soon as it was done. The answer was pretty much always right. My IQ was measured at 165.Once I got to high school calc(9th grade)I discovered creating a sort of chart worked a lot better than sequentially writing out steps. I guess I just process math more visually.Maybe that is the case with some of these students.

nbosch said...

Meep, it could be. Are you in a math related field now?

meep said...

No, I am a secretary in a private college. Some learning disabilities surfaced in college and I was unable to educate myself to the level I wanted (so far). I do, however, have access to as many journals as I want at the college and the professors send students to me to help them understand the use of statistics in the articles they read for their seminar course. I also help professors with their own articles. It is a good job where no one treats me like a curiosity for knowing too much.

nbosch said...

Sounds like you have found a good match for your skills. Thanks for visiting, N.

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dan said...

Great way to learn math. Good math article.

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