I'm sure that's the way she taught it to Christopher today.

-- CatherineJohnson - 27 Apr 2006

I'll have to do the rest of them and see what I think.

I keep forgetting: HE DOESN'T KNOW ALGEBRA

These are Math Olympiad problems, basically.

my definition of Math Olympiad problems for kids this age is algebra problems given to kids who don't know algebra

that's probably right

-- CatherineJohnson - 27 Apr 2006

I'd never try to teach a new learner this technique since it's not especially extensible

that was my next question....

I'm going to HAVE to get beginning algebra into his head this summer

-- CatherineJohnson - 28 Apr 2006

Did I do this the hard way?

I think so. I did it this way, similar to the way you did it but without algebra:

I'm going to use "integers" instead of "numbers", which she implied by her use of "one-digit numbers". If we allow non-integral real numbers, then there are other answers.

The mean of the integers = 3, and there are 5 integers, so the sum of the integers is 15.

A mode is 1, so there we know that two of the integers are 1, 1.

So we have 1, 1, ?, ?, ?

The median is 4, so we have 1, 1, 4, ?, ?. (We have an odd number of integers, and the 3rd one isn't the same as the 2nd one, so we can assume that the middle one is the mean, or 4.)

The sum of the integers is 15, so the remaining two integers sum to 15 - (1 + 1 + 4) = 9. Also, we know that these integers are greater than or equal to 4, so they must be 4 and 5.

This gives us the solution of 1, 1, 4, 4, 5; hence, the clever wording about a mode and not the mode.

BTW, if all of the integers are different, some references say that all of the integers are modes, and some references say that there is no mode. Here's a MathForum question and answer about that.

-- GoogleMaster - 28 Apr 2006

....I'm starting to define our problem as being way bigger than Ms. K & her class.

the 8th graders, now, are receiving their 'invitations' to join Honors English next fall, and of course no one's getting invited. everyone's being cut

families are getting cold, clinical rejection letters, all mailed so they arrived on the day vacation started just like our Xmas eve your-son-the-loser midterm report.

for the first time tonight, my confidence flagged in a real way

I was sitting at the dining room table, doing my own math, and I started thinking....how am I going to do this?

This Phase 4 course seems designed to be a wash-out course

It's possible The Authorities would deny that (maybe, maybe not)

But it doesn't matter what they think they're doing; all that matters is what they actually are doing.

For Christopher, this is a wash-out course.

I don't know what the high school math courses are like. I've been taking for granted that they'll better.

But what if they're not?

Plus then I got started thinking....I don't know anyone else here who's done this. I don't know anyone else in Irvington who's taken a kid flunking regular math and accelerated him to the killer wash-out course.

Unless things get LOTS worse, Ed is never going to sign off on full-time homeschooling for the next two years.

That means Christopher is going to have to spend time getting grades in IMS, AND that his high school track will be determined by IMS — true in English, too.

-- CatherineJohnson - 28 Apr 2006

GM: "I know that I would have found it fun..."

VK: I think what we have to ask is, is throwing these in front of a bunch of 6th-graders the right thing? I'd say no.

I was answering the question merely from a personal point of view. I think most sixth graders would not find this worksheet fun, since most sixth graders do not find math fun.

I probably misread the question, and Catherine was instead asking about "you" in a general sense.

But, this discussion makes me wonder: What was Ms. K told about the students in her class? What expectations does she have? Was she told (or did she assume) that because she's got a phase 4 class, that means they're all math brains and don't need as much instruction and repetition?

If she was expecting a class of gifted math brains, and what she has is 1 or 2 math brains and 25 high achievers, she's probably as frustrated as Catherine and Christopher are. She probably thought this was going to be an easy class to teach; just toss the material out and the classful of math brains will just absorb it.

-- GoogleMaster - 28 Apr 2006

Unless things get LOTS worse, Ed is never going to sign off on full-time homeschooling for the next two years.

Does Christopher have a friend who's in the same situation? Maybe you and another parent or two can tag-team homeschool. Each of you would teach all of the kids, but only 1/2 or 1/3 of the time. Then the kids get the benefit of homeschooling, but you don't get burned out by doing it full-time.

Say there are three of you. You can each teach one full day a week, for a total of three instruction days per week. Is NYS flexible enough so that you can set your own class schedules? If they don't allow homeschooling-by-other-than-a-parent, then you just tell them your class schedule is one day a week and conveniently forget to let them know that your kids are sitting in on each other's "classes" two days a week.

-- GoogleMaster - 28 Apr 2006

Maybe Ms. Kahl's class is designed for the gifted/high achievers, but in that case, they either need a "Phase 3.5" that ends up with calculus in the 12th grade, or they need to accelerate the Phase 3 program so that it ends up with calculus in the 12th grade.

no kidding

I wish I'd said that when I was talking to the math chair

Obviously he doesn't belong in this class. Nobody belongs in this class as far as I'm concerned; she shouldn't be teaching here.

However, it's possible that the gifted kids are being taught well. There's no way for me to know.

Christopher can learn this material.

But he can't learn it from her, in this way.

-- CatherineJohnson - 28 Apr 2006

Does Christopher have a friend who's in the same situation? Maybe you and another parent or two can tag-team homeschool. Each of you would teach all of the kids, but only 1/2 or 1/3 of the time. Then the kids get the benefit of homeschooling, but you don't get burned out by doing it full-time.

The problem isn't burn-out; the problem is that there isn't a living soul in all of Irvington who would even consider homeschooling their kid.

People are shocked. They're so shocked they almost can't talk to me about it.

-- CatherineJohnson - 28 Apr 2006

I probably misread the question, and Catherine was instead asking about "you" in a general sense.

oh no, I'm definitely asking all of you 'Math Brain' types how this strikes you, for you

I'm also interested in what everyone has to say about giving these problems to a high-achiever type.....

But I definitely wanted to run these by people whose strength is math

-- CatherineJohnson - 28 Apr 2006

oh...I was unclear about the homeschooling issue

what I meant was, Christopher is going to be spending more time at IMS (barring a miracle; never say never)

if things stay this bad, that is all lost instructional time

I'll be trying to teach to crammery AND TEACH WRITING 'on the side' while he spends hours going to school and doing homework that doesn't teach him to write or do math and does earn him the low grades and poor reputation that will cause him to be cut out of honors courses etc. in high school

-- CatherineJohnson - 28 Apr 2006

I'm in BLEAK MODE!

-- CatherineJohnson - 28 Apr 2006

People are shocked. They're so shocked they almost can't talk to me about it.

Irvington being where and what it is, is schooling one of those getting-your-hands-dirty kinds of tasks that you're supposed to pay other people to do, like diaper your children, clean your house, mow your lawn, wash your car, and fill out your tax form?

-- GoogleMaster - 28 Apr 2006

You should collect all of those Saxon 8/7 problems and get them on one or two sheets. They're scattered in many chapter mixed practices.

DEFINITELY

I'll pull them all, and we'll do them

-- CatherineJohnson - 28 Apr 2006

There is a HUGE difference in teaching the "truly gifted" vs. the "try hards."

My honors students catch on after only one example and can, from there, extrapolate the technique to much more general settings without being explicitly taught.

My general-population students need to see many more examples before they catch on and need to do a LOT of practice before they can extend the idea.

In KTM-lingo: my honors students develop flexible knowledge almost instantly.

The "try hards" are the easiest students to teach: predictable, no surprises. With the truly gifted, it's much more challenging but WAY more fun.

-- RudbeckiaHirta - 28 Apr 2006

I'm going to dump BLEAK MODE & figure out my Next Actions.

• call the homeschooling novelist in Riverdale

• debrief as many high school parents as I possibly can

• look into Catholic schools

• start pressing the district for precise numbers & data on who gets 'accepted' into what tracks in high school & on what basis decisions are made, what grounds for appeal we have (none)

• ask for precise data on college admissions from IHS & courses taken (i.e. are colleges downgrading Irvington AP courses - which have open enrollment - and upgrading honors courses)

• file Freedom of Information Act if info isn't forthcoming

etc.

I think it's also time to talk to the advocate who handled Jimmy's case. She was great. Used to be a teacher, majored in math in college.

She told me her boss always says the problem with teachers in this country is they don't understand their job isn't Tour Guide to content.

-- CatherineJohnson - 28 Apr 2006

It sounds like IMS has some vertical alignment issues between the elementary school, the middle school and the high school.

Our district has six elementary schools (K-5) that feed into one junior high. However, the 6th grade year is seen as a transition year. In sixth grade the students are in teams of 50-60. Two teachers share responsibilities for teaching the 5 primary subjects, in classes of 25 to 30. Then in 7th grade, they have separate teachers for those five subjects. I think it's an effective way to transition the kids. It's not the "cold turkey" approach that IMS seems to use.

Also, I wonder how much real discussion is taking place between the schools as to the content knowledge that is needed to survive Ms. Kahl's math class. If this is the expectation for that class, then that needs to be clearly communicated to the elemtary school teachers. Same way with the writing instruction.

Another question--is Ms. Kahl teaching math to the other sixth graders? If so, what is their experience? That is, are they having the same kinds of teaching issues?

-- KarenA - 28 Apr 2006

Irvington being where and what it is, is schooling one of those getting-your-hands-dirty kinds of tasks that you're supposed to pay other people to do, like diaper your children, clean your house, mow your lawn, wash your car, and fill out your tax form?

hardly!

the moms are teaching day and night!

-- CatherineJohnson - 28 Apr 2006

My honors students catch on after only one example and can, from there, extrapolate the technique to much more general settings without being explicitly taught.

My general-population students need to see many more examples before they catch on and need to do a LOT of practice before they can extend the idea.

I think this is exactly right.

The problem with most K12 programs today is that they refuse to acknowledge this difference. They just try to teach the general ed kids with the same techniques they use with the honors kids.

The honors kids are able to tolerate much more educational nonsense -- discovery learning, whole language, and the like -- and still survive.

-- KDeRosa - 28 Apr 2006

Then in 7th grade, they have separate teachers for those five subjects. I think it's an effective way to transition the kids. It's not the "cold turkey" approach that IMS seems to use.

I think they're moving to something like that for next year, in fact.

I think it's accurate to say there's ZERO discussion amongst the schools - that's Ralph Napolitano's mission, to address the integration issue.

I'm going to have to dig out the strategic plan & read it.

My impression is that it's all differentiated instruction & portfolio assessment & data warehousing, so .... I don't know what's become of the plans to integrate curriculum

There's just no interest in subject matter content knowledge at all.

-- CatherineJohnson - 28 Apr 2006

Another question--is Ms. Kahl teaching math to the other sixth graders? If so, what is their experience? That is, are they having the same kinds of teaching issues?

I AM THE ONLY PARENT WHO'S COMPLAINED!

MAYBE CHRISTOPHER DOESN'T BELONG IN PHASE 4 MATH!

-- CatherineJohnson - 28 Apr 2006

Actually, I've been able to cess out a little about the other kids.

Christopher's class has the super-smart girls in it, and they seem all to be doing well.

I can't tell if there are any boys in his particular class who are doing well (there are in the other 2 sections).

Talking to Christopher it sounds like it's almost half-and-half, but I can't tell.

His friend M. 'lasted longer' this fall, but is now in the same boat as Christopher; I know there are several other boys who 'aren't smart' (this is their perception, and is how Christopher puts it).

I also know that the 'Homework Nazi' mom is working basically for hours and hours on every course. Says her son 'struggles every day' - she's talking about everything. She's miserable, and he's miserable, and this is a brainy kid.

So.....my guess is that half the class is either suffering, or doing badly on tests but taking it in stride.

I know I've mentioned that the one reform for this year was that grades went up. I'd bet the ranch she's weighting homework much more heavily than she did last year.

I can't tell much from the class averages, unfortunately, because she never gives the range.

The average is typically an 84 (it's been as low as 80, AND it's been lower in other classes).

Now that I know this class is filled with brainy girls, I'm thinking it's possible there's a 'bimodal' distribution (is that the right term???)

-- CatherineJohnson - 28 Apr 2006

The problem with most K12 programs today is that they refuse to acknowledge this difference. They just try to teach the general ed kids with the same techniques they use with the honors kids.

The honors kids are able to tolerate much more educational nonsense -- discovery learning, whole language, and the like -- and still survive.

It is a horror.

I just had no idea how bad it is, or would be.

After all this time writing ktm (oh my god - did we miss our anniversary??? Space Cadets of the World Unite!)....

ok, start over

after all this time I still had no idea how bad it is when you experience it

-- CatherineJohnson - 28 Apr 2006

ACTUALLY.....next year is going to be better as far as math goes. (English will be worse.)

They teach the same course again next year, with less b*s.

We could have Ms. K again for 8th grade after that.

although I tend to think she'd refuse to teach Christopher (teachers have an opt-out on a kid; at least they do in K-5)

My neighbor has had a much, much better year with math.

Unfortunately, the teacher, who everyone thinks is fantastic, is retiring

-- CatherineJohnson - 28 Apr 2006

My 5th grade daughter is what I would consider to be gifted, but she still needs to be taught, she doesn't teach herself. She would have a hard time with these questions if she hadn't been taught how to do them first. I was unhappy with her teacher last year because he was basically expecting her to teach herself. He used Accelerated Math in his classroom almost exclusively. At first I thought that was great, Hannah would be able to go at her own pace. But he wasn't preteaching any of the material she was working on. He would hand her some worksheets and then go over the questions that she missed afterwards. So she had to try to figure it out on her own first. She is smart enough that she could figure out many of the answers because it was all multiple choice, but she didn't know why she was doing what she was doing. When I asked her questions about her work I could tell that she didn't really understand it. I had to do a lot of explaining at home.

I was told once that the difference between a gifted child and an average child is in the number of repetitions that it takes for them to learn something new. A gifted child may only need to be told once or twice how to do something and they "get it". While others need to hear it 5 or 6 times or more before they "get it". Thats why gifted children can go at a faster pace. But they still need good teaching and they still need practice, just maybe not as much of it. She also pays attention, takes good notes, and rarely forgets anything, which is a huge advantage at school. I would guess that focus, memory, and organization are the biggest factors outside of good teaching that contribute to good grades. If you have poor teaching then they are vital.

RebeccaR^?

-- KtmGuest - 28 Apr 2006

oh - back to money....

(Google Master)

I think money is the issue, but for a different reason

Number one, almost everyone here could swing private school if they absolutely had to, and a lot of people can do it easily

There's plenty of talk about pulling kids out of the middle school, but that talk centers on private school

After that, people here are pretty conservative. They vote Democratic, but are personally conservative. Homeschooling is still in the 'Innovator' phase here - and not even there.

.....

time to go watch INVASION again

-- CatherineJohnson - 28 Apr 2006

Tracy's list looks cool - just checked it!

-- CatherineJohnson - 28 Apr 2006

actually, it's quite interesting -

-- CatherineJohnson - 28 Apr 2006

Rebecca hi!

thanks so much for your comment (I've added it to the post)

That's exactly what I was asking

I always hear that gifted kids get things incredibly fast....but I've heard exactly what you say: they do need some instruction.

But he wasn't preteaching any of the material she was working on. He would hand her some worksheets and then go over the questions that she missed afterwards. So she had to try to figure it out on her own first.

EXACTLY!

Why are they doing this?

That's Ms. K's class.

When a friend of mine assumed Ms. K had taught the problems before assigning them, Ms. K. acted as if my friend was some kind of idiot. Her tone of voice was, Of course I don't teach them how to do the problems before they do them.

I don't know where her teaching method comes from.

Is it constructivist?

Is it some special approach for gifted kids?

Is it the way she was taught?

Does she think word problems aren't something to be taught?

I think this last one is a possibility. It jibes with what I've experienced often enough. Word problems are kind of like a little 'test' unto themselves. Word problems are assigned to 'test' whether the kids can apply a procedure or concept....

-- CatherineJohnson - 28 Apr 2006

from Tracy's table:

high achievers: Six to Eight repetitions for mastery

gifted: One to two repetitions for mastery

-- CatherineJohnson - 28 Apr 2006

"Enrichment Worksheet"

Is this what the teacher called it? Was everyone supposed to do it? Was it going to be graded? Would they see these questions on an exam?

I would never call them "enrichment". They are basic problems that all students should be able to do AT SOME POINT. Although I have very few facts about their curriculum, it sounds like this isn't the point. In fact, the best point is when they are doing algebra; define the governing equation or definition, assign variable(s), and solve. Very simple.

Is there an "enrichment" angle to these questions (before algebra) for some students? Maybe, but I would rather see these enrichment students use the time to move on to new material. I would rather see discovery with knowledge and skills, than without. I seriously doubt that this assignment was a carefully-planned enrichment of the math curricula. It sounds like something somebody whipped up just to keep the kids busy.

Would this be good for math brains? I don't think math brains fall into any one category. Some might like the challenge and some might be completely irritated. They might be very good at absorbing new material very quickly, but that doesn't mean they like having to figure things out will little knowledge and skills. It's one thing to use algebraic skills to define and solve new problems, but quite another to discover solutions without skills, or to discover the skills themselves.

-- SteveH - 28 Apr 2006

"But they still need good teaching and they still need practice, just maybe not as much of it."

I wholeheartedly agree! My 7th grader is much more intuitively "math gifted" than our 11th grader. Honestly, I don't know if she is gifted or not. Our 11th grader had excellent math instruction K-5; our younger daughter was not getting the same instruction (we had moved from Indiana to Illinois). The difference was noticeable and alarming, which is why we enrolled the younger daughter in KUMON in third grade.

She gets math--but she still has to be taught and given sufficient practice. Gifted kids can't learn by osmosis, either.

When Meg was in first grade, she had an assignment to use her six spelling words in a sentence. She was supposed to use each word in a separate sentence, but she used all six words in the same sentence.

If I recall, she knew what she was supposed to do, but thought she could simplify matters by using them all in the same sentence. The funny thing is that she used all six words appropriately and in context--which I thought took a bit more skill than writing single sentences.

-- KarenA - 28 Apr 2006

It was interesting to look at Tracy's table link. I have seen a number of people who exhibit traits of the "Gifted Learner" who were not gifted. They are just intense, very curious, and have enormous energy. Conversely, I have seen some people who I consider to be gifted (in one way or another) and fail completely to appreciate or use their gift. Things come so easily that they never learn how to work. In fact, the more I look at the list, the less I like it. It's not that simple.

-- SteveH - 28 Apr 2006

Tracy's list looks cool - just checked it!

On re-reading it, I think it's too long. I suspect that most high performing kids are going to show items from both parts of the list.

-- TracyW - 28 Apr 2006

I do think the list is accurate, but only because there is a distinct difference between "gifted" and "successful". Very often, a hard worker ("high achiever" on that list) will be more successful at many tasks than a gifted person who figures out (often amazingly quickly and correctly) what needs to be done and how to do it, but doesn't necessarily follow through by actually doing it.

Being gifted often means less work to achieve a particular result, but as SteveH^? said, it also can mean never learning how to work and later problems.

-- AndyLange - 28 Apr 2006

"Things come so easily that they never learn how to work."

This is absolutely true. And when they finally hit a wall they often come apart, because they've never failed, never had to work hard.

-- VerghisKoshi - 28 Apr 2006

I showed the problems to my son, a fourth grader who loves math and is very good at it. They've covered mean, median, and mode in his class, but never done problems anything like this. He knew, almost immediately, how to do all of the problems except numbers 3 and 8. I'm not sure why he didn't get 3, but I saw that explaining it to him deepened his understanding of averages. I also saw that working through the other problems (without algebra) led him to understand the concepts in a way that the much more straight-forward instruction he's gotten in his class never would. For him, this is a great exercise. He had fun doing it, and he learned from doing it.

That being said, I think his abilities and enjoyment of math are unusual, and it should not take an innate talent like he's got to be on track for learning Calculus in high school.

-- DaleA - 28 Apr 2006

"That being said, I think his abilities and enjoyment of math are unusual, and it should not take an innate talent like he's got to be on track for learning Calculus in high school."

This is my problem with K-8 education. They don't believe this. Math curricula are based on the assumption that it takes innate talent (not good curricula and teaching) to get on the calculus track in high school. The top tracks or phases assume that the kids have some sort of unique or gifted qualities. Education is only sorting kids based on real or perceived qualities. In other words, if students do poorly in class, then it's always the student's fault.

"All kids can learn" does not mean that the school decides that some kids learn only at a very slow pace or with a simplified curriculum.

-- SteveH - 28 Apr 2006

Catherine,

Can you (or anyone) provide the answers for all of these? I never trust myself and the husband is a bit busy right now. I'd like to see what math kid does with them. He got the first one right, but his explanation (as usual) was weird.

Thanks

-- SusanS - 28 Apr 2006

Also, this article helped me a lot many years ago and also gave me a point from which to advocate:

http://giftedpsychologist.com/struggle.htm

-- SusanS - 28 Apr 2006

Here's what my son and I came up with for answers:

1. 95
2. 6
3. 82.7
4. 17.4
5. 35
6. 27
7. Mean = 32; Median = 37
8. 1, 1, 4, 4, 5

No promises that we got them all right!

-- DaleA - 28 Apr 2006

I'm pretty sure Dale's answers are all correct. (I'll make a minor edit to put the answers in a more accessible form.)

-- DougSundseth - 28 Apr 2006

"... there is a distinct difference between "gifted" and "successful"."

One might see these distinctions in a stereotypical way, but it depends on how you use this information.

The list is from a site on gifted and talented education. The list seems to imply that one would educate gifted and talented in completely different ways. The talented ones would need a fast-paced, but formal teaching model with a broad, specific curriculum. The gifted students would need a more free-form un-schooling approach that lets them take the lead.

Ironically, most lump gifted and talented together. My view of GATE programs is that they are used as a pragmatic escape from poor standard curricula. If one can appeal to the "special needs" of a group, then things often start happening. Rather than fix the low expectations of public schools, they look for a special needs way to escape. One could argue that a program is needed only for truly gifted students who make up a very small fraction of the population.

One could also argue that the common thread for gifted and talented is the need for acceleration of the curriculum. But there is no quantum jump or gap between the abilities of regular students and talented (not gifted) students. Talented students are just better regular students. It's always a BIG problem where you draw this line. What if this gifted/talented line should be drawn between subjects?

In terms of educating 99% of the population, I prefer to focus on the basics of a quality education. Talk of enrichment and discovery (or any kind of teaching process) masks some really basic problems with curricula, expectations, and teacher competence.

-- SteveH - 28 Apr 2006

Thanks Dale (and Doug,

My son just did the first three and it looks like he got them right, but I want to give him the rest and if I doubt him he can talk my head into circles with his various ways of doing things, little stinker.

Hey Catherine and Carolyn,

I just now am able to get on from earlier today. Whew, that was a close one. The withdrawal would have been tough.

-- SusanS - 28 Apr 2006

was he super-brainy in Math and all other things??

Carl is about 5 years younger than me, and when I was 11-12 he knew a lot more math than I did.

I see via Wkipedia: Carl Feynman is the son of Richard Feynman. He has consulted on various computer ventures including supercomputer manufacturer Thinking Machines. He holds an SB degree in Linguistics and Philosophy and an SM degree in EECS from MIT.

So I guess he is smart.

-- BenCalvin - 28 Apr 2006

From my personal experience, I see value in discovery learning for gifted kids. However, I think it is ridiculous for normal, individual students to be expected to solve untaught problems as a graded assignment. This will only produce frustration because the problem is “unsolvable” given the tools the student possesses.

For a group of gifted students, however, discovery learning can be valuable. As long as the problems are not graded on a “percentage right” basis, gifted kids can learn some valuable lessons from discovery learning.

When I was in elementary school, school was easy for me. I finished my English worksheets half way through the allotted time period and then read my own book silently. In 6th grade, I never had math homework because I finished it during the lecture or the 10 minutes at the end of class when we were supposed to start our homework. I had no concept of what it meant to study for a history, spelling, or science test, because for me it was pointless repetition.

Then, in 6th grade, I was placed in an enrichment-style pullout GATE program one day a week. For the first time, I was exposed to discovery learning. It was sometimes frustrating and definitely pushed me out of my comfort zone, but it taught me some valuable things, such as:

Empathy: Until I was exposed to concept I hadn’t been taught, I never “hit a wall” in any subject in elementary school. Thus, I had trouble empathizing with my classmates to whom concepts weren’t immediately clear. When I actually had to work to find a solution and experienced the frustration of not understanding, I learned how to better relate to my age-level peers.

Humility: When you spend 7 formative years in school with adult authority figures who praise you and hold you up as an example, you’re bound to get a big head. Discovery learning was useful to remind me that at the age of 12 I did not, indeed, know everything.

Teamwork: I did NOT learn teamwork in my regular elementary school classroom. I learned to teach/threaten the other kids (too stressful or time consuming) or do it all myself. After being hung out to dry by uncooperative teammates enough times, my default mode became “benevolent dictator”. When assigned to a group, I would immediately take charge, dole out assignments, and ask for input, but make the final decisions myself. I remember the teacher talking about “everyone contributing” and “using everyone’s gifts” but all in all it was just blather. A heterogeneous group elementary school kids discover that it’s easier to just rely on the “smart kid” than to contribute. Since the “smart kid” cares about the grade, he/she will ensure that the work gets done. In my gifted class, I finally understood teamwork. Since I couldn’t solve the problem myself, I learned how to work with others to draw on our collective knowledge and experience. I learned to relinquish control and let others lead. Once was able to step back see others at work, I was able to go back to my regular classroom groups and encourage my teammates rather than discounting them automatically. I learned how to be more of a project mentor than a dictator.

More realistic expectations: When I was engaged in discovery learning, I was not expected to get everything right by my teacher, classmates, or most importantly, myself. Thus, it was a “safe” time for me to fail. Somehow, this made it easier for me to accept less than 100% on things that did matter to me, such as tests in my regular classroom. I think experiencing “failure” and discovering that the world didn’t end helped me develop a more balanced, realistic view. This helped relieve some of my self-created stress. (The man who administered my IQ test told my mom I would probably commit suicide during my freshman year of college, if not during high school, because of my unrealistic perfectionistic demands on myself.)

Logical reasoning skills: When things came easy to me, I didn’t have to break things down into steps and think through them. However, when I was exposed to a problem to for which I didn’t have all the tools, I had to use logic and strategy to develop a plan of attack. I had to figure out what relevant knowledge I already possessed and discover how to acquire the rest of the knowledge. I didn’t learn this skill in regular classroom work, because I always had the information I needed and could “plug it in” when asked.

I think there are more, but these are the first benefits of discovery learning for the gifted child that popped into my head.

-- AndyJoy - 28 Apr 2006

The problem with learning something after a couple of times is that the gifted kid can forget it just as quickly. The gap problem in gifted kids is often more hidden and causes a great deal of frustration down the road, and as mentioned earlier, gifted kids often don't have the resilience. So, while I agree that discovery learning is very valuable to them, they can often "dazzle" teachers a bit and conceal what they don't know.

The other problem is overthinking. Some very bright kids miss obvious grade level questions looking for more than is there. I am constantly telling my son that he is overthinking and that what is wanted from him isn't so complicated. Standardized tests can be a problem for just this reason.

-- SusanS - 28 Apr 2006

I took a look at the list comparing Talented and Gifted. I found characteristics in both groups that applied to me. The one thing that the list doesn't seem to include is motivation/drive. I was certainly not super-genius material, but by most folks' standards, I was a gifted child. However, I also had (have) what I like to call a pathologically laid-back personality. On top of that, I've got a pretty good efficiency streak. (Some call it laziness, but what do they know? (: ) Also I had a tendency to be a bit of a procrastinator. (In my younger years, procrastination seemed to like the most efficient way to deal with being a self-critical. I tended to start things with just enough time to get the work done, but not enough to be able to obsess over how good it was. This only worked because I was laid-back about the work once I turned it in.)

I guess I would like to suggest that not all gifted students are self-motivated and/or driven to be high acheivers outside of a structured environment. I usually did what I needed to in classes, but unlike some of my peers who seemed to be a little less 'gifted' but had a lot more motivation, I did not do well with independent work. I could accelerate as fast as they would let me as long as I was in a classroom setting (I did this by skipping classes), but it rarely seemed worth the effort to accelerate on my own time or do independent studies. Maybe I would have done better with a mentor that could find ways to motivate me, but that's not what I had.

-- MattGoff - 29 Apr 2006

I think one of the things the list is supposed to do is to get people to broaden their criteria when trying to identify gifted kids.

There was an early ('70's) book about teaching gifted kids that mentioned a study going around about how many gifted were in schools according to the teachers. Most teachers said they had no children that they considered gifted and when they did identify a student it was always the perfect, bright, straight A kid in the class. The authors then went on to say that 9 times out of 10 teachers would miss the actual gifted kid who could very well be the disorganized mess on the back row.

I wish I could remember the name of the book and the study.

-- SusanS - 29 Apr 2006

Dale

I showed the problems to my son, a fourth grader who loves math and is very good at it. They've covered mean, median, and mode in his class, but never done problems anything like this. He knew, almost immediately, how to do all of the problems except numbers 3 and 8. I'm not sure why he didn't get 3, but I saw that explaining it to him deepened his understanding of averages. I also saw that working through the other problems (without algebra) led him to understand the concepts in a way that the much more straight-forward instruction he's gotten in his class never would. For him, this is a great exercise. He had fun doing it, and he learned from doing it.

wow!

interesting

what do you think about.....the contribution of his education to his understanding of these problems??

in other words, do you have any sense of whether this is 'him' or this is 'him plus good teaching'?

I first saw problems like the first one about a year ago, when I ordered a book on bar models. (Haven't even looked at the rest of them yet.)

I almost immediately figured out how to calculate the next score, which told me I had decent conceptual understanding of averages.

In my case, that would mean that either I was taught the concept well years ago, or that I've used it enough over the years (which I have) that I've come to understand it.

-- CatherineJohnson - 29 Apr 2006

Karen A

When Meg was in first grade, she had an assignment to use her six spelling words in a sentence. She was supposed to use each word in a separate sentence, but she used all six words in the same sentence.

If I recall, she knew what she was supposed to do, but thought she could simplify matters by using them all in the same sentence. The funny thing is that she used all six words appropriately and in context--which I thought took a bit more skill than writing single sentences.

I love it!

Did I write a Comment about the 2nd grade assignment being given out here?

I think I did.

They give the kids a list of spelling words that are related by a spelling rule (all ending in 'ing' or some such).

Then they tell the kids to write a paragraph using all of the words, with a thesis statement and 3 pieces of evidence.

-- CatherineJohnson - 29 Apr 2006

I agree with Dale (I think!) - doing algebra problems without algebra has been helpful for me in relearning elementary math.

I don't know that it's helpful for kids learning arithmetic for the first time, but I assume it probably is....just so long as the kids can actually do the problems, rather than being clobbered by them.

-- CatherineJohnson - 29 Apr 2006

On re-reading it, I think it's too long. I suspect that most high performing kids are going to show items from both parts of the list.

yup, and people cross-over the list.....but it's interesting

I haven't read it closely, but just skimming through I found myself in both columns

-- CatherineJohnson - 29 Apr 2006

Susan

The problem with learning something after a couple of times is that the gifted kid can forget it just as quickly.

I never thought of that!

But of course it makes sense.

I'm sure that happens to 'brainy' people all the time, as well as to people who've gained some expertise in a field or avocation.

Overthinking is another issue!

I'm not sure I'm gifted in any particular realm (possibly in writing/reading?) but I can definitely overthink!

-- CatherineJohnson - 29 Apr 2006

Actually, I wonder if that explains a conversation I had with my friend Kris.

We were talking about practical intelligence, being practical, etc.

She's got amazing practical intelligence; I'm constantly STUNNED by her insight into Basic Reality.

I said that, and she said, 'You're very practical yourself.'

I don't feel practical at all. It's true, however, that the instant Kris makes a practical observation I instantly 'get it' and use it if at all possible.

I was thinking that I'm not practical, but I 'appreciate' practicality.

Given what you've said, I wonder if Kris is right. Maybe I do have practical intelligence, but mess it up by overthinking things.

(I hope I'm not making it sound as if Kris is less intelligence. She's brainy AND she took & passed calculus in college! However, she's not as bookish as I am.....which is probably part of my problem.)

-- CatherineJohnson - 29 Apr 2006

Some very bright kids miss obvious grade level questions looking for more than is there. I am constantly telling my son that he is overthinking and that what is wanted from him isn't so complicated.

We, meaning a fair chunk of my class, used to have fights with our chemistry teacher over this. Most class tests, there would be a question which a chunk of us had gotten marked wrong in the same way, and we'd have a discussion with the teacher going something like: "But our answer is right! Look it meets the letter of the test!" "You're not meant to give that answer. You're meant to give the most obvious answer." "For heaven's sake, it was a test. We did give the first answer that came to our heads."

Unfortunately I can't remember any of the questions. Partway through the second year we had him for chemistry he figured out how to stop giving questions like that.

My mum was a teacher, and said that one thing to be aware of when writing questions was that if the smartest kids in your class consistently got a question "wrong" you'd written it badly, and should eliminate it from your pool of questions.

Your son probably isn't trying to be overcomplicated or overthinking. He's just, under somewhat stressful situations, putting down the first answer that is right. I don't think he's going to be able to switch that off.

-- TracyW - 29 Apr 2006

I'll give you an example of a question for which I received no credit for my answer:

"Which is heavier, a pound of feathers or a pound of gold?" (Actual extra-credit question from my horrible Minnesota Jr. High.)

The answer I gave was "Feathers". Feathers are weighed in avoirdupois pounds, each of which is 454 g weight; gold is weighed in troy pounds, each of which is 353 grams weight. Therefore, a pound of feathers is heavier than a pound of gold (neglecting differences in local acceleration).

I received no credit, because the approved answer is, "They weigh the same".

-- DougSundseth - 29 Apr 2006

Good one, Doug. Here are a couple more:

In 4th grade, I got wrong a question that asked how many days there are in a year. Smarty-pants that I was, I answered 365.25.

I've got a friend who was marked wrong on what a comet is in 5th grade. She said it was a ball of dirty ice flying through space. Her teacher marked that wrong, and said it was a star with a tail.

-- StephanieO - 30 Apr 2006

I got marked wrong on one of the questions on my school certficate science exam (taken at age 15/16).

The topic was air circulation, and there were a series of questions about air circulation in a mine with two shafts to the surface and a fire lit below one. The final question, for 1/2 a mark, was "would air circulation improve if the mine owner lit a fire under both shafts?" I replied "No" and that was marked wrong.

I could have had the exam remarked, but that cost something like $70 for only 1/2 a mark. It rankled still, though now it makes me grin.

-- TracyW - 30 Apr 2006

My 5th grade daughter is what I would consider to be gifted, but she still needs to be taught, she doesn't teach herself.

If you think about it, it would be absolutely astounding if any kid, no matter how gifted, could teach themselves much mathematics compared to our society's knowledge. Mathematics has come so far in human history. Pythagoras, Aristotle seem to have been pretty smart, but they didn't have the concepts of infinite series, or the square root of -1, or algebra at all. While I'm sure your daughter is gifted, I suspect she's also human.

-- TracyW - 30 Apr 2006

"what do you think about.....the contribution of his education to his understanding of these problems??"

"in other words, do you have any sense of whether this is 'him' or this is 'him plus good teaching'?"

Well, our school district uses Mathland. As I understand it, the idea behind Mathland and many of the other fuzzy curricula was that they would boost the performance of lower achievers, by helping students understand the reasoning behind the math, rather than focusing on memorization and drilling. What we've seen, of course, is that it didn't work out that way, and that without the facts that can only be learned through memorization and drill, the reasoning and concepts just don't stick for the non-math-brains.

Ironically, though, this not-nearly-rigorous-enough curriculum, which bores my son to pieces, has probably provided him the deep conceptual understanding it was supposed to give everyone else. Since he comes to the table with the facts solidly ingrained within him, he has the ability to soak up the concepts and really make sense of them.

So, to answer your question, I would reluctantly have to admit that the curriculum I've spent so much time complaining about, (and which I will continue to complain about because too many kids in our district just aren't learning what they need,) is probably part of the reason my son can handle questions like the ones this thread started with.

I have to say that before you asked your questions, I never would have thought that I had anything good to say about Mathland!

-- DaleA - 01 May 2006