Gifted Issues Discussion homepage Forums Parenting and Advocacy Piggy-Backing on HK's Epiphany re: Challenges

HK's Epiphany relating to the flip-side of "What a Child Doesn't Learn" has officially drawn me from lurking mode. (I've been following the "To Skip or Not" threads for awhile.)

I must also echo her experience with what I consider to be some sort of a reinforcing effect when a grade skip fails to yield meaningful challenge: HK -- "Then in the wake of acceleration, if there is an unresolved lack of challenge, the child interprets this as normal."

I think we are battling this same issue, which, if anything, makes me much more confident that the early grade skips were an absolute necessity. Although now I am finding that they have not been enough.

Our son is in 8th grade @ age 11 (Fall BD), and takes Geometry across the street @ the HS everyday as his first period. Depending on the comparison state, he's two or three years ahead of his age peers.

He's maintained a 4.0+ throughout 7th & 8th and as I look back, it's almost like 2nd & 3rd grade all over again: this stuff is just not challenging enough for him. (Either that, or he is just *that* good at making it look easy!)

Geometry, however, has proven to be the leveling factor. He has maintained a B, but only because the teacher gives credit for *completed* homework, rather than *correct* homework. As a result, the A for homework masks the C for quizzes and tests, giving him a B in the class. And because it's considered an Honors-level course for an 8th grader, he gets 4 pts, hence his 4.0 GPA.

BUT... (cue HK's Epiphany)... because he has been conditioned by his other classes that hard work is not necessary... that note-taking is not necessary (unless graded)... that actual *STUDYING* is not necessary... he doesn't have a gosh-darned clue how to tackle his Geometry debacle. And I guarantee that the total-fantasy B he's getting in Geometry doesn't help the situation much.

Unfortunately, I have no bloody idea where to go with this. When I raised my concern with his Algebra teacher last year, he said, "Bah! It's a maturity thing -- he'll pull it together. After all, he understands the material." And his Geometry teacher this year essentially plagiarized the Alg teacher's answer.

Bottom line for me is that DS is screwed when he runs into real educational challenge -- like those pesky college courses -- if he doesn't get his poo together NOW! Heck -- I'm not so sure he'll have to worry about college classes if he bombs his SAT math section.

So there. That's what's been percolating in my head for the past several weeks (months?). Thank You to HK for sharing her epiphany.

What now? Any suggestions?

Dandy

I don't have any suggestions, but just my sympathies. I wasn't a HG kid (IQ about 130 back in the 1970s) but was gifted enough to get through most of my schooling without effort. I *still* have a hard time dealing with frustration. (In fact, I was just fantasizing about quitting my job the other day because I can't figure something out that I think is really important.)

That all being said--I *did* eventually figure it out, once I got a 2.0 GPA my first year in college and totally freaked out. I'm still not amazing at dealing with frustration, but I can do it when I need to. And, I can make myself work when it's required, though I do still procrastinate. And, I'm pretty successful in my chosen field, well-liked by my colleagues, respected by my boss, good at what I do. (AND--beyond all that, I'm really happy with my life--my work, my family, my home... which really, isn't that what we want for our kids?)

Hmm... Depends, really. *Does* he understand the material (but make slips in tests?) do you think? What happens when you talk to him explicitly about the need to work and needing to work being fine, etc? I asked my DS what he'd advise (mostly, of course, wondering whether anything would come out of relevance to his own situation) and, interestingly to me, he immediately assumed your DS was just not interested in geometry as things are, and suggested books, e.g. the AoPS geometry book, or DVDs e.g. Great Courses Maths of the Visual World, that he might find interesting. Anything in that? What does he say about it? As a practical matter, I wouldn't let errors in homework go, even if the teacher does.

I never really got geometry, but I got tutored for credit in geometry (so that I could take a trig class the next semester).

I got a 740 on the math portion of the SAT's back in 1991 (?). I also got an 800 on some other college test math achievement whachamdaoo (I remember this because I was angry at not getting an 800 on the SAT math section).

As long as he can sleep through calculus, then he will be fine on his SAT's.

For some reason, geometry is different.

I talked about this with Val (?) somewhere else here.

My outcome is whatever the opposite of staceychev's outcome is.

My college GPA shows a *very attractive* straight line down from a 3.75 first semester, which also caused me to totally freak out. Fortunately, I was able to freak out very effectively and self-sabotaged down to a 1.75 one of my last semesters, with a number of Withdraw-failure and F's (I just had to obtain and look at my transcripts lately when I asked myself - hmm, I wonder if I could go to med school, so this is quite fresh in my memory).

More specifically, it caused me to give up, as I was no longer able to get a 4.0, so was there even a point to college anymore?

I mean, if you can't get a 4.0, aren't you already dead and haven't you *already failed*?

My outcome has been whatever the opposite of *staceychev's* outcome is (permanent teenage angst and existential despair?).

So, the moral of the story is to learn that failure isn't equivalent of death and that it's best to learn this early in life rather than when you are a practicing attorney.

Me neither. Geometry was brutal, yet somehow I did fine in calculus.

I loved geometry, but I suppose it played right into my areas of strength. Compared to other maths, it was long on concepts and formal logic, and short on computations. My brain likes to hide the occasional stupid computational error at random locations, but could immediately visualize and grok the concepts of geometry, so it was basically made for the subject.

Geometry lays the conceptual framework that was used to build trig, but that doesn't mean you necessarily have to master that framework in order to use trig, any more than you need to master the concepts of metallurgy and the Carnot cycle to drive a car. You can just accept that it works, and use it.

I was thinking about Geometry yesterday because HK had mentioned not knowing how her daughter goes from knowing nothing to everything on a subject. It was in freshman geometry when I figured out how my brain did that stuff.

For a topdown/abstract thinker all these facts come in like random cards in a card catalog. Until the index system is identified and understood, that information is inaccessible. Once the brain works through some models and hypotheses and some obscure point of balance is passed this whole scaffolding pops into place and all that data is accessible.

Geometry rewards a very topdown perspective with bonuses for visualization skills. To my memory 90% of year 1 geometry can be derived from Pythagoras' Theorem.

I think the best way to have challenge is to throw out the motivation of satisfying the school's requirements and to rather drive for one's own complete understanding while encapsulating the inadequate expectations of the class.

I think there are two problems here. One is the concept of challenge at school. The other is what I call thinking in a new way as distinct from "studying." (Actually, there could be a third, which would be subpar teaching, but I'll ignore that here).

Personally, I've been wondering if a HG+ kid can be consistently cognitively challenged in a school environment. The material just isn't that hard (for a HG+ kid). By cognitive challenge, I mean stuff that's hard to understand, not just lots of homework. Increasing the volume of the workload doesn't make the material harder to understand.

For many or most HG+ kids who are paying even a bit of attention, most everything makes sense on the first pass. I'm not saying they absorb the information completely, just that the ideas make sense. In that situation, all that's required is a bit of cramming during lunch or on the bus or while watching TV or whatever. Presto! Another good grade.

Suddenly, a kid meets something that doesn't make sense on the first pass. Now a bona fide cognitive challenge may exist, but it's isolated and the child has no idea how to approach it. Complicating the problem, he has only his limited experience to interpret what's going on. If geometry is the only class that's ever posed a problem for your son,he may decide that he's reached a limit. In this situation, it's natural to misinterpret what's going on (Example: "Those other kids are doing better than I am in Geometry, so they must be smarter than me."). Remember that based on his lifetime experience, getting a good grade results from being smart. Yeah, I know he's got a B, but it's from homework and he sees how the other students are doing on tests.

This is the part where thinking in a new way comes in. A student who always gets the basic idea on the first pass may have no concept that it's even possible to look at something that's completely baffling and figure it out by simply staring at it and thinking. This is very different from the idea of "studying," which, to a HG+ kid, can mean "cram it in" or "do the worksheets as quickly as possible." There's a subtle difference between studying and thinking in a new way, but it's a savage one. Until a person actually groks the idea of "stare and think in order to understand," he'll be hindered by misconceptions about his abilities. And yet, once he gets the idea, he'll have made a huge cognitive leap. See? Subtle, but savage.*

Schools do not teach this idea to HG+ kids.


*With thanks to Truman Capote for this phrasing. He was describing the difference between writing that is merely very good and writing that is true art. See Music for Chameleons.

If you get stuck, you can also toss it into your subconscious and wait a few days for a solution to magically appear.

This is so true! They are so used to getting things the first time they hear it they just don't know how to go about figuring it out. My son gets very frustrated and he won't let us help him. Partly because he thinks he knows everything and he doesn't need help. Trust me I am working on this with him as well.

I am very glad that we accelerated him this year to 4th grade. He still really doesn't need to work hard at anything. After being put in a Math Plus class (for gitfted students) 1/2 through he is being challenged a little bit more. There have been just a couple problems that he had to look at longer. He just doesn't do well. As much as I wanted him to be challenged so he doesn't become lazy and he learns how to work for something early on he really has trouble with it. In the end he ends up leaving to calm down and coming back to it later. At that point he still won't let us help him but he normally has figured it out by then.

He expects to know it right away. I hope he figures out a way soon to learn how to learn and deal with the things that don't make sense the first time. He is still young so I hope we made the change early enough.

I would love to hear suggestions on how to teach a child to learn or see things differently when they are used to knowing things very easily. If anyone out there has ideas I would love to hear them!!

Regarding Geometry... This was the only Math class I struggled with. I do think it is different kind of thinking and you are either good at it or not. Just my take. I got through the class never really learning it. However ended up fine with everything else. It will be intersting to see how my son does with it.

In both Algebra & Geometry, his teachers said he participated in classroom discussions while always demonstrating an understanding at a level that left neither teacher concerned.

When asked about his favorite subjects, Geometry is always right up there with concert band. It was the same with Algebra last year. He's moved beyond the visceral hatred he had for the subject when he was quasi-homeschooled for the subject for 5th, 6th & 7th grades.

Part of me thinks I'm over-reacting, but the rational me is fearful that, placated with easy As, he'll not develop the discipline required for success in STEM. Admittedly, there's a bit of reflection, as I vividly recall bolting from my first college Calculus course, realizing that I had absolutely no idea how to work that hard.

How do you look a kid with a 4.0 and say, "I think you need to work harder!"?

The thinking in a new way is using the metacognitive skills that schools seem to hope kids will accidentally learn. These skills advance under challenge and quite slowly for most kids (half the reason there are 12 years of math, imho), but can be taught directly. It may also be a case where mixed ability group problem solving could benefit HG kids.

I think this is what his math teachers are seeing. When I discuss particular problems, I see it too: he understands the material. And he's not shy about saying when he's unclear on a concept. But getting him to move from "clarity in understanding" to "accuracy in execution" has me stumped.

The last formal instruction he had for math was in 3rd grade, and he finished all the year's work in the first quarter. He used EPGY & ALEKS for 4th, 5th, 6th & pre-Algebra. He clearly missed out on the classroom & teacher aspects -- especially the required performance on testing. Both ALEKS & EPGY utilize "second chances" throughout, so he always had an extra shot if his wild first serve didn't score. He never had a teacher TEACH him how to attack problem solving. He never had to "show his work" until Algebra.

Suddenly, a kid meets something that doesn't make sense on the first pass. Now a bona fide cognitive challenge may exist, but it's isolated and the child has no idea how to approach it. Complicating the problem, he has only his limited experience to interpret what's going on. If geometry is the only class that's ever posed a problem for your son,he may decide that he's reached a limit. In this situation, it's natural to misinterpret what's going on (Example: "Those other kids are doing better than I am in Geometry, so they must be smarter than me."). Remember that based on his lifetime experience, getting a good grade results from being smart. Yeah, I know he's got a B, but it's from homework and he sees how the other students are doing on tests.

Yup -- he particularly lacks the persistence when faced with problem-solving. I would love to place him in a classroom version of AOPS... I swear that would help him a ton. No make-believe As for homework masking an underlying deficiency.

I appreciate all the comments on this issue. It seems so minor in the grand scheme of things, but I feel if he can just come down with a slight case of perfectionism, he'd be much better off!

Dandy

Perhaps you're looking at this the wrong way. Maybe he needs to work better.

If he understands everything so well, why is he getting Cs on quizzes and tests? And why do his As on his homework result from doing the assignments but not necessarily getting the answers right? (This question may not be a simple one.)

What do you know about the quality of teaching and the quality of his textbook? Have you looked closely at his book? Is it a classical book (e.g. author = Richard Brown, but there are others), where each section has a lot of explanatory text and lots of problems of increasing difficulty? Or is it a new book with constant distractions like lots of LOUD COLOR GRAPHICS and fluffy examples about Geometry in Real Life! and little text?

What do the homework assignments and exams look like? Do the kids have to write proofs from scratch or fill in blanks in a partially completed proof? Do things like the word "postulate" count for points, as in "Side-Angle-Side" is an incorrect answer but "Side-Angle-Side postulate" is correct? My very mathy son got a C on an exam last year because of multiple point losses due to this kind of thing. He should have scored 100.

If kids are writing proofs from scratch and the difficulty of problems in each section increases, it sounds to me like your son doesn't understand the material, in spite of what the teacher said (teachers can be wrong). If he's getting a C because "SAS" is wrong and "Side-Angle-Side postulate" is correct, the entire problem is, IMO, moot because he's not being taught real geometry anyway, and learning how to score high on fluff is pointless (this is why my son is homeschooling this year).

A lot of kids end up in remedial math during their first year of college. IMO, part of the problem is that they got As and Bs in marshmallow math courses starting way back in grade school, and reasonably believe that they can do math. Yet colleges are still unforgiving this regard, and I suspect that the students are at a loss to understand how they could bomb a placement test when they did so well for all those years.

That's me. Geometry was the only math class I truly enjoyed the whole way through.

I sometimes tell my DD5 "if you focus and try hard, you become smarter and difficult problems become easier."

I sat down with him during the first quarter and went line-by-line through the tests. His errors were generally careless. He knew the material & how to solve a particular problem... he just made sloppy and/or careless errors (same thing?) at every turn. He hadn't come to proofs yet, so no clue there.

It was near the end of the first quarter that I first raised my concerns with the teacher and was told that DS is doing fine; accuracy will come with maturity; he's understanding everything just fine -- DON'T WORRY! And I did pretty good about not worrying until now as we are in the middle of the 3rd quarter and I'm not seeing any improvement.

The geometry text is nearly devoid of unnecessary splashy graphics. Don't remember the text, but I recall admiring how clean the text appeared. (His Algebra, in contrast, was filled with all the colorful claptrap you mentioned.)

I had no idea until recently that his homework was not graded for accuracy. The few times I saw <100% on a homework assignment & reviewed the errors, it looked as though the teacher was going through the problems. Now, however, I understand that the teacher is looking for all the required steps, with little regard to the final answer. I'm guessing my son locked onto this early on. He rarely gets less than 100% on homework, which, to me , means that he was able to make it look like he knew what he was doing. Or something to that effect.

This is precisely what I hope to avoid. That is, of course, assuming he does well enough on his SAT math section to get into college!

I'd say you're right to be concerned, and your teacher is wrong for not being concerned. If he's demonstrating mastery of the concepts, great, but if he's doing so and getting the wrong answers anyway, he needs to know that, and be held accountable. If not, he never learns anything from the mistakes, keeps on making the same ones, never learns how to check his answers, and eventually runs into a situation in which results matter (SAT score, college class, engineering project), and can't cope. Disaster results.

I tell my DD8 that mistakes are the best teachers.

This is DD's preferred method.

Heck, I get it-- this is the relatively painless way, when you can afford it. I'll just wait until it all falls into place... I have plenty of subconscious bandwidth to only be peripherally aware of the learning process, if I consider it at all, and it works just as well.



Mostly.



For things which don't have deadlines attached, I mean, and for which there are not external consequences/procedural requirements.

Yeah, okay, so this has limited application. On the one hand, rumor has it that this is how Kekule determined just how aromaticity "works" but depending on epiphany is a risky strategy-- and one that feels like it isn't an earned understanding, if that makes sense. So it doesn't do anything positive/authentic for our sense of competence/worth, either.

This is why we have tried to work on the metacognitive skill set to understand that distinction posited by Val-- that changing the HOW of your thinking is just as important as changing the direction or intensity of it.

Ahh, but according to my son, he doesn't need to check them because he makes no mistakes! And apparently he doesn't remember what he needs to do in order to "check his work."

My wife & I discussed this today and figured that he'll have problems with anything computational, like Chemistry & Physics. For everything else, he gets to rely on his processing speed and freakish memory.

Perhaps the workload of AP courses will prove taxing, but probably more related to the volume rather than complexity.

I think this behavior is normal. My 12-year-old is only now beginning to get the idea about checking his work. I typically push him to check problems and his usual response is akin to what you wrote. But recently, he's actually checked them and found errors. He seems pleased when he finds the errors and even more pleased when we check what he did against an answer key and he gets, say, 100%. I can see he has a real sense of accomplishment.

I don't think he's going to suddenly check his work as a matter of course, but I think that he's finally on the path to that place.


I steer my son away from AP courses. Why take an AP course when you can just take an actual college course? Yes, I know why people take them, IMO, they aren't generally worth it.

*Sigh*
I had a nice meeting with the teacher in her classroom today while DS watched a ball game. She's been teaching in the district for a couple decades and is well-liked & respected by even the most demanding parents. She has a solid reputation for being a hard-nose and is known for high-expectations.

Her initial reaction to my questions -- after talking about DS coasting in all his other classes; getting a "misleading" A in her class and Algebra last year; etc. -- was that she can't spend too much time & energy with our DS because he seems to grasp all the concepts, while there are so many others that do not.

In reviewing the most recent test, she said that DS missed out on some half-credit because he didn't show all the required steps. She would definitely like to see him improve his organization in presenting solutions, etc., and promised to be more rigorous in her criticism.

I asked if she could correct his homework and she said that she has too many students and can't start down that road.

She closed with saying that DS really does a wonderful job and that he's a delight to have in her class.

Dandy

In our case, we aren't near any college campuses, so I look to AP as an opportunity to expose him to some of the rigor -- at least in comparison to the usual HS courses. There's no GATE program around these parts... and no Honors. So it's either CP, with little if any ability grouping, or AP.

I could have been clearer. There are a lot of online options that may make AP less relevant for kids on the far right of the bell curve.

This has been our exact experience, with a few exceptions.

I also agree that at about 12-13yo is when my DD began to be capable of actually "checking" her work using something besides a basic reality/sanity check.

The responses here have been great as always!

As DS starts 9th grade + Alg II in the fall, he's gonna be in a sink or swim situation and I'm really hoping to get him at least treading water before then.

To his credit, after a discussion last night, he acknowledged that his A/B in math the past couple years aren't a fair representation of his performance because of the giveaway homework portion of the grade that has been masking his underlying problem.

Another email from the teacher reiterated her confidence that the accuracy on tests and the neater work habits were issues related more to maturity than anything else and that they would likely resolve on their own in a few years. (!?!?!)

The challenge for us, of course, is that he'll be a junior in a few years, which might be cutting things a bit close.

I know (or at least think I know) that he can do the work now, but nothing his dear old ogre of a dad can say will help. I've already begun reaching out to other people within his school.

The suggestion I'm running with is to lock him in a smaller box at night and also require that he work out all missed problems on his test with me, step by grueling step. The teacher that suggested this said that he definitely missed a lot of the "process" drilling during the years he did on independent study. He said his pre-alg classes will often only get one or two problems per night, but that they must be 100% complete, showing every blessed step along the way.

I suspect that I can blather on all I want about "show your work" and "take your time" but that he'll be better served by actually going through the process. And then, suspects the teacher, DS will decide that it's better to take a little more time on the actual test, and NOT have to teach his ogre-dad Geometry at night.

Along these lines, I've always been explicit when defining "check your work." My definition has been drummed into my kids: "Yeah Mom, I know: it means REDO THE PROBLEM."

IMO, a better phrase would be "Redo your work and compare your answers."

"Check your work" implies that you should go through what you wrote. This is a great way to overlook your mistakes, because it encourages you to replay your original thought processes, and therefore miss your mistakes. Starting from scratch helps avoid that pit.

Starting from scratch and using a different method is good. But not if you've been stuck with 40 more or less identical problems.

Yeah, I was thinking I wouldn't redo many problems that were boring the first time without a serious incentive, too! I'd be tempted to suggest writing a program that took as input the variable numbers in the problem and gave as output the correct answer, where that's practical; this could be quicker if there are 40 problems, besides being metacognitively interesting.

Dandy, does your DS do maths competitions? For my DS, these raise the stakes in the right way to encourage carefulness.

Too me check your work doesn't mean all the time redoing the problem...if it was long division I check by multiplying, if it is an equation, I might plug the answer in to the original question....I might check by estimating and see if my answer is reasonable...like 20% of a number and my answer is bigger than my number I know I have done something wrong.

And sometimes I just spot check random problems by redoing them. But I did not and do not expect my son to do every problem twice. No one is perfect, go through slowly and carefully the first time and with a minimum of checking what you produce should be good enough.

And the US Dept of education says that 3 to 5 problems done correctly is the optimal number of practice problems...so if you have 3 different types of problems for one concept then your homework should be 9-15 problems long.

I've raised the topic a few times, but he's not been interested. He holds math merely as a tool to use in other pursuits.

Another heart-to-heart last night clarified his understanding of just how much math he will face in non-math courses and that his weakness will be felt in all those areas.

So far, he's on board with the idea of re-doing incorrect problems each night with me. We reminisced about his first major math challenge, which was 3-digit long-division. That dragon was slain by working carefully through a couple problems every night for 2-3 weeks.

We also looked at the various universities that interest him, noting the SAT score ranges of accepted students. He has big dreams and I think the importance of math in reaching those goals is slowly sinking in.

In the 6 weeks since I started thread, we've been working 3 or 4 nights each week carefully reviewing any missed problems on his Geometry homework and tests. For any problems we must re-visit, he has to show every glorious step so that I can follow exactly what he's doing. And it must be *legible*. To add an extra twinge of pain, when he has to re-work, he must do so from scratch, without the benefit of seeing what he'd done on his first attempt. By going through these exercises, he's starting to recognize the difference in quality when he SLOWS DOWN even slightly.

So far, the remedial work seems to be helping, as he's improved both his homework grade AND his test scores. He still needs to increase the consistency of his work, but he's definitely headed in the right direction.

Again, many thanks to all the support!

Dandy

Glad to hear it's going well!