Anyhoo, things have taken a little turn for the worse. Thus the

I'd discuss in p.m. if interested.

Neato

Neato:
First of all I would step away from the internet and from this board for 48 hours
It has helped me gain the perspective as to what the "really" important things are. I am not preaching here, this comes from experience.

I agree with others saying that Calculus Trap applies more to middle/high school kids but our story put Ghost in calculus trap in 5th grade!
From what I gather, your DD is 8 years old and in 4th grade, never grade skipped, correct?

Our story, and I think I have posted it here but am unable to find it now, began in 5th grade when Ghost changed schools from private to charter and was immediately placed in Algebra 1. We were extatic, but stupid. We have never done any extra work in math with him up to this point, unless you are counting math problems I was doing with him in my native language which were purely to keep him fluent. But even what I was working on with him was "on a grade level", just the language was different.
So he was in 5th grade and doing Algebra and really struggling with it. Not struggling in a sense of understanding concepts, but he was a guy who has hardly done any work on fractions and negative numbers. He has jumped straight from regular 4th grade math curriculum to this class full of 8th graders. And he was the best of them all, had highest grade (A+), did all his homework - but at what cost. Sometimes he went to bed at 11 P.M.
I wanted to talk to the teacher that the homework was too much but my DH was adamantly against it - you learn math by doing difficult problems, he would say.
Things got easier by winter, Ghost got a hang of it all and started cruising. We have only realized that he needed additional challenges and additional instructions by the time he was in 6th grade. We have realized that school was was only breezing the subject and for a guy who really has a potential in math he needed to work much, much, much more deeper.
In 6th grade he waqs doing Geometry but also had to do regular 6th grade stuff. He absolutely hated it, it was so repetitive, so not intelligent, pure busy work. We told him he had to stick with it (learning for the future I guess, not all work is fun and you DO have to be responsible) and he resorted to doing 6th grade math homework, the busy work, in the hallway right before the class. Every single day. I repeat again - he hated it - but I don't think it did any damage. If anything, he has learned that not all that we do in life is fun and interesting.
By the time he was in 6th grade we started a math club at school as a vehicle for him to participate in math competitons.
He also started AoPS classes at that time and we started working on math at home - mostly competition math.

What I would do if I were you now? I would have my kid do Aleks and Singapore math at school, if possible, with my guidance. I have achieved that when my DD was in 4 th grade. I think that it is of paramount importance that kids use the school time to the fullest. I do not believe that it is fair to them to unschool them. I would involve my kid in math competitions. You are saying that your DD is not ready. Some of them are very, very friendly. Look at Math Kangaroo questions . I know, you have to pay for them now, but they are still quite cheap.
What is that pull out for math that you are doing? Please write more about it.
Do not rush with curriculum. Ghost is in pre-calc now - it is great, only two students plus the teacher, every day, can you imagine? But he is looking at writing his SAT II this year, and he doesn't even know what SAT II is! And there is going to be accomodation issues in HS, I am sure of that.
I do not know what book your child is using, but most of the math books in US (awful, awful texts really)have a section with challenge problems at the end of each lesson. Those are really challenging problems, requiring much more knowledge/thinking to solve. Look through her book for those.
Keep bugging the faculty. Look at the things I have manage to achieve - under Success Story.
Have your DD play math games. Make her become really comfortable with numbers. Krypto is great. Buy fraction ones if she has already mastered the one with double digits.

Ooooh, sorry for the bad turn there Neato!!!

We are well into the calculus trap here as well, but I still say where DS is today has GOT to be better than where he would have been without The Trap. The thought of him in 4th grade math....with 4th grade math enrichment just boggles the mind, .

Again for us, it's about A, B and C choices. I can't compare A to B, when we only have A or C. We do what we can on the home front, but we are holding the rest together with duct tape. And it's working. (Duct tape is amazing!) At 9, I think we have plenty of time to fine tune the plan.

And I'll say it again, as I so often do: every child is different, and every school situation is different. What works for one may work for many others, but it won't work for all. All that matters is that the solution you have in place works for YOUR child.

It seems like you've got that licked, Dottie! And good on ya' for it!

Dottie - you are already involved in AoPS, so you are going sideways/deeper from the regular track.
Once your kid is done with Geometry - work on proofs.
Tales theorem - seems to be very easy. Have them look for three proofs. Teach them how to write those.
Neato - PM me with your problem.

So it's only a trap if you don't go wide and deep? I think we've been doing that all along, thanks to DS's interest and my own abilities (and hindsight benefits from being a third child). I really do think we have a good situation going at the moment. Thanks for the geometry tips.

I hope things will be looking better (or least more approachable) for Neato after a good night's sleep. (I plan on grabbing one myself here in a minute, .)

Thanks Kriston!

I think the trap refers to going fast and reaching Calc too soon. Calc is really a college course, used to be anyway...

It is quite difficult to sidetrack once the kids get into the machine and feel good in it.

Lately I frequently ask myself - why do we learn math? I ask this question with my DS in mind. There are many different answers that I am coming up with but the one that is usually up there on top is to have a deep understanding if its function and application in everyday life. Sadly, one is not going to accomplish this by following a standard curriculum.

Kriston - I think that the "what works for your child" idea is fine, but kids also need to learn to function by doing things that are not necessarily pleasing to them. On occasions.
Sheltering them from this is harmful, in my opinion.

Agreed. I just don't happen to believe that giving them boring schoolwork is the place to give them things that are not necessarily pleasing to them.

Treating learning as a chore to be gotten through is harmful, in my opinion.

Keeping in mind, of course, that I'm dealing with a 7yo. My attitude might be different with an older child who would just prefer to play video games or go to the mall or something than to do anything even remotely work-related. As I said, I suspect much of where people stand on this debate has to do with the age of the child in question...

This could be why I strongly advise a child should do the drudgery work given them, while you are advocating to get level appropriate work. GS was 5.5 when we got custody and had to learn to respect those in authority. He had good reason not to respect those in authority up to that point, but that's another subject. Part of learning respect was to do the tasks assigned to him, then receive an appropriate reward as he learned to internalize feelings of self-pride and accomplishment.
I didn't want to offend anyone with my views, but wanted to make a point that often there is value in doing those boring, repetitious tasks.