How fast is too fast?

[lewelma]

why not speed them through elementary math and then really wallow in algebra for a few years and enjoy it?

 

This is exactly what my ds did. He has been studying AoPS Intro Algebra for 2.5 years, doing all the challengers, teaching himself, and looooving it. No hurry, no pressure, just loving learning at the perfect pace for him.

[boscopup]

Add me to the camp of "go at his own pace". You may find he slows down when he hits harder math... or he may not. :) He may hit a wall, or he may not. There is only so much to elementary math - your basic 4 operations, fractions, decimals, percents, and some geometry. Some kids pick those things up very quickly and really don't need 6 years to study them.

 

Accelerating does not necessarily mean early graduation. You can still graduate him whenever you want! I have NO plans to graduate my sons early. When they complete "12th grade" by age, we'll graduate. Until then, we will keep plugging along at whatever pace they need. My oldest will definitely be doing algebra before he has "hair under his arms". ;) I plan for calculus to be no earlier than 11th or 12th if possible. That means I'll be filling in with some AoPS courses. It shouldn't be too hard to do. I think AoPS will slow him down sufficiently (I'm going through the prealgebra book myself now, and once I got to chapter 2, it actually took ME time to do some of the lessons, and I know prealgebra :D).

 

Remember that there is always more to learn. Unless you just use a boxed curriculum (ie, A Beka grade X), you won't run out of material. There is plenty of math, literature, history, and science. :)

[KAR120C]

So I guess what I'm trying to say is, listen to your gut, follow your kid, and don't worry too much about what everyone else thinks is the right way to do it.

Absolutely. The only thing I'd add is that we need to recognize that there are real risks to making choices that don't fit the kid -- too fast or too slow. If I ever come across as stridently in favor of radical acceleration, I certainly don't mean that it's the right approach for everyone... only that I really bristle when faced with the "what's the harm in waiting" argument. For some kids there is harm in waiting. Real, serious, more-important-than-everything-else harm. It's why some of us will call radical acceleration a "least worst" option. There are certainly downsides too, but sometimes those downsides pale in comparison to the effects of not accelerating.

 

Whether that's true for your kid or not has to be something you figure out for yourself, and I have to trust that a mom who is even asking this question is paying attention and can make the call for her own child. But there is no "safe" choice that can be applied across the board.

[MissKNG]

I'm in the "follow your gut, follow your kid" camp...do what you think is right and don't worry about what others think. I'm sure there's a hundred things I do that would cause people's heads to shake on this board (gasp!)! You know your kiddo, not anyone else.

 

I have an aggressive learner as well, especially in math and science. I always have lots of materials, resources, books, etc. available. I have been letting her choose her science topics and that has worked out well. I do keep on the lookout for stuff that I think she would enjoy. Right now, I'm trying to get my hands on Horrible Science and Horrible Geography books.

 

After much trial and error, I found that my roll is her facilitator. I have stuff available and am there for guidance and some teaching. I am blessed that she is doing well on her own and she just turned six last week! It's a ride with these kids but it's soooo worth it when you just watch them thrive!

[EKS]

 

I was just reading somewhere (can't for the life of me remember where) that rather than dragging out elementary math for so many years then expecting kids to speed thru algebra, why not speed them through elementary math and then really wallow in algebra for a few years and enjoy it?

 

 

This is exactly what accelerating elementary math allowed my older son to do. He started algebra three years ahead in 5th grade and we did Algebra I over two years, so he finished two years ahead. Then we had a few false starts with geometry, while I mucked about finding a text that *I* could live with. During this time he also worked through Jacobs MHE on his own. He finally finished geometry in the first semester of 8th grade. Then we had another false start with Algebra II, which took us to the end of 8th grade and he finished Algebra II with the book we ended up going with by the end of 9th grade, making him only a year ahead. In 10th grade he did the first half of precalculus but then entered a school that teaches "integrated math." So he did their 10th grade math, which was sort of a combination of Algebra II and precalculus. Anyway, he'll graduate right on schedule. And we had the luxury of time to figure out which resources worked best for us. And FWIW, he took the ITBS/ITED every year he was home and scored at the 99th percentile on all of the math sections, so he never lost his arithmetic skills.

 

Another kid could use the time to explore all that cool stuff that AoPS has to offer, or dabble in computer science, or whatever. I honestly don't see why people want to drag out elementary math. Much better to drag out the upper level stuff.

[Crimson Wife]

There seems to be a great divide on this board, those who are in favor of radical acceleration, and those opposed.

 

I'm not actually opposed to radical acceleration. I don't believe there is a magical age where all kids are ready for algebra after and none prior. If you've got a student who zips through Singapore with the IP's, or MEP, or AOPS Pre-Algebra or other challenging curriculum and still gets to algebra by age 9 or 10, then more power to that kid.

 

I just think that it's far better to be only a bit accelerated in a challenging curriculum than radically accelerated with an easy one. It's like with weight-training. I could do a lot of reps with a really light weight or a few reps with a really heavy weight.

[beaners]

 

I just think that it's far better to be only a bit accelerated in a challenging curriculum than radically accelerated with an easy one. It's like with weight-training. I could do a lot of reps with a really light weight or a few reps with a really heavy weight.

 

But here's where that comparison is more appropriate than you realize. Lifting weights in different ways in useful for strengthening and conditioning different systems. As a distance runner in college, I wasn't doing the same workouts that the football players were. We were both in the weight room, lifting weights according to our own needs.

[poetic license]

I'm really benefitting from reading the experiences of those of you whose kids have completed elementary math, and reading about the different approaches to advancement: whether radical acceleration or going deeper into each grade's topics.

 

I realized that I have been locking myself into the linear, "school" mentality--recently, due to my husband's sparking interest in DS, he's been wanting to do decimals and DH has been doing some stuff with him in that regard. I was all like, "Nooo, how can you jump into decimals with him when he's barely finished grade 1 math?" and now I realize that I just need to relax and let him go where he needs to go. I've literally been dragging out 1st grade for almost the last 2 years because of my fear of "letting him" accelerate too fast. I think I need to step back a little bit and see where he takes me. :D

 

Also, it may be just me, but I bristle at the assertion that many people who accelerate or do Kumon or whatever are doing it to make their kid into some trophy kid. It's easy to judge what someone's doing by looking from the outside in, but I'd bet that a lot of these parents, rather than being pushy-pushy, are merely being dragged along by their eager kids.

[Iucounu]

My first recommendation whenever someone asks about their child flying through math is to find more challenging materials, and it's likely this is the best solution for most kids. However, absent other concerns, I don't see the point of slowing them down or making them do every problem or even every unit, or keeping them at grade level, just because. But simply finding a more challenging program isn't the best approach for all children, and until you've seen a child crying in frustration because because they crave more knowledge -- they want to see the point rather than just tackle another set of somewhat tricky problems -- that might be difficult to understand. There's just not that much in elementary math that it needs to be drawn out through six years of incremental problem sets (and Singapore is incremental from year to year) for very bright kids.

I agree. I think children should be challenged as much as they can handle; the appropriate balance of challenge to rote memorization and procedural drill-type work will vary for each student, and the drill should be carefully managed to take up as little time as possible while comfortably assuring proficiency, or one wastes the student's capacity for growth. I think this is one reason, among many, why public schools lag behind correctly conducted homeschooling: lack of efficiency due to decisions about student readiness made in the aggregate.

 

Since more talented students can learn the more fact- and procedure-based skills much more quickly, or even in passing while working on challenging problems, it frees up some time that can be devoted to extra challenge or extra conceptual progress. In my opinion one can provide plenty of challenge at any conceptual level; there's no shortage of problems, so no need to stay at a certain conceptual level just to do more challenge problems there. Thus some of the extra freed-up time can and should be devoted to learning new concepts; otherwise conceptual progress is artificially limited.

 

ETA: Part of my weariness regarding "broader rather than deeper" stems from experiences in the local public school, where it's been used as justification for some boneheaded decisions, such as suggestions that my son should do reports on the lives of famous mathematicians to "manage his pace" after he's completely mastered the material; and a math consultant, hired to bring our district out of Title I status, suggested that all students, advanced or not, should use any extra time to simply practice learning basic facts (such as practicing number bonds) more deeply before moving on to the next year's material.

 

As for early graduation, with math specifically, there's no shortage of math. It offers infinite depth. If someone wants their child to graduate at a normal age, but she's advanced in math, instead of proficiency at a normal level, one could shoot for mastery of tensor calculus or something.

Edited May 28, 2012 by Iucounu

[Iucounu]

:iagree::iagree::iagree:

Plus...challenging algebra word problems -- and computations -- are more fun for advanced youngsters than anything in cwp/ip. How fun is basic arithmetic? It is BORING. (eta: Boring compared to alg, IMHO.)

:iagree::iagree::iagree:

[Beth in SW WA]

I'm not actually opposed to radical acceleration. I don't believe there is a magical age where all kids are ready for algebra after and none prior. If you've got a student who zips through Singapore with the IP's, or MEP, or AOPS Pre-Algebra or other challenging curriculum and still gets to algebra by age 9 or 10, then more power to that kid.

 

I just think that it's far better to be only a bit accelerated in a challenging curriculum than radically accelerated with an easy one. It's like with weight-training. I could do a lot of reps with a really light weight or a few reps with a really heavy weight.

 

A sweet workout uses both methods. Light/fast, heavy/slow. On the same day or rotating throughout the week. Add some cardio and you're golden.

 

AoPS is wonderful for students who love the discovery method. Dd9 would not enjoy a full diet of that. Not now at this age. Plus, there are better options for her at this stage in the game. The hybrid approach is best for her with a combo of discovery & direct instruction taught by a fabulous teacher (of which I am not). I am able to flesh out what she is learning in her various resources. Dh & I go over her homework. We do math together often but at this point, I need a solid answer key handy. A complete solutions guide is ideal. Thankfully dh is extremely mathy and can help out when I fall short. I am keenly aware of my abilities (or lack thereof). Thank God I have so many fantastic options. I do my best w/ the DNA I am blessed with. I plan to learn through precal w/ Abi. This should be interesting. :tongue_smilie:

 

I digress...

 

This morning in her online session with Rachna, Abi 'discovered' the shortcut for multiplying certain binomials. Rachna directly instructed her in a way that got Abi's wheels turning. It is a thrill to watch.

 

Afterwards I asked Abi what she learned. She said, "Mom, Rachna said the little kid way is using FOIL for some problems. She wants me to use the grown up way like this: (she then got out a piece of paper and wrote this out)

 

(a + b)^2 = a^2 + 2ab + b^2

(a - b)^2 = a^2 – 2ab + b^2

(a - b)(a + b) = a^2 - b^2

I like it better. I'll show you. (2x - 5b)^2...."

 

Today I will have her build some problems with the MUS blocks and have her 'teach' me.

 

All this to say...She. Loves. It. All those neurons firing and it isn't even 9 AM on Memorial Day. Now they're both outside on the fort having a morning picnic and 'cuddle time' with the dog.

 

I can't emphasize enough how thrilled she is when she learns something new about algebra. Why in the world would I hold a kid back who digs special products or quadratics for the sake of 'mastering' more basic math? My only fear is that she surpasses me by age 10. I spend hours each week self-educating. It has become my passion. I'm so thankful I have the time and opportunity to do this. What a gift.

 

Pardon the ramblings. Happy Memorial Day. :)

Edited May 28, 2012 by Beth in SW WA
added link

[nmoira]

ETA: Part of my weariness regarding "broader rather than deeper" stems from experiences in the local public school, where it's been used as justification for some boneheaded decisions, such as suggestions that my son should do reports on the lives of famous mathematicians to "manage his pace" after he's completely mastered the material; and a math consultant, hired to bring our district out of Title I status, suggested that all students, advanced or not, should use any extra time to simply practice learning basic facts (such as practicing number bonds) more deeply before moving on to the next year's material.

I could have picked a better term, since we're really talking about branching out after moving on (from elementary math) not before.

[Iucounu]

I could have picked a better term, since we're really talking about branching out after moving on (from elementary math) not before.

Right. That was their term, and the "instead of" language is indicative of their whole mindset. It's a bit of a misnomer for the actual concept, though; it should be "broader instead of faster" or "deeper instead of faster", the way they talked about it, though of course doing reports on mathematicians' lives adds no depth whatsoever to math conceptual knowledge or ability. (And of course it's not bad to broaden one's focus per se-- one should just make sure that the "broadening" isn't shorthand for time-wasting filler material that has no real relevance to the subject.)