Balancing math

[Dmmetler]

DD is spurting ahead in math, often spending 2-3 hours at a stretch working happily on Singapore Math with the goal of getting to "real" algebra (not "Pawn algebra", as she puts it) as soon as possible. Today, we started school at 9:00, and she was still happily working on math at 12:30, when math is always our first subject of the day. It's even, temporarily, eclipsing her precious grammar and Latin, usually her two favorite subjects and the ones where she can often spend hours. (Admittedly, she's towards the end of MCT Island and CL 1-so I think part of the slowdown is that she doesn't want to "run out"-I suppose I should break down and get the next books).

 

DH, who has advanced degrees in pure mathematics and did a lot of math competitions as a middle and high school student, has expressed concern that she's going too fast-that she can't possibly be getting enough practice to really cement the concepts and that she's going to struggle later because of it.

 

I tend to feel that it's better to let her go at her own speed, and to go back and fill in gaps when they're needed. (And I've been surprised by her retention in spurts in other subjects, when I was absolutely sure that there was NO WAY she could possibly remember everything she was cramming in her head so fast-only to discover that she was, indeed, learning it and retaining it). I've also noticed that she's picking up on the facts, which I was CONVINCED she'd never master, just through repetition. She probably still couldn't do the 100 multiplication facts out of order in 1 minute or whatever it is that Saxon math pushes for in 3rd grade (and that I remember having me in total tears in elementary school), but she is able to get them when she needs them, accurately, and more and more seem to be automatic each week. There's enough additive that I think she's filling in the gaps herself.

 

However, DH is the expert at math. It was always, for me, a means to an end-it was the subject that got me into the magnet track at my high school, where it meant that I was with kids who actually READ the books in literature class, the subject that got me a grant to pay for getting my masters and teaching certificate, instead of having to take out loans, the subject that got me hired to teach music in the school system because I could also tutor math, and so on. But it's never been something I had a passion for or enjoyed much. I'm more than willing to believe that I'm wrong on this.

 

So, any suggestions on balancing this?

[Beth in SW WA]

I'm not a math expert by any means. I can only imagine that your hubby surely knows what is best for your dd. My dh also wants to make sure dd isn't moving too fast. It does seem a bit odd to him that dd is doing problems like these below -- when it seems like just yesterday we were working on place value.

 

4) Complete a table and graph using the following domain: {-2, -1, 0, 1, 2}.

a) y = -x + 2

b) x + 5y = 4

c) 2x – 3y = 6

 

 

5) If g(x) = x2 – x + 1, find each value.

a) g(2)

b) g(-1)

c) g(1/2)

 

How wonderful that your dd has such bright minds teaching her. I enjoy reading about her. :)

[onaclairadeluna]

Well my DS is like this. I only interfere if I think he might not be getting enough practice in other subjects. If left on his own he'll do 3-4 hours of math in the morning and this is what he really loves. Sometimes I just insist he starts with writing because, you know, mathematicians need to be able to write too.

 

Anyhow I wouldn't worry about getting too far ahead too quickly. There really is a huge boatload of depth that they can pursue. DS has been through all of the AOPS intro books and has been working on his own through the elements of mathematics curriculum. Also spent a considerable time working on the mathpath qt this past month. There really is a ton of math between algebra and calculus. You just have to hunt it out.

 

Elementary math is only a little interesting so breezing through it is usually the right thing to do. As long as she understands what she is doing and she is happy she is right on track.

 

I think it would be possible to breeze through the math sequence too quickly but you don't have to. There are hundreds of interesting detours along the way.

 

Oh and another thing to remember is they slow down when the math gets hard enough. This is a great relief. You can actually keep a curriculum for a whole year (or so). It's awesome.

 

BTW I don't know why people worry about gaps and who gets to decide what a gap is anyway. At least I wouldn't worry about it with a GT kid. They are so far ahead of grade level that it really doesn't matter what their learning sequence is. At least that has been my experience.

[quark]

Anyhow I wouldn't worry about getting too far ahead too quickly. There really is a huge boatload of depth that they can pursue. DS has been through all of the AOPS intro books and has been working on his own through the elements of mathematics curriculum. Also spent a considerable time working on the mathpath qt this past month. There really is a ton of math between algebra and calculus. You just have to hunt it out.

 

Elementary math is only a little interesting so breezing through it is usually the right thing to do. As long as she understands what she is doing and she is happy she is right on track.

 

I think it would be possible to breeze through the math sequence too quickly but you don't have to. There are hundreds of interesting detours along the way.

 

Oh and another thing to remember is they slow down when the math gets hard enough. This is a great relief. You can actually keep a curriculum for a whole year (or so). It's awesome.

 

BTW I don't know why people worry about gaps and who gets to decide what a gap is anyway. At least I wouldn't worry about it with a GT kid. They are so far ahead of grade level that it really doesn't matter what their learning sequence is. At least that has been my experience.

 

:iagree: and all the bolded are true gems. Let her at it dmmetler! You'll know when she needs a break.

[serendipitous journey]

DD is spurting ahead in math, often spending 2-3 hours at a stretch working happily on Singapore Math with the goal of getting to "real" algebra (not "Pawn algebra", as she puts it) as soon as possible.

...

 

DH, who has advanced degrees in pure mathematics and did a lot of math competitions as a middle and high school student, has expressed concern that she's going too fast-that she can't possibly be getting enough practice to really cement the concepts and that she's going to struggle later because of it.

...

 

So, any suggestions on balancing this?

 

MEP. Situate her at the right level (at least in Year2, every fifth lesson is a review/wrap-up so that may be a way to skim through) and do the lessons. Should cheer your DH up with the deeper content, and it will definitely take a while to do the lessons. :) Even with a bright kid. ;)

[chepyl]

Is she doing IP and CWP? I work to slow my son down by doingthe more challenging work in the level we are in. You can get to algebra too early. If we had just done the wkbk and txtbk this year, we would now be in level 3, the CWP top more time and he loved it. He begs to do that book.

 

Slow amd steady is really the beat way with math. If she is flying through, then gets to algebra and slows way down, she may loose her desire to do math, maybe not. I would truly wonder how much she will recall long-term, moving so fast.

[serendipitous journey]

MEP. Situate her at the right level (at least in Year2, every fifth lesson is a review/wrap-up so that may be a way to skim through) and do the lessons. Should cheer your DH up with the deeper content, and it will definitely take a while to do the lessons. :) Even with a bright kid. ;)

 

(first time I've quoted _myself_ :D)

 

for clarity: I was thinking MEP as a supplement, not as a program switch.

 

ETA: I should've just edited the first post .... zheesh, a crazy little boy & not enough sleep are not a good combo!

[Iucounu]

Your husband may be laboring under some misconceptions. He could be the most advanced mathematician in the world, but still be wrong in some respects about the right way to teach math to a gifted younger child. The book "Developing Math Talent" might be helpful, for thinking through strategies that you and your husband would both find useful in teaching your daughter, and thinking through the issues.

 

Perhaps your husband would feel better if he realized that your daughter is actually spending much more time on math than most children. In any event it's really not the time spent, or the age at which a concept is encountered, etc. that matters in terms of readiness; it's mastery of the prerequisite material. Whenever your daughter demonstrates that, no matter how long or short a period it took to develop that (in terms of biological age or hours spent in practice) is irrelevant. Many math-talented children have learned math quickly at young ages, and elementary math is particularly subject to learning at a pace that may outright terrify some people.

 

You still do need to provide a strong foundation for a gifted child, but you shouldn't have any worries about that, from what I understand of your situation. Slowing her down artificially to match an incorrect idea of what she should be ready for is the opposite of the correct approach. Math-gifted children can learn math at a faster pace than non-gifted children-- in fact, a much faster learning pace is a distinguishing hallmark for highly gifted children.

 

You're right that it is better to let your daughter go at her own pace, instead of artificially limiting her progress. As long as she's getting enough practice to demonstrate mastery of the concepts, enough practice in developing problem-solving skills along with the skills development, etc., she should be fine. It's all about mastery.

 

I personally wouldn't intentionally leave conceptual holes by skipping sections in something like Singapore Math, just because I think it's a decent arrangement made in part with an eye not to leaving them. However, I also wouldn't be afraid of leaving any as long as all the material in the SM scope and sequence is shown to have been mastered, by for instance pretesting out.

 

It seems to often be the case that young advanced math students don't master math facts as quickly as they may want to move forward (and may be ready to move forward) conceptually. This may be directly due to boredom with drill-and-kill math facts practice, to which many gifted children are prone. Functionally, I think of it as a bit similar to lagging behind grade peers in handwriting fluency. I agree with you that she practices her basic math facts every time she works a problem, and this seems to be enough for her. If nothing else, whatever lack of fluency she shows with math facts will only tend to slow her down a bit when working problems, which should help to assuage fears about her fast pace. A slight lack of fluency with facts doesn't translate to a worrisome conceptual gap.

[beaners]

Can you throw together a couple pages of mixed review at all kinds of levels? (Or is there a Singapore book for that?)

 

I wonder if he's worried about retention of material a few years from now. I know I've completely spaced on material that I knew at the time but haven't seen or done in a while. (I needed to spend a night sitting down with my unit circle from trig when I got to calculus and hadn't seen it for a few years.) Would he feel better about her moving through the material so quickly now if she occasionally did a few problems on the topic so it stayed somewhat fresh in her mind?

[La Condessa]

If she has demonstrated an ability to retain information learned at that speed in the past, my inclination would be to let her run with it. My youngest brother is a very unique learner--you could probably call him 2E--but he can do five problems to learn a concept and then never revisit it, and he will know it perfectly for the rest of his life. Some kids' brains just work that way.

[Beth in SW WA]

You can get to algebra too early.

 

Slow amd steady is really the beat way with math.

 

I respectfully disagree with both of these statements....based on experience.

[serendipitous journey]

He has a valid concern.

 

 

:iagree:

 

It sounds like the child has been moving well through one program, and quickly. She will be Just Fine, no doubt, but I think we are discussing how to help her excel. It seems to me we'd like her to both truly cement her understanding and to maintain pleasure in the subject.

 

There are lots of options here. I like adding a supplemental program b/c it is not too complicated for the parent to do and it will both introduce some new ways of thinking AND consolidate her current knowledge, by having her apply it to problems of a slightly different sort. I suggested MEP because the content is free and it is low-cost to implement; and it teaches excellent math thinking skills. My own DH uses sophisticated math in his profession, and is very very happy to see Button using MEP. DH actually thinks we could dump our MathUSee with no ill effects but I disagree :D.

 

You could also work through the livingmath.net program/books with her.

 

You could start her on early programming & programming problems, depending on her keyboarding skills &c and her enjoyment of this.

 

You could work through the Zaccaro books.

 

-- off to try to Educate somebody! good luck!

[go_go_gadget]

I've read about MM being great for accelerating, and it doesn't sound like your daughter needs to be accelerated, because she accelerates herself. Since she's going to move at a quick pace no matter what you do, you have the option to cover topics and angles outside of the usual scope and sequence of an elementary math program. I'm working on a math degree myself, and this is the approach I'm taking with my children. My son is six and left to his own devices would fly right through SM 3 and 4 within the next year, but I'm deliberately bringing in a variety of curricula that ask different kinds of questions and force him to really play with his math, rather than tearing through it. We play with logic, sets, and I adapt my own college textbooks when there's a problem that would be good for him. I consider it similar to the recommendation by the AoPS curriculum to take three courses in discrete math, even though they're not included in the typical middle/high school math sequence, because they're still valuable. No matter what we do, he's still going to be ready for pre-algebra at eight or nine, and I'm very glad we have the luxury to build the strongest foundation possible for that. Try some Martin Gardner, teach her drafting (it makes geometry and integral calculus *much* easier), teacher her the formals definitions of concepts she already knows (odd/even, for instance), and work on some basic symbolic logic, or discuss a little easy recursion (then fill it out with an Escher study). There are so many topics, even the "extra" time we're fortunate enough to have isn't enough to cover everything possible.

 

If your daughter balks at taking "detours" on her road to algebra, explain that algebra isn't the be-all, end-all of math and that discoveries in math don't usually happen while people are racing along as quickly as they can. We just watched the NOVA documentary on the proof of Fermat's Last Theorem, and it really illustrated for my kids the fact that mathematics requires an enormous skill base, one that can't be acquired with a "How quickly can I can to the next level?" attitude.

[Iucounu]

OP already does Life of Fred, Hand on Equations, and extra logic problems. There is a point at which it becomes obvious that extra work at the same conceptual level essentially just slows down a fast-paced learner. One can always find plenty of problem-solving practice at a child's appropriate conceptual instructional level.

 

I agree that a certain amount of problem solving development in key conceptual areas can be helpful in solidifying a knowledge base. Still, there are some concepts (especially in elementary math) that just don't need solidifying this way, and can't be mastered past 100%.

[Roadrunner]

I say let her move at her pace. If you are concerned above "fact mastery", just do mental math on a daily basis.

I have two boys both racing through math. My five year old did 62 pages in SM 1b several days ago only because I told him he was too young to start 1b. He proved me wrong and managed to make only 2 mistakes. I decided to let him continue. One thing he is required to do is one practice set of mental math from SM HIG to make sure we keep practicing "facts."

I don't see a reason why you should slow down. She will eventually hit the wall (or not :001_smile:). I did 180 turn on my thinking just over the last couple of days on this. What's the harm? If you start seeing holes, you go back. You can identify the gaps by periodically testing. If there are any challenging word problems she can't tackle due to maturity, write them down and go back to it at a later time.

Also, you can sign up for xtramath online (free) to provide fact practice.

[Beth in SW WA]

I agree that a certain amount of problem solving development in key conceptual areas can be helpful in solidifying a knowledge base. Still, there are some concepts (especially in elementary math) that just don't need solidifying this way, and can't be mastered past 100%.

 

:iagree:

Re-packaging basic math in a pretty bow and calling it 'challenge math' is still basic math. CWPs and the like get old quickly for some students (speaking from experience). If a kid wants to do algebra at age 7...let her.

[Crimson Wife]

Is she doing IP and CWP? I work to slow my son down by doingthe more challenging work in the level we are in. You can get to algebra too early. If we had just done the wkbk and txtbk this year, we would now be in level 3, the CWP top more time and he loved it. He begs to do that book.

 

:iagree::iagree::iagree:

 

Going "deeper" is much preferable to going "faster" in math.

 

However, you may eventually get to a point where you will pretty much have to accelerate. I wound up hitting this with my DD after finishing Singapore 5A. Even doing the IP's and CWP's, there wasn't enough challenge to satisfy her.

[acurtis75]

:iagree:

Re-packaging basic math in a pretty bow and calling it 'challenge math' is still basic math. CWPs and the like get old quickly for some students (speaking from experience). If a kid wants to do algebra at age 7...let her.

 

 

I tend to agree with this. As far as gaps are concerned as long as you are using at least one spine program (in your case Singapore) and working the levels one after another you should be fine. Our daughters seem to be similar and I'm finding she actually retains more if I let her go faster. She was just bored when we were going slower. There are periodic reviews in almostvall math curriculums. Even so called mastery programs still have some systematic review. We use MUS but i'm sure Singapore is similar. We are working on fractions but the test for the week always has a few questions about thins we learned a book or two ago. Plus, if you are supplementing, especially with word problems, you are using the skills you already learned. We do cwp and I let dd move as fast as she wants. She actually likes the problems and wants to keep going so we do. I have no doubt that she could handle hands on equations and/or a pre-algebra program but we just haven't gone there yet because we are already tackling a lot of subjects.

 

 

Eta: because the school system is set up in such a way that is counter productive for self paced learning I think having a phd in math wouldn't necessarily translate to an understanding about how a good motivated student should move through material. I think it is the mathusee founder who talks about how all the math taught in k-12 could be learned by a motivated student in a month or two if the concepts are presented when the student is ready.

Edited February 7, 2012 by acurtis75@yahoo.com

[Dmmetler]

OP already does Life of Fred, Hand on Equations, and extra logic problems. There is a point at which it becomes obvious that extra work at the same conceptual level essentially just slows down a fast-paced learner. One can always find plenty of problem-solving practice at a child's appropriate conceptual instructional level.

 

I agree that a certain amount of problem solving development in key conceptual areas can be helpful in solidifying a knowledge base. Still, there are some concepts (especially in elementary math) that just don't need solidifying this way, and can't be mastered past 100%.

 

 

I should also add-we use the IP mostly instead of the workbook, and the harder CWP problems, and we have a LOT of extra math resources, including challenge math, Sunshine math, various MEP and CSMP printouts (although I like MEP more than DD did-she hates the visual presentation of it). She's doing a lot of applications of math, all the time. What she's not doing is any significant number of plain problems that are simply "sitting on the page being boring" (to quote DD). And often, she's slower on a plain computation problem that's very straightforward than one that seems more convoluted, where she's often 3/4 of the way done before I'm done parsing it and figuring out what exactly it's asking.

 

I will admit, it bothers me that she has to stop and THINK to remember a basic fact (and even more so when she can, say, multiply 3 1/2 x 2 1/4 faster than 30x20) because it seems like it's automatic, but it really does seem like once she knows a concept, she's got it-even if she "got it" through a LOF chapter that spent the entire time talking about how Fred burned up a pizza.

[go_go_gadget]

If you have all that going on, it sounds like you're fine. Where does your husband worry the gaps are forming? Is it just a general worry, or is he worried about specific areas? Is it just because she's going so quickly, or because she can't recite the facts? I myself took a long time to memorize facts, and my DD is similar so far but she thinks more like a mathematician than my son does. I'm sure I've read on these boards about students that didn't have their facts memorized until algebra forced them to. I don't necessarily think that's ideal, but it isn't necessarily a huge problem, either.

[jennynd]

I will ask why your hubby concern about accelerate your dd.

 

my DS is on a similar path and I decided to slow him down. unlike your dd, we only get 3 hours each week instead 3 hr a day in math (we are afterschooler) so we have plenty material to work on. We did not skip any grade since 5th. and work with text/workbook and IP. I am also a bit worry to burn out my ds down bacuase it is afterschool, although he almost never bring homework home anymore, so I guess I feel justified.

 

Anyhow, it seems like all the concern I have to my son not apply to your dd.

i do a little interested on what you said she did 20x30 slower than fraction multiplication, beacuse 20x30 is not just multiplication factor but it is also place value, but it is small enough problem.

 

I use key to algebra for ds now and we are 2/3 way through. he started just when he started SM 5A. Although it is no way that it is our algebra program but more like a warm up. I like the fact it makes him self teaching and easy enough to get them hooked on algebra. after that, we will do NEM.

pm me if you want to use key to algebra ..

 

He is also 7 yo

[ebunny]

I should also add-we use the IP mostly instead of the workbook, and the harder CWP problems, and we have a LOT of extra math resources, including challenge math, Sunshine math, various MEP and CSMP printouts (although I like MEP more than DD did-she hates the visual presentation of it). She's doing a lot of applications of math, all the time. What she's not doing is any significant number of plain problems that are simply "sitting on the page being boring" (to quote DD). And often, she's slower on a plain computation problem that's very straightforward than one that seems more convoluted, where she's often 3/4 of the way done before I'm done parsing it and figuring out what exactly it's asking.

 

I will admit, it bothers me that she has to stop and THINK to remember a basic fact (and even more so when she can, say, multiply 3 1/2 x 2 1/4 faster than 30x20) because it seems like it's automatic, but it really does seem like once she knows a concept, she's got it-even if she "got it" through a LOF chapter that spent the entire time talking about how Fred burned up a pizza.

 

I will just say that the learning pattern vastly differs at home v/s school. It is because she is homeschooled, she has the luxury to go at her own pace and indulge in working at something for 2-3 hours at a stretch.

 

I think most motivated children follow a similar pattern. I don't know if drowning in information will necessary cause gaps. I haven't seen any in my DD (as yet). Weekly assessments are a good way to find and fill gaps.

 

I do know where your husband is coming from though..if he's mainstream educated, like me, there would be a certain level of worry watching a child absorb a years worth of math in the matter of a few weeks. But I've made my peace with it. I get out of DD's way when she is in a similar phase. Even if she retains half of what she works on, it's still a lot. :001_smile:

[Dmmetler]

I think what he's most worried about is that she'll get down the road and have the situation Heigh Ho mentioned-the "Oh, I know how to do that...now how do I do it?" because she didn't really get the strategy in long-term memory.

 

And I also suspect part of it is just the amazement at seeing a child jumping so fast. In many ways, I think it's easier for me because I'm tending to compare DD to other advanced kids. She's really about at a level that seems pretty typical for kids who test as she does who are homeschooled. If anything, she's a little BEHIND many PG kids her age in math. DH doesn't have that point of comparison.

 

My thought is this-if, down the road, she realizes she needs more time on X, it's not like we don't have time. She's 7. She has all the time she needs. It's perfectly OK to take a detour at some point in the future.

[ebunny]

I think what he's most worried about is that she'll get down the road and have the situation Heigh Ho mentioned-the "Oh, I know how to do that...now how do I do it?" because she didn't really get the strategy in long-term memory.

 

And I also suspect part of it is just the amazement at seeing a child jumping so fast. In many ways, I think it's easier for me because I'm tending to compare DD to other advanced kids. She's really about at a level that seems pretty typical for kids who test as she does who are homeschooled. If anything, she's a little BEHIND many PG kids her age in math. DH doesn't have that point of comparison.

 

My thought is this-if, down the road, she realizes she needs more time on X, it's not like we don't have time. She's 7. She has all the time she needs. It's perfectly OK to take a detour at some point in the future.

 

 

:iagree:

[acurtis75]

 

My thought is this-if, down the road, she realizes she needs more time on X, it's not like we don't have time. She's 7. She has all the time she needs. It's perfectly OK to take a detour at some point in the future.

 

:iagree: that is my position with dd as well. Also, she plays math bingo on the iPad which gives her basic practice on those boring math facts.

[Crimson Wife]

I think what he's most worried about is that she'll get down the road and have the situation Heigh Ho mentioned-the "Oh, I know how to do that...now how do I do it?" because she didn't really get the strategy in long-term memory.

 

And I also suspect part of it is just the amazement at seeing a child jumping so fast. In many ways, I think it's easier for me because I'm tending to compare DD to other advanced kids. She's really about at a level that seems pretty typical for kids who test as she does who are homeschooled. If anything, she's a little BEHIND many PG kids her age in math. DH doesn't have that point of comparison.

 

The bolded is exactly why I go "deeper" rather than "faster" in math. I see no point in rushing through arithmetic at a very superficial level for what- to have bragging rights that my 6 y.o. is doing "4th grade" math? :rolleyes: My goal is to build a rock-solid foundation for higher-level math work, and I frankly don't care that going "deep" rather than fast puts my children "behind" other HG+ kids. It's not a race where the child who starts algebra the earliest gets some big trophy :rolleyes::rolleyes:

[Iucounu]

It's not about racing; it's about not holding someone back who's mastered material. As an example, take a child who has learned all the math facts in a particular area, as well as the concepts, and is very good at problem solving. There's likely to be no way to go "deeper" on elementary arithmetic; the only thing to do is to go on.

 

Take another child who knows concepts cold, has practiced them plenty enough to get them into long-term memory, but whose memorization of math facts may be behind because the child finds it boring. This is true of many highly gifted children. Lower calculation fluency does not equal a shaky math foundation either-- and practice with basic math facts will often occur enough to cement them when doing higher-level problems.

 

You have to look at math as involving different though complementary strands and skills, as someone else has pointed out in this thread IIRC. Calculation will ideally be fast enough so that the student doesn't have to focus on it when thinking about higher-level math, but calculation fluency will and can develop at a different speed from thorough conceptual mastery.

 

How about someone with dyscalculia or some other issue with calculation, fluency or otherwise-- can they never go on to higher math because they haven't "mastered" arithmetic?

 

A faster pace doesn't necessarily indicate a shaky math foundation, although it could if a teacher were intentionally glossing over important material. Highly gifted children very often show a much faster learning pace than average; it's not due to skimming, it's due to actually learning much faster. On a discussion board for parents of gifted children, I don't see much value in wagging a finger at parents whose children may be ready to learn, and master content, much faster than normal.

 

Or, in other words:

 

gifted ≠ superficial

actual fast learning pace ≠ bragging about it

faster learning pace ≠ threat to other children or parents

Edited February 8, 2012 by Iucounu

[jennynd]

The bolded is exactly why I go "deeper" rather than "faster" in math. I see no point in rushing through arithmetic at a very superficial level for what- to have bragging rights that my 6 y.o. is doing "4th grade" math? :rolleyes: My goal is to build a rock-solid foundation for higher-level math work, and I frankly don't care that going "deep" rather than fast puts my children "behind" other HG+ kids. It's not a race where the child who starts algebra the earliest gets some big trophy :rolleyes::rolleyes:

 

 

I agree and disagree

 

I agree go deeper but not when they are grade 1-4. I personally can not imaging to have my kid work on his "age" grade level. and you can only go so far with the 4 operations whole numbers.

 

However, I fully agree that 5+, now you adding decimal/fraction/percent/proportion/ratio all that in the mix. You really can't run out the questions to do. We see countless time on this board that a Mom asking how to solving a question without using algebra. To be honest, in many instance, I think some of the question SM put out is much tougher than algebra question when u considering no algebra can be used. That makes kids think math rather than solve a equation. I myself think it is super fun thinking through those question without using algebra.

 

I agree that there is no point rush into "real" algebra. But a "easy and soft" introduction like "Key to" or "TT" is good compromise if you have a kid begging to move up a grade.

 

And the last, I do FULLY agree that it is not a race. It is your kids' future and you know your kid the best. There is no reason to compare kids because each of them are so different

Edited February 8, 2012 by jennynd

[quark]

The parent with a child who has finished "real" algebra younger than age 10, rarely has the opportunity to brag even if she wants to. When a child is really working at this level of math fluency, math understanding and intense math adoration, believe you me, it's very lonely. The younger the child, the more lonely. Because there is such a small population of parents in any homeschooling or parenting list who can relate to working with such a child.

 

I was once in the "move on only when you master it" camp. But that's not how some children learn. What is mastery? >95% in a singapore placement test? >90% in an AoPS-based test? Or 100% in another test out there that has lower standards than AoPS or some other respected program? Mastery is so subjective. Does mastery ever end? Do we ever reach a perfect level that cannot be improved upon even more?

 

And algebra is not some "way out there" abstract math. It's not as complicated as many people think. A complete program has a significant amount of built-in review of prealgebra concepts. And it doesn't stop there. Math is a fluid subject. When a child has a chance to move on, she will encounter other math that will make her grasp of earlier math more meaningful.

 

A child working on division, needs to see what's coming up in say, fractions to better appreciate division. A child who is working on algebra, needs to know why she needs it, what will happen in geometry, are the two related and so on. There must be some meaning to the math other than just daily review and regurgitation of concepts she's already quite familiar with.

 

Maybe I'm babbling here. And perhaps I won't ramble about math on these boards much anymore LOL but I really want to say, please trust your child. If it worries you to move on, use another program on the side for a little practice of concepts you think she sorely needs (3-5 daily problems are usually good enough) but don't force a child to remain at "your level of comfort" if she's really excited to move on. Once you lose her excitement, you are going to be working so much harder to bring it back.

 

This isn't to address anyone in particular. Trying to add the voice of a "reformed" mom to the discussion.

Edited February 8, 2012 by quark

[Crimson Wife]

Someone who goes through Singapore only doing the textbook and not the IP's I think *IS* giving their child a more superficial math education than someone who goes more slowly by doing the IP's. My DS was working in the 1A IP book today and I was really impressed by the problem-solving skills it helps develop. Sure, I *COULD* skip the IP books like some people who set themselves up as know-it-alls about GATE do :rolleyes:, but that doesn't serve my long term educational goals for him.

[Beth in SW WA]

When a child has a chance to move on, she will encounter other math that will make her grasp of earlier math more meaningful.

 

 

Amen!

Dd was working on some alg problems today which included basic arithmetic operations. It is much more interesting/meaningful/fun when you can actually do something slightly creative algebraically with fractions, decimals, etc. It comes alive at that point.

 

I know I'm preaching to the choir. Just had to chime in again since this topic is front & center in my world currently.

 

As to the notion of 'bragging rights'....It is all relative. We should boast in the fact that we have found the sweet spot between challenge and exasperation. If you find the sweet spot, brag away! I'm :bigear:.

[Tattarrattat]

The parent with a child who has finished "real" algebra younger than age 10, rarely has the opportunity to brag even if she wants to. When a child is really working at this level of math fluency, math understanding and intense math adoration, believe you me, it's very lonely. The younger the child, the more lonely. Because there is such a small population of parents in any homeschooling or parenting list who can relate to working with such a child.

 

Maybe I'm babbling here. And perhaps I won't ramble about math on these boards much anymore LOL but I really want to say, please trust your child.

 

:iagree: quark, just want to say I appreciate your insights on parenting your child and really enjoy reading your posts!

[Roadrunner]

Someone who goes through Singapore only doing the textbook and not the IP's I think *IS* giving their child a more superficial math education than someone who goes more slowly by doing the IP's. My DS was working in the 1A IP book today and I was really impressed by the problem-solving skills it helps develop. Sure, I *COULD* skip the IP books like some people who set themselves up as know-it-alls about GATE do :rolleyes:, but that doesn't serve my long term educational goals for him.

 

I agree here. I think without IP and CWP SM isn't a whole program. Workbooks are too simple. My kids are prohibited from moving on to another level until the corresponding level of IP and CWP is completed. My little one that moved on to 1B completed 1A IP (minus some challenge problems which he will be working through in the summer when he is closer to 6 if he wants to move on to 2A).

So yes, I agree. But I won't hold them back just because of age anymore.

[Iucounu]

Someone who goes through Singapore only doing the textbook and not the IP's I think *IS* giving their child a more superficial math education than someone who goes more slowly by doing the IP's. My DS was working in the 1A IP book today and I was really impressed by the problem-solving skills it helps develop. Sure, I *COULD* skip the IP books like some people who set themselves up as know-it-alls about GATE do :rolleyes:, but that doesn't serve my long term educational goals for him.

I'm sorry you feel the need to personally attack me, and that you apparently feel threatened in some way by my child's progress. That's the balance all of us parents have to strike, I guess-- say too much, and you can offend someone; but you have to be honest in order to discuss some things.

 

I've never claimed that faster progress always translates to mastery, and I've never compared my child to someone else's here. He is what he is. Many of the problems in the IP / CWP books are not challenging for him. I find that selected problems from MEP tend to be plenty challenging most of the time, and I have other sources for problem-solving practice.

 

My son's an excellent problem solver; that's actually his strongest area. He scores at the 99th percentile multiple years ahead on MAP tests even after his grade skip, and was young for his age before the skip; the closest student in his top math group for his grade, where some of the kids are two years older, pulls to between 30 and 40 points away from my son's MAP score, according to his teacher. This is with on-again, off-again afterschooling for my son. He just picks things up quickly. It's not his fault, and it's not my fault for truly discussing it.

 

What would you do, for instance, with a polymath like John von Neumann? Make him plod through every IP section to achieve "mastery" of arithmetic he'd mastered nearly instantaneously upon learning of the concept?

 

My son is bored to tears by drill and other work that he considers to be fluff. I choose not to bore him. FWIW, he's quite fast on calculation, so I could easily have him do plenty of extra problems from the same-leveled IP book. It just doesn't lead to more mastery, and the up-level IP books tend to rely on notation and concepts he may not have encountered yet. I have picked a few of the more challenging IP problems-- they just tend to not be necessary with the other enrichment I also do.

 

There's no need to feel threatened by anything anyone says here. There's also no need to misrepresent me as claiming to be a GATE expert, just because I am knowledgeable on the subject and can point someone in the direction of accepted info. :chillpill: It's just a fact of life that many HG+ children thirst for knowledge and go at a very fast pace by nature when they're engaged. Don't shoot the messenger.

 

ETA: I recommend the book "Developing Math Talent", and also reading up on acceleration, perhaps starting with A Nation Deceived. It's never wrong to go at an appropriate pace for a particular child. For some, that's just faster than for others. Acceleration can lead to extremely positive academic and emotional results. This applies also to the study of math.

Edited February 8, 2012 by Iucounu

[quark]

It's just a fact of life that many HG+ children thirst for knowledge and go at a very fast pace by nature when they're engaged. Don't shoot the messenger.

 

ETA: I recommend the book "Developing Math Talent", and also reading up on acceleration, perhaps starting with A Nation Deceived. It's never wrong to go at an appropriate pace for a particular child. For some, that's just faster than for others. Acceleration can lead to extremely positive academic and emotional results. This applies also to the study of math.

 

Exactly! Well said.

 

Addressing the whole deeper vs faster issues brought up in this thread to anyone who is interested:

 

If you keep going deeper and deeper without moving on and your child remains in an academically and emotionally positive state, then good for you! Obviously, acceleration is not the answer for your child.

 

To add to Iocounu's

gifted ≠ superficial

actual fast learning pace ≠ bragging about it

faster learning pace ≠ threat to other children or parents

faster is not always equal to shallow or superficial

deeper is not always equal to slower pace

 

I think some of the confusion is due to how some kids are PG level in more than one area. If you take a kid who is strong in both math and critical reading for example, who "gets" things immediately due to very high processing speed, you just can't keep that kid looping on and on without moving further. You'll HAVE to challenge that kid or risk a sort of break down in spirit (if you've been there you'll know what I'm talking about). If he's already showing you he needs to go further and you keep putting walls in his way saying no, you have to climb this first and then there's another and another wall and only then will I open the following door...wow, you cannot imagine how frustrating it is for a kid until you've seen it for yourself.

 

Moving on to a higher level does not mean you are giving up lower levels. The lower levels will be practiced again and again whenever there are problems to solve, esp. problems that need more creative thinking.

 

Also as the OP said, when dealing with younger kids, it's not as though you don't have the time. Since it's not a race, why worry about where you start, where to jump to and to which level to jump back to?

 

As to the notion of 'bragging rights'....It is all relative. We should boast in the fact that we have found the sweet spot between challenge and exasperation. If you find the sweet spot, brag away! I'm :bigear:.

 

Beth, I'm starting to see so much maturity now in my child. He seems to have finally hit his sweet spot. It's so wonderful to see him work so hard and take responsibility over his learning. Sure, he gets frustrated. Yes, we have those "it's SO hard, I'm not good enough" teary, perfectionism moments. But an hour or day or week later, he's risen to the challenge somehow. It's so humbling to see this happening before my eyes. I'm so grateful to be able to homeschool this boy.

[Runningmom80]

Thank you for this thread! My ds isn't nearly as advanced in math as others here, but even he is bored of number bonds below 10. He keeps asking to learn how to add big numbers and asking about multiplication. I feel more confident jumping around. I kind of felt liked needed to follow a straight line with math. We do cwp, and ip but he is over it.

[onaclairadeluna]

:grouphug:

 

We are all just trying to figure it out for our kids.

 

I'd like to chime in as another one who "raced ahead to algebra" even skipping CWP and it was the most awesomist thing I did.

 

Not to say that CWP and IP is not a great thing for kids to do. I'll probably make DD do them before going on to AOPS. (or maybe not depends on how great beast academy turns out to be)

 

Actually I didn't do algebra first. We started first with Inro to Probability and Counting. My son went from being pretty good at math and liking it ok to it being his reason for waking up in the morning and his life's quest. He would talk to his math book he was so happy. It was the cutest thing in the world and a sure sign that it was a good fit.

 

Every kid is different. Some will need the extra practice and repetition. Also different kids have a different sequence for what they need to learn. My son had to figure out arithmetic by using Algebra. It was kind of the other way around from most kids. People with kids like this are NOT the norm. But we do exist. So yes of course you have to be the own judge of what kind of kid you actually have.

 

There are many great ways to learn math. It's not necessarily better to do it all backwards and turned around the way my son did. But it was better for him. That's all that really matters.

[jenbrdsly]

Just to add my two cents... My philosophy at the moment is to choose and complete an entire math program so my kids don't "miss anything", but to start it early enough with them that they are appropriately paced. Houghton Mifflin Math Expressions is what my DS6 is using at school. While it's not my favorite, it is comprehensive. Then we supplement with other things like LOF, HOE, Right Start etc.

My own experience with math, even in a very good GATE program, was the old, "put her in the corner and let her work by herself" methodology. This worked very well for some of my classmates, but not for me. I vividly remember being in 10th grade and missing a question on a test because I did not know the difference between horizontal and vertical. So now of course, I'm a bit paranoid and don't want the same thing to happen to my own kids.