what is the "sign" that a kid is ready for Algebra

[jennynd]

There are a lot discussion on Algebra need maturity and other stuff.

What will you define what is "required" to be successful in Algebra

DS is almost done with Key to Algebra. He seem understand the concept. He certainly can do the problems and found the question are very easy without much my instruction. He start to write his steps done neatly after few instance that he tried to skip step and loss track on numbers. Do you think he is ready for "formal" algebra program like AOPS?

He has done SM through 6B with IP/CWP. He actually think SM IP/CWP is more difficult than Key to algebra. Which I kinda agree with him. He enjoy Geometry very very much, so the other thinking I have is to do Geometry first...

 

Any thought?

[regentrude]

What will you define what is "required" to be successful in Algebra

 

Prerequisite for algebra is a thorough mastery of arithmetic (addition, subtraction, multiplication, division) with positive and negative integers, fractions (including decimals and percent), plus some basic knowledge about exponents, laws of exponents, etc. The above should be mastered without calculator.

[abbeyej]

If he can do the word problems in CWP/IP6 and the equations in Key to Algebra, he's more than ready for algebra 1. :)

[fractalgal]

There are a lot discussion on Algebra need maturity and other stuff.

What will you define what is "required" to be successful in Algebra

DS is almost done with Key to Algebra. He seem understand the concept. He certainly can do the problems and found the question are very easy without much my instruction. He start to write his steps done neatly after few instance that he tried to skip step and loss track on numbers. Do you think he is ready for "formal" algebra program like AOPS?

He has done SM through 6B with IP/CWP. He actually think SM IP/CWP is more difficult than Key to algebra. Which I kinda agree with him. He enjoy Geometry very very much, so the other thinking I have is to do Geometry first...

 

Any thought?

 

How old is he? There are other books that are available from AoPS that are challenging but more at a Pre-Algebra level, and perhaps going through those would give him more time to mature.

 

If you think he is ready, then you could start AoPS Algebra slowly. If he has completed the IP and CWP through 6B he will be used to solving multi-step math problems.

 

The*'d problems in AoPS Algebra do require a certain amount of maturity, because they may take him more time and be more complex than he is used to. It is helpful to have patience and determination so as to not give up when he may feel discouraged.

 

You know him best. If you attempt it, but he feels too much frustration, it may be best to wait a year.

 

You could also email the author of the AoPS books. I did so when I had questions about placement for my daughter. He was very helpful.

 

Good luck.:)

[SuperDad]

Prerequisite for algebra is a thorough mastery of arithmetic (addition, subtraction, multiplication, division) with positive and negative integers, fractions (including decimals and percent), plus some basic knowledge about exponents, laws of exponents, etc. The above should be mastered without calculator.

 

If he can do the word problems in CWP/IP6 and the equations in Key to Algebra, he's more than ready for algebra 1.

 

:iagree: with both of the above.

 

Not that age is a huge player in algebra readiness, but it would be nice to know how old your ds is. Are you trying to "put off" algebra? If so, there are a number of excellent resources I could recommend. Is your ds mathy/do you see him pursuing math to calculus and beyond? Are you already set on which algebra text you'll use if you do decide to go ahead with starting algebra?

[lakotajm]

I'm not sure I would include needing to understand and be proficient in negative integers and exponents. But the rest, yes. It depends on if you are going to start with Algebra 1 or pre-algebra. A basic understanding and some exposure to those problems would suffice for pre-algebra. But definitely needs to be proficient with the four major operations and decimals, fractions and percents.

[wapiti]

Here is a handy list of "prealgebra" skills to have mastered before starting Alg 1: http://cty.jhu.edu/sebin/a/y/prealg.pdf

 

There are also pre- and post-tests for the AOPS prealgebra and algebra books.

[jennynd]

I read from another thread that because Algebra require certain logic thinking and it only happen when a kid reach certain age. And rush into it will make a kid hate math or become a skilled question solving technician rather than mathematician.

 

I do not want to rush the kid to Algebra and fail and go back. I want him ready and when he start it, he can fully enjoy it. But the same time I don't want to keep having him working decimal/fractions.

[jennynd]

How old is he? There are other books that are available from AoPS that are challenging but more at a Pre-Algebra level, and perhaps going through those would give him more time to mature.

 

)

 

What are those book you refereeing to??

[fractalgal]

What are those book you refereeing to??

 

 

This page is helpful:

 

http://www.artofproblemsolving.com/Store/curriculum.php?mode=recommendations

 

Also if you look in the section for grades 4-6:

 

http://www.artofproblemsolving.com/Store/age.php?age=elementary

 

This is also from the website:

 

Start with Prealgebra. After this, you will be ready to continue with Introduction to Algebra.

 

After Prealgebra

 

 

Start with Introduction to Algebra. After the first 11 chapters of Introduction to Algebra, you will be ready for both Introduction to Counting & Probability and Introduction to Number Theory, as well.

 

Your son sounds highly advanced to me, so perhaps the above path would also work.

[regentrude]

I read from another thread that because Algebra require certain logic thinking and it only happen when a kid reach certain age. And rush into it will make a kid hate math or become a skilled question solving technician rather than mathematician.

 

I do not want to rush the kid to Algebra and fail and go back. I want him ready and when he start it, he can fully enjoy it. But the same time I don't want to keep having him working decimal/fractions.

 

Why don't you just start with algebra and see how it goes?

 

I find the compartmentalizing of math that is done in the US completely and utterly stupid. In my home country, math is simply "math". Easy algebra concepts are introduced earlier (linear equs are taught in 7th grade), harder algebra concepts are introduced later (quadratics in 9th grade). In between, students work some geometry (triangles, proofs and congruency in 6th grade). This way, the student can still advance in math without waiting to be "ready" for the hard concepts and being bored to death by three years of fraction worksheets while waiting for the maturity to come.

[jennynd]

Are you trying to "put off" algebra? If so, there are a number of excellent resources I could recommend. Is your ds mathy/do you see him pursuing math to calculus and beyond? Are you already set on which algebra text you'll use if you do decide to go ahead with starting algebra?

 

I do have AOPS-algebra, and thinking chalkdust also . The plan was using NEM1 supplement with AOPS-algebra and we did start with NEM1. And mostly seem review at this point from NEM1, and based on how he did with Key to algebra. I was thinking have him using AOPS algebra solely but the comment from another thread make me rethinking maybe I should put him off for another year. I do see him does calculus and beyond and I have no problem teaching him.

[jennynd]

Why don't you just start with algebra and see how it goes?

 

I find the compartmentalizing of math that is done in the US completely and utterly stupid. In my home country, math is simply "math". Easy algebra concepts are introduced earlier (linear equs are taught in 7th grade), harder algebra concepts are introduced later (quadratics in 9th grade). In between, students work some geometry (triangles, proofs and congruency in 6th grade). This way, the student can still advance in math without waiting to be "ready" for the hard concepts and being bored to death by three years of fraction worksheets while waiting for the maturity to come.

maybe I can break the algebra in half also... does first half and jump to geometry for second half year....

[Cosmos]

I read from another thread that because Algebra require certain logic thinking and it only happen when a kid reach certain age. And rush into it will make a kid hate math or become a skilled question solving technician rather than mathematician.

 

I do not want to rush the kid to Algebra and fail and go back. I want him ready and when he start it, he can fully enjoy it. But the same time I don't want to keep having him working decimal/fractions.

 

I think that's a problem more in an institutional setting. A child with questionable readiness who enters an Algebra I class in a school must go forward at the pace of the class. A later decision to back up in math would mean changing classes and the possible embarrassment and sense of failure to accompany that. A decision to stay in an unsuitable class could mean falling further behind and poor grades.

 

If you are homeschooling, you can work on the material at his pace. You can take the time to revisit topics of difficulty or take a break when necessary. You will be working with him every day and will know if he's getting it or not. Stepping back to review or taking a break or adjusting the pace are all options you have as a homeschooler that a public school program does not.

 

I don't think that algebra is particularly special in this regard, only that as in most of mathematics the topics build on previous ones. So getting behind can have a snowball effect quite quickly.

[Cosmos]

maybe I can break the algebra in half also... does first half and jump to geometry for second half year....

 

NEM follows this pattern. NEM 1 is beginning algebra concepts in the first half and geometry in the second half. NEM 2 continues with more advanced algebra in the first half and geometry in the second.

[quark]

I do have AOPS-algebra, and thinking chalkdust also . The plan was using NEM1 supplement with AOPS-algebra and we did start with NEM1. And mostly seem review at this point from NEM1, and based on how he did with Key to algebra. I was thinking have him using AOPS algebra solely but the comment from another thread make me rethinking maybe I should put him off for another year. I do see him does calculus and beyond and I have no problem teaching him.

 

I believe my son would have found AOPS Algebra frustrating after Key To Algebra (which he used at 7yo). He completed about half of Key To Algebra (along with other prerequisites of arithmetic others have mentioned) and found it much too easy. We moved on to the Dolciani text instead and it was at the suitable level: easy enough conceptually (with the exception of a few challenging chapters) but more challenging than Key To and not as difficult as AOPS.

 

He also developed the ability to show his work gradually over several months, graduating from showing steps for only a handful of problems a week to all his problems about 1/4-1/3 way through the program. I personally don't believe it is required to show all your problems but that ability cemented my conviction that he was more than ready for it.

 

In my experience, if you have a very interested, high-ability student younger than 8 or 9, showing work is probably the most challenging aspect of starting algebra early. Everything else falls into place as long as they are not overly frustrated. Motivation is key.

 

We are doing the same for Geometry. He tried a few of the Key To Geometry books, found them too easy and is now thriving on Jurgensen's Geometry. AOPS Geometry is hard.

 

But you know your child best. And these books are just tools to see what whets their appetite and keeps them engaged and challenged.

[jennynd]

I believe my son would have found AOPS Algebra frustrating after Key To Algebra (which he used at 7yo). He completed about half of Key To Algebra (along with other prerequisites of arithmetic others have mentioned) and found it much too easy. .

 

So... AOPS Algebra will still too hard but typical Algebra might work...Sound like U went through what we are going through now,, Key to algebra is not enough to prepare a kid to work AOPS Algebra independently. Do you might I asking what you used for elementary series?

Edited April 7, 2012 by jennynd

[jennynd]

NEM follows this pattern. NEM 1 is beginning algebra concepts in the first half and geometry in the second half. NEM 2 continues with more advanced algebra in the first half and geometry in the second.

 

 

I get the feeling first part NEM1 is PreA and first part NEM2 is Algebra??

[Laura Corin]

According to the writer of Life of Fred: hairy armpits.

 

Laura

[Cosmos]

I get the feeling first part NEM1 is PreA and first part NEM2 is Algebra??

 

Could be. I'm not very familiar with those distinctions. NEM 1 covers linear equations, NEM 2 covers quadratics. The Singapore math website has samples and topics covered if you need more detail.

[jennynd]

According to the writer of Life of Fred: hairy armpits.

 

Laura

 

:confused:

[regentrude]

According to the writer of Life of Fred: hairy armpits.

 

 

Yes. I have heard this one, too. By the time my DD develops hair armpits she will be finished with calculus, LOL.

But then there is also the myth that losing teeth is a sign for reading readiness...

[regentrude]

I do have AOPS-algebra, and thinking chalkdust also . The plan was using NEM1 supplement with AOPS-algebra and we did start with NEM1. And mostly seem review at this point from NEM1, and based on how he did with Key to algebra. I was thinking have him using AOPS algebra solely but the comment from another thread make me rethinking maybe I should put him off for another year. I do see him does calculus and beyond and I have no problem teaching him.

 

Maybe I missed it: how old is your child?

My son did just fine with AoPS Intro to Algebra in 6th grade - for the first 12 chapters, then we took a break and did some discrete math. (DD did the whole book in 7th)

[quark]

So... AOPS Algebra will still too hard but typical Algebra might work...Sound like U went through what we are going through now,, Key to algebra is not enough to prepare a kid to work AOPS Algebra independently. Do you might I asking what you used for elementary series?

 

My observation about AoPS is from reading lots of messages about the program on various forums. It seems that with the high ability kids, 5th-6th grade (chronological age) seems to be the norm for Intro to Alg although I do know a couple of kids who are already completing Intro to Geometry (a harder course) by then (and they have completed most of Intro to Alg too). So again, it really depends on the kid. Mine seems to prefer the Dolciani and Jurgensen books and just picks the occasional challenging problem from Intro to Alg and Intro to Geometry. I love what Cosmos says about how you can customize it when you are homeschooling. So true and easy to forget.

 

We used almost everything there is out there for elementary (except Saxon). Just picking and choosing according to interest and not finishing anything from cover to cover. Worked best for him.

[jennynd]

Maybe I missed it: how old is your child?

My son did just fine with AoPS Intro to Algebra in 6th grade - for the first 12 chapters, then we took a break and did some discrete math. (DD did the whole book in 7th)

 

I will like to keep Ds's age of of the picture but just focus on the mental readiness. i supposed... I think first 12 chapter might be doable..

[chepyl]

I will like to keep Ds's age of of the picture but just focus on the mental readiness. i supposed... I think first 12 chapter might be doable..

 

 

We are unable to evaluate his mental readiness, knowing his age and what he has successfully completed helps to evaluate without meeting him.

 

I would say, if he has mastered pre-algebra concepts from some of the links provided, and can pass a placement test into algebra he is probably ready for the material. However, what is his attention span like. I know that some of the CWP problems take a while to do, we are currently using level 2 and they take a few steps; but Algebra and Geometry problems can take a lot longer. I remember two page proofs from Geometry. Can he handle problems that take longer? You may have to move a lot slower if his focus is not there.

 

Try it, but if he spends 15 minutes solving each problem I would assign a few problems a day and let it take more than a year to complete a book.

[jennynd]

a placement test into algebra he is probably ready for the material. .

 

AOPS's algebra placement test is unfortunately very very misleading. DS past that last year about the same time. and there is NOWAY he can do the book 1 year ago.

[wapiti]

AOPS's algebra placement test is unfortunately very very misleading.

 

I agree. Can he do the prealgebra post-test? IIRC, it's slightly more difficult/more comprehensive (and, check out the post-tests for Prealg 1 and 2 - Prealg 2's post-test contains a bunch of geometry that's not on the book post-test)

 

The prealgebra book - even just doing the chapter reviews - may make a nice transition to the algebra book if you really don't want to start the alg book yet.

[abbeyej]

Yes. I have heard this one, too. By the time my DD develops hair armpits she will be finished with calculus, LOL.

But then there is also the myth that losing teeth is a sign for reading readiness...

 

These sorts of things make me crazy. I happen to have kids who are slow to develop physically, but quick to develop academically. And, obviously, there are perfectly normal kids who develop the other way around.

 

*headshake*

[chepyl]

These sorts of things make me crazy. I happen to have kids who are slow to develop physically, but quick to develop academically. And, obviously, there are perfectly normal kids who develop the other way around.

 

*headshake*

 

My son is almost 7 and finally has loose teeth (3 or 4 of them - he is going to have the biggest hole in the front of his mouth:D), but he has been reading fluently for nearly 2 years....I do find the hairly armpit comment very funny even though it is not a solid rule. If it came from the author of LofF, I think it may be a joke. He has an odd sense of humor (one that my son totally gets!)

[Candid]

I get the feeling first part NEM1 is PreA and first part NEM2 is Algebra??

 

At some point long in the distance past on an old long gone forum Jenny at Singapore Math posted a rough sequence for the NEM books. The forum and post are long gone, but I captured it. Here's what she said:

 

Pre-algebra: PM 6 and NEM 1, Ch. 1-4

Algebra I: NEM 1, Ch. 5-8; NEM 2, Ch. 1-7, 12-14

Geometry: NEM 1, Ch. 9-14, NEM 2, Ch. 8-11

Algebra II: NEM 3, Ch. 1-6, 14; some of NEM 4

Advanced Math/Trig: NEM 3: ch. 7-13, NEM 4, ch. 1-4 (precalculus)

[Candid]

I read from another thread that because Algebra require certain logic thinking and it only happen when a kid reach certain age. And rush into it will make a kid hate math or become a skilled question solving technician rather than mathematician.

 

I do not want to rush the kid to Algebra and fail and go back. I want him ready and when he start it, he can fully enjoy it. But the same time I don't want to keep having him working decimal/fractions.

 

I think this is somewhat incorrect. As noted in another post it has something to do with a school setting where all children must move up at the same time together, and quite the reverse can be true too: a child who is ready for algebra but has to twiddle his thumbs with easier material will possibly tune out of math class.

 

I also have a question about the technician and mathematician part. Many, maybe most, folks who are very skilled in math are technicians. True mathematics has a huge helping of creativity which is not, I suspect, suppressed by being rushed ahead into math. For more on this see:

http://www.maa.org/devlin/LockhartsLament.pdf

 

A mathematician, like a painter or poet, is a maker

of patterns. If his patterns are more permanent than

theirs, it is because they are made with ideas.

 

Those who have become adept at it

derive a great deal of self-esteem from their success. The last thing they want to hear is that

math is really about raw creativity and aesthetic sensitivity. Many a graduate student has come

to grief when they discover, after a decade of being told they were “good at math,†that in fact

they have no real mathematical talent and are just very good at following directions. Math is not

about following directions, it’s about making new directions.

 

While this second paragraph may seem like what you've been told, I doubt the problem is rushing children ahead. But read the article to find out more.

[quark]

I read from another thread that because Algebra require certain logic thinking and it only happen when a kid reach certain age. And rush into it will make a kid hate math or become a skilled question solving technician rather than mathematician.

 

I do not want to rush the kid to Algebra and fail and go back. I want him ready and when he start it, he can fully enjoy it. But the same time I don't want to keep having him working decimal/fractions.

 

I agree with Candid. And also with regentrude about compartmentalization of math here in the US. I was so disgusted with the pre-algebra materials available that we completely skipped a formal program in it (we used LoF Fractions and Decimals/ Percents over 2 summers instead).

 

I suppose it also depends on what one means by "mathematician". Math professor? Math researcher? Both? Number theorist in your spare time with some other primary career? To my son, mathematician (his current career aspiration) means observing and finding relationships in numbers, proving theorems for the fun of it, and reading about and surrounding his life with math in its many forms which includes artistic and musical pursuits. Hence, the curriculum (including the "it" curriculum of the moment like AoPS) is simply a means to discovering as much as he can. He couldn't care less where he is in his math progression as long as it feeds his thirst for challenge and fun. It's not about finishing a curriculum or textbook but using the best parts of it to help him move on to the next step in his journey. And if that means going back to pre-algebra at some point, hey, even going back to spend months practicing addition and subtraction just for the fun of it because it will lead to some other mind-blowing bunny trail, why not?

 

I don't know if that makes sense. But that's where we are. I of course don't know how realistic his aspirations are. He will need to earn enough to feed himself at some point.

 

The world needs skilled technicians. The world needs mathematicians. I just don't think there's any need to doubt yourself too much about what to use to get there based on what others say, as long as your standards are high enough to use good quality materials and strew them regularly so your child has sufficient variety. Enjoy the journey. Don't be afraid to take leaps and risks. And don't be afraid to try, and try again!

[besroma]

:lurk5:

[Laura Corin]

:confused:

 

... that readiness for algebra is a developmental stage linked to the physical and mental changes associated with puberty.

 

FWIW I was a late developer who had taken GCSE maths (containing lots of algebra) before I had started my periods.

 

Laura

[abbeyej]

... that readiness for algebra is a developmental stage linked to the physical and mental changes associated with puberty.

 

Right. ... And it may be that *generally* speaking, across populations, puberty and algebra readiness happen around roughly the same time.

 

When it comes to *individuals* though? I think it's total nonsense.

 

I know children whose physical maturation far outstrips their academic and abstract thinking ability (look at the 5th graders in almost any school and you will see a few who have bodies that are very nearly adult) -- and kids whose bodies lag years behind their mental development. Ds did honors algebra starting just before he turned 10yo. He has continued on through honors geometry and honors algebra 2 at a standard pace with solid A's and good understanding of the material. It seems to come to him more easily than most of his classmates (who are 1-4 years older). Physically, he will likely mature at the later end of average... I'm simply trying to show that physical maturation and an ability to think logically and use abstract reasoning are *not* linked on an *individual* basis. (While my daughter will not do algebra as young as ds -- she does not have his intuitive grasp of the subject or his desire to excel -- her physical development is significantly delayed compared to her peers, so she will likely also complete algebra well before puberty.)

[SuperDad]

Right, but it would still be helpful to know the child's age.

 

Oh, wait. I just stumbled across this thread:

 

DS is 8.

Posted by jennynd.

 

Is this the ds we are discussing?

[abbeyej]

Even if the child is 8, I would have no particular qualms about starting a high school algebra course with a child who had completed Singapore 6 including CWP and IP and the Key to Algebra series (which covers exponents, negatives, and other advanced arithmetic topics not covered in Singapore). An ability to work the CWP and IP word problems demonstrates a good grasp of abstract reasoning, while the arithmetic covered in Singapore 6 and Key to Algebra is more than adequate preparation for a standard algebra course.

 

That said, it's certainly possible to delay a bit by using AoPS. Actually, because ds has finished alg1, geometry, and alg 2 at a young age, I've decided to stop and do a year of "discrete math" topics (mostly using AoPS) before heading into pre-calc. I have no doubt that he *could* do pre-calc and be completely successful, but I also don't see a *reason* to push through and finish AP calculus with years of high school to spare. We'll be starting the the Number Theory and Counting and Probability books.

 

Math Olympiad is another great supplement for elementary students who have completed the standard arithmetic topics. There are a huge variety of interesting and challenging problems that can be solved in creative ways without algebra. Many of the same topics that are covered in AoPS are touched on in the MO practice problems.

 

But don't be *AFRAID* to let an academically advanced child continue to work ahead. The nice thing is that they have lots of time. You can start a high school algebra course and they can do great. If not, you can set it aside and do something else. Nothing bad will happen. :) Although, again, I doubt that will be an issue for a kid who can handle the complexity of CWP and IP 6.

[SuperDad]

Even if the child is 8, I would have no particular qualms about starting a high school algebra course with a child who had completed Singapore 6 including CWP and IP and the Key to Algebra series (which covers exponents, negatives, and other advanced arithmetic topics not covered in Singapore). An ability to work the CWP and IP word problems demonstrates a good grasp of abstract reasoning, while the arithmetic covered in Singapore 6 and Key to Algebra is more than adequate preparation for a standard algebra course.

 

That said, it's certainly possible to delay a bit by using AoPS. Actually, because ds has finished alg1, geometry, and alg 2 at a young age, I've decided to stop and do a year of "discrete math" topics (mostly using AoPS) before heading into pre-calc. I have no doubt that he *could* do pre-calc and be completely successful, but I also don't see a *reason* to push through and finish AP calculus with years of high school to spare. We'll be starting the the Number Theory and Counting and Probability books.

 

Math Olympiad is another great supplement for elementary students who have completed the standard arithmetic topics. There are a huge variety of interesting and challenging problems that can be solved in creative ways without algebra. Many of the same topics that are covered in AoPS are touched on in the MO practice problems.

 

But don't be *AFRAID* to let an academically advanced child continue to work ahead. The nice thing is that they have lots of time. You can start a high school algebra course and they can do great. If not, you can set it aside and do something else. Nothing bad will happen. :001_smile: Although, again, I doubt that will be an issue for a kid who can handle the complexity of CWP and IP 6.

:iagree:

[Sebastian (a lady)]

I will like to keep Ds's age of of the picture but just focus on the mental readiness. i supposed... I think first 12 chapter might be doable..

 

FWIW, the Intro to Algebra book includes more than just the material for a standard Algebra 1 course.

 

If you compare the table of contents to the topics for the AoPS online classes, I think that Algebra 1 covers up through chapter 13. The Algebra 2 class is still in the Intro to Algebra book. The Intermediate Algebra book is used for the Algebra 3 class.

 

My plan for Algebra 1 is to get through chapter 13. And I think that is a pretty full year too.

[jennynd]

Thank you all for the advise and encouragement. I think I have a pretty good idea what I gonna do for next school year. You girls are the best !!!;)

[NittanyJen]

But don't be *AFRAID* to let an academically advanced child continue to work ahead. The nice thing is that they have lots of time. You can start a high school algebra course and they can do great. If not, you can set it aside and do something else. Nothing bad will happen. :) Although, again, I doubt that will be an issue for a kid who can handle the complexity of CWP and IP 6.

 

I would agree with that statement as well. The beauty of homeschooling is individualizing instruction for our kids. It's nice to remember what outside factors might be at work if things head south.

 

As far as a PP goes, I would agree the world needs technicians as well as real mathematicians. It's just sad when a person gets mixed up and thinks he is one but is really the other due to unnecessarily accelerated instruction (I am NOT saying this is the case with your son; I do not know you or your son) or other factors. My husband and I have seen this at all levels of kids and young adults from grade school up through grad school students who didn't make the cut 2 years into a PhD program in math, when they learned the difference between really understanding and being really good at the plug-n-chug.

 

I have argued multiple times on this board that it is a huge mistake to hold a child back for artificial reasons such as age (and my earlier post in the other thread should be read in that context; it is SO very difficult to 'interpret' someone's entire philosophy and meaning based on one message board post, now isn't it?? :) ) but yes, it can definitely be true that algebra can be a logic stage skill. If your son is ready for logic stage work in mathematics at age 8, then great, go for it! If it doesn't work, just remember it does NOT mean he isn't a mathematician; it just means he may need another year to be ready and there is lots of other math that can be done in the meantime that he will enjoy and still find challenging.

 

And no, that idea has zero to do with being based in a classroom. Different kids develop differently, even at home :).