Gifted Issues Discussion homepage Forums Parenting and Advocacy Math acceleration -- age & abstract thinking

I think there are levels of abstraction. In this case, the first level is, "Can he understand that x is a variable, and what that idea means?" A higher level of abstraction requires solving word problems in algebra, which often aren't straightforward in the way that other math problems are (BTW, I see this as a fault of lower-grade math curricula; there should be a few harder problems for the stronger students).

My then DS9 did a formal algebra class last year (more this year, plus geometry soon). I wouldn't say he struggles -- he worked harder last year, but also says his teacher this year is much better.

Second thing: I think your son's teacher has some flaws in her reasoning. Sure, the vast majority of nine-year-olds (or ten-year-olds, for that matter) can't handle that level of abstraction. But if your son is HG+, he isn't in the vast majority and she shouldn't judge him by the standards she uses for other kids.

If he skipped a grade and is doing well, he obviously has the mental function of the kids a year older than him (at least), so why is she suddenly worried that this isn't the case?

If he wants to do it, and you and your husband are also on board, I'd say let him try. He can always step back if he's miserable or over-challenged. You could even do some after school work with him to introduce him to concepts. I did this with my son starting when he was 8-ish.

Val

I would agree for algebra, geometry, statistics, logic, and probably other stuff we haven't tried, like calculus . I'm saving the Calculus for Young People books for a snow day this winter.

DD is 8 and finishing up 5th grade math supposedly in the next week or so. (She is in school, so I've heard she is most probably moving up in Nov, but don't know exactly what that means.)

I have seen a big jump with her computation speed and organization in the past 6 months. (This is more of a typical development area for her.) Last spring, she just couldn't do long division or multiple digit multiplication in any sort of timely or accurate fashion and we dropped it for a few months. This fall she's doing the same stuff, but also with decimals no problem. Not speed demon fast, but solid. So I do think there is something to the math and brain development thing, but not in the way I hear educators talk about it.

There are some Abstract Reasoning and Algebra readiness test out there - I know dd took some at school - but I don't know exactly what they are called.

I think this is Piaget raising his influential head again. There was a thread on here about his developmental theory, so I did some reading on it.

He claimed there are four stages of thinking,

Sensori-motor
(Birth-2 yrs)

Pre-operational
(2-7 years)


Concrete operational
(7-11 years) Recent research suggests that children in Western cultures tend to achieve conservation of number by age 7, conservation of mass and length by age 7 or 8, and conservation of area by age 8 or 9.

Formal operational
(11 years and up) Can think logically about abstract propositions and test hypotheses systemtically

And the last stage, formal operational is where they're supposed to be able to do entirely abstract things like calculus.

I found a couple of articles talking about precocious math children, and it seems that they might be as much as two years early with entering the concrete operational stage, they can get everything through to conservation of area within months (which puts them 3 or 4 years ahead). Then they spend years at that stage before the next switch to formal operational.

I haven't read up on that yet, but I think it's where the teacher's coming from, and I'm interested to hear if it's true or not. Is this the time to delve into other interesting math?

DD12 is doing geometry. She struggles with the logic parts of the proofs. She is getting an A so I think it is a good challenge. She did not have trouble with the abtract parts of algebra I. It has been a good experience for her to be accelerated and I would do it again. Her school used saxon math and they had tests that decided what levels the student was ready for. I think u can get some of those materials from ebay or other used books on line. sent from my very small phone....

I may be way off on this, but I think the schools (Not All) get the Algebra thing wrong. They give very little time in 1st through 7th grade in problem solving skills. Most of what they teach is operational in nature. So you take a gifted math student who has it easy (Mostly just follow the operations to get the answer). They cruse along with little to no effort. Then Algebra hits and they have to use effort, and try and solve a problem, and they hit a wall. They think I am not smart enough, or I am not good at math. When it was the schools who never taught them how to problem solve, or how to work on a problem and give effort towards a math problem or puzzle. I hear of this Algebra wall, and what I see it is self created by a short sighted belief in operation over computation. That�s my 2 cents it, and I've been paid well.

Cookiemom,

One more thought:

Have you read Developing Math Talent? It is a book that comes up on this site frequently. It might have some ideas for you.

Chrys

I don't agree with OP's teacher. Gifted kids are all over the place, and as the comments on this page show, not all gifted kids even walk the same path, let alone with NT kids. I would try to informally assess him at home and if the results are good, letting the teacher in on them to convince her. Collinsmum posted an excellent readiness test from the art of problem solving website. Her post, along with the readiness test website is here:

http://giftedissues.davidsongifted....ion_on_demonstrating_gift.html#Post87936


Here's our experience:
DS7 is much better at problem solving than at arithmatic. In his case, he needs practice and drill for arithmatic skills, but he hates it to the core. So that's why he finshed the entire Primary Grade Challenge book by Ed Zacarro last year when he was 6 - every question provides a different take (luckily he has zero problems with the basics, like multiplication tables). He started on EZ's Real World Algebra before the questions on percentages floored him (yes that's his bugbear too). I'm not a teacher so I never realized children could have problems with the abstract "X".

According to the Gifted Math Specialist from the Ministry, math should be lock step and he should work with number puzzles first. But my son has vision issues and (I now realize) can't see straight lines, so try telling him to do a Magic Square. Apparently, kids who are 6/7yo should not understand probablity, but my son loves!

What he finds challenging at this stage - Singapore Math word problems for Primary 5 and above, so we are leaving them off till he's more develpmentally ready. Instead, he seems to really love the Math Olympiad style questions because they are short, sharp, and usually bring some imagery to him. These are not algebra per se, but they are bursting with abstraction.

So I don't think all young kids are not developmentally ready for abstraction. It's finding the appropriate level to offer them that's the key. Your son's scores are terrific - beginning algebra may not require such a great leap at all for him.

Good luck!

I forgot to mention earlier, you might want to try the ALEKS online math curriculum (www.ALEKS.com) either at home or with the school. DS8 does ALEKS at school during his regular class' math time and in the 5th grade math class that he goes to. It is great because it checks to see what you know and then you just keep moving ahead--you can start anywhere from basic addition and subtraction to graduate level Calculus and stuff. It fills in the gaps as it goes, and when you demonstrate that you know something, it goes on. You can register at home for $20 a month, or if the school has an account or is willing to get one, it's only $40 for a whole year that way.

Thanks again to all for the helpful posts. I don't think we had considered all of our options before this. As a couple of people have pointed out, why worry now about next year? None of us think he'll have any trouble with this year. If it turns out he struggles next year for whatever reason, there are tons of options, including EPGY. We don't have any experience with ALEKS, but our older son did EPGY for a year and it sounds similar.

I can't imagine why we hadn't thought of some of this before. My husband and I talked and agreed we'd reopen the conversation with the teacher. We're pretty sure she'll go along if we feel strongly (she's proven that she really wants what's best for him). IF he makes the cut-off, that is. He has a few more weeks to go.

Thanks thanks thanks for the help.

Whew, yes, does that sound familiar. Add to this the fact that the gifted kids coast through computational math without studying at all, ever, and you end up with students who have no concept of "studying."

I struggled to get Bs in Algebra in school, and at the end of the year, I finally sat down and really studied for the first time the weekend before the final. I got the highest grade in the class on it (I was shocked).

I've noticed that the word problems in math books I've looked at over the years are generally quite trivial and straightforward. I struggled to find books for my kids that have problems requiring thought.

Val