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

Tallulah I was just talking with the hubby over breakfast this morning about the discussion in that thread about the conservation of area. �The first Singapore math book has it right near the beginning and we're stuck on that page. �It said to place blocks in different patterns to see if the child recognizes equal amounts in different arrangements. �I threw down 2 sets of 5 blocks a week ago and my boy thought the spread out one had more. �Yesterday I threw down 6 pieces of cereal and he still thinks the scattered one's have more. �I said to the hubby that's why we go so slow, when he gets stuck I just ask him again later until he can answer right. �There's a reason they put that there so we shouldn't just skip it. �We'll go for several pages then get stuck again and it could be two weeks or two months before he answers right. �The hubby said, just tell him to count it because he's kind of right in a way. �The scattered one is more, it's more area. �I told him about the water experiment (it's not in the math book, but along the same lines) I know he wouldn't know it's the same if I poured 1/2 c water in a tall glass and 1/2 c water in a short glass because the tall glass would look bigger. �The hubby works in the oilfield and measures pressures and volumes for a living and knows too much about hot rod motors. �Practical daily math applications only. �He explained that the static pressure is more at the bottom of the smaller glass because the wider glass has room to spread out. �So, the hubby's no kind of math genuis but he makes a good point about math having so many applications the answer your looking for may change depending on what you want to use it for. �But you can't quote dh against Piaget and some math teachers and expect to win.

To each her own... But, I can only say for our family the idea that "they" put something in a book so the child should do it makes absolutely no sense. "They" don't know my child. "They" may have not been thinking of an asynchronous learner. "They" may have been assuming that the child would be working with a flexible teacher who would be able to adapt or let go assignments that don't make sense.

Forcing a child to march lock step through a curriculum produces a kid good at worksheets.

Thanks for pointing that out. We use what works until it's not useful anymore or we need something else. I'm never too attached to anything that I can't change my mind within 15 minutes. (cross-eyed emoticon:)
We have so many other things to learn and do I just set that book aside for awhile whenever he's stumped and we pick it up later.
Eta: he's just going through that book slower than some of our other stuff.

Yeah, that's good that you aren't too married to any curriculum. There really are these moments in child development when it is like a light switch. Yesterday they couldn't do it; today they can (or in gifted kid style... today it is too easy). It can be frustrating in the early homeschool years because so much is too easy or too hard... that "just right" category can be hard to find and when you do by tomorrow it is too easy!

La Texican, I would just skip the conservation stuff and have him learn what he is ready to learn. I don't think that conservation of area, as a concept, could possibly be a precursor to so many other math concepts that it can or should hold your son back.

From what I read before, it's just an indicator or milestone if you buy into the Piaget developmental levels-- and so a strict follower of Piaget would probably say that even a math supergenius is perfectly normal if he doesn't get conservation of area at a young age. Do you think someone with Einstein Syndrome would necessarily be able to answer correctly about conservation of area at your son's age?

FWIW I don't think my five year old would possibly have gotten such things right at three, which I ascribe largely to the fact that I hadn't started teaching him about math yet at all, so he knew only a bit of counting and simple math that he'd picked up in passing. I would bet that if you teach him about area and he does some more work with it, conservation will just dawn on him.

I agree with passthepotatoes about doing a curriculum in lockstep. As long as you hit everything he needs to know in time, and he understands fully what he learns, you're doing a great job if you just keep his learning time full of fun and productive.

My goal for my daughter is success in college and post-college. She wants to be a surgeon.

Learning should not always be "fun and productive" for our kids. They will grow up and will need to work according to a boring teacher. I teach in college and I really tire of seeing these kids fail.

They need to work problems that take time - many, many steps and respect the inabilities of some teachers. This is a really tough part of being gifted.

Not that I think they should be in classes they should not be in, but they must learn subjects that they don't care for.

My daughter is now in 8th grade and has never liked Social Studies - but she knows the subject. I teach students who know nothing about social studies. It is so hard to explain the feudal system 10 minutes before an exam.

La Texican - patterns are the most important part of math and you are right about that. Most of upper math is looking for the pattern based on many types of principles. I help college students with their math. If they cannot decipher a pattern, they really never get the entire solution - maybe they can just answer the homework. but the big picture - never.

So many gifted kids are procrastinators (if they ever turn their work). They have been taught to only work the interesting work and carry that idea through their lives. If this is their "rule", they cannot be successful in a job.

I generally believe that parents should make educational choices for their children. Most parents (in the US) believe that a child may choose to take the courses or clubs that the child chooses. A child - no matter how intelligent - does not have the overall picture. They get used to making their choices and are unbearable when they hit puberty and basically think that they should make their own decisions.

I don't agree with your logic, and I certainly don't think that if your idea were valid for some, that it would ever be valid to apply it to a three-year-old. One of your mistakes is assuming that a child can't learn to be thorough in the course of a fun lesson.

I liked this quote from one of the links on the inspiration thread, "Too often we give our children answers to remember rather than problems to solve." � Roger Lewin
But you do have to give enough answers to keep them going. �And you have to give them enough problems to keep them involved. �I want to help give him all the tools, but it's gotta come mostly from what's inside him. �I'll admit it's more like training than teaching. �I've only taught people how to do crafts because I love to do crafts. �I taught them what I know, then they went on to do their own thing with it. �
I think in the case of this workbook page I'll do like my husband suggested and tell ds to count the pieces so it's clear what I'm asking. �I also think I'll hand him a calculator in the grocery store because he wants to learn big numbers. �He wrote down 1000 and told me it was 10,000. �He's not that advanced to add them, but he knows you can add more than 2#'s together. �Boy, was he shocked when he saw me add up a few prices to make a catalog order. �("Mamma! �Equals", he tried to remind me, his eyes wide as he saw me writing in a third addend. �Lol)
I guess I'm trying to guide him from the edge of his proximal development. �I'm afraid if I tell him too many of the answers it will skew what that looks like. �So I give him something and if he doesn't get it we put it up for later. �(overthink things much?).
Maybe I'm gauging it from too close. �Maybe that's supposed to interpret from a broad range birds eye view. �Maybe that's what the teachers are doing; they're trying to expertly judge a child's edge of proximal development from the vantage point of a single subject and a single year. �They need to look from a more wholistic angle.

La Texican, I totally agree. For example, I was pretty upset when I found out that my wife had "helped" my son understand how to do a certain kind of problem (making the largest or smallest positive number using a collection of digits). I felt like she'd robbed him of the chance to figure it out on his own-- after that actually doing the problems is essentially make-work. I was quite despondent over something that probably seemed really trivial at the time!

I also won't let his grandmother do anything learning-wise with him when one of us is not around, because she has a strong tendency to "help" him, even when he doesn't ask for it.

With learning math and problem-solving skills, basically my main approach is to find something that's a little beyond his easy grasp, but which I think he can figure out on his own with a little intense focus. My hope is that this will result in lasting superb self-confidence in addition to increasing his general problem-solving skills, and so far it seems to be going that way.

I dunno what I'd do with the conservation / counting idea. It seems to me that telling him to count up the units is really giving him the answer. I think I would tend to just teach him (or learn him) how to do area, and wait for him to realize on his own that the little regions can all be added up, or something, leading to the general concept of conservation. I think it would happen naturally then, and he'd be allowed to discover it. I just know that after DS5 had learned a fair bit about area, conservation was a no-brainer.

Yeah. �You gotta let it go. �I try not to censor how ds interacts with other people in the world. �Glad you can't hear my brain screeching and grinding as I tell myself that sometimes (over religion).�As you know after they turn five you gotta let them go and trust them with their own mind around other people's questionable teachings. �That's why I just focus on the basic tools so he will hopefully be equipped to take charge of his own education despite all of our adult help. I don't know if this is the right thread to ask but you've mentioned how you teach your son logics and stuff and I'm interested in hearing more of your methods and resources.