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Joined: Jun 2010
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Interesting thread and articles. Without being an expert or assigning any special significance to it (because I see so much evidence that precociousness does not always or perhaps even generally equate to maximum potential), I would say that my five-year-old has been in the Formal Operational stage, to the extent that these classifications are valid, since at least age four and a half and perhaps significantly earlier. Then again, I have exposed him to a wide range of material not, shall we say, in the mode of "Blue's Clues" and "The Wiggles". Thus in our case "training effects", whatever those are, may have confounded the results as mentioned in passing in the article.
The thing that was actually the most interesting to me from the articles I read was the idea that the Formal Operational stage may not be reached by some children. I think that all children of at least fairly normal physical development could be fairly easily taught Formal Operational thinking, and at a younger age than 11 or even 7. I suspect that the difference between Concrete and Formal Operational stages has much more to do with training than the differences between the earlier stages do.
Last edited by Iucounu; 10/04/10 05:17 AM.
Striving to increase my rate of flow, and fight forum gloopiness. 
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Under Sensorimotor: Object permanence is the awareness that an object continues to exist even when it is not in view. This was our first clue that DD was advanced within Piaget's stages. She had severe separation anxiety when she was 3-4 months old. Her Dr. freaked out and said that she was very very early for this phase. Most babies don't exhibit this until at least 8 months. Under concrete: Categorical labels such as "number" or "animal" are now available to the child. DD understood this way before age 2. She understood animals were different and could categorize them from an early age. And numbers beyond rote counting was right before age 2. I don't exactly remember when but when it came to classification of breeds within the dog category such as the example in the article ... she just seemed to understand. Dogs were not just dogs but clearly different. She was under age 3 when she figured that out. Piaget determined that children in the concrete operational stage were fairly good at the use of inductive logic. Inductive logic involves going from a specific experience to a general principle. On the other hand, children at this age have difficulty using deductive logic, which involves using a general principle to determine the outcome of a specific event. I joke that logic is DD's middle name. She has no problem deducing either. As for Formal Operational Stage, I think she is showing signs of this but I wouldn't say she is fully into this stage. Back when I didn't really see her advancing with noticeable work, such as jumping into multiplication or really reading beyond her starting phase ... I did see the conceptional side advancing quickly. She is very much about imagination and could always play for long periods entertaining herself with whatever scene she had created in the moment, but during this period of no real academic growth her thought process advanced like crazy. She has always had advanced speech but during this period her ability to really communicate and asked relevant questions to the topic of the moment showed her abstract thinking.
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Tex, I love the story of your DS and his giant. I don't know what to say, with respect to resizing, though. Are you saying your DS is tinkering with the concept of conservatism? Are you familiar with that classic test with the glasses of water? Never heard of it. And google's letting me down on this one. Are you describing empathy in your daughter? Empathy is understanding someone else's perspective. I have a friend who is so empathetic that she finds it hard to argue because she see's the other perspective too easily. She's a Libra, go figur. I wish the whole world had a little more empathy Tbh.
Youth lives by personality, age lives by calculation. -- Aristotle on a calendar
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Oh yeah, scanning the piaget's overview I saw "recognizing an object's permanence" in the first stage, but I didn't see anywhere that said "all items and situations are for a limited time only." Like if I ask you do you want to see a movie I mean now, not next week. Or, you should try to eat your cereal pretty soon after you add the milk.
Youth lives by personality, age lives by calculation. -- Aristotle on a calendar
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Lucouno, unfortunately, my sister married a man who we are convinced does not have formal operations. Not a good thing.  KatelynsM_om, I hadn't thought of it in terms of object permanence, but DD had extreme separation anxiety, too, from day 3. She also quieted to my voice, beginning day 3, that was our first day home. Amazing that your DD is in formal operations, although I'm not totally surprised.  Back when I didn't really see her advancing with noticeable work, such as jumping into multiplication or really reading beyond her starting phase ... I did see the conceptional side advancing quickly. She is very much about imagination and could always play for long periods entertaining herself with whatever scene she had created in the moment, but during this period of no real academic growth her thought process advanced like crazy. She has always had advanced speech but during this period her ability to really communicate and asked relevant questions to the topic of the moment showed her abstract thinking. Talk to me... we are here. This seems like a argument for play. DH and I are counselors and DH used play therapy with puppets for part of his graduate work, so we are big into vignettes and role play with supervised play. My gosh, we do it every day. My current role, however, is glorified referee. Every time I try to have some meaningful time with DD 3.5, DS 14 months - who took his first step at 7 months, has been walking since 8 months and is now climbing up onto the kitchen table, going out the cat door, and running around the house - tries to join the fun. Just call me Mama Mediation. I have read how extremely important sibling relationships are with respect to adult abilities to get along with others, so this is taking the lion's share of my energy these days. Tex, empathy? Yes, DD is an empathetic being. But I think empathy is different than loss of egocentricity.
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Tex, I love the story of your DS and his giant. I don't know what to say, with respect to resizing, though. Are you saying your DS is tinkering with the concept of conservatism? Are you familiar with that classic test with the glasses of water? Never heard of it. And google's letting me down on this one. It's simple. You take two glasses, one squat, one tall and thin. You half fill one with water, then pour it into the other glass and ask them if there's more or less. From what I just read they shouldn't be able to say it's the same until age 7? Can that be right? That must be why this sort of thing is my DD's favorite ATM, it must be very new to her to understand it. I'm interested to test her with the conservation of area tomorrow. Hopefully she fails. (ETA: I'm relieved, she failed)(ETA#2: now she passes. Oh hell) By six or seven, most children develop the ability to conserve number, length, and liquid volume. Conservation refers to the idea that a quantity remains the same despite changes in appearance. If you show a child four marbles in a row, then spread them out, the preoperational child will focus on the spread, and tend to believe that there are now more marbles than before.
Or if you have two five inch sticks laid parallel to each other, then move one of them a little, she may believe that the moved stick is now longer than the other.
The concrete operations child, on the other hand, will know that there are still four marbles, and that the stick doesn�t change length even though it now extends beyond the other. And he will know that you have to look at more than just the height of the milk in the glass: If you pour the mild from the short, fat glass into the tall, skinny glass, he will tell you that there is the same amount of milk as before, despite the dramatic increase in mild-level!
By seven or eight years old, children develop conservation of substance: If I take a ball of clay and roll it into a long thin rod, or even split it into ten little pieces, the child knows that there is still the same amount of clay. And he will know that, if you rolled it all back into a single ball, it would look quite the same as it did -- a feature known as reversibility.
By nine or ten, the last of the conservation tests is mastered: conservation of area. If you take four one-inch square pieces of felt, and lay them on a six-by-six cloth together in the center, the child who conserves will know that they take up just as much room as the same squares spread out in the corners, or, for that matter, anywhere at all. This discussion is really fascinating, and ties into something I was thinking about a few weeks ago. Until you have these developmental stages, you can't do certain types of math. Like area is usually fourth grade, because it's kind of pointless to teach if they think it's fluid.
Last edited by Tallulah; 10/05/10 05:00 PM.
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That link clarified it nicely, thanks Tallulah. Ds is definitely egocentric. I would have thought he wasn't since he can read upside down or sideways, and he seems to understand family relationships (although he could be parroting what he's heard). But sometimes when he's on the phone he'll hold the phone up to a drawing he's working on to "show" his grandma, and he expects they can see it.
Youth lives by personality, age lives by calculation. -- Aristotle on a calendar
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Yesterday DS5 was doing some area-related math learning. I remembered this thread, and tested him on knowledge of conservation of area, and he passed the first time. He looked at me like I was a little loony for asking... Tonight I will double-check with conservation of substance (we will be having fun with clay).
Striving to increase my rate of flow, and fight forum gloopiness.
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I took 10 of his Yellow Trio blocks and put five in one pile, five in the other (one pile with all of them close, one pile all spread out). �I asked, Which pile is bigger? �He quickly pointed out the larger looking one. �Count them, I told him, 12345, 12345. �He realized they were the same and without hesitating smiled and took another yellow trio block and put it in the pile that he had called bigger. �Oh, I'm sorry. �I didn't see that one. �You are right. �That one's bigger.�
I'm going to have to tell him smarty pants isn't the samething as smart. Get an education boy.
Last edited by La Texican; 10/19/10 11:47 AM.
Youth lives by personality, age lives by calculation. -- Aristotle on a calendar
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