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28 Jul 2005 - 20:15 Scientific American article about manipulatives & symbolic representation now:
About 20 years ago I had one of those wonderful moments when research takes an unexpected but fruitful turn. I had been studying toddler memory and was beginning a new experiment with two-and-a-half- and three-year-olds. For the project, I had built a model of a room that was part of my lab. The real space was furnished like a standard living room, albeit a rather shabby one, with an upholstered couch, an armchair, a cabinet and so on. The miniature items were as similar as possible to their larger counterparts: they were the same shape and material, covered with the same fabric and arranged in the same positions. For the study, a child watched as we hid a miniature toy--a plastic dog we dubbed "Little Snoopy"--in the model, which we referred to as "Little Snoopy's room." We then encouraged the child to find "Big Snoopy," a large version of the toy "hiding in the same place in his big room." We wondered whether children could use their memory of the small room to figure out where to find the toy in the large one. The three-year-olds were, as we had expected, very successful. After they observed the small toy being placed behind the miniature couch, they ran into the room and found the large toy behind the real couch. But the two-and-a-half-year-olds, much to my and their parents' surprise, failed abysmally. They cheerfully ran into the room to retrieve the large toy, but most of them had no idea where to look, even though they remembered where the tiny toy was hidden in the miniature room and could readily find it there. Their failure to use what they knew about the model to draw an inference about the room indicated that they did not appreciate the relation between the model and room. I soon realized that my memory study was instead a study of symbolic understanding and that the younger children's failure might be telling us something interesting about how and when youngsters acquire the ability to understand that one object can stand for another.
[The] capacity [to] create and manipulate a wide variety of symbolic representations .... enables us to transmit information from one generation to another, making culture possible, and to learn vast amounts without having direct experience--we all know about dinosaurs despite never having met one. Because of the fundamental role of symbolization in almost everything we do, perhaps no aspect of human development is more important than becoming symbol-minded.
The first type of symbolic object infants and young children master is pictures. No symbols seem simpler to adults, but my colleagues and I have discovered that infants initially find pictures perplexing. The problem stems from the duality inherent in all symbolic objects: they are real in and of themselves and, at the same time, representations of something else. To understand them, the viewer must achieve dual representation: he or she must mentally represent the object as well as the relation between it and what it stands for. A few years ago I became intrigued by anecdotes suggesting that infants do not appreciate the dual nature of pictures. [snip] .... the Beng babies, who had almost certainly never seen a picture before, manually explored the depicted objects just as the American babies had. The confusion seems to be conceptual, not perceptual. Infants can perfectly well perceive the difference between objects and pictures. Given a choice between the two, infants choose the real thing. But they do not yet fully understand what pictures are and how they differ from the things depicted (the "referents") and so they explore: some actually lean over and put their lips on the nipple in a photograph of a bottle, for instance. They only do so, however, when the depicted object is highly similar to the object it represents, as in color photographs.... [snip] it takes several years for the nature of pictures to be completely understood. John H. Flavell of Stanford University and his colleagues have found, for example, that until the age of four, many children think that turning a picture of a bowl of popcorn upside down will result in the depicted popcorn falling out of the bowl.
Period of Concrete Operations. (Often you'll see the word 'developmental' used to designate constructivist curricula. Apparently that's a reference to Piaget.) Wayne Wickelgren says this is nonsense; children can handle abstract concepts long before age 11. But constructivists are the people time forgot, and they're still basing their pedagogy on work done in the 1950s. That's bad enough in itself, seeing as how the field of cognitive science was just getting started around that time, and Piaget's work hasn't fared so well over the past 60 years. But the more glaring misstep, it appears, is that they failed to grasp the nature of the concrete. The reason constructivists think children should spend their grade school years working with manipulatives is that manipulatives are concrete. But they're not. Manipulatives are symbolic objects that require the child to have mastered the concept of dual representation. Skinnies and bits are not concrete. They are symbolic representations of the Hindu-Arabic numeral system. Worse yet, they are more intellectually demanding, and hence more confusing, symbolic representations than pencil marks on paper. They're harder to understand, not easier. Lost in translation.
CA state study on manipulatives
Quick Thought about Fraction Manipulatives
Fraction Manipulatives Part 2
New Study on Manipulatives Part 2
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