More often than not over the last month, when Helena is tucked into bed she tells me, "Pas une histoire, Mama. Bonne nuit." I may have to establish storytime at some other time of day.
Counting
Some fascinating research is discussed at Collision Detection, and it happens to be remarkably relevant to weird stuff Helena does.
The experiments started after witnessing behaviour I've seen for myself, and puzzled over, in Helena: exploring and attempting to interact with pictures of objects as if they were the objects themselves.
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.
(Helena has done this with less-than-realistic pictoral representations — perhaps a more intensive exploration of the relationship between it and the referent. Huge philosophical implications are likely also being considered: when does the cat picture, in all its petting-worthiness, stop representing a cat? when it's not furry? when it's purple? when it has no legs? when it's a stick cat? when it's stretched unbelievably long? Humour starts here too — to delight in the unusual, one must know what is normal and expected first. She continues to "play" with pictures, to enter into them, but with a wink and a smile — she's in on the secret now.)
A subsequent experiment is summarized nicely at Collision Detection:
When teachers try to show kids subtraction or addition, they typically use objects — like coins, sticks, whatever — to represent quantities. But DeLoache suspects many children cannot easily yet separate the symbolic nature of numbers — the "threeness" of a trio of apples, for example — from the actual objects themselves. In an even more mindblowing experiment, she taught two groups of six-and-seven-year-old kids to do subtraction problems that involve borrowing, a rather sophisticated concept. One group of kids was taught using pencil and paper; the other was taught using blocks. Both groups learned the concept, but the kids with blocks took three times longer. Why? Because learning the concept with pencil and paper requires the kids to immediately interact with abstract symbolic concepts. The kids working with blocks, paradoxically, had to do more mental work — since they had to separate the concept of numbers from the blocks they were working with.
A girl who used the blocks offered some advice to the researchers after the study: "Have you ever thought of teaching kids to do these with paper and pencil? It's a lot easier."
Helena is definitely better at counting off the top of her head than at counting objects. This has improved significantly over recent weeks, but counting with objects is considerably slower.
Puzzling
Last week, my sister gave Helena a couple of amazing jigsaw puzzles she's brought back from Bishkek recently, and we're proud to note they're made in Poland.
This one has 20 pieces. The pieces are bigger than my hand. I love that the edges aren't straight, but follow the line of the treetop. (The other puzzle has a few hundred pieces and will have to wait a while.)
Helena's 12-piece puzzle was no longer a challenge for her, so just before we went away I got her a 24-piece puzzle featuring Dora the Explorer. I've seen her complete it on her own, but she still still struggles with it, as well as with the above "Bambi" picture.
We're still working on figuring out clues as to what piece goes where. What doesn't work: suggesting to Helena that she look at the picture on the box. Just as the above-mentioned research would indicate, Helena has trouble mapping.
6 comments:
VERY interesting! My lad can easily count to 10, sometimes to 20, but he can't count objects at all. He will just keep counting until he runs out of numbers or interest.
Yesterday, I bought D. a stuffed cow which obviously looks cartoonish. She loves it, kisses it and asks for it. When we discovered that Casey actually "moos" very realistically, it bothered her tremendously. She pushes the toy away as if this should not be happening. She only wants Casey if the toy doesn't sound like a cow. This makes much more sense now in light of the article.
She just turned two but she does count objects and, in fact, insists on doing so.
Go figure!
Interesting re: the counting. The first children's book I illustrated was an educational mather reader published by Harcourt Canada. The title of the book is 'Fifty Little Penguins' and its goal is to help grade ones count, in sets of 10. Is it easier for kids to learn to count if they do it in sets? I'm not up on these things.
I often wondered why the math consultants for this book chose penguins as the objects to be counted. Because kids like penguins? The are an easy shape to recognize? I do know that in order to make it more enjoyable for kids reading this book, I made an extra effort to make each penguin look different in their expressions (this was no small feat, especially once I got beyond the number 25....ugh). My husband works for the Toronto Public Library, and he sometimes uses my book in his kids' programs. According to my husband the kids have a great time counting all the penguins in the book.
One more thing. At the back of the book there is a section entitled: 'Notes for teachers and parents' where the consultants provide further suggestions to help kids with their counting. Examples provided are:
'Provide the children with 20 to 50 objects (e.g. counters, popsicle sticks) and hve the arrange the objects in groups of 10's.
Interesting subject. Sorry I blathered on.
If anyone's reading this, you may be interested to see what comments Rachel has garnered.
I really love the way you write about your daughter. It makes me incredibly nostalgic.
This is interesting. For teaching addition and carrying I like Math-U-See, which I find works better than regular manipulatives. As for pictures, when my kids were tiny loved to look at them both right side up and upside down, and my eldest would get quite upset if a well-meaning adult turned an upside down book she was looking at back the "right" way.
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