Yesterday, Lily lined up 9 babies on three steps, instructed me to sit next to them, got out a pack of addition flash cards (the kind with the answer missing, and a box on slick cards that one can write the answer in), and announced she was going to teach her babies stuff.
She proceeded to pick a card, pick a student, instruct them (including me) to raise a hand and answer. She read the task on the card (1+5=_____) and asked the baby (or me) to solve. I assisted with some, working through the process. Then, after a couple or three, she took over. She encouraged and coaxed the babies along as each and every one of them was chosen, presented with the task, assisted by Cecily to solve, and then when the answer was determined, she wrote the number in the box.
I didn’t know she could write numbers. Well, maybe 1, 7, 3, and 0. She has demonstrated letter writing for a few months now, but not numbers.
Ok, well, so much for the theory that the only way a child will learn to write or read characters and digits is to “teach” them and have them do it over and over again.
The boxes were blank, the numbers of each problem present, but many of which required a completely different number than shown on the card (i.e., 2+7=9). She generated each of the numbers and, with only slight deviation, was dead on accurate. Each could easily be determined as to what number she intended to write (and not just because of the number being the known answer), even if it was a bit loopy or not entirely proportionate.
Russ got some video of her leading the group in the exercise. I’ll upload when he gets me the files.
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After yesterday, I decided to pull out some of her mathematically related toys. She has a peg board that accepts cylindrical blocks, painted and sized different into groups, each about 1/2″ in diameter. We began with patterns.
She has exceptional ability to recognize and generate patterns, including complex (6+ series) sequences. She started demonstrating her virtual and abstract pattern related skills about a year ago when she first discovered Team Umizoomi on NickJr. Prior to that however, she provided tangible examples of her comprehension frequently, and from about the age of 13 months. Her first demonstration was with a toy that uses lights, language, and color (it was her dinner time toy). She progressively demonstrated a comprehension that, while accurate, seemed to be limited to the specific sequence; when asked, she would not replicate or associate the pattern beyond the original object/sequence/language repetition. However, she could generate a pattern when asked, with alternative objects/other than the original pattern example that had been discovered/understood.
From pattern work, we moved to grouping. First, we played with recognition of greater/lesser amounts within a group. Comparison between two and then three groups (color and size of cylinder/woodblock indicate group). After she reliably demonstrated comprehension of comparison and identification of which group was bigger/smaller, in a responsive manner, I switched and requested she generate the same.
I placed (for example) three yellow cylinders/blocks in a specific (though random) pattern on the board and asked her to pick a different color and match or replicate my pattern. Some responses included the exact number of blocks, in an exact pattern mirroring mine. Some responses the same amount of blocks, but in a completely different pattern. Some responses included more or fewer blocks than my pattern, but arranged in such a way that her contribution became a new pattern situated around my own. (For instance, I placed 2 red blocks on the board and she placed a blue block on either side, then a yellow block directly opposite (right angle) to the blue.)
Finally, I began asking her to “compute” precise amounts within a given group. I would place a given number of blocks of a specific color on the board and then add a second (different color/size) group of a differing amount to the board. Her task? Do whatever necessary to make the two groups identical. Her options? Add to one, subtract to another, or some other solution (up to her). I got some of each.
She added and/or subtracted a few times to even out the groups. A couple times, she decided to tell me the exact opposite of what was necessary to complete the task, instead of physically solving. Additionally, she determined a couple times to completely modify the task. At one point, she split one of my groups into equal halves and then placed the blocks from the second group I’d provided in-between the two halves.
At one point, during the original request for her to assess patterns and do something with them, she began to build vertically. These blocks are not easily stacked, and require extreme dexterity (significant for me, really cool to watch her succeed). At first, I observed, and assumed she was just “building”. But, as I watched, I realized that more than just stacking for the sake of building, she was replicating and/or generating the specific patterns she’d been requested to (or a logical modification of one which invariably increased the complexity of the pattern I’d provided).
– I didn’t know she could do that either.
I have a natural interest in sociology, history, writing, and neuroscience… not math. I’m working tonight to locate exercises and ideas on how to encourage this aspect of her development through creative and intriguing play.