Saturday, 24 April 2010
Working with Larry for the past three months, I’ve had the unique privilege of watching five years of cognitive development be shrunk down into a ninety-day period. This remarkable little boy is astounding us daily with his ability to learn. One area where we’ve seen an enormous amount of growth is in the area of numbers, to the point where we are now entering into the world of addition. Here was Larry’s progression in the field of numbers and math:
1. Naming Numbers: We used a basic 10-piece wooden number puzzle. We would dump the numbers out, and as Larry put them back in, I would name them aloud and he would repeat the names. Eventually, he was naming the numbers on his own as we put them into the puzzle.
2. Counting: Larry had previously learned to count to 100 aloud, although the actual concept of counting meant nothing to him. If you started 1,2,3 he would keep going until he felt like stopping, but if you placed five toys in front of him and asked how many, you would get a blank look. So we took a book his old BSC had made, with pictures of cars, increasing from 1-20. Hand-over-hand we pointed to the cars and counted how many there were, saying the last number again. He caught on to this process quickly, and within a week he was counting on his own.
3. Connecting counting and numbers: With the ability to name written numbers and verbally count numbers aloud, we needed to find a way to cross the barrier between the two. This took a bit more creativity, because the first process we tried we found he was merely memorizing the order he needed to put numbers down in, rather than counting and matching. So I ended up taking twelve index cards and making each one into a set of two dice fronts, with the first having one dot and the last having two sets of six dots. Then we had the printed numbers from an old set, and they were arranged next to the stack of index cards. Hand-over-hand Larry and I counted the dots, then moved the number card bearing the result on top of it. A month later and any set of objects Larry can count, name the result, and put the matching number next to. It’s time to move onto addition.
4. Addition: Addition doesn’t seem to lend itself to teaching in as simple and concrete a way that other skills do. Addition is more about concepts, and less about stimulus discrimination. At least at first glance. But after spending some time thinking about the skills Larry has and the visual nature of his learning, I came up with a plan. I took 100 strips of paper and five crayons and set to work. Each fact looks just like this, with an identical color scheme:
Larry counts the first box, puts the matching number on top, then the second, with the number on top, and then the answer, putting the number on top. Then hand-over-hand we read the math fact. “1+3=4″. We started Friday afternoon, and he was very excited about this activity, holding each strip up to his face before we did it. We did 1+1=2 hand-over-hand. 1+2=3 he was able to put the numbers on himself and we read the fact together. By 1+3 =4, he had stopped counting the dots and was able to place the corresponding numbers on directly, and he read the numbers while I read the signs. On 1+4=5, he did the entire thing on his own, laying down the strip, placing the numbers on top, and then reading the resulting fact.
My plan is to do ten strips a day, five of which will be a review from the day before, and five of which will be new. Slowly but surely we’ll work our way up to 10+10=20. Then we’ll move onto the next skill, which is filling in the answer when the first two numbers are given. Then we’ll take out the dots all together and simply add numbers. Finally, we’ll move from horizontal to vertical addition. Once that happens, I have a dry-erase board with all 100 math problems on it. Once those are gotten, he will hopefully have the concept of addition down, and we will be able to start on the rules of complex addition, like adding in columns and carrying numbers. Placing this on a time frame, I would say a minimum of 6 weeks, with a good probability of completion in 3 months. Then we’ll tackle subtraction and we’ll do it the exact same way.
This is a very tedious, repetitious way to teach addition. But it’s also a good reminder that even topics which seem abstract (like math), can, with a little creativity, be broken down and taught with discrete trials. I’m very excited about this new skill we’re working on, and I’ll be posting updates about how the process is going.