Wednesday, February 24, 2010

The Ah Ha

I am a little tired of educators referring to the "Ah ha! Moment." I don't know where the expression originated, but it's overused at this point.

Even my jaded, cranky old teacher self has to admit, though, that sometimes it perfectly expresses the moment when a new idea crystallizes into something understood. Tonight I watched that moment happen over and over again as I ran a math activity at Math Night. Families and children came out to play math games, eat dinner, and catch up, and I was working the giant hundreds chart, which is exactly what it sounds like -- an enormous hundreds chart (from 1-100) that you can walk on.

As each child approached, I asked their grade level, and started them on a series of tasks. Anyone in grades 1 or higher started like this:

"Stand on 23. Okay, now what is 23 + 10?"

Once they told me it was 33, I asked, "What is 33 + 10?"

Then, 43 + 10.

53 + 10.

63 + 10.

And so on.

Several children came and dutifully walked ten steps from 23 to 33. When asked what was 33 + 10, they counted carefully as they walked along the numbers to 43. 43 + 10? Once again, they counted by ones to arrive at the answer.

I watched Elijah do these problems, painstakingly counting by ones 7 times.

63 + 10?

64, 65, 66, 67, 68, 69, 70, 71, 72, 73.

Then, 73 + 10. He looked ahead, looked down, and stepped directly to the 83. Bam. There it was. I grinned.

"83 + 10."

He stepped on the 93. He looked at me. I looked at him. We smiled.

"How about 45 + 10?" I asked.

He walked to the 45. He paused, frowned, and stepped to the 55.

"55 + 10." He stepped to 65.

I started to mix up the order.

47 + 10.

82 + 10.

15 + 10.

Then, I switched to subtraction. "73 - 10." He stood on 73. He looked around. He thought. "Hmmmm," he said. And then, he stepped to the 63. Each subtraction problem took a little while, and I am pretty sure if I asked him tomorrow, he would have to repeat the process of counting by ones until he relearned the pattern.

But to be there for that moment, that split second when a look passes over a child's face and something new is realized, is precious. Then to throw my arms in the air in celebration and exchange a high five? Priceless.

I knew there was a reason I was a teacher. I was just having a hard time remembering it.


  1. The new school I'm working at uses Think Math, which uses an upside-down hundreds chart -- 100 is at the top. They say that way it's like the floors of a building, starting at the bottom number and climbing. Thoughts?

  2. I think it's good for kids to have many different mental models of each concept. So they need to do the plus-tens and minus-tens with hundreds charts, then number lines, then manipulatives. (Not necessarily in that order.) So 2 different hundreds chart is probably a great idea. The more ways they see it, the more deeply and flexibly they understand it.

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