Christian – Part 2

In my previous blog I introduced Christian. He had a prescribed method for solving addition tasks, but many times his answers were not accurate.

In our second session with Christian our primary goal was for him to use a counting strategy when adding two numbers. We began by presenting cards to him with the numerals 27 and 9 printed on them and asked him how much altogether.

He starts by saying “Let me use my brain,” then sits and stares at the numbers for 45 seconds, then says, “40. I was using my head.”

I turn the first card over revealing 27 worms printed on the back side and ask him to count them. After he’s done, I point to the number 9 and ask, “Now can you continue and count these also?”

Christian reaches out to turn it over.

“Can you count without turning it over?” I ask.

He then begins counting out loud: “28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39,” and here he pauses.

“How do you know when to stop?” I ask.

He starts counting again, “40. [pauses] 41.”

“How do you know when to stop?”

He responds, “I count 9 in my head.”

“Okay. Do that for me out loud so I can hear you count the 9. So how many were here?”

Christian says, “27.”

“Okay, count these 9 out loud for me.”

He starts counting, “28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.”

I ask him, “Is there any way you can count and know when to stop at 9?”

He sits for a few seconds looking up and then says, “I think I’ll use my fingers.”

He then proceeds to count and extend fingers sequentially, “28, 29, 30, 31, 32, 33, 34, 35, 36, 37.”

He stops, stares at his fingers, and realizes all 10 fingers are extended.

“So how many do you have here?” I point to the 9.

He replies, “9.”

“So how could you know with your fingers that you have counted 9?”

He looks at his fingers and pulls back one, leaving nine fingers extended.

Christian begins his count again while extending fingers sequentially, “27, 28, 29, 30, 31, 32, 33, 34, 35,” stopping with 9 fingers extended.

At this point he doesn’t look confident in his results.

I ask, “Do you want to try it again?”

He starts over, “27, 28, 29…(slowly) 35.”

I ask “Are you sure?, Do you want to try again?”

“One more time…28, 29, 30, 31, 32, 33, 34, 35, 36.” Now he looks very confused.

Again, “28, 29, 30, 31, 32, 33, 34, 35, 36.”

“So is it 35 or 36?”

He says, “I think it’s 36,” and counts the images of the worms, ending up with 36.

“Hey, it worked!”

It’s not an exaggeration to say he was surprised. I would say he began constructing a way to use his understanding of number to solve the problem. His journey continues in my next blog. What strategies do your students use to “know when to stop” when adding two numbers?

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