The following sample dialog is adapted from a transcription of a
classroom videotape. Students are solving the problem 59 + 62.
Linda: It's 59 plus 62 equals 22.
Students: No, too low. And it's higher.
Teacher: No? How come I hear all these "no's"?
Jacob: No. It's too low because 59 and 62 are big numbers, and 22 is too low.
Teacher: Right. Jacob says 59 and 62 are big numbers, so you
can't end up with a number smaller like 22. Linda, how
did you get that 22?
Linda: See, I counted, I think, 5 in my head and then I counted
up 6 more. It was 11 and then 9 and 2 and it was 22.
Teacher: Oh, so you went 5 plus 6 equals 11 and then you
went 9 plus 2 equals 11 and then you said 11 plus 11 is
22.
Students: That's wrong.
Teacher: Yes, there is something wrong here. Linda, point to
the 5 in the 59 and the 6 in the 62. What do those numbers
mean? Are they really just 5 and 6?
Linda: Yes, 5 and 6.
Teacher: The same as the 9 and 2?
Linda: Um.
Teacher: I’m glad that you are trying, Linda. Can anyone help
Linda here? Tanya?
Tanya: 5 and 6 are like 50 and 60. I could put, um. I could put, a
hundred...
Teacher: Watch what Tanya is doing, and you should be thinking
in your head how you would figure it out.
Tanya: I'm just trying to like...count in my head.
Teacher: Try to say it out loud, what you're thinking in your
head. Or try to write down notes. Go ahead up to the overhead.
Tanya: [Walks up to the overhead.] Like you could put, um, one
hundred and then you could put 121.
Teacher: 121. But how did you get 121?
Tanya: Because I just counted and then...
Teacher: What did you count?
Tanya: I counted um, 50 plus, plus 60 and...
Teacher: Count it for me. How do you do 50 plus 60?
Tanya: I went 6, I went 7, and then um, 80, 90, so then I went a
hundred and then I counted the ones.
Teacher: Okay, so Tanya went 50 plus 60. She put 50 in her
head and went 60, [students chime in and count with
teacher] 70, 80, 90, 100, 110. And then what did you do?
Tanya: Then I added the 2 and then...It had um...121.
Teacher: So you went 110 plus 2.
Tanya: ... is 112. And then 9. 121.
Teacher: Okay, very good, Tanya. Good way to think about it.
