Chapter 7, page 169
gives a summary of a paragraph without explaining how she got the answer. On the right side of Figure
7.10, she does explain how she came up with her summary, thus showing her cognitive work.
How can teachers encourage students to make their thinking public? Asking the questions as our
hypothetical teacher did can elicit students to reveal their thought processes. Additional questions and
statements that teachers use to help students verbalize their thoughts are illustrated in the transcript
presented below. This transcript, based on research by Taylor and Cox (1997) shows a teacher (T) working
with fourth graders (J, R, L) solving relatively complex math problems. In the transcript, the students are
working on this math problem: Amy has $28. She plans to save $3 each week. In how many weeks will
she have enough money to buy a telescope that costs $49? Notice what the teacher says to elicit students’
public thinking.
Dialogue Analysis
T: OK, how’s his math? Everything OK up there [on the
whiteboard where the student has written his
answer]?
J, R: [together] Yeah.
L: I don’t know yet.
T: What do you mean, we don’t know yet?
L: Well, it could be wrong. We didn’t check it yet.
T: We didn’t check it yet, but as for his division, 21
divided by 3, is that correct?
L: Yeah.
T: What about the subtraction 49 minus 28?
L: Well, we only gotta go 7, minus 14, minus 28 to check
it.
T: Well, we’re not up there yet are we? So, what’s the
answer to our question so far?
L, J, R: [together] Seven.
T: OK, Linda, you can go up there [to the whiteboard **]
and give it a good ol’ try. Talk to us. Tell us what
you’re doing while you check it.
L: 7 times 3, so if it’s 21, then we know it’s the answer.
And it is 21!
T: OK, but how do you know?
Å The teacher asks other students
to evaluate one student’s work.Å The teacher asks the student to
explain why she doesn’t know.
Then the students try to explain
their thinking in the next several
turns.Å Here the teacher gives explicit
instructions asking Linda to make
her thinking public by telling what
she is doing as she works at the
board.Å The teacher prompts the
student to explain her thinking
even more.
L: Because 7 plus 7 is 14, and then you add another 7 and
it’s 21.
T: Right, but how do you know she has enough money?
L: Well ....
(The teacher continues working with the students to understand
why they have come up with this answer.)
Taylor and Cox (1997, pp. 209-210, underlining added)
Å The teacher wants more
elaboration and therefore prompts
the student to explain further.The teacher encourages students to make their thinking public in several ways:
Ɣ by generally asking students to show their thinking out loud
Ɣ by asking for further clarification of their ideas (“What do you mean?)
Ɣ by having students explain their thinking while working out the problem on the board (“tell us what
you’re doing while you check it”)
Ɣ by insisting that the students come up with explanations for their answers (“but how do you know....”)