The challenges of instructional leadership school renewal

Focus on Learning Problems in Mathematics, Wntr, 2002 by Roland G. Pourdavood, Lynn M. Cowen, Lawrence V. Svec

John: I don't know about that.

T: I don't know either. You folks have me most confused. Lam going to have to think about this. I never thought about it this way. I think we will have to continue this discussion sometime tomorrow. [Her way of ending lessons when she is unsure about how the students are thinking and how she needs to continue the instruction.]

The next vignette describes a conversation between fourth grade students and two teachers about "time." In this situation, the teacher-leader (TL) was modeling a lesson for her mentee. The intent of the lesson was to investigate what students already knew about "time" and to use their understanding to create lessons. The students were required to dialogue with each other and to explain/defend/justify their ideas. The unanticipated result was a perturbation of teachers' understandings about students' prior experiences and present thoughts.

Setting: Fifteen potentially underachieving fourth grade mathematics students are sitting in a circle, on the floor, with two teachers. One teacher-leader (TL) is the mentor of the other teacher (T). The teachers are preparing students for the state mathematics test. Each student has a small, yellow plastic clock.

TL: So, what do you know about time?

S I: There is twenty-four hours in a day. Seven days in a week. 30 or 31 days in a month. Four weeks in a month. Twelve months in a year.

TL: Anything else that needs to be added? Anybody know other things about time?

S II: He left out ten years in a decade.

S I: Oh, year. And one hundred years in a century. Thousand years in a .....I forget.

TL: Anyone know? [Students, thinking, are silent.]

TL: Well, I'm not sure either. So, let's go on. What about this thirty or thirty one days in a month? Why those numbers?

S II: I think it has something to do with the earth or sun.

S III: Yeah, it does. Um, let me see if I remember. It's how long it takes the earth to spin around.

S IV: No, that's the time for a day-one complete spin-12 hours a day, facing the sun, 12 hours of night, facing away from the sun equals one complete day. But I can't remember about months. Maybe it has something to do with orbit about the sun.

S V: Yeah, it has to do with orbit. Like where in the orbit the earth is.

S VI: Yeah, whether it is close or far from the sun.

S V: It never gets close to the sun or it would burn up!

S VIII: But it has to get close sometimes because we have summer and winter. [Students are silent.]

TL: Hum, I don't know about this orbit. Let's go back to one complete spin. Does everyone agree that one day is measured when earth spins completely around one time?

Students: Yes.

TL: And that one full day is measured in hours?

Students: Yes.

TL: And that one spin takes 24 hours?

S VIII: Not always.

TL: Oh, tell me when it doesn't take 24 hours?

S VIII: Well, sometimes it goes faster. Sometimes it goes slower. But most of the time it takes 24 hours. [Teacher leans forward and responds to student's comment.]

T: That's not right! Where did you get that idea?