night to confirm their observations. But for the moment it was agreed to assume—with the majority—that the North Star didn't seem to move at all.

With these observations, Ms. B. said, they were ready to try to find the circumference of the earth. She challenged each group of four to use their globes to answer the question: ''Since the North Star didn't appear to move, what direction would it be if you were standing at the North Pole?" After some time for thinking, discussing and moving the globe around, the class shared their answers. Several groups said it would be right overhead. Asked to explain why, they used their globes to illustrate that if it were not, it wouldn't stay due north as the earth turned.

Ms. B. then drew a sketch of the earth, with the familiar Western Hemisphere facing her, on the blackboard. She drew an arrow straight up from the North Pole, pointing to the North Star, and she also made a dot on the equator at the edge of her sketch on the Gilbert and Ellis Islands in the Pacific. She asked: "Which way is the North Star for someone in the Gilbert and Ellis Islands?"

Figure 1.

Ms. B.'s Sketch of the earth

Each group was directed to reach a consensus of where to draw the arrow from the Gilbert and Ellis Islands on the sketch, but some could not. Each group, and the holdouts, put an arrow on the board to illustrate their answer. One arrow pointed straight up, and the rest pointed at a range of angles, most toward a point near the top of the blackboard. How could they find out who was accurate? Ms. B. suggested that they use what they knew to try to decide who among the groups might be right. To help the students get started on this task, she asked each group how high up they thought the North Star was. According to where their arrows pointed, most had assumed that the North Star was only a few earth diameters above the North Pole. Ms. B. then asked what the students thought the distance to the North Star really was compared with the size of the earth. Now many students said that it must be very far away because it's a star and stars are very far away. In the end consensus was reached that if the North Star were very far away—a great many earth diameters—the straight up arrow in the sketch would point to this star, no matter where one was on the drawing of the earth.

Then Ms. B. drew a line straight across the top of the earth in her sketch to indicate the horizon at the North Pole, pointing out that on the blackboard the angle from the horizon to the North Star was 90 degrees. If you were standing on the North Pole you would look straight up to see the North Star. She asked the students where the inhabitants of the Gilbert and Ellis Islands on the equator, ¼ of the way around the earth away, would look. She also made a mark on her diagram



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