SPG 2010 Class 2- January 25, 2010

Today was the second class day of the PBI course for the Spring 2010 semester of class. Professor Petrosino opened the class by telling a heartfelt story about his childhood love of the then Baltimore, now Indianapolis, Colts – based entirely upon an aunt’s gift of a Colts football helmet when he was 4 years old. The story culminated with his excitement that the Indiapolis Colts beat the New York Jets last night to return to advance to Super Bowl XLIV, a nice win against the old rival who beat them back in 1969 during Super Bowl III. Although he does have a soft spot for the NY Jets- thus making yesterday's victory a more subdued for him than expected. 

The class continued with Professor Petrosino breaking the class up into groups of three students each to solve how Eratosthenes figured out the circumference of the Earth. Eratosthenes was able to calculate this number to only an error of a few percent, knowing only that, at noon, a meter stick in Syene cast no shadow while a meter stick in Alexandria, roughly 800 km away, cast a shadow of 0.1219 meters.

In each group, two students were assigned to work together to solve the problem. The third member, however, was to observe the interactions of the other members of the group during problem solving, paying careful attention to four aspects: Discourse, Inscriptions, Engagement, and Learning. 

While Professor Petrosino introduced this problem to the groups, Teddy Chao, the teaching assistant for the course, took the observers outside the classroom to discuss the particulars of the role of observer.

Then, the groups were given about 30 minutes to solve the problem, with the observer taking notes and not participating in the problem solving in any way. At the end of the 30 minutes, Teddy once again met with the observers outside of the classroom to listen to what they had observed.

Students then re-grouped to present their strategies and thinking on the doccam to the rest of the classroom. Professor Petrosino elicited students’ thinking and representations throughout the process, and then opened up space for the observers to add what they observed and interpreted was happening during the problem-solving process.

Professor Petrosino then handed out a packet of various Middle School Science TEKS that showcased how the Circumference of the Earth activity involved multiple standards in deep ways.

And, as the class came to a close, Professor Petrosino reminded students that two Discussion Board postings were due on the class website before Wednesday’s class.

The purpose of the class is to set up a couple of discussions that will continue throughout the course, including:

1) a clear example of inert knowledge

2) modeling how motivating cross-discipline problems can be used in class. 

3) development of observational skills related around ill structured and extended problem solving

4) discussion of assessment practices. 

5) showing how extended activities extend over a fair amount of curricula standards (TEKS).

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Eratosthenes and the The Circumference of the Earth

 Eratosthenes,  an ancient astronomer, historian, geographer, philosopher and mathematician, was also the directore of the great library of Alexandria. One day he read that in the southern frontier outpost of Syene, near the first cataract (waterfall) of the Nile, at noon on June 21 vertical sticks cast no shadows. This observation may have been easily past over by others but Eratosthenes was no ordinary guy. Eratosthenes had the presence of mind to conduct an experiment, actually to observe whether in Alexandria vertical sticks cast shadows near noon on June 21. And, he discovered that sticks do.

 Eratosthenes asked himself how, at the same moment, a meter stick (length = 1 meter) in Syene could cast no shadow and a stick in Alexandria, far to the north, could cast a shadow. Consider a map of ancient Egypt with two vertical sticks of equal length, one struck in Alexandria, the other in Syene. Suppose that, at a certain moment, each stick casts no shadow at all. This is perfectly easy to understand…provided the Earth is flat. Two shadows of equal length would make sense as well, since the Earth would be inclined at the same angle to the two sticks. But how could it be that at the same instant there was no shadow at Syene and a substantial shadow at Alexandria? The Earth must be curved…

 Eratosthenes figured out that the shadow length of the stick in Alexandria (in today’s terms, about .1219 meters or 4.8 inches). Eratosthenes also knew that the distance between Alexandria and Syene was (in today’s units) approximately 800 kilometers (@500 miles).

 Eratosthenes, using only sticks, eyes, feet, and brains (plus a taste for experiment) was able to deduce the circumference of the Earth with an error of only a few percent. How did he do it?  (no outside resource help on this one please)

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