## Sunday, January 31, 2010

### Meeting with Manor Teachers- Thursday Jan 28

## Wednesday, January 27, 2010

### SPG 2001- Day 3 January 27

Today, Profesor Petrosino started the class by giving student the same quiz from the very first day of class, this time as a post-test of their factual knowledge to solve the Circumference of the Earth problem. The class average for the pre-test from the first day was 95% and the class average for the post-test after working with the actual problem was a 98.1%, showing a mild increase.

Professor Petrosino then opened up a class discussion about why students did so well on test of individual facts, but not so well on actually finding the circumference of the Earth even though they knew all the facts. After all, if problem based learning was so good in terms of helping students connect their factual knowledge to actual concepts, then why is what we’re seeing when we visit actual classrooms more aligned with the factual recall quiz questions rather than the deep concepts from the problem? After some thoughts by the students, Professor Petrosino posed that, perhaps it’s the fault of all of us in the room. This class, and the UTeach cohort in general, is filled with students who have excelled in math and science, namely because we’ve done well at these sorts of factual recall based tests. All of us, including the Professor Petrosino, have been systemized to teaching and learning math and science into bite-size factual chunks.

Professor Petrsoino then started to talk about how we know that experts and novices in fact hold the same sorts of factual and often conceptual knowledge. But what differs in experts is their ability to transfer this knowledge to different situations. Students then broke up into smaller groups to discuss what they thought about this framework: Is it possible to teach basic skills through complex problems? Or, is it more important to teach basic skills first before solving problems.

After the discussion, Master Teacher Denise Ekberg introduced the logistics of the Field Teaching Component of the course, in which students would be responsible for observations and implementation of a problem-based lesson at Manor New Tech High.

## Tuesday, January 26, 2010

### Supplement: June 19, 240 B.C.: The Earth Is Round, and It’s This Big

By Randy Alfred June 19, 2008 | 12:00 am | Categories: Uncategorized

**240 B.C.: **Greek astronomer, geographer, mathematician and librarian Eratosthenes calculates the Earth’s circumference. His data was rough, but he wasn’t far off.

Eratosthenes was an all-around guy, a Renaissance man centuries before the Renaissance. Some contemporaries called him Pentathalos, a champion of multiple skills. The breadth of his knowledge made him a natural for the post of librarian of the library of Alexandria, Egypt, the greatest repository of classical knowledge.

His detractors, however, mocked Eratosthenes as a jack-of-all-trades and master of none. They called him Beta, because he came in second in every category.

Envy? Perhaps. He invented the Sieve of Eratosthenes, an algorithm for finding prime numbers still used in modified form today. He sketched the course of the Nile from the sea to Khartoum, and he correctly predicted that the source of the great, life-giving river would be found in great upland lakes.

Eratosthenes knew that at noon on the day of the summer solstice, the sun was observed to be directly overhead at Syene (modern-day Aswan): You could see it from the bottom of a deep well, and a sundial cast no shadow. Yet, to the north at Alexandria, a sundial cast a shadow even at the solstice midday, because the sun was not directly overhead there. Therefore, the Earth must be round — already conventionally believed by the astronomers of his day.

What’s more, if one assumed the sun to be sufficiently far away to be casting parallel rays at Syene and Alexandria, it would be possible to figure out the Earth’s circumference. Eratosthenes computed the shadow in Alexandria to be 1/50 of a full 360-degree circle. He then estimated the distance between the two locations and multiplied by 50 to derive the circumference.

Of course, his measurements were slightly off. Alexandria was not due north of Syene, but 2 degrees of longitude off. Syene was not precisely on the Tropic of Cancer but 39 minutes of latitude north of it. The distance between the cities was an estimate. The Earth is not a perfect sphere, but an oblate spheroid flattened at the poles.

And we don’t know today the exact size of the measurement unit Eratosthenes was using when he came up with the final figure of 252,000 stades. (We know he knew it was just a rough estimate, because he adjusted his initial number of 250,000 upward by 2,000 — or 0.8 percent — to make it divisible by 60 or 360 for easy computation.)

So how big is 252,000 stades? Depending on which classical source you trust, it’s somewhere between 24,663 and 27,967 miles. The accepted figure for equatorial circumference today is 24,902 miles. Pretty darn good for a guy without modern measurement tools.

Eratosthenes went further and computed the tilt of the Earth’s axis to within a degree. He also deduced the length of the year as 365¼ days. He suggested that calendars should have a leap day every fourth year, an idea taken up two centuries later by Julius Caesar.

Grade-school tales aside, it was thus known long before Columbus that the Earth was round and even how big it is, approximately. But it was just not widely known among the masses in 15th-century Europe. One reason is that Eratosthenes’ very own library of Alexandria had been destroyed, and there was no complete backup of its data.

### 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

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## Friday, January 22, 2010

### SPG 2010 Class 1- January 20, 2010

## Wednesday, January 13, 2010

### Obama References UTeach

In announcing the expansion of his "Educate to Innovate" campaign, the president applauded several new public-private partnerships that will help meet the goal of moving American students from the middle to the top in science and math achievement over the next decade.

One of those exemplary partnerships is leading to the replication of the UTeach math and science teacher-preparation program, which began at The University of Texas at Austin in 1997, to 19 universities nationally.

Thirteen universities in nine states implemented UTeach programs during the 2008-2009 school year. A newly announced second cohort of six universities includes the University of Tennessee Knoxville, Middle Tennessee State University, the University of Colorado at Colorado Springs, University of Texas at Arlington, University of Texas at Tyler and Cleveland State University.

View a full list of UTeach replication sites.

Support and funding for these replications come from the UTeach Institute, the National Math and Science Initiative, the Texas High School Project, the Texas Education Agency, the Greater Texas Foundation, Exxon Mobil Corporation, the Bill & Melinda Gates Foundation, the Michael & Susan Dell Foundation, Texas Instruments Foundation, the Tennessee Higher Education Commission, the Tennessee Department of Education and other private philanthropy.

UTeach allows students to graduate in four years with both deep content knowledge in their major and a teaching certification.** **Ninety-two percent of UTeach graduates have become teachers, and 82 percent are still in the classroom after five years.

Enrollment in UTeach has nearly doubled nationally in just two years, attracting more than 2,100 math and science majors into the program.

Projections indicate that, by 2018, UTeach-like programs around the country will have produced an estimated 7,000 new math and science teachers, and those teachers will have affected more than one million students by 2017 and more than 20 million during the course of the new teachers' careers.

At The University of Texas at Austin, UTeach has graduated more than 500 students, and has more than doubled the number of math majors and increased by six times the number of science majors being certified as teachers at the university.