Eratosthenes and Us,
It Just Keeps Going and Going and Going…

Conclusion

In one sense, there is no conclusion to this project as it is still going on and we are still going on together. Be that as it may, there are some things that we have noticed about pursing such a project as this.

The project has enriched everyone who has been involved with it, scientists, teachers and students beyond their initial expectations. The challenges we encountered were motivating and allowed us to grow as professionals and students. We all learned about ancient science and mathematics. The students had the opportunity to be science detectives as they rediscovered how to apply the same concepts Eratosthenes used to measure the circumference of the Earth. The constructivist approach gave the students the responsibility for his/hertheir learning and the freedom to think critically and creatively. In the process of evolving their understanding and applying the mathematics and physics concepts, the students developed the ability to think criticallylogically. For example, students questioned that the Sun's rays were parallel, the need to average the data, and why Eratosthenes's size was not the same as today's value. Teachers, with the aid of the scientists, worked together to understand these concepts and created lesson plans to teach the concepts the best way possible.

We feel the students benefited from being having an integrated unit that included science, math, social studies and art. We made it relevant to them and put it in an historical-scientific context. From this, the students appreciated the input of ancient science and scientists to our current knowledge. They learned how to use angles in real life application, something lacking in elementary education. The students were encouraged to use information and concepts learned in math and apply them in science, thus encouraginghelping them to make transferences of concepts learned in different areas and to apply them to concrete problems. Students also felt motivated to think and question, intelligently, all the possibilities. When they graduating graduated from sixth grade the great majority acknowledged that the Eratosthenes project was the best and most influential project they had done. One unexpected benefit for the students was an increase in self-confidence. Figuring out the geometry behind the measurement on your their own and being able to measure the circumference of the Earth to within 10% of the correct value with tomato stakes makes a big and lasting impression.

We worked closely as a team and were able to show this to our students. The benefits of group work became clear to them when they saw how teachers reached out to the scientists and vice versa. The students also took this project very seriously because a "real" scientist was involved.

This project has had an effect on the teachers that has been carried beyond the classroom. They have trained other teachers and encouraged them to do this project unit. They have held workshops at local and national levels (NSTA and NCTM conferences) promoting the project and to encourage encouraging collaborations of this sort between scientists and educators. One of the teachers had local astronomers come to her class and demonstrate how telescopes are were made and persuaded local amateur astronomers to hold a night star show for students and their families to enjoy and learn. Liliana has become involved with NASA as an educator for the Solar System Educator Program (SSEP).

Teachers were grateful to have a scientist and vice versa. Teachers found in Paul and Karl sounding boards to ask questions and check understanding. Teachers want to teach accurately and understand in-depth the concepts. They feel more secure when the information comes directly from a working scientist. It was important that teachers feel free and safe to openly talk with the scientists and that their questions were not going to be taken as "dumb" questions. Scientists should be sensitive in talking with non-scientists on how to explain concepts in non-technical language but maintaining the high level and sophistication that the concepts demand. Teachers do not want to be talked down to or be given dumbed down explanations. Paul was also grateful to work with teachers. Paul was able to see the project take shape in ways he did not imagine could be done. The teachers gave Paul the pedagogical theory behind the reasons for teaching in certain ways by addressing the audience's age, knowledge and interests.

The benefits of explaining intricate concepts to teachers in simpler terms have been substantial benefits to Paul. He recognized that in order to explain certain concepts to the teachers he needed to have them clear and organized himself in order for the teachersothers to follow. There is nothing like having to teach a topic to make youin order to learn it.

There are, however, the inevitable sacrifices and difficulties, no matter how surmountable they may be. Time, scheduling, and weather were our "challenges" (i.e. enemies) with time being the worst. The amount of work that the teachers and scientists placed in it was significant. . Paul put extra hours to do this, in addition to his regular job. Scientists may feel that teaching in schools or collaborating with teachers will rob them of precious research hours. It is a realistic aspect of this collaboration. However, scientists interested in outreach should know that these projects are short lasting, a few months or weeksfrom four to 10 weeks, and but the benefits for the teachers and the students are priceless. Time Scheduling constraints are also problematic on the teachers' side. The project needs to fit the time of the year so that testing and other scheduled activities are not in conflict. In this project we were also weather dependent and the students needed to be were available to go outside for an hour to measure the shadows. We worked together to find solutions to these scheduling difficulties. The teachers, as much as possible, taught their units in an integrated way giving more flexibility to the times and days they could use for instruction. For example, angles were taught during math, Christopher Columbus during social studies.

Even though the team had not met prior to doing the project, the distance between Paul in Maryland and the teachers in Massachusetts was not a problem to our collaboration. The teachers in Amherst and Paul had not met before. We did most of our communication via e-mail and phone. At the end of the project, Paul went to visit the Amherst students and teachers. It was a great experience to finally see each other face to face.

This project was indeed special, but not unique. The same project or the development of similar projects can be reproduced in any place. What is needed are scientists, teachers and students. They should all have in common, the desire to learn from each other, explore new ideas, let anybody be able to lead the project into new directions, communicate without fear or insecurity about shortcomings or lack of understanding and support each other. We have discovered new aspects of ourselves through this collaboration that we would have never known otherwise. Unlike Eli our participation was voluntary, but like Eli, we are grateful for such wonderful opportunity.

"This project taught me that math and science are fun and that I am good at them." - Liza

"I want to be an astronomer when I grow up." - Chelsea

"This was the best project I've ever done." - Joel

Bibliography

Fraknoi, A. (editor) 1995. The Universe at Your Fingertips: An Astronomy Activity and Resource Notebook, A Publication of the ASTRO Project at the Astronomical Society of the Pacific.

Lasky, K. The Librarian Who Measured the Earth, Little, Brown and Co.

Yue, C. and D. Yue 1992. Christopher Columbus, How He Did It., Houghton Mifflin Company, Boston.

Brooks, J. and M. Brooks 1993. In Search For Understanding - The Case For Constructivist Classrooms. ASCD Alexandria, VA.

Paul Romani
Mail Code 693
NASA-Goddard Space Flight Center
Greenbelt, MD 20771
E-mail: Paul.Romani@gsfc.nasa.gov

Liliana Klass
Fort River Elementary School
70 South East Street
Amherst, MA 01002
E-mail: ljaf@javanet.com

Tamara Kaplan
E-mail:kdanford@k12.oit.umass.edu

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