|"...Why do we have washboard (some say corduroy) dirt
roads, should you vote in an election about whose candidates you know nothing,
if light from the sun is parallel when it falls on the earth, how come
it flares out when it shines through a hole in the clouds, why don't bugs
have lungs, what does the weatherman mean when he says there's a 20% chance
of rain, how can it be that the water level is going down when the tide
is coming in, etc....? All these questions and thousands of others require
for their explanation a bit of science married to a bit of mathematics.
Like a poem you come to love even more after study, such understanding
heightens your appreciation for the world around you and provides a never
ending source of joy. In the process you come to treasure both..."
Professor of Mathematics
Stevens Institute of Technology
Hoboken, New Jersey
Last march I helped host a collaborative Internet project (The Noon Observation Project1 ) in which schools from all over the world re-created Eratosthenes' famous measurement of the circumference of the earth. It was an impressive example of what the marriage of modern technology and ancient tools can produce; Internet resources, software tools, sticks, eyes, feet and common sense. (Without Eratosthenes' input it is impossible to know which generation would be more awed by the performance of the other!) Re-creating the mathematics necessary to support scientific phenomena certainly has the potential to help students appreciate how mathematics helps us understand the way the world works.
However, to pull this off, a teacher has to know and be good at many things. In this paper I will discuss what we have learned from our ìgrass rootsî efforts (as part of our NSF funded Internet project here at Stevens) to incorporate collaborative Internet projects into conventional classrooms that are not quite ready yet for "prime time" and describe what still needs to be done to help make this vision reality.
The Collaborative Internet Project Vision
In a 1989 article entitled "Observations on Educational Electronic Networks: The Importance of Appropriate Activities for Learning" the authors2 explored how the new communication revolution in the form of computer networks can be most effectively used in education. An example that they thought had potential was called the "Noon Observation Project." This project had students re-create an experiment that was done over 2000 years ago in Ancient Greece by Eratosthenes. Here students made simple measurements of the sun's shadow, shared their data with schools from other latitudes, and then calculated the north-south circumference of the earth.They saw this as a real, practical experiment which would provide lots of practice using trigonometry.
They wrote that such a network based project had many educational benefits
motivation would be high, students would collaborate on solving real world problems, they would keep a diary of their efforts and then report back their results in the form of a presentation. These conclusions were drawn from observations of Kathleen Smith's (one of the co-authors) class doing the experiment.
I discovered this project in 1994 when I read Kathy's email inviting me to participate. Having unsuccessfully tried to do the experiment back in 1972 when I first learned about Eratosthenes and his remarkable measurement, I was eager to get involved. At the time of the email, I was managing an NSF funded project3 whose aim was to help 40 middle and high school teachers in 16 school districts take advantage of technology mostly in the form of computer software to enhance their students learning. Our goal was to see how many of teachers we could encourage, nurture, cajole, etc. to go through the six stages and master the six areas of professional development.4
At about the same time CIESE5 received another NSF grant6 to pursue the potential of the Internet in science classrooms. Since the mathematics project was in its last year and I was becoming intrigued with how the Internet (especially the World Wide Web) might help in the mathematics arena, I decided to get my feet wet by enrolling some of my teachers in the Noon Observation (or Noon Day) Project7 . This would also give me an opportunity to see first hand what the authors of the article had experienced and how the project had changed as the World Wide Web was making its initial impact. That year I was able to observe two high school teachers take their classes through the Noon Day experience. More about that later.
Things we learned in general from our experience with working on two NSF funded projects.
This past March, I had to chance to share my materials including an article that I wrote with a number of teachers who participated in the project, correspond with them as they carried out the project, and discuss with them their efforts and how they might improve them in the future. Several of the teachers that I was not able to visit, sent me short email accounts of how the project went.
Areas of Professional Growth
In the earlier mentorship project, we identified six areas of teacher proficiency that seemed to correlate with successful implementation of technology. These are:
The first three areas - resources, teacher's knowledge and interest in math, and the way the room is set up for classroom activities - is the "background" for the classroom event that will take place. The school offers a script - either very specific or in broad strokes - that suggest to the teacher what is important to teach. The curriculum may offer suggestions as the kind of discourse that students have with their teachers and each other. It may include guidelines for assessment to determine whether the mission of the school is being carried out. The resources, teacher"s math knowledge, and the learning environment set the stage, while the dynamics of the curriculum (context), the discourse (engagement in the activity), and assessment (reflection) determine the success of the project.
From this perspective, I observed how teachers implemented the Noon Observation Project and reflected on what I learned from the endeavor. I also compared my observations with the vision that the authors of the 1989 article described.
Vision and Reality
(The quoted statements below are from the 1989 article referred to earlier.)
"In general, the network allows us to use the diversity present in the world in powerful ways for education... We would like to increase this sort of student involvement in the post-data collection aspect of the project. Students should be encouraged to look in detail at the overall data, try to identify patterns, and interact with the other sites to clarify any problems or issues that arise..."
The results I observed in the recent noon day classrooms were mixed. I didn't see as much personal contact between the various schools involved as I had originally thought would be there. One nice feature was the use of a listserv which made it easy to get information from anyone who submitted data. This helped to avoid the disappointment of students missing the posting of data.
"...Students should be encouraged to work jointly with other students
to develop presentations of the project, which could be a project for a
school's science fair... This is a science fair activity conducted on an
electronic network, with project descriptions submitted electronically,
judged by distributed judges, and then "visited" by students, teachers, and
other adults electronically."
Some of this happened, but not much; probably because there is not enough web page creation skills out there. Some groups of students managed to put together web pages that demonstrated what they did. One creative teacher, Ken Coles, put together a Noon Day Quilt8 of the pages that were submitted.
"...It is already clear that electronic networks are very good for conducting certain kinds of educational activities that would be very difficult in a conventional classroom. It is also clear that they are not suitable for all possible activities. Discovering appropriate network-based activities is the most important challenge to those exploring education on the electronic frontier..."
Things I learned from observing teachers implement the Noon Day Project (Also, some questions that I now know the answers to):
Though the project was highly motivational for most students and they did learn some procedural skills (like measuring angles and how to use a spreadsheet), I didn't see evidence of what I what was hoping to see: students gaining a deeper insight into what scale drawings, protractor measurements, and trigonometry had in common. There are many reasons why I think this didn't happen. But in my opinion, the most important were the lack of the teachers fully understanding and appreciating how mathematics and science worked together to help Eratosthenes make his wonderful discovery and not being able to come up with effective strategies that would encourage students to appreciate, understand, and imagine the significance of his discovery. So the timeless problems of teachers needing to know more mathematics and being able to teach it effectively surfaced in my observations of this 21st century activity. So what is it that we can do on this the eve of the 21st century to make our teachers more engaged in learning and discovering mathematics and adopting more effective teaching strategies? Share good examples via the Standards document.
One of the challenges facing the Standards writing team is to find worthy examples of what students ought to be doing in mathematics classrooms. For me, the Erastosthenes measurement project is such an activity. What made this activity so engaging was using a variety of resources to tell the story that set the stage for the activities that followed. For example, Carl Sagan in the first episode of the PBS series Cosmos tells the Eratosthenes story in a highly engaging way that I could not equal with my less than adequate story telling skills. Sharing the seven minute segment with students can make a big difference if the story is intimately woven into the tapestry of the lesson. (It can also be a dud if not done right.) Also, students can play with Geometer's Sketchpad models of shadow measurements at two different spots on the globe to discover how one can determine the central angle of the earth (Eratothenes' major insight) by knowing the measures of the sun's angles. What I would encourage the writers to do is to include in their examples as much detail as possible to really capture the spirit of the activities that are shared. Getting a teacher excited about trying something different in the classroom is really at the heart of the reform movement and given the power of the World Wide Web as a publishing vehicle, this is more possible than ever before.
And one last thought
After reading the last paragraph, I was reminded of my favorite assessment "yardstick" that I used as a classroom teacher. If my children left my classroom after a lesson was over still talking about the mathematics we had just discussed, then I knew something special had happened and that the class lesson was a success. My vision is that the impact of Standards 2000 will be to make this kind of conversation about mathematical ideas more commonplace than it currently is.
1 For more details on this project visit the website: http://k12science.stevens-tech.edu/noonday
2 James A. Levin and Michael L. Waugh, University of Illinois, Al Rogers, San Diego County Office of Education, and Kathleen Smith, Champaign School District. (The Computing Teacher, 1989, volume 16.)
3 Enhanced Mathematics Instruction Through Computer Oriented Active Learning Environments (ESI #9253265)
4The six stages we adopted were: awareness, exploration, experimentation, implementation, and institutionalization. We defined the six areas of professional development as: Ability to use resources, Math background and attitude toward learning, managing the classroom environment, personalizing the curriculum, discourse & pedagogy strategies, and assessment.
5 Center for Improved Engineering & Science Education, Stevens Institute of Technology, Hoboken, NJ, Ed Friedman, Director
6 Networking Infrastructure for Education Testbed within the context of Statewide Systemic Reform in Mathematics, Science, Technology Education (RED #9454719)
7 web site address is: http://k12science.stevens-tech.edu/noonday
8 Web site: http://www.geocities.com/Athens/8231/noonschs.htm
Web site: http://www.geocities.com/Athens/8231/noonschs.htm