Prelude to a Project by Ihor Charischak

Back in 1972 I came across an issue of the Mathematics Teacher in which there was an article that described one teacher's effort to collaborate with another school in order to recreate and confirm the results that a libriarian in Alexandria, Egypt named Eratosthenes came up with around 200 BC. What he was able to do was to determine an extremely accurate approximation for the circumference of the earth.This activity inspired me to try this out with with a second year Algebra class that I was teaching at that time. I tried to make contact with these schools - one in Pontiac, Michigan and the other in Gainsville, Florida. But because my telephone messages were not returned, nothing materialized. 

Fast Forward to 1995. While creeping along the Internet (I hadn't discovered surfing as yet), I read that a high school mathematics teacher in Illinois was hosting something she called the Noon Day Project. What this turned out to be was a world-wide collaboration among schools to try to recreate what Eratosthenes' did so long ago. Since the experiment requires that participating groups measure shadows at about the same time (when the sun is at its highest point in the sky), "real time" communication is extremely important. As it turned out email was a great way to do this. 

I found out later that the project dated back to at least 1988 when Jim Levin at the University of Illinois with the help of Al Rogers and his ubiquitous Fredmail network made such an experiment practical. 

Since I was working in staff development with elementary and middle school teachers, I was tempted to get involved, but held off because I thought the use of trigonometry would be a barrier for most of my teachers. So I put this project on the back burner. 

A year later while visiting my favorite library, Barnes and Nobles, I came across a children's book with this intriguing title: The Librarian who Measured the Earth. I stood in the aisle and read the book. (One of the delights of children's books is their brevity.) It was wonderful, but I did have one problem with it. All the mathematics was contained on one page and was probably beyond the understanding of the intended audience. This gave me an idea and a challenge... I wanted to explain the mathematics behind this story in a way that would be understood by children reading it. Little did I know what I was getting myself into. (That explanation turned into this website! ) 

The process of making the mathematics comprehensible took me on a fascinating learning journey. One thing that I learned is how important it is to have good physical models to represent real world phenomenon. Ideas like how the earth revolves around the sun seem simple on first glance, but can be very hard to conceptualize unless you have something to look at and turn in your hand. The other hurdle is language. I've read many descriptions of the phenomena that I describe here. Most of them are intended for a sophisticated audience. The challenge for me was to try to explain it at a level where my use of language invites understanding. Unfortunately, I don't think I accomplished my goal. Most kids who would find the Lasky book interesting would still not be able to understand most of what I describe here. But I think this is a step in the right direction. My attempt at getting at the essence of ideas and trying to explain them in a kid friendly way is very useful. I admire writer's of children's books because they think about this more than anyone else.

The other thing I learned was about the relationship of mathematics and science.  Seperating mathematics from science deprives the student of seeing how the two are intimately linked. 

A colleague of mine shared these thoughts with me when I asked him about the way math and science go together.

"...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 explantion 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...

Roger Pinkham,
Professor of Mathematics,
Stevens Institute of Technology,
Hoboken, NJ

I hope that this website will give you an example of what Roger is talking about.

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