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Newsletter: Math Forum Internet News 2.37 (Sept. 15)
Posted:
Sep 13, 1997 10:54 AM


15 September 1997 Vol.2, No.37
THE MATH FORUM INTERNET NEWS
Rainbows  New Prime  Middle School POW  Grading/Nongrading
CIRCLES OF LIGHT: THE MATHEMATICS OF RAINBOWS
http://www.geom.umn.edu/education/calcinit/rainbow/
How are rainbows formed? Why do they only occur when the sun is behind the observer? If the sun is low on the horizon, at what angle in the sky should we expect to see a rainbow?
This lab helps to answer these and other questions by examining a mathematical model of light passing through a water droplet. The contents include:
 How does light travel?  Reflection  Refraction  Rainbows: Exploration  Rainbows: Analysis  Conclusion
Objectives of the lab:
 to examine the use of Fermat's Principle of leasttime to derive the Law of Reflection and the Law of Refraction
 to experimentally determine the angle at which rainbows appear in the sky
 to understand geometric properties of rainbows by analyzing the passage of light through a raindrop
 to apply a knowledge of derivatives to a problem in the physical sciences
 to better understand the relation between the geometric, symbolic, and numerical representation of derivatives
This lab from the Curriculum Initiative Project at the University of Minnesota is based on a module that was developed by Steven Janke and published in "Modules in Undergraduate Mathematics and its Applications" in 1992.
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NEW LARGEST KNOWN PRIME NUMBER!
http://www.mersenne.org/prime.htm
On August 24th, Gordon Spence, using a program written by George Woltman, discovered what is now the largest known prime number. The prime number, 2^(2976221)1, is one of a special class of prime numbers called Mersenne primes; it is 895,932 digits long.
An introduction to prime numbers can be found in the Dr. Math FAQ:
http://forum.swarthmore.edu/dr.math/faq/faq.prime.num.html
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MATH FORUM MIDDLE SCHOOL PROBLEM OF THE WEEK
http://forum.swarthmore.edu/midpow/
A project designed to challenge middle school students with nonroutine problems, and to encourage them to verbalize their solutions. Responses will be read and assessed and comments will be returned; incorrect solutions will be sent back with an explanation of the error and students will be urged to try again.
The problems are intended for students in grades 69 (ages 1114), but may also be appropriate for students in other grades. A variety of problemsolving techniques are encouraged, including:
 guess and check  make a list  draw a picture  make a table  act it out  logical thinking  algebraic equations
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GRADING VERSUS NONGRADING  A MATHTEACH DISCUSSION
http://forum.swarthmore.edu/epigone/mathteach/frehkherdwimp
A conversation about the merits of giving grades, student motivation and interest, the need for grades for college admission, what grading does to the grader, the illusion of absolute truth, the effects of praise in the classroom, GPA, SAT and IQ tests, and the effects of testing.
Grading vs. nongrading was first mentioned in the context of grade inflation by Michael Paul Goldenberg, during a discussion of "Atrisk Algebra Students":
http://forum.swarthmore.edu/epigone/mathteach/khunclerverm
The archives of the MathTeach mailing list are hosted by the Math Forum:
http://forum.swarthmore.edu/epigone/mathteach/
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The Math Forum ** 15 September 1997
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