Math Forum Internet News

Volume 2, Number 37

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15 September 1997                                Vol. 2, No. 37

                 THE MATH FORUM INTERNET NEWS

Rainbows | New Prime | Middle School POW | Grading/Non-grading


       CIRCLES OF LIGHT: THE MATHEMATICS OF RAINBOWS

    http://www.geom.umn.edu/education/calc-init/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 least-time 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://mathforum.org/dr.math/faq/faq.prime.num.html


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         MATH FORUM MIDDLE SCHOOL PROBLEM OF THE WEEK

             http://mathforum.org/midpow/

A project designed to challenge middle school students with 
non-routine 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 6-9 (ages 
11-14), but may also be appropriate for students in other 
grades. A variety of problem-solving 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 NON-GRADING - A MATH-TEACH DISCUSSION

http://mathforum.org/epigone/math-teach/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. non-grading was first mentioned in the context
of grade inflation by Michael Paul Goldenberg, during a 
discussion of "At-risk Algebra Students":

http://mathforum.org/epigone/math-teach/khunclerverm

The archives of the Math-Teach mailing list are hosted by
the Math Forum:

http://mathforum.org/epigone/math-teach/


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