6 September 1999 Vol. 4, No. 36
THE MATH FORUM INTERNET NEWS
Newton Basins  Joyce  TI86 Graphics Calculator  NCRTL  Michigan State
NEWTON BASINS  David Joyce
http://aleph0.clarku.edu/~djoyce/newton/newton.html
Newton basins are fractals  kinds of Julia sets. David
Joyce, of the Department of Mathematics and Computer Science
at Clark University, provides a description of Newton's
method for finding solutions to equations, and an interactive
Newton Basin generator.
Newton's method leads to some fantastic images when applied
to complex functions. This program colors the complex plane
according to where an initial guess will eventually take you,
and gives each solution a different color so that all the
initial guesses that eventually lead you to that solution
are colored the same. A Newton basin is just a set of
initial guesses that leads to one solution.
The site includes background on Newton's method, some
examples for a quick idea of the possibilities, and a form
that allows you to generate Newton basins for polynomials.
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THE HIGH SCHOOL STUDENT'S GUIDE TO PROGRAMMING
THE TI86 GRAPHICS CALCULATOR
Jim Bowen, Stillwater H.S., Stillwater, OK
http://members.fullnet.net/jbowen
A site "dedicated to the premise that one of the defining
characteristics of mathematics education during the early part
of the 21st century will be the full integration of
programming throughout the high school mathematics curriculum
as an accepted and fundamental problemsolving technique."
Lessons and subjectoriented projects take students
stepbystep through programming lessons such as:
 input/output
 ifthen
 for loop
 while and repeat loop
 functions and graphs
 draw menu lessons
 miscellaneous special instructions.
Project Menus are available for algebra, trigonometry,
calculus, and miscellaneous projects (e.g. write a program
that will simulate flipping a coin and display the results).
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NATIONAL CENTER FOR RESEARCH ON TEACHER LEARNING (NCRTL)
College of Education, Michigan State University
http://ncrtl.msu.edu/
NCRTL brochures and publications  special reports, craft
papers, research reports, technical series, issue papers,
conference series, and video packages  include articles
and essays such as:
"Developing Mathematics Reform: What Don't We Know About
Teacher Learning  But Would Make Good Working Hypotheses?"
"Beyond Exhortations Not to Tell: The Teacher's Role in
DiscussionIntensive Mathematics Classes"
"Halves, pieces, and twoths: Constructing representational
contexts in teaching fractions"
"Knowing the subject and learning to teach it: Examining
assumptions about becoming a mathematics teacher"
"Research on teaching mathematics: Making subject matter
knowledge part of the equation"
"Unlearning to teach mathematics"
"Using hypermedia technology to support a new pedagogy of
teacher education"
All publications are in PDF format, and a link to the free
PDF Acrobat Reader is provided.
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