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Newsletter: Math Forum Internet News No. 2.12 (March 24)
Posted:
Mar 22, 1997 11:20 PM
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24 March 1997 Vol.2, No.12
THE MATH FORUM INTERNET NEWS
SCORE Mathematics | Nils Ahbel | Plausibility Arguments
SCORE MATHEMATICS
http://www.kings.k12.ca.us/math/
From The Schools of California Online Resource for Educators.
The contents and links are intended to reflect the California
Mathematics Framework.
An archive of Internet Math Resources for grades K-4, 5-8,
and 9-12 may be browsed or searched. It includes information
on assessment and education organizations, and features a
database of math lessons.
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NILS AHBEL - KENT SCHOOL
http://www.kent.pvt.k12.ct.us/fachmpag/ahbeln/homepage.htm
Nils Ahbel teaches mathematics at Kent School in Connecticut.
He and his students have generated some interesting new math
materials for the secondary school level:
UNI- AND BI-VARIATE DATA ANALYSIS
A fall term computer project for Nils Ahbel's honors class
in Functions, Trigonometry and Statistics. Students chose
a topic, searched the Internet for relevant data, performed
a statistical analysis, and displayed the results.
- NBA draft picks by Mike Harley '98.
- German traffic safety by Philipp Hasskamp '97.
- Ice cream consumption by Sarah O'Neil '98.
EXCEL FILES FOR THE MATH CLASSROOM
Microsoft Excel files to download: annual vs. compound
interest, arithmetic and geometric sequences and series,
height of a falling object over time, Pascal's Triangle,
polynomial differences, a simulation of rolling two dice
and one about a family with three children, synthetic
division, transformations, and trigonometric modeling.
Images of sample output let you view the content of many
modules before downloading them.
GEOMETER'S SKETCHPAD FILES
Downloadable v.3.0 files, with samples for viewing.
Subjects include a variety of tessellations, and Versiera,
better known as the Witch of Agnesi.
The work of some of Nils' students is among the pages
featured in the Math Forum's Student Showcase:
http://forum.swarthmore.edu/students/showcase/
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PLAUSIBILITY ARGUMENTS: A MATH-TEACH DISCUSSION
What is really meant by the phrase "plausiblity
argument"? We can see just how thorny this question
really is by recasting it: What is a proof?
- Lou Talman
On March 7th Ron Ward initiated a lively discussion on
the MATH-TEACH mailing list (formerly NCTM-L) about
student assessment as addressed in the 1989 NCTM Evaluation
Standards.
http://forum.swarthmore.edu/epigone/math-teach/jaltweldjax
Ward's message focuses on Standard 7 - Reasoning: "What is
really meant by a 'PLAUSIBILITY argument'? What is the
difference between 'use reasoning to develop plausible
arguments' and 'use deductive reasoning to construct valid
arguments'?"
The discussion ranges through a number of issues:
Can a good teacher be precise without being pedantic?
Aren't almost all proofs really plausibility arguments?
Is rigorous proof still important? What is the role of
logic? How should we deal with students who invent
plausible, convincing false proofs?
Ted Alper contributes a simple false proof that constructs
a triangle with two right angles, and Andre Toom offers a
false proof that an arbitrary triangle is isosceles.
See "Plausibility Arguments" in the Math Forum archives:
http://forum.swarthmore.edu/epigone/math-teach/fersusnim
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The Math Forum ** 24 March 1997
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