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Q&A #6278


Teaching and learning of the circle theorems

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From: Marielouise (for Teacher2Teacher Service)
Date: May 08, 2001 at 18:08:45
Subject: Re: Teaching and learning of the circle theorems

Prof. Clements:

Your questions intrigue me because I love geometry at all levels and the
teaching of it in high school in particular.  I will try to answer some of
your questions.

1:  The NCTM Standards

www.nctm.org/standards

has a strain of geometry from K-12.   At different levels different aspects
from vocabulary, recognition, to properties of geometric figures, proof are
discussed.   At the NCTM site you should also be able to find references to
research articles that have been published in the Journal for Research.
Since your topic is so wide, I don't know where to begin in research.   In the
United States there has been much discussion on the how and why of proof in
high school geometry.   Van Hiele (from the Netherlands) has had extensive
studies on five levels of geometric understanding.   You might search the
internet with "Van Hiele" as your source word.

2:   I am not sure what you mean by circle theorems.   Do you mean measures
of angles formed by intersecting chords, by two chords meeting on the circle,
by two secants to the circle meeting outside the circle, by a tangent and
secant meeting outside the circle?   If you do, yes, these are proved.  If you
mean lengths of intersecting chords within the circle, etc. these are also
proved.

3:   About this I have no idea.

4:   Many teachers / texts do not think that these are important for high
school students.   For all high school students I think that they are not
important.   For some high school students I think that they are important.
Who are the some?   These are students who will spend time in mathematics /
science / architecture.   Surprisingly I solved a problem for a contractor
whose son was in my class.   He gave me the height of a window and the width
of its cross-section.   He wanted to figure the angle / location of the center
of the circle so that he could cut the opening for a "Palladian-style" window
in a wall.   Yes I used my knowledge of angles, trig and chords of a circle!

As these the most important theorems to be taught?   No.   Should they be
mentioned?   Yes.   Should they be proved?   Only to some students.

-Marielouise, for the T2T service.

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