Peer Review

Thales' Circle

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Overall Rating:

Content Quality:

Effectiveness:

Ease of Use:

Overview:: This site is one of 17 Java applets which can be used to demonstrate
mathematical theorems.
Type of Material:: Simulation or animation
Recommended Uses:: Provides a "hands-on" visualization of Thales' Theorem.
Technical Requirements:: Java-enabled browser, level 4 or higher.
Identify Major Learning Goals:: This learning object provides an opportunity for students to see a visual
representation of a theorem. The student will see an infinite number of
examples that demonstrate Thales' Theorem, "A triangle inscribed in a semicircle
is right."
Target Student Population:: This would work for middle school students and teacher education courses in
mathematics.
Prerequisite Knowledge or Skills:: The site requires a knowledge of geometry and geometric terms. It also
presupposes that students are able to recognize the commonly used symbols for
terms, such as a square for a right angle. The site requires some technical
savvy in that users must be able to drag an object.

Rating:
Strengths:: The learning objects on Walter Fendt's site are superb. While basic, they are
illustrative of the theorems. Actually the portion of Fendt's site from which
mathematics teachers can choose more learning objects that illustrate important
theorems can be found at http://home.a-city.de/walter.fendt/me/me.htm This
specific material provides the visual for Pick's Theorem. It enables a quick
demonstration of what the theorem means.
Concerns:: The content only provides the visual. It assumes that the viewer has the
requisite mathematical understanding. A teacher may misuse the resource and not
provide adequate or appropriate accompanying information (e.g. a lesson plan).
A teacher who is not a strong mathematics educator may struggle with how to
incorporate this learning object and how to assess whether the student achieved
the objective (of being able to explain or apply the theorem).

Rating:
Strengths:: Pick's theorem can be demonstrated quickly and graphically. Using concrete
materials facilitates students' learning of mathematical concepts. The
advantage of using concrete manipulatives is that students can physically touch
the manipulatives. Using electronic learning objects has the advantage of
providing examples of the concept or principle to be learned. Thales' Theorem
is presented to students in middle grades (Stigler, J. W. & Hiebert, J. (1999).
The teaching gap: Best ideas from the world's teachers for improving education
in the classroom. New York: Free Press).
Concerns:: There are no accompanying lessons. If a teacher did not have the requisite
knowledge, they might be satisfied with demonstrating the theorem. This
learning object should be inserted into a lesson activity that has been planned
by the teacher.

Rating:
Strengths:: The Java applets are easy to use. They are simple and focused on the
mathematical concept or principle being illustrated. Because the student can
alter the picture (moving the vertex of the triangle that lies on the
semicircle) this learning provides a means for the student to visualize the
result of numerous different positions of that vertex and observe that the
result remains unchanged.
Concerns:: The teacher will probably need to describe or demonstrate how to drag the vertex
of the triangle lying on the semicircle.

Other Issues and Comments:: This site has a great many Applets that can be used to demonstrate mathematical
theorems. It is a useful tool in the hands of someone with a mathematical
background.

Additional physics and astronomy examples are in another section of Fendt's
website: http://home.a-city.de/walter.fendt/homepage.htm

The site was viewed using both Netscape and Internet Explorer without any
problems.
Creative Commons: