A collection of ten modules based on JAVA applets illustrating "advanced configurations" in plane geometry:
A cubic spline construction
Intersections of exterior common tangents to 3 circles
Intersections of interior common tangents of 3 circles
An isosceles triangle theorem
A theorem using the Pythagoras diagram but yielding a surprising triangle
A derived quadrilateral
Napoleon's Theorem
Circle through three points
4 special points of a triangle
The shape of birds' eggs
Many of the modules are organized as questions for students to explore.
Please see the associated reviews of the main href="http://www.merlot.org/artifact/PeerReviewDetail.po?rOid=1010000000000021523"> Geometry Gallery site and the href="http://www.merlot.org/artifact/PeerReviewDetail.po?rOid=1010000000000021521">Basic Geometry modules.
Type of Material:
Interactive modules based on JAVA applets
Technical Requirements:
Computer with browser supporting JAVA.
Identify Major Learning Goals:
To provide challenging and informative exercises for advanced geometry students.
Target Student Population:
Advanced students in Plane Geometry.
Prerequisite Knowledge or Skills:
Good understanding of elementary euclidean geometry, including circle and triangle theorems. Some practice with attacking multi-step geometry problems. Ability to read instructions and to handle a mouse.
Content Quality
Rating:
Strengths:
The better modules are excellent learning tools for well prepared and motivated students. These include:
A cubic spline construction
Intersections of interior common tangents of 3 circles
A theorem using the Pythagoras diagram but yielding a surprising triangle
Napoleon's Theorem
Circle through three points
4 special points of a triangle
Concerns:
The problems are all challenging but some are harder than others. Some indication of the level of difficulty would be useful to teachers assigning this material.
Some of the modules are unsatisfactory as adjuncts to coursework. In particular:
Isoceles triangle theorem applet (There are no points to move, but rather numbers to input; students may need direction as to what numbers to try - moving points seems much preferable.)
Intersections of exterior common tangents to 3 circles (Needs explicit directions to student: prove that ...)
A derived quadrilateral (Not clear if there is a theorem to be proved, or what the point of the module is, beyond a demo of the software.)
The shape of birds' eggs (Needs more explanation of what is going on mathematically: how do the movable points determine the shape? Is there anything for students to try to discover?)
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The better modules (see above) are very effective in bringing to life complex constructions and phenomena. Good students will find pleasure and emlightenment.
Concerns:
Beyond the concerns stated above, the modules could be enhanced by a several-step approach to the problems, with for example some elementary experiments to perform with the configuration. In this way students could be "shown the path" to a certain extent; this could make the modules more useful in learning how to prove geometry theorems (instead of how to prove this one theorem) than abandoning the students to sink or swim.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
Explanations are clear and useful although, as mentioned above, in some cases more elaborate agendas would be useful.
Concerns:
None.
Creative Commons:
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