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MERLOT II


    

Peer Review


Geometry Gallery-Advanced geometric configurations

 

Ratings

Overall Rating:

5 stars
Content Quality: 4 stars
Effectiveness: 4 stars
Ease of Use: 5 stars
Reviewed: Jun 02, 2002 by Mathematics
Overview: 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.

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.
Type of Material: Interactive modules based on JAVA applets
Technical Requirements: Computer with browser supporting JAVA.

Evaluation and Observation

Content Quality

Rating: 4 stars
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:

  1. 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.
  2. 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: 4 stars
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: 5 stars
Strengths: Explanations are clear and useful although, as mentioned above, in some cases more elaborate agendas would be useful.
Concerns: None.