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This site is a sub collection of a larger set Manipula Math containing a variety of learning material, both textual and visual. It is a self-contained collection of Java Applets that can be used in the teaching and learning of geometry.

The Manipula Math-Geometry 2 applets are designed to help the user explore the elementary geometry concepts.

Target Student Population:

Students in a geometry course.

Prerequisite Knowledge or Skills:

The applets are self-explanatory. Any geometry student can work with these applets.

Type of Material:

Simulation, animation, and exploration

Recommended Uses:

These applets could be used as classroom demonstration tools or as aids to students problem solving on homework assignments.

Technical Requirements:

A "Java-enabled" browser is required.

Evaluation and Observation

Content Quality

Rating:

Strengths:

Manipula Math-Geometry 2 contains two groups of applets: Circles and Pythagorean Theorem. The groups have 20 and 16 modules, respectively. The applets illustrate the geometry concepts very well, demonstrating the theorems and properties in a simple style. The user will have a more hands on visual knowledge of geometry concepts after exploring with the applets.

The applets vary in their approaches. Most involve the moving of a point or rotation of a figure to demonstrate the principle. A few involve watching as the computer demonstrates a proof one step at a time. Many are activities that could be assigned in a laboratory setting or as homework. For many of the applets, the student can decide whether or not to get a hint. The computer will then sketch the key angle, line, or triangle involved in the solution. The diagrams are well structured in that they contain all the necessary information without being cluttered. In particular, there are eight demonstrations of the proof of the Pythagorean Theorem. The Peaucellier Apparatus applet provides a historical perspective as well as activities for the student. This is an excellent and very useful package.

Concerns:

Occasional grammatical and spelling errors exist.

The Pythagorean Theorem applets all include various misspellings: Pythagoriean, Pytharoras, Pythagrean.

Shortest Distance has errors in terminology, referring to line BC as side BC. The directions should be restated to, ?The points A to G are vertices?.?

Problem of Two Circles (3) does not make the entire conclusion visible when pressing the Next button.

Quoits is a good idea but it only shows purple beads on one side. A bead counter would assist this applet.

Eye Ball Theorem is a dead link.

Potential Effectiveness as a Teaching Tool

Rating:

Strengths:

This site provides a truly excellent teaching tool. The modules are easy to use, have a standard interface, and most come with an explanation section. The activities are exploration based and most can be used without the aid of the instructor. Students can play with the applets to get an intuitive understanding of the geometry concepts and follow-up with a traditional proof. Many of the applets require the student to develop their own conclusion after having manipulated the geometrical objects and are therefore suitable as assignments. These applets will be particularly instructive for the kinesthetic learner. An instructor has the option of selecting from a large variety of visual approaches to the proof of the Pythagorean Theorem.

Concerns:

Feedback is not provided for some of the applets and the student could develop an incorrect conclusion. Instructor intervention to provide the correct answers and require development of proofs for the conclusions generated is necessary to guarantee that the concepts are correctly mastered.

Ease of Use for Both Students and Faculty

Rating:

Strengths:

The applets have controls that are easy to use, clearly labeled, and self-explanatory in function. Hence, the operation of the applets is fairly intuitive. A short explanation section is always found at the beginning of the more complex applets. Available options give the user good control over the appearance of the graphical output of the modules.

A single user license is available for use offline. Network/site licenses are available for schools, teachers, and researchers. These licenses allow the purchaser to place the applets on home pages and to make changes to the applets by editing the HTML files. The license may be purchased for the Geometry 2 applets only, or for the Manipula Math Applet Collections, which includes additional applets in Geometry,
Trigonometry, Vectors and Calculus.