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 Ratings
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| Reviewed: |
Apr 17, 2003 by Mathematics |
| Overview: |
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 vectors.
Please see the related reviews of the main href="http://www.merlot.org/artifact/ArtifactDetail.po?discipline=Mathematics&oid=3000000000000000348">class=SpellE>Manipula Math with Java site, as well as the following
sub-sites:
- href="http://www.merlot.org/artifact/ArtifactDetail.po?discipline=Mathematics&oid=3000000000000000349"> class=SpellE>Manipula Math - Calculus
- href="http://www.merlot.org/artifact/ArtifactDetail.po?discipline=Mathematics&oid=1010000000000085651"> class=SpellE>Manipula Math - Conics
- href="http://www.merlot.org/artifact/ArtifactDetail.po?discipline=Mathematics&oid=1010000000000085670"> class=SpellE>Manipula Math - Middle School (Geometry)
- href="http://www.merlot.org/artifact/ArtifactDetail.po?discipline=Mathematics&oid=3000000000000000351"> class=SpellE>Manipula Math - Geometry I
- href="http://www.merlot.org/artifact/ArtifactDetail.po?discipline=Mathematics&oid=3000000000
000000352"> class=SpellE>Manipula Math - Geometry II
- href="http://www.merlot.org/artifact/ArtifactDetail.po?discipline=Mathematics&oid=3000000000000000350"> class=SpellE>Manipula Math - Trigonometry
- href="http://www.merlot.org/artifact/ArtifactDetail.po?discipline=Mathematics&oid=1010000000000073413"> class=SpellE>Manipula Math - Vectors
- href="http://www.merlot.org/artifact/ArtifactDetail.po?discipline=Mathematics&oid=1010000000000085655"> class=SpellE>Manipula Math - Complex Numbers
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| Learning Goals: |
The Manipula Math-Vector applets are designed to help the user explore vector concepts and applications using vectors. |
| Target Student Population: |
Students in a precalculus course and higher. |
| Prerequisite Knowledge or Skills: |
The applets are self-explanatory. Understanding of basic vector concepts, such as sketching and vector addition is helpful. |
| 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: |
Requires a "Java-enabled" browser. (JDK 1.1 compliant) |
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| Strengths: |
Manipula Math-Vectors contains 29 applets. These applets are in three categories: Basics of Vectors, Inner Product (Dot Product), Vectors in 3D. The groups have 19, 8 and 2 modules, respectively. The applets illustrate the vector concepts very well, demonstrating the theorems and properties in a simple style. The user will have a more hands on visual knowledge of vectors and their applications after exploring with these applets.
The applets include both algebraic and geometric interpretations of the concepts. Most applets allow the user to determine an initial vector(s) by dragging the terminal point(s). Many are exploratory activities that could be assigned in a laboratory setting or as homework. The computer will then sketch the key vectors involved in the solution and provide the supporting algebra.
Area of a Parallegram (2) provides key concepts used in many of the other applets, particularly the geometric relationship between vectors and the area of a parallelogram. Cramer?s Rule incorporates the use of vectors and area of a parallelogram into a geometric interpretation of the process. Linear Independent is excellent in demonstrating the algebraic and geometric relationships of the vectors. Problem of a Regular Hexagon and Distributive Law for Inner Product make nice use of animation in their demonstrations. |
| Concerns: |
Linear Independent would be better titled as Linearly Independent or Linear Independence. Attempting to use dependent vectors may cause the applet to crash.
Problem of Dot (Inner) Product has a spelling error, ?poing? rather than ?point?. Other grammatical errors were also found. |
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Potential Effectiveness as a Teaching Tool |
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| 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 vector concepts, many of which are difficult to visualize without the technology. These applets will be particularly instructive for the kinesthetic learner.
Unit Vector clearly relates a vector to a unit vector by simultaneously sketching a vector, the vector in standard position, and the corresponding unit vector. Vector and Circle defines a circle in terms of the sum of two vectors, one for the center and one for the radius; the user can modify both the center and radius and view the resulting vector as it sketches the circle. |
| Concerns: |
Subtraction of Vectors is not effective in demonstrating the concept. Addition of Vectors is cluttered and does not demonstrate the concepts as clearly as other applets. Midpoint of Side of Quadrilateral and Parallelogram shows two proofs at a total of 17 steps that are too difficult for the general student. In Euler Line gravity center, circum center, and orthocenter need to be defined in words. |
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Ease of Use for Both Students and Faculty |
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| 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 for 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 Vector applets only,
or for the Manipula Math Applet Collections, which includes additional applets in Geometry, Trigonometry and Calculus. |
| Concerns: |
No concerns |
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