- Peer Review: Manipula Math - Trigonometry
Manipula Math - Trigonometry
- Apr 17, 2003 by Mathematics
- 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 trigonometry.
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
- 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=3000 000000000000352"> 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
- Type of Material:
- Simulation and animation.
- 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
- Identify Major Learning Goals:
- The Manipula Math-Trigonometry applets are designed to help the user explore trigonometric definitions, graphs, and some of the identities.
- Target Student Population:
- Students in a Trigonometry course.
- Prerequisite Knowledge or Skills:
- The applets are self-explanatory. Any trigonometry student can work with these applets
- Manipula Math-Trigonometry contains four groups of applets: Definitions, Equalities and Inequalities, Further Trig Functions, and Triangles. The groups have 11, 6, 5 and 3 modules, respectively. The applets treat the concepts of the basic trig functions, their graphs, and relationships very well. The user will have a more hands on visual knowledge of trigonometry after exploring with the applets. The applets vary in their approaches. Most involve the moving of a point around a circle and watching how various trig functions are graphed. The sin, cos, and tan function box applets are a simple but effective way to understand how these functions are evaluated. They allow the user to input angles both larger than 360 degrees and less than zero. The sin t = a and cos t = a applets entice the students into playing a game while they are learning trig. This is an excellent and very useful package.
The applet sin (A+B) is excellent in demonstrating a graphical interpretation of the identity and also includes a similar demonstration for cos (A+B). Other applets graphically demonstrate the addition of two trig functions, justification for the Law of Sines and Law of Cosines, and effects of amplitude, period and shifts on a sine function?s graph.
- There are some grammatical errors in the applets, particularly the ?Crane Ship? applet. In general, these errors are obvious and do not significantly hinder the effectiveness of the applets.
The applet titled y = Asin (Bx ? C), instead demonstrates y = a sin b(x ? c). This error could result in a major misinterpretation by the student user who often is already convinced the C in y = A sin (Bx ? C) is actually a horizontal shift.
The applets sin t = a and cos t = a imply accuracy to the tenths place by allowing the user to guess angles with that accuracy. However, the success response is activated if the user guesses an angle in a 5 degree range.
These applets use only degree measurement for angles and do not support radian measurement.
In about half of the applets the auto feature is turned on so fast that the user cannot see what is happening. Using the + and ? buttons instead is tediously slow and requires two activations of the buttons for each increment displayed.
Also there is no response to trying tan(90) in the tan function box applet. An ?undefined ? message would be appropriate here.
In the ?Law of Cosines? applet the word ?prove? should be change to ?demonstrate?.
Potential Effectiveness as a Teaching Tool
- 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 all except the ?Law of Cosines ? and ?Law of Sines? applets can be used without the aid of the instructor. Students can play with the applets to get an intuitive understanding of the trig functions before working on traditional paper and pencil work.
The Transform feature in the applet y = a sin b(x ? c) is very effective in visualizing the sequence of amplitude, period and horizontal shift in creating a graph. This applet, as well as many others on the site, demonstrates concepts that are difficult to understand without visualization using technology. Many of the simulations provided could be incorporated into a classroom lecture to enhance student understanding of the concepts.
- The ?Law of Sines? applet has a small bug in menu 3 in that a graph sticks after it has been sketched. Students using the ?Law of Cosines? applet will need a lot of guidance from the instructor.
Ease of Use for Both Students and Faculty
- Most of 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 Trigonometry applets only, or for the Manipula Math Applet Collections, which includes additional applets in Geometry, Vectors and Calculus.
- The applet Graph of y = tan x does not function properly in some browsers as the graph approaches infinity and causes the computer to crash.