This site is a subcollection of a larger set titled 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 undergraduate Calculus.

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=Mathemati
cs&oid=3000000000000000352"> 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.

Technical Requirements:

It requires a "Java-enabled" browser.

Identify Major Learning Goals:

The Manipulate Math-Calculus applets are designed to help the user visualize many basic concepts of Calculus.

Target Student Population:

Students at and above the calculus level.

Prerequisite Knowledge or Skills:

This varies from one applet to the next. Some require knowledge of functions, other of single-variable calculus, multi-variable calculus, or ODE's.

Content Quality

Rating:

Strengths:

Manipula Math-Calculus contains three groups of applets: Limits, Derivatives, and Integrals. The groups have 4,18, and 8 modules, respectively. Topics include, but are not limited to, visualization of limits, visualization of the derivative, numerical and geometric explanation of specific limits, the relationship of secant lines and tangent lines, L' Hopital's Rule, the chain rule, involutes, and Riemann sums.All applets are excellent, fast implementations that illustrate corresponding Calculus concepts very well. Almost all the modules have introductory sections giving necessary Calculus background of the problem as well as activity sections that require users to actually use the applet to solve a particular problem. The user has good control over the appearance of the generated graphs (domain, range, color, variable names, etc.). This is an excellent and very useful package.

Concerns:

The collection would benefit from the unified style and design of the modules.

Potential Effectiveness as a Teaching Tool

Rating:

Strengths:

This site provides a truly excellent teaching tool. It could be easily implemented in the standard Calculus sequence, and in a wide range of science and engineering classes. The modules are easy to use, have a standard interface, and always come with an explanation section. Users can quickly and efficiently explore a wide range of situations. Most of the activities contain simple assignments with answers provided at the end of the section. Features such as the ability to see and overlay different plots and/or examine numerical output open up learning opportunities in a wide variety of situations. Because the introduction in each module is terse, students would benefit most if these were used by the instructor for demonstration purposes or in a lab where an instructor could point out some interesting facts.

Concerns:

None of the applets has an arbitrary function input option. Providing this option together with the standard function input syntax would definitely broaden the usage potential of the site.

Ease of Use for Both Students and Faculty

Rating:

Strengths:

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.

Concerns:

Again, a unified look of the applets could reduce possible confusion. Adding button arrays would help to navigate the site.

Creative Commons:

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