This is a collection of tools to visualize graphs in two and three dimensions. Included are applications to first, second, and third semester calculus.
Type of Material:
Collection of applets
classroom demo; student exploration
Flash Player Version 8 or higher although some of the applets will run on Flash Player 7
Identify Major Learning Goals:
To visualize concepts from calculus.
Target Student Population:
First, second, and third semester calculus
Prerequisite Knowledge or Skills:
A basic knowledge of calculus.
Evaluation and Observation
This is a collection of about 25 activities; some were authored in collaboration with Doug Ensley of Shippensburg University. Most of them allow the student to type in the formula for a curve or surface or series and then the computer will sketch it. The activities include parametric curves and surfaces that can be defined in the main coordinate systems: rectangular, polar, cylindrical and spherical. Several of the activities include a gallery of pre-programmed curves and surfaces. The user has the ability to change the scale and rotate the objects. Some of the activities include an exercise where the student is asked to provide the equation for the displayed object. The author did an excellent job of displaying an extensive list of functions for each activity. The displays of the graphs are easy to see. Included on the site is a link to the code for the activities and a tutorial on how to create such code
Potential Effectiveness as a Teaching Tool
This collection can be used by the student who is working on a project or homework problem that involves graphing. An instructor can also create curriculum where the student is asked to visually explore a curve or surface. Some of the activities are exploratory in nature. For example, one of the activities displays the graph of a function. The student uses a slider to graph the derivative and show a piece of the tangent line at the point.
Ease of Use for Both Students and Faculty
Although there is a lot going on with each activity, the buttons and text fields are easy to use. For the activities that ask the student to enter a function into a text box, there is a syntax button. When the mouse hovers above this button, a full set of instructions is provided. The instructions include examples of functions that could be inputted. The main page that contains links to the activities also includes brief explanations of what the activity demonstrates. The lessons for faculty on how to create the activities are well written. Anyone with math background and with experience using Flashs Actionscript language will be able to create their own 3D animated graphics.