CyberCalc: Poster

Review Documents Written by:

Michele Williams

Interactive Quizzer Created by:

T. J. Willis

Advisor:

Edward A. Bogucz

Abstract for final paper:

An interactive computer-aided environment has been developed for calculus instruction. CyberCalc combines Mosaic and Mathematica to provide a powerful and convenient way of accessing calculus instructional material via the Internet. The CyberCalc environment includes two main elements: a Concept Reviewer and an Interactive Quizzer.

These create a much shortened calculus textbook which was written as a companion to a Calculus I course. These documents contain:

graphs
text
1. Review of Needed Topics
  - coordinates, slopes, and distance
  - equations, functions, and graphs
  - trigonometry review and absolute value
2. Limits
  - properties and one- and two-sided limits
  - at infinity and rational functions
  - continuous functions
  - maxima, minima, and the Intermediate Value Theorem
  - formal definition
3. Derivatives
  - slope, tangent lines, and the derivative
  - rules and rates of change
  - L'Hopital's Rule
  - trigonometric functions and the Chain Rule
  - implicit differentiation
hyperlinks to relevant definitions

The following are three of the graphs, all of which happen to be in chapter one:

A graph of a piece-wise defined function:

A graph showing the shifting of the cosine function into the sine function:

This combines Mosaic, Mathematica, a client, and a server to provide students with an on-line Quizzer which gives immediate feedback.

The connections established for the Quizzer.

Mosaic
- user interface
- form support needed
- fill in form space for answers
Mathematica
- generates questions
- checks answers
client
- tasks
  - asks for answers
  - checks answers for syntax
  - checks answers for correctness
- html documents created
  - questions
  - answer is wrong
  - possible answer
  - answer is correct
server
- starts-up Mathematica
- sends requests to Mathematica
- returns Mathematica's questions and answers

This is the work we hope to see take place in the future:

complete the Calculus I syllabus
- 4. Application of Derivatives
  - related rates of change
  - maxima, minima, and the Mean-Value Theorem
  - graph sketching
  - maximization (area and volume)
- 5. Extension: Expanding into n-Dimensions
  - functions, limits, and continuity
  - partial derivatives
  - general form of the Chain Rule
extend to Calculus II and perhaps Calculus III
expand into other fields
- physics
- real analysis

Michele Williams, Saint Michael's College, mx_williams@smcvax.smcvt.edu

T.J. Willis, Syracuse University, twillis@npac.syr.edu

Edward A. Bogucz, Syracuse University, bogucz@npac.syr.edu