Working Description of OpenMath JavaBean Function Plotting Environment


Motivation:

The function plotting implementation is intended to:

1. provide the students with an environment in which they can explore functions (2d to start) and their properties in a way that reinforces the set-mapping metaphor of function construction and composition and...

2. present students with a real programming environment (albeit a GUI) in which they will develop their understanding of how computers deal with the tasks associated with plotting functions.

If the first goal is met, then students will have an environment for which exploration activities can be constructed that will challenge them to increase their understanding and appreciation of function and function properties. Evidence for this increased understanding would be improvement in their ability to describe the general properties of a function before graphing it. The second goal is woven into the nature of the interface itself. If the second goal is met, studemnts will aquire an appreciation of the relationship between objects and the information flow issues which surround objects' event handling. While this level of understanding touches on abstract concepts of computer programming, preliminary research by Jorgenson, Sinclair, Braham, and Balka (?) suggests that even middle-school aged students are capable of developing some understanding of these ideas. For this reason, the function plotting interface is not envisaged as simply a JavaBean implementation of a graphing calculator. Rather, it is a genuine graphical programming environmemt.

Features:

1. Students will have (be required to have) a high degree of control over the output of their plot. They will be required to specify parameters determining:

  1. Domain
  2. Range
  3. Resolution (step size)
  4. Grid layout (independant variable)
  5. choice of independant variable
  6. background colour
  7. grid colour
  8. axes colour
  9. plot colour(s)

2. Students will be able to have more than one plot displayed at a time on the same grid and be able to plot piecewise continuous functions.

3. Students will be able (forced?) to deal appropriately with restrictions

4. Students will be able to display an (active in both columns) table of values

5. Students will be able to reprogram to plot inverse

6. Students will be able to display nicely-formatted math representation of their function.

7. Students will be able to program to plot orthogonal tranlations as simple compositions

8. Students will be able to program to plot general compositions. f(x) = sin(x^2)

9. The programming environment will reinforce the set-mapping metaphor (as opposed to black box or input-output metaphor).


Return to Graphing Calculator Mock-ups.