# Dynamic Visualizations

Dynamic visualizations are those in which the graphical elements being displayed can change with time. The most obvios type of dynamic visualization is a simulation (here the term simulation refers to both the underlying calculation of parameters and the mapping of those parameters to visual entities. Simulations can take many forms and different types of learning can take place given the form of simulation. In general learning can occur by two means of interaction with a simulation

• Writing the simulation
• Dynamically interacting with the simulation during its execution
An example of a simulation where the student learns by writing the simulation is Logo. Logo was designed to allow students to explore goemetrical relationships. It consisted of a small triangle called the "Turtle" that could be moved about on the screen using commands(the original "turtle" was actually mechanical and moved about on the floor). The turtle could be told to move foward by some amount, turn left, turn right, put its pen up or down. If the turtle moved with its pen down a line would be drawn on the screen tracing its movement. The commands could be combined to form procedures, and could be stored and run sequentially in the form of a program. By having to achieve certain tasks, draw a triangle, square, pentagon, ..., with the turtle the student was required to apply knowledge about the geometry of the shapes. If the student did not have the needed knowledge Logo served as an environment for the student to explore the relationships between length of a side and the angle of intersection in the shapes. Logo also served as an introduction to programming. Although the language was very simple, it introduced the ideas of iterative execution and functional decomposition.

An example of a simulation where the student learns by dynamically interactiong with the simulation is the Dynaturtle, diSessa[4]. The Dynaturtle is a similar envirnoment to Logo. One major difference is that insted of usinf the forward command, student put the turtle in motion by applying impulses or "kicks" to it in the direction it was facing. Expirements would be set up in which the student would be required to have the dynaturtle hit a target. The arrangement of the expiremnt would be such that the dynaturtle could not be aimed directly at the target. In order for the student to achieve the goal they would have to display an understanding of Newtonian mechanics that is in conflict with there intuitive Aristotelian view of physics, diSessa[4]. This environement allowed the student to form and test hypothesis' about the environment. Through such expirements and careflu guidence from the instructor the students were able to construct there own knowledge about the world consistant with the Newtonian ideas being taught.

Simulations can also display multiple representations of the same concept. By linking the changes in one representation to the appropriate changes in the others, A student is able to manipulte the environment in a context in which they are familiar and whitness the effects those manipulations have on the other representations.