Doctoral Candidate in Mathematics Education

University of Illinois at Urbana-Champaign

Applets on this site are available for use by teachers, students, and education researchers, provided they acknowledge the source. If you find any of this material particularly useful, if you have questions, comments, or suggestions, or if you are interested in using any of this material in a published paper or a commercial venture, please contact me at ldmurphy@uiuc.edu.

The MovingMan applet is the most versatile applet available on this site. It can be used in the study of functions, line graphs, slope, the derivative, and basic motion concepts.

Using a mouse, the student drags a stick figure back and forth across the top of the screen between its home and its school. Below, graphs of the motion appear as the motion progresses. Using the menus, the student can opt to display one, two or three graphs. Each graph can be independently set to display the figure's distance, velocity, or acceleration with respect to time. The graphs are automatically scaled appropriately.

Since the figure can be in only one place and have only one velocity and one acceleration at any one time, the graphs are all **functions**. This provides an easily understood example to emphasize the difference between functions and other types of curves.

Beginning students can start with a single graph showing the figure's distance from home with respect to time. By experimenting with different motions, the student quickly learns how the **line graph** represents the motion: the direction of motion determines whether the graph goes up or down, the speed determines the steepness, etc.

Giving attention to the connection between the speed of motion and the steepness of the graph can lead to a lesson on **slope**. By associating a concrete physical concept with the abstract graph, this approach may help students understand difficult points, such as the often misunderstood distinction between vertical lines, which have** ***no* slope, and horizontal lines, which have** ***zero* slope. (There is** ***no* finite speed of motion that will produce a vertical line; a horizontal line is produced by standing still, which means moving at** ***zero* speed.)

The **derivative** can be introduced by starting with the concept of slope or steepness of the distance graph and linking that to the velocity graph. I have had some success with this approach in introductory calculus. Materials I have used for this purpose are available. This approach will be explained in greater detail in my forthcoming doctoral dissertation. A preview is available.

By displaying the distance, velocity, and acceleration graphs together and comparing how each represents motion events such as speeding up, slowing down, standing still, and changing direction, the student can develop an improved understanding of **basic motion concepts**.

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**The Water Flow applets**

The flow of electricity is often explained via an analogy to the flow of water. Voltage (also known as potential) is compared to pressure, flow of charge is compared to flow of water, and electrical resistance is compared to something that impedes the flow of water, such as a narrow spot in the pipe. As part of a unit on basic electricity and Ohm's Law, I have created a few applets depicting the flow of water.

The **Picnic Cooler** applet shows water flowing out of a canister with a spigot near the bottom. When the water level is high, this produces greater pressure which results in rapid flow. As the level drops, the flow slows. The flow rate is shown in two ways: the stream of water from the spigot appears larger and extends further across the screen to depict a greater flow rate, and the water level inside the canister drops more rapidly when the flow rate of water out of the canister is greater.

The **Water Tower** applet shows a water tower supplying water to a house. Outside the house is a stick figure using a garden hose to water flowers. The flow of water from the hose depends on the water pressue, which in turn depends on how high the level of the water tower is above the hose nozzle. The student can use a slider to set the level of the water in the tower, and can use the mouse to drag the figure with the hose around the screen. Eventually, I plan to add a partial clog in the pipe, which the student will be able to control with a slider, to model resistance.

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**The Current Flow applets**

These applets depict the flow of positive charge. They could be easily modified to depict electron flow, but that's low on my priority list right now because I haven't met anyone who wanted it. If you do, let me know.

The **Light Bulb** applet depicts the effect of voltage on flow rate. It shows a battery connected to a light bulb. The student uses a slider to control the battery voltage. Greater voltage produces greater current flow, which is shown by a larger number of charges moving in the wire and a brighter bulb. I also intended to make the charges move more rapidly to depict greater current flow, but depending on twhat kind of computer you are using may not work due to the limitations of the processor speed.

The **Resistance** applet depicts the effects of voltage and resistance on flow rate. It shows a battery connected to a variable resistor. (I left the light bulb out of this one because light bulbs are also resistors, and I thought two types of resistance would be confusing.) The resistor is modeled by a narrow spot in the wire, analogous to the narrow spot in the pipe which provides resistance in the water flow example. The student can control both the battery voltage and the resistance with sliders.

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These applets were written by Lisa Denise Murphy at the University of Illinois. The current versions were last revised in January of 2000. Permission is given for students and teachers to use these applets, provided acknowledgement is made of the source. Anyone interested in using these applets in connection with any published paper or commercial venture should please first consult the author. Thank you.

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This page last revised January 19, 2000.