Reusability and Student-Centered Learning

Two ideas are discussed in the Virtual Earthquake pages.

• Determining the location of an earthquake.
• Determining the magnitude of an earthquake on the Richter scale.

An earthquake produces two kinds of waves -- P-waves and the slower moving S-waves. The graph above shows these two waves as detected by a detector in Eureka, California some distance from an earthquake.

The time required for each wave to arrive at the detector can be expressed as a linear function of the distance from the earthqauke to the detector as shown in the graph below.

The difference between the two arrival times is also a linear function of the distance from the earthquake to the detector as shown in the same graph.

Because it is easy to measure the difference between the two arrival times, it is easy to determine the distance from the earthquake to a detector. With measurements from three detectors we can determine the location of the earthquake as shown in the map below.

This basic situation is very rich and engaging. It can be used or reused in a variety of different educational settings -- in courses in different subject areas and with students at different levels.

The Virtual Earthquake pages are designed for use in a science course. They minimize the time that students spend on the underlying mathematics by providing interactive tools that do all the computations -- and even draw the circles on a map as shown above. The pages lead students through the process step-by-step, so that they should develop an understanding of the ideas and process involved.

We discuss several different situations in which this basic idea might be used in mathematics courses and in the process build up an argument for reusability -- that is, for developing resources like the Virtual Earthquake in a form that makes it easy to use them as a base for, or as a component of other resources for learning in science, mathematics, engineering, and technology (SMET).

• In a middle school class looking at linear relationships.
• In a high school class studying quadratic equations.

• Playground experimentation.
• Thunder and lightning.
• The Global Positioning System.

Reusability involves many different problems.

• Material needs to be available in a form that enables adaptation and reuse.
  • Electronic formats are a big step forward.
  • Smaller units that can be used or combined in different ways.
  • Open source code.
  • Using generally available tools.
• Intellectual property rights.
  • The original writer should continue to receive credit.
  • Contributions of second generation writers should be recognized.
• Economic property rights.