Assessing the Use of Technology and Using Technology to Assess

A Case Study

Alex Heidenberg
Michael Huber

Department of Mathematical Sciences
The United States Military Academy
West Point, New York

Appendix C      Example Modeling and Inquiry Problem

Scenario:  Your friend borrowed a 1 kg mass and two springs from the Physics Department.  The springs have the following properties:

Spring

Spring Constant (N/m)

A ( B (2

She wants to build an undamped harmonic oscillator to keep time like a watch.  After displacing the mass an initial 5 cm and letting it go, she wants it to move through the position of the system's natural length (equilibrium) every second.  Which spring will accomplish this?  Justify your answer with appropriate differential equation(s), solution(s), and/or graph(s).

Follow-up:  What‚s fundamentally wrong with your friend‚s plan to build a spring-mass system to keep time?  Explain your answer using terminology from the course.

The format used for assessment is broken down as follows:

Part I:  Modeling the Situation

1.  Draw a picture.

2.  Define variables with appropriate units.

3.  What are you trying to find?

4.  What information is given?

5.  What are your assumptions?  (They must be valid and necessary.)

6.  Describe the technique you will use to solve the model.

Part II:  Determining a solution

1.  The solution follows logically from the equations.

2.  The solution to the follow-up question follows logically.

3.  No magical "leaps of faith".

4.  The solutions are given in correct units.

Part III:  Inquiries and Discussion

1.  Summarize your answer to the MIP in the context of the problem.

2.  Discuss your solution to the follow-on question in context.

3.  Perform a common sense check.

4.  Explanations are communicated clearly.

This format is given to the students.