I. Constant Velocity Paradigm Lab

A. Pre-lab discussion
Students observe battery-powered vehicle moving across floor and make observations. The teacher guides them toward a laboratory investigation to determine whether the vehicle moves at constant speed, as it appears, and to determine a mathematical model of the vehicle’s position.

B. Lab investigation
Students collect position and time data for the vehicles and analyze the data to develop a mathematical model. (In this case, the graph of position vs. time is linear, so they do a linear regression to determine the model.) Students then display their results on small whiteboards and prepare presentations.

C. Post-lab discussion
Students present the results of their lab investigations to the rest of the class and interpret what their model means in terms of the motion of the vehicle. After all lab groups have presented, the teacher leads a discussion of the models to develop a general mathematical model that describes constant-velocity motion.

II. Constant Velocity Model Deployment

A. Worksheets
Working in small groups, students complete worksheets that ask them to apply the constant-velocity model to various situations. They are also asked to prepare whiteboard presentations of their problem solutions and present them to the class. The teacher’s role at this stage is continual questioning of the students to encourage them to articulate what they know and how they know it.

B. Quizzes
In order to do mid-course progress checks for student understanding, the modeling materials include several short quizzes. Students are asked to complete these quizzes individually to demonstrate their understanding of the model and its application. Students are asked not only to solve problems, but also to provide brief explanations of their problem-solving strategy.

C. Lab Practicum
To further check for understanding, students are asked to complete a lab practicum in which they need to use the constant-velocity model to solve a real-world problem. Working in groups, they come to agreement on a solution and then test their solution with the battery-powered vehicles.

D. Unit Test
As a final check for understanding, students take a unit test. (The constant-velocity unit is the first unit of the curriculum. In later unit tests, students are asked to solve problems using models developed earlier in the course, emphasizing the spiral nature of the curriculum).

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