MODSIM is a promising approach for several reasons. The first is that it allows instruction to be student-driven. Students can explore a model or simulation at their own pace and in a manner that makes sense to them. Another is that models and simulations today use state-of-the-art technology. It seems more “real” to the students because the models and simulations use the same types of technology that they use in other areas of their life—computers, Web-based programs, and gaming systems. Finally, using a MODSIM approach to study a phenomenon mirrors what happens in the world of science and engineering outside the classroom. Students can think and act like scientists and engineers as they explore for themselves how varying conditions affect a process or system without having to have the physical system available to them.
This chapter will examine some sample models and simulations using two different programs, Squeak and STELLA®. Each program represents a different approach to using MODSIM for instruction. Squeak is an animation-based program while STELLA is a mathematics modeling based software package. For each program there is background information for the instructor, activities for students, and an answer key. The student activities are written as pull-out sections from the other two sections.
Squeak
What is Squeak?
Squeak is a free, open-source, object-oriented, multimedia authoring environment that runs on many platforms and can be used to construct active learning environments for all ages. Programs can be written in the Squeak environment by novices using graphical programming tiles or by experts using Smalltalk. Developers around the world are continually adding functionality to the open-source Squeak image. In fact, Squeak is written in Squeak. Everything in the Squeak world is an object. Each object has properties and can send messages to other objects. The objects are like actors on a stage. Each object can be imbued with actions that create interactive experiences for learners and authoring is always on. Squeak is currently being rewritten from the ground up and is the basis for many new collaborative programming environments and exciting developments.
Two activities have been developed using Squeak. The first activity introduces students to the use of lasers to measure aerosol and cloud thickness. The second activity introduces students to Squeak programming through the study of motion in one dimension. These programs can be opened by following this link, http://www.pcs.cnu.edu/~rcaton/flexbook/flexbook.html.
Using Lasers to Measure Aerosol and Cloud Thickness
In this activity, students will use a Squeak program to investigate how lasers are used to measure the thickness of aerosols and clouds. Students will investigate the mathematical relationship between aerosol/cloud thickness and laser signal attenuation. The Squeak program also contains a mathematics review book for student reference. This activity is divided into six parts:
Calibration
Challenge 1: determining the relationship between laser intensity and aerosol/cloud thickness
Challenge 2: determining the thickness of an aerosol and/or cloud
Challenge 3: developing the algebraic equation that relates laser intensity to thickness
Challenge 4: developing the exponential equation that relates laser intensity to thickness
Challenge 5: writing a Squeak script to make a fifth test cell.
Directions and Questions to Accompany Laser Simulation
To access the laser program, follow this link: http://www.pcs.cnu.edu/~rcaton/flexbook/flexbook.html.
There are six parts to this activity. The directions for each activity can be found in the “book” on the left-hand side of the simulation. It will make more sense if you first read the directions then complete the activity. Each activity has one or more questions that are listed below. Be sure to answer the questions for one activity before moving on to the next activity. As part of the simulation, there is a mathematics review “book” for your reference.
1. Calibration
For both the aerosol and cloud calibrations, make a data table that includes number of cells (thickness) and laser intensity. Be sure to record laser intensity values as you take measurements.
2. Challenge 1
Make a graph of laser intensity vs. number of cells (thickness) for both the aerosol and cloud calibrations. Determine whether the relationship between intensity and thickness is directly proportional, inversely proportional, always decreases by the same factor, or none of these. Show work to support you answer.
3. Challenge 2
In the calibration activity, each cell was cm thick. In real life, clouds and aerosols can be meters or even kilometers thick. Scale the cell thicknesses to meters using the following information:
For aerosols,
For clouds,
In the Squeak program, click on the “aerosol challenge” and “cloud challenge” buttons to measure the laser intensity as it passes through aerosols/clouds of various thicknesses. Record these intensities and determine the corresponding thickness in meters. Explain the method you used to determine the thickness in meters.
4. Challenge 3
Based on your graphs, write an algebraic equation for the relationship between laser intensity and thickness for both aerosols and clouds. Show work to support your answer.
5. Challenge 4
Plot the natural log (ln) of intensity vs. thickness for both the aerosol and cloud calibration data. Write an exponential equation for each relationship.
6. Challenge 5
Construct a fifth test cell using Squeak. Save the edited program and submit it to your teacher.
Answer Key for Laser Simulation
Aerosol Calibration Data Table Number of Test Cells Laser Intensity
1
2
3
4
Cloud Calibration Data Table Number of Test Cells Laser Intensity
1
2
3
4
Challenge 1 The intensity decreases by the same factor every time the thickness increases by the same amount.
Challenge 2 Below is a sample calculation for aerosol and cloud thickness. Students’ answers will vary depending on the thickness of the aerosol or cloud they measure. They may also determine the thickness using the graph they created.
Aerosol
From the data table above, a thickness gives a laser intensity reading of , so
From the information provided in the simulation, in the simulation is , so
Cloud
From the data table above, a thickness gives a laser intensity reading of , so
From the information provided in the simulation, in the simulation is , so
Challenge 3
Aerosol equation:
Cloud equation:
Challenge 4
Transformed Aerosol Calibration Data Table Number of Test Cells ln (Laser Intensity)
1
2
3
4
Equation: or
Cloud Calibration Data Table Number of Test Cells ln (Laser Intensity)
1
2
3
4
Equation: or
Learning About Newton’s Second Law by Exploring One—Dimensional Motion
In this activity, students will explore one-dimensional motion and at the same time learn about programming in Squeak. The program explores the interrelationship between position, velocity, acceleration, force, mass, and time as well as touching on the relationship between force and energy. Students work through the program at their own pace and then are given a challenge to demonstrate their understanding of the physics concepts presented by being challenged to write their own Squeak program.
Directions and Challenge for Newton’s Second Law
Click on the following link to access the Squeak program for Newton’s second law: http://www.pcs.cnu.edu/~rcaton/flexbook/flexbook.html.
You should read through the "book" and complete the activities described. There are no questions for you to answer; you are simply learni
ng about motion and how to model it using Squeak. On the last page of the book, you will find the challenge to complete. The only item you need to turn in is the program you write for the challenge. The following is an overview of how to use the programming controls found in the book:
Any value that can be changed is next to a blue box with a description of the value.
Once you have changed the values, click and hold the “!” in the yellow circle to run the simulation.
Click the yellow reset button to return to the original conditions.
The scripts that are running the simulation are in the green boxes.
The challenge you are given is:
“Use Squeak to create a simulated microworld that shows how a body moves under the action of a force law of your choice. Illustrate the motion with graphs. Write an instruction manual for your project and be sure to include an explanation of how your project works. To be sure your instructions are clear, test your manual on others not familiar with your project to see if they can follow your instructions. As an additional challenge, explore the relationship between Newton’s second law and energy in your microworld.”
STELLA
What is STELLA?
STELLA is a software package used by thousands of educators and researchers for model building and simulation. It can be used to study everything from physics to economics, literature to calculus, chemistry to public policy. Based on Systems Thinking and System Dynamics, STELLA is a powerful tool for creating environments that allow students at all levels to learn by doing. STELLA models provide endless opportunities to explore by asking "what if" and watching what happens, inspiring the exciting ah-ha! moments of learning. Developed by isee systems, STELLA is available in both Windows and Macintosh versions. For more information, visit www.iseesystems.com www.iseesystems.com.
There are four basic building blocks to a STELLA model: stocks, flow, converters, and connectors. Each is defined as follows:
A stock is a quantity that is accumulated or depleted. The value increases or decreases over time. A stock is represented by a rectangle in the model.
A flow represents those actions or activities that cause the stock value to increase or decrease over time. A flow is represented by a large arrow with a valve in the middle. If the arrow points toward the stock then it causes the stock’s value to increase over time. If the arrow points away from the stock then the value of the stock will decrease over time. It is also possible to have a biflow, which means the value of the stock can increase and decrease over time.
A converter is used to represent additional logic important to the model. Typically, a converter modifies a flow. Converters are represented by circles.
A connector connects related items together. A connector can be an action (causes something to change) or informational (shows a qualitative relationship). Connectors are represented by wire arrows.
In order to use the models below, teachers should download the free isee Player at http://www.iseesystems.com/community/PhysicsFlexBook.aspx. The program can be saved and loaded on as many student computers as are needed. Students may also load this software on their home computers.
The Pendulum Story
This model explores the concepts behind a simple pendulum. Students can explore what effect, if any, string length, initial displacement, and pendulum bob mass have on the amplitude, period, and frequency of the pendulum’s motion. They can also explore the architecture of the model to investigate how the variables of simple harmonic motion are related.
Directions and Questions for the Pendulum Story
To complete this activity, go to http://www.iseesystems.com/community/PhysicsFlexBook.aspx and download the Pendulum Story model.
Open the model with the isee Player and read the Background and Context section.
When you go to the Conduct Experiments section, you will see that there are three inputs you can control: mass of ball, initial displacement, and string length. Your goal is to determine how each of these variables affects the movement of the pendulum. Before beginning, click on Instructions to find out how to use the functions of the model. Note that displacement is on the axis and time is on the axis. The model will display multiple trials on the same graph to make it easier for you to compare trials. If you wish to clear the graph, click on the reset button. You will know you are finished experimenting when you can answer each of the questions below. How does the magnitude of the displacement affect the period, frequency, and amplitude of the pendulum’s motion?
What happens when the displacement is a negative value? What is the significance of this in the physical world, i.e., what difference would you observe if you were actually swinging the pendulum?
How does the string’s length affect the period, frequency, and amplitude of the pendulum’s motion?
Grandfather clocks use a pendulum to keep time. If a grandfather clock was running slow, would you make the pendulum shorter or longer? Why?
How does the mass of the bob affect the period, frequency, and amplitude of the pendulum’s motion?
To answer the following questions you should look at page two of the graph, which displays velocity vs. displacement. To see page 2, click on the dog ear at the bottom left corner of the graph.
What is the displacement when velocity is at its maximum? If you were watching a pendulum, where would the bob be when maximum velocity is achieved?
What is the velocity when displacement is at its maximum? Where would the bob be at this point?
Why are velocity and displacement sometimes negative?
Answer Key for the Pendulum Story
How does the magnitude of the displacement affect the period, frequency, and amplitude of the pendulum’s motion?
As the magnitude of the displacement increases, the amplitude of the pendulum’s motion increases (it travels farther back and forth). The magnitude of the displacement has no effect on the period or frequency of the pendulum’s motion.
What happens when the displacement is a negative value? What is the significance of this in the physical world, i.e., what difference would you observe if you were actually swinging the pendulum?
When the displacement is negative, the graph starts in the trough of the sine wave rather than the crest. In the physical world this would indicate whether the bob was initially displaced to the left or right of the rest position.
How does the string’s length affect the period, frequency, and amplitude of the pendulum’s motion?
The shorter the string, the higher the frequency and shorter the period of the pendulum’s motion. String length has no effect on the amplitude of a pendulum’s motion.
Grandfather clocks use a pendulum to keep time. If a grandfather clock was running slow, would you make the pendulum shorter or longer? Why?
Make the pendulum shorter. This would cause the period to be shorter, which means the pendulum would be swinging faster. This would cause the clock to run faster.
How does the mass of the bob affect the period, frequency, and amplitude of the pendulum’s motion?
The mass of the bob has no effect on the pendulum’s motion.
What is the displacement when velocity is at its maximum? If you were watching a pendulum, where would the bob be when maximum velocity is achieved?
The displacement is zero when velocity is at a maximum. At this point the pendulum is in the middle (rest) position.
What is the velocity when displacement is at its maximum? Where would the bob be at this point?
Velocity is zero when displacement is at a maximum. The bob would be as far right or left as it was going to travel.
Why are velocity and displacement sometimes negative?
The negative sign indicates the direction of travel.
Coffee with the President and Prime Minister
This model introduces students to Newton’s law of cooling through a scenario-driven model. Students will be able to explore Newton’s law by manipulating temperature differentials and c
ontainer insulating capacity.
Directions and Questions for Coffee with the President and Prime Minister
To complete this activity, go to http://www.iseesystems.com/community/PhysicsFlexBook.aspx and download the Coffee with the President and Prime Minister model.
Open the model with the isee Player and click on Background and Context to read about the problem you will be investigating.
Return to the home screen. Before clicking on Conduct Experiments, answer the following question: Whose coffee do you think will be hotter? Why do you think so?
Click on Conduct Experiments and follow the directions. Continue to the next screen and record the coffee temperatures below. President’s coffee temperature:
Prime Minister’s coffee temperature:
Read the Understanding Why pages. After you have examined the graph, answer the following question: What assumptions are being made about the temperature of the cream added to the President's and Prime Minister’s coffee?
CK-12 21st Century Physics: A Compilation of Contemporary and Emerging Technologies Page 24
