Animated Test of Motion (draft)

Aaron Titus

1/10/02

Introduction

I have been using Physlets since Wolfgang Christian first wrote Animator. Like any technology used in teaching and learning, Physlets are not a panacea. However, they have a definite upside. Advantages include

  • Flexibilitythey can be embedded within HTML documents and can be scripted; thus, serving a wide variety of purposes.
  • Innovative assessmentthey can assess students in ways that paper-and-pencil instruments cannot.

It is this second feature that I’ve focused on. My goal was to use Physlets to create an instrument to assess students’ understanding of two-dimensional kinematics, and to develop a model by which other Physlet-based assessment instruments could be designed.

Development of an assessment instrument

A good model for developing assessment instruments is the one used by Bob Beichner to develop the TUG-K (Test of Understanding GraphsKinematics). Here are the steps he used to develop the TUG-K:

  • Recognize the need for the test.
  • Create a good acronym (this wasn’t really one of his steps, but I thought I’d throw it in).
  • Formulate the objectives.
  • Construct test items.
  • Perform content validity check.
  • Perform reliability check.
  • Distribute.

Beichner provides a useful graphic to depict the important feedback loops that are present during the design process.

Animated Test of Motion

I followed Beichner’s model for the construction of the Physlet-based Animated Test of Motion (ATM). However, due to the more general nature of the topic, there were many more objectives covered by the ATM, even though certain objectives relating to applications of two-dimensional kinematics such as projectile motion and circular motion were left out. In addition, since objectives were both numerical (requiring a calculation) and conceptual and since test items included various representations (not just graphs), objectives were categorized by type (numerical or conceptual) and representation (data, graph, vector, animation only).

In two-dimensional kinematics, there are essentially 5 topics that we wish students to have a working knowledge (i.e. understanding) of. Students should understand

  1. displacement
  2. average velocity
  3. instantaneous velocity
  4. average acceleration
  5. instantaneous acceleration

They should be able to demonstrate this understanding by performing calculations, answering conceptual questions, and interpreting graphs and vectors. Clearly, knowledge of vectors (magnitude and vector components) is essential to understanding and demonstrating understanding of two-dimensional kinematics. Although vectors are not tested specifically, proficiency with vectors is essential to performing well on the test.

For each topic, a list of objectives were written. These objectives are tasks by which students can demonstrate their understanding of the given topic. The table below lists the objectives, organized by topic.

objective
number / objective / type / data representation
1.00 / understand the concept of displacement as a change in position
1.01 / calculate displacement using x,y data for linear motion along an axis, linear motion at some angle relative to the horizontal, and curved motion including parabolic motion and circular motion / n / data
1.02 / calculate displacement using position vs. time graphs for x and y / n / graph
1.03 / draw a displacement vector as a vector from one position to another position / c / vector
1.04 / distinguish between distance traveled, magnitude of displacement, and displacement / n / animation only
1.05 / calculate a displacement component using the area under a velocity component vs. time graph / n / graph
1.06 / calculate the magnitude of displacement / n / data
2.00 / understand average velocity as the ratio of displacement divided by the time interval
2.01 / measure the x and y components of the displacement and divide by the time interval to calculate the x and y components of the average velocity for linear motion along an axis, linear motion at some angle relative to the x-axis, and curved motion including parabolic motion and circular motion / n / data
3.00 / understand the concept of instantaneous velocity
3.02 / identify whether an instantaneous velocity component is positive, negative, or zero on a position vs. time graph / c / graph
3.03 / identify whether an instantaneous velocity component is constant, increasing, or decreasing on a position vs. time graph / c / graph
3.04 / identify whether an instantaneous velocity component is positive, negative, or zero on a velocity vs. time graph / c / graph
3.05 / identify whether an instantaneous velocity component is constant, increasing, or decreasing on a velocity vs. time graph / c / graph
3.06 / identify whether an instantaneous velocity component is positive, negative, or zero by viewing the velocity vector / c / vector
3.07 / calculate speed using the x and y components of instantaneous velocity / n / data
4.00 / understand average acceleration as the ratio of the change in instantaneous velocity divided by the time interval
4.01 / identify whether a component of average acceleration is positive, negative, or zero by observing an animation and noting the direction of the change in velocity vector / c / vector
4.02 / use a graph of position vs. time to identify whether a component of average acceleration is positive, negative, or zero / c / graph
4.03 / determine the direction of average acceleration during a time interval by finding the change in velocity vector during the interval. / c / vector
4.04 / calculate the average acceleration during a time interval by finding the change in velocity during the interval and dividing by the time interval. / n / data
5.00 / understand instantaneous acceleration
5.01 / use a graph of a velocity component vs. time to identify whether a component of acceleration is constant, increasing, or decreasing / c / graph
5.02 / use a graph of a velocity component vs. time to identify whether a component of acceleration is positive, negative, or zero. / c / graph
5.03 / identify whether an instantaneous acceleration component is positive, negative, or zero by viewing the acceleration vector / c / vector
5.04 / use a graph of an acceleration component vs. time to identify whether a component of acceleration is constant, increasing, or decreasing / c / graph
5.05 / use a graph of an acceleration component vs. time to identify whether a component of acceleration is positive, negative, or zero. / c / graph

Writing Questions

Three principles guided the development of Physlets Questions (Pqs) for the test. The first principle is based on prior research. The second and third principles were developed for this project. The guiding principles are:

(1)PQs should REQUIRE the student to “collect” data in some way, whether visually (by simply watching the animation, viewing a graph, or drawing a vector) or numerically (by collecting measurements from data, a graph, or a vector). That is, the animation must be NECESSARY for the student to answer a question.

(2)One animation can be used for hundreds of different questions, simply by varying what data is displayed, what graph is drawn, or what vectors are shown; therefore, one animation should be used to create questions that test multiple objectives.

(3)The study of kinematics is not limited to the topics of one dimensional kinematics, constant velocity, constant acceleration (non-zero), and circular motion; therefore, animations, though they should include these topics, should not be limited to these topics. As a result, PQs should include linear motion along an axis, linear motion at an angle with respect to the coordinate system, and motion along a curved path, both circular and parabolic. Also, PQs should include situations with non-constant acceleration.

(4)If possible, “realistic” animations should use objects from everyday experiences such as a bouncing basketball, golf ball, car, hot-air balloon, helium-filled balloon, rocket, and a helicopter. Realistic data, at least of the correct order of magnitude, was used. Some animations include the effect of air resistance and friction.

The objectives determined the tasks assessed by the questions; however, I had to determine the contexts in which students performed those tasks. I decided on 11 animations (i.e. Physlets) that would (1) be realistic, (2) include a variety of situations from constant velocity, constant acceleration, and non-constant acceleration, and (3) include projectile motion and circular motion (although in less recognizable ways).

Each animation was then duplicated and modified to display various data, graphs, vectors, etc., and approximately one question for each animation was written for each objective. That would give 253 questions. However, at this time, 217 questions have been written. From this, a subset was used to create homework assignments.

Here is the base set of animations.

Animation
Number / Name / Description
1 / Golf ball with break and friction / A putted golf ball rolls toward the hole. Simulation includes break and velocity-dependent friction.
2 / Golf ball--linear motion with friction / A putted golf ball rolls toward the hole. Motion of the ball is linear. Simulation includes velocity-dependent friction.
3 / Basketball bounces / A basketball with an initial velocity in the x-direction bounces on the floor. The ball loses energy with each collision and eventually stops.
Simulation uses setTrajectory instead of setForce in order to show the ball at the instant that it hits the floor. Energy is lost with each collision but no particular physical model is used to determine how much energy is lost due to a collision.
4 / Rocket with constant acceleration / Rocket with constant acceleration. Rocket's path is parabolic.
5 / Square rotates with a constant speed about its center / A square rotates about its center with a constant speed.
6 / Two cars pass each other with constant velocities / Two cars pass each other; each one has a constant velocity. The animation shows the cars from a top view.
7 / Golf ball rims hole / A golf ball "rims" the hole as it catches the lip of the hole. The animation uses an inverse-square interaction to model the motion of the ball when it comes in contact with the hole. The grass is modeled to be frictionless.
8 / Hot air balloon / A hot air balloon rises with a constant positive y-acceleration for a few seconds and then a constant negative y-acceleration until its y-velocity goes to zero. It has a constant x-acceleration until it reaches constant velocity.
9 / Helicopter -- linear motion with constant velocity / A helicopter has a constant velocity with a negative x-component and a negative y-component.
10 / Helium balloon rises / A helium balloon rises. Simulation includes the effect of drag that depends on v-squared.
11 / Electron between two oppositely charged plates / An electron travels between two oppositely charged plates.

Initial Testing of Questions

To test the questions, a subset was selected and used for daily homework assignments in the General Physics course (a large-lecture calculus-based physics course for engineering and science majors) at North CarolinaA & TStateUniversity in January 2002. I taught two sections of the course with a total enrollment of approximately 170 students.

For this first phase of testing, I did not use WebAssign. Rather, the questions were posted on the course web site. Students answered the questions and submitted their responses on paper. The reason that WebAssign was not used was that additional time is needed to transfer questions to the WebAssign database. In addition, at the time of using the PQs in class, we had not yet modified WebAssign to properly grade students’ drawing of vectors.

Because the PQs include both 2-D and 1-D phenomena, I modified the order in which I presented kinematics in lecture so that they would learn 2-D kinematics first. It seems that students have great difficulty understanding the connection between 1-D kinematics and 2-D kinematics. I thought that by presenting 2-D kinematics first, they would view 1-D kinematics as just a specific case and they would immediately apply concepts of vectors and vector algebra. While I have no data to prove it, I believe that this approach has merit. I will certainly investigate it more closely in the future.

Writing the Test

Once questions were tested, they were placed on the test. However, a test of 217 Physlet questions is simply unreasonable. Rather, questions were combined into multi-part questions (a, b, c, d, etc.) so that each objective was covered (usually just once which not a good characteristic of a reliable test). The result was a set of 9 questions.

Question 1: Bouncing basketball.

Question 2: Helicopter.

Question 3: Space probe.

Question 4: Planet orbiting a star.

Question 5: Hot-air balloon.

Question 6: Golf ball rims the hole.

Question 7: Rotating square.

Question 8: Putted golf ball.

Question 9: Space probe.

Preliminary Results

Based on some field testing, there are two major problems.

(1)The test is way too long! Somehow, objectives must be eliminated or combined. For instance, if students can calculate the magnitude of a vector, they should be able to do it for displacement, as well as velocity and acceleration (average or instantaneous). In addition, asking them to interpret a function as increasing, decreasing, or constant and asking them to interpret a graphed quantity as positive, negative, or zero may give the same results regardless of the quantity being graphed. If so, then those similar objectives can be combined. However, the fact that students often have difficulty analyzing different graphs of the same motion, I do not recommend combining these objectives on graph interpretation.

(2)The test is very mathematical! Students often are asked to make measurements from an animation or graph. This not only lengthens the time required to take the test, but it also limits the validity of the test regarding conceptual understanding. On the other hand, because the objectives are directly related to kinematics concepts and not applications of concepts (such as projectile motion, centripetal acceleration, etc.), I believe that conceptual understanding is indeed necessary to getting the problems correct, mathematical mistakes not withstanding.

Where to go from here

As one colleague, Bill Junkin, said “Students understand 2-D motion when they thoroughly understand 1-D motion and that the x-motion and y-motion are independent.” Perhaps that is the only objective that we need to test, assuming that if students understand 1-D motion and if they understand that x and y motion are independent then that is sufficient to demonstrate understanding of 2-D motion.