Animated Test of Motion (ATM)

v 1.0

Information

Question Oobjectives
Mapping of questions and objectives
Test construction and design considerations
Interpretation of test results
Recommended implementation
WebAssign
Credits

Question Objectives

objective number objective
type

numerical = n
conceptual=c

representation
of
data

(data, graph, vector, animation only)

1.00 understand the concept of displacement as a change in position

1.01 calculate displacement using x,y data
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 and direction 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

2.02 calculate the magnitude and direction of average velocity
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 magnitude and direction of instantaneous velocity
n
data

3.08 Calculate x and y components of velocity using x and y vs. t graphs.
n
graph

4.00 understand average acceleration as the ratio of the change in instantaneous velocity divided by the time interval

4.01 draw the change-in-velocity vector for some interval and know that its direction is the same as the average acceleration during that interval
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 placing two instantaneous velocity vectors tail-to-tail and drawing the change in velocity vector
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

4.05 calculate magnitude and direction of average acceleration
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

5.06 calculate magnitude and direction of instantaneous acceleration
n
data

5.07 Calculate x and y components of acceleration using v_x and v_y vs. time graphs
n
graph

5.08 determine the change-in-velocity by calculating the area under an acceleration vs. time graph
n
graph

objective number	objective	type numerical = n conceptual=c	representation of data (data, graph, vector, animation only)
1.00	understand the concept of displacement as a change in position
1.01	calculate displacement using x,y data	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 and direction 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
2.02	calculate the magnitude and direction of average velocity	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 magnitude and direction of instantaneous velocity	n	data
3.08	Calculate x and y components of velocity using x and y vs. t graphs.	n	graph
4.00	understand average acceleration as the ratio of the change in instantaneous velocity divided by the time interval
4.01	draw the change-in-velocity vector for some interval and know that its direction is the same as the average acceleration during that interval	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 placing two instantaneous velocity vectors tail-to-tail and drawing the change in velocity vector	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
4.05	calculate magnitude and direction of average acceleration	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
5.06	calculate magnitude and direction of instantaneous acceleration	n	data
5.07	Calculate x and y components of acceleration using v_x and v_y vs. time graphs	n	graph
5.08	determine the change-in-velocity by calculating the area under an acceleration vs. time graph	n	graph

Mapping of Questions and Objectives

question number question
objectives

1 Bouncing basketball with x, y data 1.01, 1.03, 1.04, 1.06, 2.01, 2.02

2 Helicopter with x vs. t and y vs. t graphs 1.02, 1.04, 1.06, 3.08, 3.03, 3.02

3 Space probe with v_x vs. t and v_y vs. t graphs 3.04, 3.05, 1.05, 5.07

4 Planet orbiting a star with velocity and acceleration vectors 3.06, 5.03

5 Hot-air balloon with v_x and v_y data 3.07, 4.04, 4.05

6 Golf ball rims the hole with velocity vectors 4.03, 4.01

7 Rotating square with x vs. t and y vs. t graphs 4.02, 3.03

8 Putted golf ball with v_x vs. t and v_y vs. t graphs 5.01, 5.02, 5.06, 5.07

9 Space probe with a_x vs. t and a_y vs. t graphs 5.04, 5.05, 5.08

question number	question	objectives
1	Bouncing basketball with x, y data	1.01, 1.03, 1.04, 1.06, 2.01, 2.02
2	Helicopter with x vs. t and y vs. t graphs	1.02, 1.04, 1.06, 3.08, 3.03, 3.02
3	Space probe with v_x vs. t and v_y vs. t graphs	3.04, 3.05, 1.05, 5.07
4	Planet orbiting a star with velocity and acceleration vectors	3.06, 5.03
5	Hot-air balloon with v_x and v_y data	3.07, 4.04, 4.05
6	Golf ball rims the hole with velocity vectors	4.03, 4.01
7	Rotating square with x vs. t and y vs. t graphs	4.02, 3.03
8	Putted golf ball with v_x vs. t and v_y vs. t graphs	5.01, 5.02, 5.06, 5.07
9	Space probe with a_x vs. t and a_y vs. t graphs	5.04, 5.05, 5.08

Test Construction and Design Considerations

The test was constructed by first writing the learning objectives. Objectives were both numerical and conceptual which were distinguished by whether or not a calculation was required. Objectives covered the primary principles in kinematics, mainly displacement, average velocity, instantaneous velocity, average acceleration, and instantaneous acceleration. They did NOT cover specific applications of kinematics such as projectile motion and circular motion. They did NOT cover specific kinematics equations such as those for constant acceleration. Objectives also focused on various data representations. The learning objectives require students to use data (i.e. values), graphs, and vectors in order to answer questions.

Secondly, a base set of 13 animations were created. The set included both linear motion and motion along a curved path. They also included motion described by constant velocity, constant acceleration, and non-constant acceleration (including circular motion, motion due to a central force, and motion against a velocity dependent resistive force). Each of the 13 animations were duplicated to show data (x, y, v_x, v_y, a_x, and a_y), graphs (x and y vs. t, v_x and v_y vs. t, and a_x, a_y vs. t), and vectors (velocity and acceleration). The end result was approximately 120 variations of the base set of 13 animations.

Using the approximately 120 animations, questions were written for each of the learning objectives, approximately 220 questions were written. Those that used that tested the same general topic (like displacement) were combined into multiple parts of the same question. In the spring of 2002, a set of 6 assignments with approximately 8 questions per assignment were given to students as a trial to check the readability and technology.

From that set of assignments, questions were combined. The result was a set of 5 assignments with a total of 28 questions. This set seems reasonable as a homework set in 2-D kinematics.

From that set of homework questions were combined, a subset of 9 questions were chosen for a pretest. In order to have test most of the learning objectives, parts of the homework questions were edited. Each question was then mapped to the objectives so that we could ensure that all learning objectives were covered.

In writing the questions, the following design criteria were used:

Viewing or collecting data from the animation, graphs, or vectors should be necessary to answer the question.
Realistic situations and models should be used in order to make the animations more interesting and applicable to "real life".
Questions should be relatively straight forward with multiple choice or numerical answers.

Recommended Implementation

There are many ways of using the test depending on your goals. Here are some recommendations for a typical implementation in a classroom:

Give the test as a postest after intruction on kinematics.
For large classes, use WebAssign to collect students' answers. For smaller classes, collect their solutions and answers on paper.
Calculate the mean score for each question.
Calculate the mean score for the entire test.

Interpretation of Test Results

Interpretation of test results depends on your goals and how you used the test. Here are some ideas for how to use the test.

Give the test to two randomized groups-a control group and an experimental group--and use the two-tailed student's t-test to measure any significant differences in the scores on the test.
Give the physlet version of the test and a static version (with only images and data) to two randomized groups and use the two-tailed student's t-test to measure any significant differences in the scores on the test.
Give the test before instruction (pretest) and after instruction (postest) and measure the normalized gain and effect size for the class.

WebAssign

All of these questions are available in WebAssign. To find the questions, search for questions with the code

titus.ccli.test.physlets

Each question has also been placed on an assignment. To find the assignmaents, search for assignmaents with the code

titus.ccli.test.physlets

You may duplicate and modify the questions and assignments for your own classes if you wish.

Credits

I have many wonderful people to thank.

Kimberly Titus for her support through this long project.
Wolfgang Christian for creating Physlets. They are a lot of fun to script. I just hope they are as effective in instruction as they are fun to program.
Mario Belloni for Physlet technical support.
Melissa Dancy for evaluating the project.
John Risley for allowing me to post these questions on WebAssign and to use WebAssign to collect responses.
Brian Pittman for making changes to WebAssign that allow JavaScript to grade vectors drawn in Physlets.
Solomon Bililign and Caesar Jackson for their unwavering support at North Carolina A & T State University.
Duncan McBride and the National Science Foundation for their financial support and advice along the way.
Larry Martin--my friend and mentor in so many ways. Phillipians 4:13.

This material is based upon work supported by the National Science Foundation under Grant No. DUE-9952323
Aaron Titus | titus@mailaps.org