Game to Generate Motion
David Schuster and Betty Adams, Western Michigan University, Kalamazoo, MI
David Brookes, Florida International University, Miami, FL
Marina Milner-Bolotin, Ryerson University, Toronto, Canada
Adriana Undreiu, University of Virginia’s College at Wise, Wise, VA
otion is a topic that is taught from of the room and thus ―blind‖ to the original motion
elementary grades through to university has to translate the descriptions back into reenacted
at various levels of sophistication. It is motions.
an area that can be challenging for learning in a The game-like aspect arises from the fact that
conceptually meaningful way, and formal kinemat- students’ initial descriptions are likely to be vague
ics instruction can sometimes seem dry and boring. or incomplete, so that attempted reenactments are
Thus, the nature of students’ initial introduction to often hilarious but instructive, with the reenactor de-
motion is important in sparking their interest, shap- liberately making ―wrong‖ motions from inadequate
ing their perspective, and developing conceptual descriptions. Each reproduction attempt leads to an
understanding of motion. The kinematic concepts improved description. This eventually leads students
we want students to acquire for basic motions are: to generate collectively the basic quantities required
position, time, speed, direction, velocity, veloc- as motion descriptors, in a process of successive re-
ity change, change rate, and acceleration, all with finement. Thus, the formal kinematic concepts men-
respect to a frame of reference. In this article we tioned above arise naturally, expressed informally at
describe a challenge game used as an ―opener‖ to first. Students ―invent‖ the ideas inductively for the
motion, in which students themselves essentially task at hand, rather than being ―told.‖
generate these concepts, in everyday language, from a Thus, in a succession of fun attempts, everyone
perceived need for them. learns about basic motion types, motion concepts,
We have used the game as an initial engagement and two-way translation between real motions and
activity at Western Michigan University, Rutgers verbal representations. It turns out that the way peo-
University, Ryerson University, and the University of ple ordinarily describe motion verbally is in terms of
British Columbia. It has been demonstrated at meet- ideas much the same as the formal kinematic counter-
ings of the American Association of Physics Teachers, parts, though expressed in everyday language, casually
and schoolteachers have tried it successfully at various and less precisely. Appreciating the need for accurate
grade levels. description in science is another objective of the activ-
In the activity, fun but with serious intent, one per- ity.
son enacts a real motion in class, walking or running The game can be played at various levels of dif-
to produce one of a number of basic motion types ficulty, qualitative or quantitative, for various types of
(e.g., constant speed, speeding up, or slowing down) motion. We describe the first and simplest qualitative
and at various rates. Others observe and produce game, discuss its instructional rationale, and report on
verbal or written descriptions of the motion. This is student and instructor reactions.
followed by the inverse process; a person who was out
434 DOI: 10.1119/1.3225502 THE PHYSICS TEACHER ◆ Vol. 47, October 2009
Photographs showing some of the events during a game.
Photo 1. Photo 2. Photo 3. Photo 4. Photo 5.
Motion-Matching – The First Game words, we have added the corresponding physics
As noted, the essence of the motion-matching activ- terminology in square brackets.
ity is the translation of an observed motion into verbal The reenactor, pointing to a selected whiteboard,
descriptions, followed by translation of the descrip- asks the person to call out the instruction.
tions back into reenacted motions, in the process gen- –“Walk slowly!” [kinematic quantity: speed]
erating the necessary motion concepts. Reenactor walks slowly but starts from the
To give a sense of how the game might operate ―wrong‖ place in the room. Stumbles into a bench
in class, we illustrate its ―moves‖ for Game One, the (Photo 3).
simplest motion with qualitative descriptions. For this
introductory game it is best to prime a student volun- –―No, you’re starting from the wrongplace! Start at
teer to be ―in the know,‖ in order to take full advantage the end of the board!” [initial position]
of the game’s instructional potential and make sure it Goes to the board but to the wrong end, and starts
runs smoothly. The instructor and collaborator agree walking from there.
beforehand on the first motion to be enacted, i.e., –―That’s the wrong end! Start from the other end of
walking at a steady speed. This game serves both to the board!” [frame of reference; initial position]
demonstrate what the activity is all about and at the Goes to the correct end but then climbs up onto a
same time start generating motion concepts. conveniently placed stool. Steps off it with interesting
results (Photo 4).
The game sequence goes as follows. The instructor –“No, not from up there. Start on the ground!”
outlines the nature of the game to the class, asks for [frame of reference; three-dimensional]
a volunteer, and leaves the room. The volunteer then
enacts a basic first motion by walking at a slow steady Starts at the correct spot but then walks out into
pace alongside the board (see Photo 1) while students the room, i.e., in the wrong direction. Thus bumps into
observe. The instructor is then called back in (Photo a person.
2), available to act on instructions, and students have –“That’s the wrong direction – go parallel to the
about half a minute to come up with motion descrip- board!” [initial direction]
tions. They can write these on small whiteboards. (It Stands at the correct spot, facing along the board
enhances the game atmosphere if someone whistles or ready to walk, hesitates...and then walks backward.
plays the ―Final Jeopardy‖ theme tune from the TV – ―Silly, not backward! Walk forward this time!”
quiz show while students write). [initial direction; reference axis]
The instructor has some control of how the game Starts by walking forward but thereafter takes a
now goes by selecting from the descriptions offered wandering path.
and deciding which to act on first, ready to pounce – “No, not curvy ... walk in a straight line all the
on inadequacies by deliberately enacting ―wrong‖
motions allowed by the description. The events or
―moves‖ in any game will vary depending on class re-
sponses, but below we illustrate the kind of sequence
and dialogue one hopes for in students’ first
encounter with the activity. After the students’ own
THE PHYSICS TEACHER ◆ Vol. 47, October 2009 435
time.” [straight-line motion]
Walks in a straight line in the correct direction... Game notes and teaching strategies
but speeds up along the way. There are various teaching strategies and caveats that can
– “No, don’t speed up – walk at a steady speed all the help make the activity work well and achieve its goals.
time.” [constant speed] Note that this activity is clearly a game, so it is natural
Walks at constant speed—but much too slowly. for it to seem somewhat contrived. For the same reason one
can happily “overplay” the game events to make the point.
–“You’re going too slowly ... move faster.” [speed
Students also tend to enjoy giving instructions to the instructor.
As the class produces descriptions and refinements, stu-
Walks again but much too fast this time.
dents can put up their whiteboards sequentially at the front of
– “Not so fast! You’ve overdone it. Move at...um... the classroom. It is also useful to have a student write up the
medium walking pace.” [speed magnitude, refined] sequence of specifications as a list on the board as they arise.
The reenactor moves ―correctly,‖ fully constrained These will generally be in everyday language but in addition can
be labeled with the scientific term, e.g., initial position, etc.
There is a danger, as with any activity, that fun aspects
–“That’s it ... finally!” [accumulated descriptors all and practical details can obscure the real purpose, unless
in play] one keeps the underlying objective uppermost. Accumulating a
list of descriptors helps with this.
The reenactor has no more ―wiggle room‖ and must
move as specified by the accumulated description re- The activity, even with successive refinements, goes rap-
idly in class; students catch on quickly and descriptions
finements, i.e., from the designated initial position,
soon become tight enough to ensure faithful reproduc -
in the correct direction, in a straight line, at constant tion. There is no need to belabor points during the game.
specified speed, all relative to a specific frame of refer-
Note that since the class soon realizes what the reenactor
ence. is up to, a variation part way through is to let them in on it and
The criterion for success is that the original motion ask: “OK, what do you think I’m going to do next (to foul up)?”
enactor must agree that the reenacted motion matches In principle the reenactor could be blindfolded instead of
the original. This is more dramatic if done by direct out of the room, but this would preclude the class talking about
comparison: enactor and reenactor act out their mo- the enacted motion during that time.
tions simultaneously side by side (Photo 5). For effect
we play or whistle ―Pomp and Circumstance‖ during
this ―matching march.‖
For each motion, before going on to the next, it
is important to reflect on the concepts that arose and There are two parallel challenges in the game: how
what has been learned and how. We want the ultimate to characterize motions, and how to describe them
message to be the motion concepts, not just the game precisely in words. It is fortunate when experiential
events. One can also ask the students to write down notions correspond roughly to formal science con-
three things they didn’t understand well beforehand cepts, and when everyday vocabulary roughly fits for-
and three insights gained. mal terminology. This is not always the case in science,
but for motion, students’ existing ideas are clearly
The activity represents an inquiry-based inductive resources to be built on.
instructional approach. By contrast, in a ―direct‖ ap-
proach an instructor simply tells the students that mo- It turns out that the way people ordinarily think
tions are characterized by specified kinematic quanti- about and describe motions corresponds reasonably
ties. The concepts are received rather than generated. well to the desired scientific concepts and terms,
We note that inquiry-based instruction is advocated though expressed less formally and precisely. The game
by national and state science education standards highlights how difficult it can be to describe things
throughout K-12 schooling. At college level a number well, and the need for precision and completeness in
of reformed approaches to science instruction take science. One can mention to students that other rep-
inquiry approaches, many stemming from physics resentations such as graphs or equations can provide
education research.1-6 precision, as they will see later.
436 THE PHYSICS TEACHER ◆ Vol. 47, October 2009
Subsequent Motion Types and Game The motion-matching activity involves a variety of
Levels other ideas relevant to motion. At suitable times, or
For the initial demonstration game described above, on reflection, one can explicitly direct attention to is-
the instructor usually plays the role of reenactor. For sub- sues such as:
sequent games and different motions, students take over Point particle representation
and run the activity, playing all the roles themselves. Interval quantities and a differential perspective
After the first game there are two ways to move to on motion
the next level: either go on to motions with changing Rates of change
speed, still done qualitatively, or make the steady mo- Qualitative and quantitative descriptions
tion case quantitative. One can do these in the order Everyday and scientific language.
in which students seem to head of their own accord. Thus, this apparently simple game provides many
These cases are described briefly below, as well as com- teachable moments by injecting such ideas at the ap-
plex motions and other relevant concepts. propriate time. Each is worth discussing in its own
right to an extent that depends on objectives. One can
Accelerated motions – qualitative games
also play a ―custom‖ game focusing on one particular
If one stays in qualitative mode and tries different aspect, position-location for example.4
motions, subsequent games then involve variants of
the first (i.e., different starting points, directions, and Student and Instructor Reactions
speeds) followed by accelerated motions (speeding up
or slowing down). For speeding up, an enactor would Student and instructor reactions to the activity
start from rest and speed up to a run, gradually and have generally been very favorable. Below we give
continuously. For slowing down, an enactor would some reactions from Physics 1800, a course for pro-
already be running at the initial spot and then slow spective elementary teachers at Western Michigan
down continuously to a stop (or even reverse). In de- University.
scribing such motions, students add the concepts of A written survey asked students to comment on the
speed change and change rate to their previous set of activity and say how well they thought it succeeded as
motion descriptors. an opener to motion. Of 40 students in two sections,
32 had positive comments only, six had mixed com-
Quantitative game levels ments, one had a negative comment only, and one did
A qualitative game can move up a level by becom- not respond. Some brief extracts from comments are:
ing quantitative. Relevant quantities are then speci- Some positive comments: ―I enjoyed the activity, it was
fied numerically, in units suited to the situation. In interactive...everyone seemed interested and engaged.‖
principle there are two ways of specifying a motion ―It was something I’ve never done before...I never
quantitatively. One is to specify pairs of position-time would have thought that is so hard to explain.‖ ―Made
values, while another is to focus on intervals and refer me realize what concepts are related to motion, what is
to differential quantities (speed and acceleration) dur- required to describe motion scientifically.‖ ―What types
ing the motion. It is interesting that our students tend of motion there are.‖ ―Got the whole class involved and
toward the latter. actually laughing.‖ ―Everyone learned a lot while having
From the instructor’s point of view, the few basic
motion types above form a sensible sequence for pro- Some negative comments: ―Too simple...good for
moting the learning objectives. However, note that elementary students, a little redundant for college.‖ ―Too
students will soon want to indulge in fun with com- long...activity could be shorter.‖ ―Annoying, because the
teacher tried as hard as he could to do the wrong things.‖
plex and even acrobatic motions. They enact dancing,
Commenting as future teachers: ―Fun for young kids...
twirling, and multi-stage motions as they get into the they would enjoy giving directions to their teachers,
swing of things. Toward the end of one session, an because they don’t ever get to be the one giving
imaginative student walked on her hands and students directions, it is always the teacher.‖ ―A bit difficult for
drew hand outlines in chalk on the floor to indicate younger kids
what the reenactor should do!
Teachable moments for other relevant concepts
THE PHYSICS TEACHER ◆ Vol. 47, October 2009 437
perhaps?‖ ―Yes, an activity I would use in teaching.‖ not thought of. Photography is by Mike Lanka
A physics teacher who had seen our conference at Western Michigan University. Course develop-
demonstration tried the game at her own high school ment was supported in part by National Science
and emailed that the idea had come at just the right Foundation grant DUE 0536536 and a seed grant
time for starting motion and had been a ―smash hit‖ at from the Michigan Space Grant Consortium. Any
her school. Of course, as with any participatory activ- opinions, findings, conclusions or recommendations
ity that depends on class dynamics, it will work better in this paper are those of the authors and do not nec-
on some occasions than others. essarily reflect the views of the grantors.
Motion-matching is an engaging game that can be 1. E. Etkina and A. Van Heuvelen, Investigative Science
used as an ―invitation to learn‖ when starting motion. Learning Environment (ISLE); http://www.islephysics.
At the risk of sounding trite, we can say that the activ- net and http://www.rci.rutgers.edu/~etkina/ISLE.htm.
ity is both hands-on and minds-on. 2. Arnold B. Arons, The Various Language (Oxford Univer-
sity Press, New York, 1977).
We find that people tend to describe observed mo-
3. L.C. McDermott and the Physics Education Group at
tions in everyday language in terms of perceptually the University of Washington, Physics by Inquiry (Wiley,
evident features that correspond quite closely to the New York, 1996).
desired scientific concepts of reference frame, initial 4. W. J. Leonard, R. J. Dufresne, W. J Gerace, and J.
position, direction, speed, speed change, and rate of P. Mestre, Minds-on Physics: Motion (Kendall/Hunt,
change (acceleration). This intuitive tendency can be Dubuque, IO, 1999), Activity 2A.
seen as a resource to build on in instruction. 5. Priscilla W. Laws, Workshop Physics: Activity Guide Mod-
It is interesting that, from a mathematical perspec- ules, 2nd ed. (Wiley, Inc., New York, 2004).
tive, both velocity and acceleration are differential 6. David Schuster, Mechanics, Inquiry and Insights, Physics
quantities (being rate of change of position and rate course pack (Western Michigan University, 2004).
of change of velocity, respectively). This also seems to 7. R.W. Bybee et al., Science and Technology Education for
reflect what people notice when they observe actual the Elementary Years: Frameworks for Curriculum and
motions: how things are changing. Instruction (The National Center for Improving Instruc-
tion, Washington, DC, 1989).
Note that motion-matching is envisaged as an PACS codes: 01.55.+b, 45.00.00
―overture.‖ For science instruction that explicitly uses a
learning-cycle approach, such as the 5-E cycle,7 it can David Schuster is an associate professor in physics and
serve as a wonderful Engage phase, with a good admix- science education at Western Michigan University.
ture of Explore and Explain aspects as well. However it email@example.com
need not necessarily form an integral part of the ―main Marina Milner-Bolotin is an assistant professor in the
movement‖ conceptual development sequence. After Department of Physics at Ryerson University in Toronto.
the overture, we go to our planned kinematics teach- firstname.lastname@example.org
ing sequence, which the game complements. Betty Adams is an engineer working on graduate degrees
The challenge game works well in both small classes in physics and science education at Western Michigan
and large lectures, can be adapted to a range of levels,
and can be used in both science courses and teaching David Brookes is an assistant professor in the Physics
methods courses. Department at Florida International University.
Acknowledgments Adriana Undreiu is a teaching fellow in the natural sci-
ences department at the University of Virginia’s College at
The authors would like to thank Bill Merrow, whose Wise and is completing her doctorate in science educa-
toy car activity sparked a train of thought; Eugenia tion.
Etkina, who does her own version of the game at email@example.com
Rutgers; Philip Kaldon, who spontaneously whistled
the two theme tunes during a game; and our many
students, who came up with good ideas we had
438 THE PHYSICS TEACHER ◆ Vol. 47, October 2009