Physics
Applets
for Drawing
Features | Exercises
| Examples
The Physics Applets for Drawing (PADs) are a set of modular,
auto-grading Java applets for drawing graphs, sketching diagrams and capturing
motion. While they can function perfectly well in stand-alone applications,
they are particularly designed to work as an element within web homework
where they provide a graphical alternative to numerical boxes and multiple-choice
buttons.
Features:
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Web-friendly: PADs are designed for use by everyone,
not just those with computer savvy and the latest equipment. They are written
in Java 1.1, which is supported by virtually all 4.0 and higher browsers
without any need for downloading plug-ins or other software. This can be
a problem for older computers and users in locked-down environments such
as university computer labs. They are relatively small; both GraphPAD and StrobePAD
are 38 KB and TablePAD is 27 KB, enabling relatively fast downloads even for users
with modem connections. Because they share a lot of code, the three applet can be
bundled into an archive of 53 KB. (Photos on the web can easily reach 40 KB and larger.)
They can be used with or without JavaScript, a problem for Macintosh users
and those very concerned about security.
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Focused: each PAD does one and only one thing such
as drawing a single graph or moving a single object. This both keeps the
size down and minimizes what users must learn to use them.
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Flexible: A large number of options can be set through
parameter tags, from titles to specification of what a correct answer is.
This means that they can be customized to a specific exercise without changing
the applet code.
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Common storage and code: Behind the different
faces the PADs present, they will all handle data points and curve fits
the same way and use the same code for grading. This will enable
easy communication, reduce the total code needed to download when multiple
PADs are present in a page, and make authoring exercises easier.
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Modular: They are designed to work together, so that
interactions with one can set the display value or correct value of another.
For example, moving the object in the MotionPAD could cause a graph of
the motion to be plotted in real time (similar to RTP) or the VideoPAD
could output to a table for a simple version of video analysis. Alternatively,
a student could be allowed to draw an arbitrary position graph, but then
required to draw a velocity graph for that particular position graph.
This capability will allow flexibility in creating applications as simple
or as complex as appropriate to the exercise.
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Self-grading: Internal code compares the current state
to the specified correct state and the allowed tolerances. The evaluation
is done using the linear or polynomial parameters (slope, intercept, etc.)
which is more tolerant of small errors in point placement. Each parameter
and tolerance is specified independently, allowing different levels of
specification, from simply requiring a positive slope of a graph to a strobe
diagram where the object moves downward at precisely y(t)=10m – ½(9.8
m/s2)t2. A mentioned above, the correct value
can also be made dependent on the state of another PAD. Self-grading
allows these to work as stand-alone applets for classroom or extra practice
use where no permanent record is needed, and it means that web homework
systems do not need to add much code to be able to use these. Alternatively,
the system could get the status of the applet and evaluate it directly,
for higher security.
Exercises enabled
What matters in the end, of course, is not having the latest
computer technology in the classroom, but the ability to employ effective
pedagogical methods. The value of the PADs is that they will facilitate
the use of a number of different types of exercises to be administrated
and evaluated on the computer; exercises that are already used in research-based
physics curricula will now be available as part of computerized homework.
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Visual conceptual questions: These are exercises
such as, “Draw a position graph of a person walking away from the origin
at a steady rate,” or “Draw a vector to indicate the direction of the electric
field at point ‘A.’” There are no numbers—the only things that matter
are direction and perhaps relative magnitudes. Math can sometimes
be a crutch by students plugging numbers into a calculator without really
thinking about it, or cause cognitive overload in which thinking about
both the concept and the numbers at the same time is really too much to
handle when everything in new. This type of exercise allows/forces
them to focus on the concept, is visual so it can have more intuitive
meaning and still can be a fairly challenging exercises as it does not
present the correct answer as one of a few options. Curricula such
as RealTime Physics, and Tutorials in Physics use these sort of exercises
frequently.
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Semi-qualitative questions: These exercises are similar
to the conceptual ones, but some numbers are introduced, such as there
are numbers on the graph and the line must cross certain points, or the
vector needs to have a certain magnitude. They require some simple
math to complete, but not complex calculations. These exercises serve
as a half-way point between the conceptual questions and standard numerical
exercises. These are also used with RealTime Physics and Workshop
Physics.
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Problem visualization: Sketches and diagrams are useful
tools for helping to set up and visualize a problem. The most common
example is drawing free-body diagrams, but curriculum such as the ALPS
kits also use motion, energy, momentum and rotation diagrams to help visualize
the situation and identify the essential physics in the problem before
writing down and solving the equations. Novice problem solvers tend
to skip this stage and go directly to the equations, without always choosing
the correct equations to solve. PADs would enable instructors to
require a sketch as part of solving a numerical problem.
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Multiple representations: By viewing multiple representations
of a situation—for example the live motion of an object and a real-time
graph—students can be helped to focus more on the phenomena being represented
rather than the representation itself. This is an important reason
for the real-time graphing of RealTime Physics and a valuable component
of video analysis and simulations that include graphs and other representations.
The flexible, modular structure of PADs would enable several different
uses of this:
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Real time representations: The user draws in one PAD
and another one is updated simentanuosly, as in computerized laboratories,
linking the two representations in the user’s mind.
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Representation conversion: In this case the user is
requested to draw one diagram based on another, for example a strobe diagram
from a graph, and the correctness of the second one is checked. The
first diagram could even be one the user drew first, and the correct answer
in the second depends on what was drawn in the first.
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Combination: This combines features of the two previous
ones; for example, a user could be presented a ball moving across one applet
in an animation and be requested to draw a graph representing its position.
Then once done, a second ball would move according the graph drawn, allowing
the user to visually compare and judge the correctness of the graph.
This sort of feedback can be particularly valuable
Examples