|
Swing
Low, Swing High, Sweet Pendulum
By Clint Luscombe
|
Science has determined the formula that adequately
describes the
relationship between a pendulum's period, P, to its
length, L, while
under the influence of a specific gravitational filed, g.
This formula
alone is hard or most students to appreciate. (Not many
students
would look at the formula and think, "The period of a
pendulum
is solely dependent upon its length and gravitational
field in which
it swings!") Going to a neighborhood park to
experience the
pendulum motion of various swings would perhaps help
create more
of an appreciation and understanding of the formula.
However, the
park swings only offer one gravitational field, the
earth's! I suggest
introducing this formula to secondary science and math
students
using a great computer software called, Widget
Workshop—The
Mad Scientist's Laboratory. With this software teachers
can create
a pendulum environment that can be manipulated by students
in their
search for the "pendulum truths."
What follows is a lesson plan and activity that can easily
be implemented
by any secondary teacher. Also included are some results
of this
lesson implementation in an eighth grade algebra I class.
Instructional
Goals
Students will be working with an engaging software
environment that
will aid them in discovering the effect of a pendulum's
length,
weight and gravitational field upon its period of motion.
During
this activity the students will:
a)
change the pendulum's length, weight and gravitational
field to
determine their effect on the pendulum's period,
b)
find a direct relationship existing between a pendulum's
length
and period,
c)
find an inverse relationship between a pendulum's
gravitational
field and period,
d)
find no relationship between a pendulum's weight, and
e)
learn the value of isolating variables by holding all but
one variable
constant.
Software
Description
Widget Workshop offers a "safe" work station for
students
to hook together dozens of gadgets that perform both
meaningful
and fun outputs! Each gadget or widget part can easily be
connected
to other parts to create realistic experiments and
activities. Widget
Workshop is a great experiencing software. With this
specific activity
students will be able to see the pendulum swing and
experience the
real time motion of its period! [trying things out and
seeing what
happens. What's the basis of the simulation? What laws,
rules, etc.,
does it follow?]
Lesson
Plan
Widget Workshop can be a powerful tool in aiding the
discovery of
many mathematical and scientific truths. It gives the
students the
opportunity to test their conjectures and collect real
data. The
pendulum in this activity realistically reflects the
students' thinking
as it swings based on the students' input.
Teacher
Focus for Pendulum Activity
The teacher will help the students discover that there is
a direct
relationship between the pendulum's length and its period,
that
there is an inverse relationship between the gravitational
conditions
and its period, and that the weight of the pendulum has no
effect
on its period. The teacher will focus on seeing that the
students
isolate variables by holding others constant as they
change the
pendulum's parameters; that the students collect data;
that the
students communicate with their partner during the
activity; and
that the students make and test their conjectures.
Desired
Outcome for the Students
The teacher not only is interested in that the formula be
understood
but is just as interested in having the students be
self-disciplined
and organized as they perform the activity. Specifically,
the teacher
desires that the students learn the value of studying
multiple variables
by isolating them one at a time. The teacher also desires
that the
students verbally make and test conjectures throughout the
activity.
Teacher
Actions During the Activity
The teacher observes the students as they interact with
the software
and communicates with the students by asking questions
such as:
"Is your strategy working?, How can you be more
efficient?,
and, How can you be more confident about your
conclusions?"
The teacher must make sure to not give away answers.
Class
Discussion After the Activity
During this discussion the students can share both their
findings
and their problem solving strategies. Students should also
be encouraged
to share poor strategies that they used.
Results
My algebra I class of fourteen eighth graders paired up
and performed
the pendulum activity. Each pair spent from ten to twenty
minutes
on the activity. All seven pairs of students came up with
the same
successful conclusions regarding the relationship between
the variables.
Some pairs were much more efficient at isolating one
variable by
changing it and holding the other two constant. Those
pairs that
did not begin by isolating one variable eventually
realized the
futility of their work and soon began to isolate
variables. At times
I had to refocus them by asking, "Are you sure that
your strategy
is a good one to use?"
One pair of students collected a large amount of
disorganized data
before trying to make any conclusions and as a result
found it harder
to seen any patterns to their work. All but one pair wrote
down
their data. That pair decided to take notes when I asked,
"to
what are you comparing that result?" To each pair I
had to
specifically say, "Now, say your conclusion again and
write
it down!" Some had a difficult time articulating
their results
until they worked at writing them down. The writing of
their conclusions
seemed to help them clarify their thinking as they
compared the
three relationships.
Class
Discussion
A class discussion was held after the completion of the
pendulum
activity. The results were shared and the 'best'
strategies were
discussed. It was decided that the best strategy to use
was the
one that held two variables constant while changing only
one. It
was also mentioned that taking notes, making predictions
(hypothesizing)
during the activity and verbally sharing ideas with one's
partner
were key components to finding the relationships.
Conclusion
All fourteen students said they enjoyed the software
activity. It
was a rather new learning experience for them. However,
without
the follow-up class discussion there would not have been
as much
learning taking place. The discussion helped to solidify
all that
they experienced. At the very least, I needed the feedback
to be
convinced that the activity accomplished some or all of
what I hoped.
Finally, setting up the widget is quite easy. If the
teacher does
not want to do so most students would gladly do so as the
initial
step to performing the activity.
Software
Citation
Widget Workshop—The Mad Scientist's Laboratory,
Win3.1/Win95/Mac
by Maxis, 2121 N. California Blvd., Walnut Creek, CA.
94596-3572.
Editor's note: Maxis is not currently marketing Widget
Workshop.
The software remains available from numerous online
sources and
in many traditional software outlets.
Widget
Workshop Activity
"Analyzing the relationship of a pendulum's length
and with
to its period while under the influence of various
gravitational
fields."
Directions: Use the software, Widget
Workshop, to
find the relationships of a pendulum's period to the
following three
parameters (items): pendulum length, pendulum weight and
gravitational
conditions. You will use a teacher designed widget to
perform the
activity. Simply use the mouse to double click on the
pendulum to
make any adjustment you would like. Both parameters,
weight, and
gravity, have three possible settings while the pendulum
length
has seven possible settings which include a
"custom" one
in which you may determine its length. For simplicity
sake, the
widget you will work with is set up to time one-fourth of
a period
and then to automatically multiply the data by four in
order to
display the total period value. Be sure to collect data to
support
your conclusions. (See the picture of the widget.)
Copyright © 2001, ISTE (International
Society for Technology in Education).
All rights reserved.
|
