A Digital Mathematical Performance to Support the Physical
Embodiment of Balanced Equations
Stephen Chen, Steven Khan, Alireza Moghaddam, Immaculate Namukasa, and
Darren Stanley
One of the topics of exploration at the UWO Symposium on Digital
Mathematical Performance was on how the combination of physical
performances and digital technologies could improve mathematics
teaching. Our working group developed, performed, and recorded a
skit that attempts to help students learn the concept of
balanced/imbalanced equations with respect to the process of solving
equations.
The following eight video clips in .wmv (original recording and smaller
downloads) and .avi formats represent the key highlights of our
presentation at the UWO Symposium.
Video 1 -- The Skit
In the skit, one of the actors is carrying a heavy load of single items
and grouped items. The actor wants to balance this load -- i.e.
carry the same amount in each arm. Upon reaching his destination,
the actor needs to be unloaded in such a way that he remains in balance
at all times. A result of this unloading process is that a set of
single items eventually balances a set (of one) grouped items -- and
thus isolating and solving for the unknown. In the process of
unloading, several common errors are enacted that cause the actor to
become imbalanced. The actor over reacts to these situations and
creates a physically embodied understanding for the concept of
balanced/imbalanced equations.
There are several goals to this skit. First, there is the goal of
teaching the topics of balanced/imbalanced equations and the solving of
equations. To help students learn the concept of imbalanced
equations, a physical movement/full-body gesture is created. It
is hoped that teachers and students will be inspired by our performance
and re-enact the skit. It is hypothesized that the physical
embodiment of the mathematical concept and the opportunity to role-play
will both help the students to learn the mathematical material better.
.wmv format
.avi format
Video 2 -- The Mathematics of the Skit
The actor in the skit is carrying one bag and three cups in one hand
and two bags and one cup in the other. Thus, the equation is x +
3 = 2x + 1. To isolate x quickly, a student might take the 3 away
from the left hand side -- which leads to an imbalance. Upon
learning that they have to take away from both sides, a common error is
to take away a unit from one side and a group from the other.
These two common errors are part of the skit. Another error that
was not acted is to remove all of the units (e.g. 3 from the left and 1
from the right).
It is hoped that the students will enjoy the skit. And, just as
important, it is hoped that by performing the skit, it will help them
learn the associated mathematics more easily. Similar to the
expected classroom use of this digital mathematical performance, the
skit and the role playing are done first and then followed by the
mathematical lesson.
.wmv format
.avi format
Video 3 -- The Digital Mathematical Performance
In this video, we discuss the purpose of the skit.
.wmv format
.avi format
Video 4 -- The Lesson Goals
In this video, we discuss the objectives of the skit in terms of a
classroom lesson plan.
.wmv format
.avi format
Video 5 -- A Relevant On-line Resource
To follow up with the skit, we suggest the following on-line
resource
which we believe is highly relevant. This on-line resource allows
equations to be balanced and solved in an animated visualization.
.wmv format
.avi format
Video 6 -- Why use Digitial Mathematical
Performances?
In this video, we discuss the potential benefits to using a digital
mathematical performance to teach the topic of balanced/imbalanced
equations.
.wmv format
.avi format
Video 7 -- David Pimm discusses Physical
Rituals as a part of Learning
In this video, David Pimm provides an example of how a gesture used to
help students learn a mathematical concept then become almost a
required physical ritual that was a part of the mathematical concept.
.wmv format
.avi format
Video 8 -- John Mighton discusses how to handle
Negative Values
One of the limitations of the skit (and of the selected model/metaphor)
is that it doesn't handle negative values. In this video, John
Mighton describes how he has taught the topic in such a way as to avoid
this limitation.
.wmv format
.avi format
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