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 Discussion: Research Area Topic: Action Research -- Balances

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 Subject: balance applets Author: Kristin Smetana Date: Nov 23 2003
I recently worked with three seventh graders on the applets.  Two of the seventh
graders are in the 8th grade math curriculum.  I gave all three of the students
a worksheet to serve as a pre-test.  The worksheet had two balances that were
balanced with different shapes that showed different relationships.  The
objective was to balance the third balance by adding only one shape.  The
students were able to figure this out by finding one relationship at a time and
then substituting shapes until they were able to discover all of the
relationships of the different shapes.  The two accelerated math students,
helped the other girl for the first problem.  However, once she saw the
successful thought process, she easily completed the second problem.

Then, I worked with each student separately on the applets.  The first student,
“Ann” is in the 8th grade math curriculum and is currently studying algebra.
First she worked on the Algebra Beam Balance.  This program requires students to
work on balances to solve an equation.  All of the students found this program
to be very confusing at first.  They did not know how to use the program or what
the program wanted them to do.  Once Ann figured it out, she was easily able to
use the balances and solve the system of equations and find x.  Ann was able to
figure out exactly what x was equal to but had a hard time using the program to
do so.  If anything, I would say that this program confused all three students
rather than help them.  Ann also used the MSTE balance applets.  She was able to
confidently complete each problem by finding relationships between the shapes
and then solve the problem.  However, she said that she liked the worksheet
problems better because it was easier to see the relationships between the
different shapes.

The next student, “Beth” is also in Algebra this year.  Beth also had a hard
time figuring out how to use the Algebra Beam Balance program.  Again, it was
not that she did not understand the concepts, she merely did not understand how
to use the program. When using the MSTE applet, she used the same method as Ann.
Beth said that all of the programs were the same, meaning that she did not find
one program superior to another in helping her understand relationships between
objects.  She also said that it did not matter if there was an algebraic
equation with the balance or not.  From working with Beth, it was obvious that
she is a very bright student who relies on a systematic way of solving problems
which is why she found this activity to be relatively easy.

The last student, “Cara” is in the highest level of 7th grade math and is
currently studying Pre-Algebra.  She is very successful in this class and is
being currently being considered for the accelerated track.  When given the
pre-test, she did not understand the thought process that the other girls were
using, i.e. the method of finding one relationship and then substituting.
However, once Beth explained it to her, she was easily able to apply it to the
future problems and solved all of the successfully.  When Cara worked with the
Algebra Beam Balance, she was very confused by the equation and the balance.
She explained to me that she did not have a lot of experience solving equations.
However, she immediately was able to solve for x in her head but she had
difficulty using the applet to aid her in completely the problem.  However, she
did very well with the MSTE applet.  When talking to her, she told me that she
did not prefer pictures (the balances) over algebraic equations, but when both
were present, she became very confused.  She also said that the balances did not
help her understand solving equations better because when she solved equations
she did not see them as a balance, but merely numbers that she had to
manipulate.

Overall, the three students were able to successfully complete all of the
problems by using a systematic approach by finding one relationship at a time.
The students said that they did not have a preference for an applet, but they
clearly had trouble using the Algebra Beam Balance because they did not
understand the directions.  I think that these applets might be beneficial for
younger students to help introduce the idea of relationships, but these students
already understood the concept and did not find them very beneficial.