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Even after the biased data from the factorial problem is thrown out, it is evident that the
students' scores on individual quiz questions did not show a significant improvement over the
corresponding opener problems. This in itself suggests that my instructional intervention did
not make any noticeable difference in student performance and understanding. Another possible
interpretation of the lack of improvement is that many of the students weren't paying attention
or making any attempt to retain the material taught, a conclusion which would be supported by my
own observations of the class during the mini-lessons. Since the students knew that the results of
the study would not affect their grade, perhaps they felt it was unimportant and did not attempt to
learn the information. Alternatively, the lack of improvement may just be due to the increased
pressure of a six-problem quiz instead of single-problem openers.
I also tracked the percentage of the class that reported using a graphing calculator on each
problem, to check if there was any change between opener and quiz. Strangely, the percentage
of students using a calculator increased on every problem except for simplifying factorials,
even the ones for which I suggested calculators would be useless in the mini-lessons. This may
suggest that the only idea students retained from the mini-lessons is that Mr. Davis thinks that
calculators are useful on some of these problems. The lack of actual improvement implies that
students do not actually understand how to effectively use calculators in this context.
If the results from my study are at all representative of high school students as a whole, then
frequent student use of graphing calculators is not beneficial to an Algebra II class. Low performance
on the problems emphasizing appropriate use or non-use of the calculator matches trends seen in the
initial survey. Students repeatedly mentioned the complexity of the calculator, the difficulty of
finding the one function they need from the myriad of buttons they know nothing about. Programming
tools are completely superfluous for students who know nothing about programming, and window settings
confuse students even after they have been shown several times how to adjust them. Graphing on a
calculator only prevents students from learning how to graph without one.
Of all the functions of a graphing calculator used in an Algebra II class, the only ones that cannot
be duplicated on an ordinary scientific calculator are graphing and matrix operations. While the
graphing calculator may save time on these two procedures, students need to learn how to do both by
hand anyway; when a graphing calculator is available, many do not. It is therefore my inevitable
conclusion that a graphing calculator is not beneficial, and may even be harmful, to the mathematical
progress of an Algebra II student. Within the Algebra II curriculum, a scientific calculator can
accomplish just as much, and may encourage better understanding, deeper thinking, and less
dependency. Furthermore, due to its significantly lower price, it would be more widely available to
students from low-income families, and its relative simplicity means that less class time would
be spent explaining how to use the various functions. As a final piece of anecdotal
evidence, I note that of all the students in my class, the two with the highest grades
do not have graphing calculators of their own.