Coming into this semester, I felt
like I really didn’t understand the prevalence of the big issues we talk about
in our education classes, particularly the math-specific classes. We have talked about how tricks and mnemonics
might actually hinder the learning of students because of the lack of
understanding and the reliance on blind memorization. The role of calculators in the classroom has been
a hot topic of debate. How much students
learn and retain information about basic computations from year to year has
also been discussed. All of these ideas,
and more, were running through my mind as I came face-to-face with the reality
I didn’t think I knew anything about.
When she showed me her first
problem, I knew I had a lot of explaining to do. The student I was tutoring had gotten a poor
grade on one of her first quizzes of the semester, and she told me she had no
idea where she went wrong. As a
sophomore in college, she was struggling with understanding how exponents work.
She needed help figuring out how to
rewrite the fourth root of x as x to some power. It seemed as though she didn’t remember
anything about radicals like that from high school. After some explanation, she eventually showed
me that she could convert other examples of roots to exponents, so we moved on.
Next, we looked at a problem she
got wrong that involved expanding an expression, namely 2(x+3)^2. Looking at her previous work, I noticed her
first step was to distribute the 2, so she had written (2x+6)^2. When I asked her why she did that, she said,
“Well, in ‘Please Excuse My Dear Aunt Sally,’ parentheses come first.” Our discussions of PEMDAS have mentioned how
confusing it can be for students, such as in this situation. I had never really been given the opportunity
to explain to a student where the mnemonic can be tricky, so I finally had the
chance at this tutoring session. I don’t
know if my explanation was adequate enough for her to make the right
calculation in all situations, but she seemed to grasp the content for at least
this specific type of problem.
The last major problem
I came across in my tutoring session was how to simplify 125^(1/3). The answer she had written was 41.67, which
is actually found when dividing 125 by 3.
I knew right away where her mistake was, but I wanted to know what she
thought she did wrong. “I typed it in my
calculator, and it gave me the wrong answer.”
I had her show me how she input the information in her calculator, and
sure enough, the answer she got was 41.67.
What was her problem? No one had
taught her how to use the technology!
She had no idea that she needed to use parentheses for fractional
exponents, so I showed her how to input it with parentheses to get the correct
answer. Of course, the point of this
problem was to have students rewrite 125 as 5^3 and solve by combining the
exponents, but I wanted to make sure she knew how to use the little technology
she is allowed to prevent further mistakes.
I never thought I would
see so many of the issues we discuss in one tutoring session, but it happened. All of the important information we want
students to know may actually not be getting across to them. I am hoping throughout this semester in MATH
371, and other math-education classes, that we as future math teachers are able
to finally understand the prevalence of these problems and make great strides
toward finding solutions.
Ashley Larson
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