Analytical
and Integrative Thinking
My
Introduction
to Research
I
clearly
remember my
admission interview in December
2008.
In
explaining one of my many reasons for applying to the Ph.D.
program, I said, "I want to do research; but, I don't know how."
Certainly, I had much to learn; but, my desire to learn has
made
the journey much more satisfying than I could have imagined.
Although I had done data recording and some video
transcriptions,
my summer internship with Dr. Suh, at the COMPLETE summer institute, in
the summer of 2010, was really the launching point for my active
involvement in research. I learned how to observe
and kept
daily records of my
observations. I
watched the techniques which
the instructors used when interacting with the participants.
And,
I attended the daily meetings at the end of each day, through which I
gained considerable insight into how the instructors evaluated
their sessions; how they assessed the understanding of the
participants;
and, how they used the information from the day to plan for future
days. This came full circle when I was an instructor
at the
COMPLETE institute in the summer of 2012.
I was a GRA for Dr. Smith for two years. I have also been an
archivist for several COMPLETE and ESTEEM sessions. I have
successfully, and not painlessly, gone through the HSRB process.
And, I have had a research article published.
My
Timely and Enlightening
Introduction to Qualitative, Quantitative and Mixed Methods
Research
First,
I experienced qualitative
research. I was surprised by amount of researcher personality
and
interpretive leeway which exists in qualitative research.
In
my qualitative research course, we discussed the very real possibility
that two researchers who viewed the same research coming to two
different, and possibly contradictory conclusions. This is
due to
the
differing perspectives, opinions and experiences of the researchers.
Initially, I thought this may be a significant
drawback.
However,
after studying several qualitative research pieces, I came to
see
that
the self description of the researcher, which usually appeared
at
the
beginning of an article, set the tone for the interpretation of the
research. Everyone is biased, no matter how much we think we
are
not.
I found this phenomenon to be most evident in culturally
situated
research. I specifically remember one piece in which the
author
extolled the superiority of the mothering skills of a certain tribe of
American Indians over their Caucasian counterparts. The
researcher
herself was from that tribe. And, while her bias was at times
excessive, her early acknowledgment of her ethnic loyalty gave me a
tolerance for her sometimes gushing praise which would
otherwise
have
been saccharine. For me, the important lesson here, though,
was
to not
do that myself.
EDRS
812 Final Project:
Polynomial Dancing
My
paper discusses interviews with three high school Algebra teachers and
their views on calculator use in the classroom.
My introductory quantitative class was enjoyable and enlightening.
I learned much about statistical tests which I did not
previously know and I got a very useful introduction to SPSS software.
Dr. Dimitrov's explanations of some concepts which I thought
I knew actually gave me more in-depth understanding. I got
the chance to work on some real data sets and not the small, pristrine
ones I use in the high school statistics classes I teach.
Interpreting the results has also given me an appreciation
for the difficulty my own students havein doing the same thing.
Just what is this test telling me? Did I use the
right variables? Did I use the right test? It is
ironic that while doing some quantitative tests, I thought about
qualitative data which could be used to help clarify the results.
In my final paper for this class, I used data from the high school
classes which I teach to run Chi-Square, ANOVA and multiple
regression tests. I looked for correlations or associations
among AP Calculus Exam scores, class grades, science courses, sex,
minority status, participation in school sports, and,
participation in school arts.
I learned a great deal from manipuating data to see how the
results would vary. I was pleasantly surprised that this
course went well beyond the curriculum of the AP Statistics course
which I teach. I learned a great deal and consider this
course to be one of my favorites.
EDRS
811 Final Project:
What Factors in Predict AP Calculus Students’
Grades on the National AP Calculus Exam and How Well Do They Predict?
Lastly,
I registered for the
mixed methods course. I had come to the realization that I
did
not was to limit my research to just one or the other. In my
summer experiences and in my own research projects at work, I had seen
how the results from both methods could clarify each other or even make
sense of something. But, I was a long way from well-informed
on
this. I thought that mixed methods was much simpler than it
actually is.
My uninformed view: use
quantitative to explain things which could be explained with numbers
and use qualtiative for anything else. I
knew there had to be more to it than I was realizing.
I thought that mixed methods indicated that some research
questions were stated and addressed qualitatively and other
research questions were stated
and addressed quantitatively. And, maybe there might be some
overlap which could help clarify the findings. I
have read
a
few dissertations and several articles which are formatted
this
way. The quantitative research was
accompanied by tables of values, hypothesis tests, p-values,
means and standard
deviations. The qualitative research, invariably much, much
more
voluminous, was replete with detailed descriptions of
environments, personal data on the subjects, human behaviors,
personal affect, appearance, attitudes, emotions, and reactions.
The researcher's own perspectives and opinions were often
included.
So, I found my Mixed Methods Research course to be most enlightening.
I learned an incredible amount in this course and was glad to
have taken it in the summer when I was not working full time.
The
twice-a-week class meetings, coupled with the volume of required
reading would have been difficult to complete otherwise. But,
back to the enlightenment: it seems so obvious to
me now that
qualitative and quantitative research should inform each other and not
be distinct parts of a whole. One can actually provide
possible
explanation for the other. The interaction of the
two, the
reciprocity of clarification is actually the most valuable feature of
mixed methods, in my opinion.
EDRS
797 Paradigm Reflection Memo
EDRS
797 Research
Matrix
EDRS
797 Validity Matrix
My
Growth as a
Researcher
As
I re-entered the world of academia, I
worried
about what I could possibly study or discover which has not already
been done. I have to laugh at myself now for not realizing
that
the world has an infinite number of possible topics which I would find
relevant.
Several
of my cohort colleagues
have known their dissertation topics for several years; others seemed
to have a good grasp of where they wanted to go. I did not.
I feel passionately about calculus and statistics; but, I did
not
know exactly how to approach a possible combination of the two.
Although I have several areas of general interest, I just was
not
honing in on anything in particular. I decided to not worry
about
it and see if my coursework and research experiences would help guide
me. In my internship, I was introduced to teacher
professional
development at several levels. In working with the ESTEEM
courses
and as a GRA, I have become enlightened about teacher content
knowledge and how I might contribute to making improvements.
Through my research with my own high school classes, I have
learned how differing teaching approaches can be used effectively
communicate mathematical ideas. Throughout my coursework, I
have
come to appreciate the value of reflection. When reading my
own
reflections, I was stunned at what was written there which I had
completely forgotten.
Sometimes, when I am preparing my
lessons for my students, I momentarily will dismiss an idea as
"obvious." Then, I remind myself that just because
it is
obvious to me does not mean it is obvious to my students.
This is
new to them and worthy of exploration, even if I think it is trivial.
Now, I as the student, did not get some of the "obvious"
things.
When I entered this program, I was a bundle of questions.
Working in independent schools, I was unfamiliar with public
school terminology, procedures and policies. These things
were
obvious to my colleagues, but not to me. And, on top of
that, I did not know how to write using APA. I did
not know
how to try to get an article published; and, I had never given a
presentation at an educational conference. Now, I reflect
back at
those questions I had and how much I have learned but do not even
realize that I have learned them. To clarify, I certainly
realize
that I have learned them; but, they have become such a part of my daily
thoughts that they re starting to fall into that "obvious" category.
I have
found I must admit that as
I was closing in on the end of my coursework, I did start to have
serious concerns about my dissertation. Then, I was invited
to be
one of the two teacher-participants in the Research Experience for
Undergraduates (REU) at GMU, sponsored by the NSF. Dr.
Seshaiyer
asked my area of interest and led me on a journey of discovery.
I
wanted to combine statistics and calculus and was especially interested
in regression analysis. My eye-opening experiences in this
program have led me to decide to delve deeper into these
research
ideas. I really want to expand my own mathematical knowledge;
but, I realize that I need to tie this research to education.
I
am thinking about possibly developing a training module, perhaps for
teachers, perhaps for students, to understand the logic of different
types of regression, of how regression is used in real world
applications, or how calculus and statistics are closely tied together
through regression. Through my discussions with Dr. Rantou, I
have seen many possibilities for studying regression or Normal
distributions. I intend to spend the autumn doing appropriate
reading to be
ready for the proposal class in the spring.
For my
dissertation, I also am
adamant that I choose
something which truly interests me. I have no interest in
simply
going through the motions to finish something which is nothing more
than a means to an end. And, my mentors have told me that I
would
be wise to choose a topic which is interesting to me because I will be
sharing company with it for a long time. I take their advice
seriously.
I do not need a huge topic. It is much wiser to hone in on a
small
chunk and build on that. I have been laboring over this for quite a
while and was working on an idea involving statistics education.
But, I just was not finding relevant research and
my enthusiasm was dwindling. I just did not know where to
turn. Then, voila, I was at the AP Calculus reading in June
discussing the advantages for students whose teachers are AP readers.
So many teachers assert that the AP Calculus reading
experience is wonderful professional experience which helps them to be
better teachers. I think it is true; but, I wonder if it
really is true. If it is, then why is it true. What
changes in the classroom? It dawned on me that my
dissertation topic had just taken root.
It is a
feeling of releif to finally have a topic which genuinely interests me
to my core. In the weeks since June, I have been searching
for relevant research. I am looking for recent research to
add to my growing list. And, I have been using the AP
Calculus reader list to try to build a list of potential participants
for my study. I have my baseline HSRB documents finished and
it seems that all I do is read, write and sleep, and eat mac and
cheese. It is exhausting and exhilarating at the same time.
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