Having spent the past several semesters, this is my
teleprompter. Uh reading research, learning various research methods and
delving in research methodology in general. Excuse me
I embarked on my own lonely journey of writing
my prelims. Part of the prelim process requires and in
depth discussion about textbook analysis, for me. However,
not only have to figure out what textbook
analysis was, I had to relate the analysis to my particular
area of interest, the real numbers. So after
reviewing several textbook analysis in the literature world, I
discovered two important things. I discovered that the constant
comparative method was a tool often employed by
researchers in this area. Um, and B, I
discovered that none of the methods or the theoretical frameworks
fit what I was trying to do. So it
was a dilemma for me, and one I'm still working,
trying to work out. So in addition to
this dilemma, I felt like many of the studies
either lack or failed to disclose methodological uh methodological rigor
for whatever reason. And some of them I know
have issues with publishing and they have to cut this
and that. But what I needed most was the
methodological rigor, at least a path
to it. So, for instance, what was
meant by the constant comparative method? Lots of people
say I used the constant comparative method, but then when
I was looking for, Okay, that's great,
I get pretty excited. It wasn't clear to me
what, how they used or where they used it or when
they used it. Also another thing and I'm guilty of
it. I've said, you know, I've coded
in theories emerged. What does that mean?
without telling the reader it's a magic show. So
it took me a while but eventually realize that I
would have to go back to the literature and
re-examine the various research methodologies and based upon several discussions
that we've had in here. I thought it might
be nice to discuss some of it. It's an ongoing process
for me and by no means am I an expert at it.
Uhh so um before I move on, I'll just
tell an interesting story. I think the graduate students
will appreciate it. I had this this research that
I was doing at the time, and I was
taking a qual II class maybe, qual III by then,
I don't remember, a lot of qual, I was trying
to fit it in. So I was trying to figure
it out. I didn't know that much about quantitative
research really when it comes down to it, or
qualitative beyond what I had a few classes. So
I went to three different professors who will go unnamed
and each one said, no, that doesn't
fit this paradigm. You know, that doesn't fit
this paradigm. This isn't quantitative, this is qualitative
or this isn't qualitative. Then I went to the
qualitative. No, no, no, this isn't
qualitative, it's definitely quantitative and it really rattled me.
I thought, okay, I don't know what I'm
doing. So finally, and I will say Jay
I finally went to Jay and I was told Jay
I was so frustrated, so frustrated. I said
Jay, I'm getting one guy says its qualitative.
Another guy says its quantitative and I'm so angry.
It's really yeah, it was because well mainly out
of fear because it just like struck fear in my
heart, I don't know what I'm doing. So
Jay said why are you taking that instrument to this
person? He doesn't care about your research. I
mean this is my own rephrasing now, it's not his
research. He's not going to get excited about it.
Because that was one of my complaints, he didn't understand what
I was doing. That wasn't Andy. So uh he said
it's your research. He said it's up to you
to decide where it fits in in which paradigm and
how. And that really helped me a lot.
It relieved me. So on we go. So first
um I'd like to talk a little bit about methodological
rigor which involves internal validity. And now I will be
mixing. I have no trouble and I'm gonna say
it up front. I feel like I should for
anybody who considers themselves a pure anything belongs to a
camp. Um one of the things that I was
told in one of my qualitative analysis classes, I
said well what about generalizabilityability? Well that's
not that's not a term we use in qualitative analysis, however they use
the term or terms like it just depends on who
you talk to and how far I go in the
qualitative world, there are some who abandoned positive thinking,
which I won't go into, altogether. What for for those
of us in math education. I feel like we
need method, methodologicall rigor. And
some of the things that help build that rigor
are internal validity, external validity, reliability and objectivity
. And I did use quantitative terms I suppose.
And I did it. They're the most meaningful to
me to describe these things that we all need in
our research regardless of what the response boston. Um
, so internal validity deals with generally and very generally
how trustworthy are conclusions that are drawn from your dad
. So that's important thing to let your read or
no. Otherwise, you know, I could maybe
stand up here and recite a poem which which I'm
all for it and call it method research and I
doubt that anybody is going to, you know?
Yeah. Especially if I'm talking about look at home
, external validity deals with how well can findings be
generalized. What are the implications? And you see
the terms on the left are actually we're part of
a natural, I think it's called the naturalistic,
anybody knows correctly, naturalistic terminology, which has been
changed since. But this was basically one of the
first attempts to capture. It turns on the right
because it 10 seconds uh reliability I guess for math
education, the way I see it is how to
what extent is your research based in Yeah, in
the literature and objectivity. Well, I guess again
, I don't don't think I need to say much
about objectivity. I'm not subjectivity objectivity, we know
what that is. And I suppose the way I
go about handling that in my own research is reflective
memos along the way on a reflexive memo is what
what's my position in this research? What is my
biased? Okay. You know, and you'll discover
them? I know we all have we've done research
along the way, so it's important to address this
those those um myself. So, uhh another term
is triangulation and we hear that we've heard that in
seminar several times. Um and you see it in
the literature quite a bit. And what is it
, what is triangulation? Does anybody have any input
? They'd like anything they'd like to say about triangulation
? I loved here we all have four people people
in the class now and I know his Lexus have
used it quite often in her research, Maybe I'll
take a shot. Yeah, that's good. How
uh Okay, okay, so Alexis has a job
. So did you go, So the root of
the word, suggest three things involved. Um but
I would also say that, I mean it's it's
kind of looking for more things if you don't mind
. Well, so it's not three specifically. Right
. It's three distinct things all support the same.
Like you wanna you wanna you wanna look at a
situation from at least case three perspectives. three results
for like three samples. Do you have that all
confirmed that all support and say help of how it's
I'm asking the question yeah there is no right answer
. So I mean my kind of the way I
understood it we were talking about it walk glass was
like you you can like do interviews to collect data
right? And you can look at historical records took
like or you can look at so like interviews like
two different populations like males and females in the same
community or teachers and students in the same classroom and
see if they like see if they see the like
what are you investigating the same what you're doing?
But you also want to support that with evidence like
student work. Yeah maybe reservation. Yeah observation yeah
things that you see. So how did you see
the related to math education research? Because one thing
that I found when I first started especially in the
fall classes there a lot of them were designed around
Margaret instead which none of which I was familiar with
at all. And so when I saw that I
thought well my initial reaction was I'll know if I
ever go to a ethnography this would be great from
monday social setting. Classrooms are socialists. Can you
be specific about something different about looking at this first
current master And so you interview students to talk about
what types of questions to use the pressures. Then
you wake up repeated questions you know as a students
. No. Yes. And then you might observe
and then you might go into the please exams,
all of things that students right now to seem like
other questions in those that might evolve from those that
types of discussions. So that might be an example
of using regulation. But your thing is in those
questions you're actually seeking a lot of times you're not
seeking an ethnography except for what is happening and what
you can take the data and say this. Your
decisions about it are grounded in it. But in
your case the things that you're saying is you're going
to ask questions. What kind of questions do you
ask because you're trying to find out something mathematics is 184 --> A:middle L:90% .