Methodology.tex

\chapter{Methodology}
\section{Big picture}
analytic lens is phenomenography, i.e. Professor Marton and perhaps others
\subsection{How Many Interviews}
how many interviews\\
So far, approximately 30 interviews have been conducted.
\subsection{Pool}
pool -- I think this means characterize the participants\\
The participants were mostly students, mostly undergraduate, but some graduate; also some former students and some faculty participated.
The participants were mostly male. 
The participants were mostly traditional aged.
The participants included domestic and international students.\\
The participants included Asian, Caucasian, Latin and Middle Eastern students.\\
A small number of students had disabilities, including being on the autistic spectrum.
\subsection{Interview Protocols}
For  IRB approved H13-065, as approved on 4/2/13, the interview protocol is:\\
When you took course "x", as far as you can remember, was there any discussion about proofs?\\
Do you remember whether you had to furnish proofs of any kind?\\
What kinds?\\
Do you remember any example proofs?\\
Why do you think course "x" treats proofs?\\
Why do you think course "x" uses the examples it does?\\
Have you noticed any use that you make, of the material related to proofs, in any course you take, or any activity you do?\\
Have you noticed material, related to proofs, from a previous course supporting work in a later course?\\
If you have to choose mathematical symbolic formulation, or software code, \textit{to articulate carefully} a concept you were trying to express, would you find one easier than another? Which?\\
If you had to choose mathematical symbolic formulation, or software code, \textit{to read for precise understanding} a concept you were trying to understand, would you find one easier than another? Which?\\
Does it ever arise that you wish to convince yourself, or someone else, of a technical point?\\
If so, what techniques do you employ?\\

For  IRB approved H15-022, as approved on 2/12/15, \\
I think the same questions were used.



\section{Analytic Technique}
\subsection{Interviews}
This phenomenographic study is a qualitative study, in which thematic analysis, a kind of basic inductive alaysis, will be performed upon the transcripts of the interviews.
The result of the analysis will be descriptive of the students' remarks.
In a phenomenographic study, the outcome is a set of categories, with a description of each.
In this case, the categories will be about student conceptions related to proofs in computer science.
Consistent with qualitative analysis, analysis begins as soon as there is any data, i.e., one interview.
Basic inductive qualitative analysis, in particular, thematic analysis as by Braun and Clarke will be applied to the texts of the interviews.

ideas that recurred were given a name and labeled with that name (termed, "generating initial codes"). One may imagine gathering synonyms, or synonymous phrases, into an equivalence class, and generating a representative of that class. The representative may be chosen from among the class members, or, can be different from each member, but the essence of the class should be retained. These representative are called codes.
For each code, create a memo, that explains the meaning of the code, as derived from the usages, within the transcript, of the phrases labeled by that code.
As codes abstract information, a memo is less detailed than the original text; ideally the gist remains.
(The forward and back checking process is important for rigor in qualitative analysis.)
A check was carried out, that each memo captured the essence of its origin.

With the codes, also called categories, a process named axial coding is carried out. In this process, one-by-one, each code is placed as if it were the hub of a wheel, and every other code is arrayed about the hub, with a spoke to it, indicating a pair-wise relationship. 
The spoke is annotated with the relationship between those codes, as found in the transcript.
After each code has taken its turn as the center category, an assessment can be made as to which approximately four codes have the most salient relationships, i.e., those relationships that seem to capture the character of the transcripts.
Those categories participating in these most prominent relationships are promoted to the rank of main theme.
A memo can be written about the network of relationships in which each main theme finds itself. This is a forward step.
These memos can be reviewed in the light of the relationships that inspired them. This is a back step.
Using the main themes and the memos, a rich description of the topics mentioned in the ensemble of interviews is created.\\
When thematic analysis is used in support of phenomenographic inquiry, there is an expectation that a partial ordering by inclusion will characterize the graph of the main themes and their relationships.
With this structure, the pairs of adjacent themes and their incident relationship are pondered to extract a critical factor.
A critical factor is that item, awareness of which permits a student to grasp the broader conceptualization.\\ 
The product of a phenomenographical study is the rich description, the graph of themes (called conceptualizations) and the critical factors.
\subsection{Homework}

Homework questions related to proofs were selected for examination.
Examination consistent in looking for how logical reasoning is applied, and the kinds of mistakes, for example, omissions.

\section{Used to be first}
Knowledge about how students conceptualize has a qualitative nature. For
qualitative research, methodology varies, but has standard parts: design of the
study, sources and their selection, data, the process of analysis, the interpretation,
and the approach to validation. Sample selection is recorded and reported
so that others may judge transferability to their own context. Interviews are
the principle technique used by phenomenographical research. Documents
can also be used. Normal conduct of teaching can also provide data that can
be used, if in an anonymous, aggregate form. Both deductive and inductive
analysis provide qualitative data.
\section{Design of the Studies}