Writing Problem Statements and
Statement of the Problem
Your first chapter will give a brief background to contextualize and problematize your research question(s). It will end with a statement of your research questions.
The net effect of your problem statement should be that readers
understand the intellectual motivation for your study.
agree that the field's state of knowledge is such that your research questions are timely and important.
agree that answers to your questions will be interesting and important regardless of what the answers might be.
Writing Literature Reviews
The literature review should do work for your study. However, there are
various kinds of work it might do. It should:
- Convince the reader that you know the relevant literature.
- Assume that some readers do know all the relevant literature.
This assumption will ensure that you at least acknowledge
literature that you will not rely on heavily but that others might
think is germane to your topic, thereby satisfying the
knowledgeable reader that you are at least aware of it
- Assume also that other readers know little about the relevant
literature. This assumption will focus your attention on the
literature that you do rely on, thus helping less knowledgeable
readers understand the intellectual context for your study.
- Build an intellectual framework for your study.
- Explicate important constructs that you will draw upon or employ
in your study
- Explain results from studies that have important implications
for your study
- Help readers understand how your present work connects to and builds
upon the work of others.
This third point is important. You can do a good or poor job of it,
and the job you do is strongly shaped by how you construct your
citations. There are three ways to cite other work:
- Ambiguous or gratuitous citation. A citation is ambiguous
when you cite an article or book, but the reader cannot tell why you
cited it. Is it because the authors provided results that back your
statement? Is it because they made a claim that you also are
claiming (and hence want to credit them with the original idea)? Is
it because the article raises issues that are somehow related to the
point you are making? Ambiguous citations should be rare. Whenever
you cite an article without discussing it, the context should make
it clear why you are citing it. A gratuitous citation is one that
you feel compelled to include because you think it is important, but
you have no particular reason for citing it. You should never
include a gratuitous citation.
- Citations of work that you are building upon. These are the
most important. They do two things. They educate the reader about
the issue or question you are investigating and they give
appropriate credit to the person who did this work. Think that you
are explaining these articles to readers. Investing the effort to
explain work upon which your study builds will have the added
benefit of crystalizing in your own thinking the distinction between
what others have done and what you are adding to it that is yours.
Your writing will reflect this distinction, and both readers and the
field will benefit.
- Citations of work that you know the field thinks should be
pertinent to your study, but which you will not use. These
citations are nearly as important as the second type. You should
discuss these works thoroughly in order to convey how they do not
comport with the framework your study uses. Often, discussions of
these types of studies can be cast as differences of perspectives,
and it is the perspective from which the study was designed or
conducted that makes it less important for your study. For example,
Scott Courtney discussed Ball & Hill's framework for
mathematical knowledge for teaching extensively in order to make a
case that its non-cognitive perspective did not support his attempt
to get at teachers' mathematical thinking. The framework is well
known and widely accepted in the field, so Courtney needed to review
it in order to make his stance sensible to readers.
Finally, Keith Leatham wrote an excellent commentary on citation
practices that covers other issues than those listed here. See:
Leatham, K. (2015). Observations on citation practices in mathematics
education research. Journal for Research in Mathematics Education,
on citation practice.pdf