Writing Problem Statements and Literature Reviews
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.
Other Resources
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, 46(3), 253-269.
Leatham-2015-Observations
on citation practice.pdf