Deciding+how+to+conduct+the+study

= Making Decisions About How the Study Is To Be Conducted =

Start With Your Research Questions
How your study should be conducted depends heavily on your research question(s). One convenient way to categorize your questions to help decide on appropriate methods is by their orientation in time: are they past-oriented, present-oriented, or future-oriented?
 * Past-oriented questions focus on the state of something in the past, or how some present state of affairs came to be. For example, you might want to know how (or if) the teaching of geometry changed as a result of the New Math movement, how the //Agenda for Action// published in 1980 affected the teaching of problem solving, why many modern mathematics textbooks have a section on elementary set theory, or whether grades really have been inflated in mathematics classes over the past half-century.
 * Present-oriented questions focus on understanding some current situation in more detail. For example, you might want to know the different conceptions students have of decimal fractions, whether there is a relationship between students' beliefs about problem solving and their problem solving behaviors, the nature of conversations between student teachers and their cooperating teachers, how students come to understand justification in a mathematics class focused on writing conceptual explanations, or why mathematics teachers leave the profession.
 * Future-oriented questions deal with how situations might change from their current state, especially because of actions taken now. For example, you might want to know how an instructional unit on the various meanings of "variable" at the beginning of an introductory algebra class affects students' ability to write equations for story problems, or whether taking a course in problem solving in their undergraduate preparation programs affects teachers' approaches to teaching problem solving, or whether a particular in-service program for teachers results in better standardized test scores in their students. Note that many of these questions have an element of prediction, or of causality -- showing that one things causes another to happen.

Methods for Past-Oriented Questions
Past-oriented questions are comparatively rare in mathematics education, but can be quite insightful (for examples, look for the work of George M.A. Stanic in the mid-1980's). Such questions call for the methods generally employed by historians, which include not only finding historical artifacts, but subjecting them to careful and critical analysis to determine their nature and validity. For example, written accounts of events need to be compared and contrasted, examined for patterns, and analyzed for consistency. If you choose to address a past-oriented question, you should expect to spend some time learning historical methods, and might consider a committee member who is well-versed in these methods.

Methods for Present-Oriented Questions
Present-oriented questions are probably the most common in current mathematics education research. Depending on the research question, there are a great number of methods that are appropriate to study relationships in some current state of affairs. Among the most common are:
 * Survey
 * Interviews
 * Observation
 * Participant observation/Ethnography
 * Case study
 * Grounded Theory
 * Discourse analysis
 * Constructivist Teaching Experiment
 * Design Experiment