Doctoral students in Mathematics Education must conduct research in Mathematics Education. Research in education, however, is by nature quite different from research in Mathematics. In education, there are several different theoretical viewpoints and research paradigms that govern the conduct of educational studies. Articles in Mathematics Education typically begin by stating the author’s research framework or theoretical paradigm. Students conducting such research might learn about the theoretical paradigms on which social research is based in one of the following:
- SOC 5243, Social Research Design
- SCFD 6113, Theoretical Foundations of Inquiry
Educational research can be either quantitative, that is, based on analyzing numerical data, or qualitative, that is, based on an analysis of data involving more words than numbers, such as answers to interview questions, observations of classroom situations, etc. Both methods, along with studies that explicitly mix the methods, are conducted in educational research, and students doing educational research should have a foundation in both modes of inquiry.
Training in qualitative research methods might be undertaken in the following courses:
- SOC 5273, Qualitative Research Methods
- SCFD 6123, Qualitative Research I
- SCFD 6193, Qualitative Research II
The following course emphasizes mixed methods but also helps compare and contrast the two research styles and helps students understand the research paradigms:
- CIED 5730, Conducting Mixed Methods Research
Training in quantitative methods can come from courses in Sociology or courses in REMS (in the College of Education), but the Mathematics Department encourages Mathematics students to take advantage of the rigorous foundation and more thorough treatment provided by graduate courses in Statistics. The foundational applied sequence, covering analysis of experimental data, is
- STAT 5023, Statistics for Experimenters II (STAT 5013 or 4023 is a prerequisite)
- STAT 5303, Experimental Design
To go along with these classes, it would be helpful for the student to have computational experience with large statistical data sets:
- STAT 5091, SAS Programming (or STAT 4091)
Many educational studies involve surveys and construction of questionnaires. The following course could be very helpful:
- STAT 5043, Sample Survey Designs
These courses are very good starting points, but they tend to deal with a single varying quantity. Advanced quantitative studies in education might perform statistical analysis on multivariate quantities instead, or on data that are not normally distributed. These research methodologies are taught in:
- STAT 5063, Multivariate Methods
- STAT 5073, Categorical Data Analysis
- STAT 5033, Nonparametric Methods
The Graduate Advisor in Statistics will usually be able to help graduate students in Mathematics with questions of placement in Statistics courses.
As a final note, we remark that the theoretical Probability sequence in Statistics is currently allowed as one of the core course sequences on a Mathematics Education Ph.D. plan of study:
- STAT 5123, Probability Theory
- STAT 5223, Statistical Inference
These courses serve as a valuable theoretical foundation to all future study or future teaching in Probability and Statistics but do not explicitly cover the data analysis techniques for quantitative educational research beyond those contained in STAT 5013.