The research design for this project is descriptive [observational: observing mathematics professors, grad student teachers, and undergraduate students], and includes tutoring as an intervention. This project collects original data using assessments of learning, achievement tests, observation [personal observation, videography, web logs], and survey research [paper and pencil, self-completion questionnaires, and face-to-face semi-structured/informal interviews].
This project is developing assessments of student relational understanding of several DE solution techniques. These involve multiple choice, short-answer, and longer written or sketched answers questions administered pencil-and-paper or electronically.
There is a variety of data here. The transcripts of tutoring are analyzed for tutorial goal structures and linguistic phenomena manually. Tutoring pre-tests and post-tests are analyzed by simple statistics for learning gains. Interviews with professors are analyzed manually. Assessments are tested for validity and reliability both internally and against other measures.