Assessment of Student Understanding Through Written Reports and Oral Presentations in Upper Division Math Courses

Carl Lienert, Fort Lewis College

Stan Yoshinobu, Cal State University Dominguez Hills

Two courses, one topic driven, one introduction to proofs, will be used to illustrate how oral and written assignments lend themselves to encouraging a student-centered classroom and to assessing the progress of the level of students understanding of mathematical material. Specific activities will be illustrated and results will be discussed.

In one course, an Introduction to Proofs class, students choose a term-long project.

Students’ level of understanding, particularly at an abstract level, is assessed through both oral presentations and written work. Throughout the term students give oral presentations that detail their progress on their project. Their level of understanding is assessed both through questioning and the manner in which they choose to present their material. Ideally, the level at which students attack the term-long problem becomes more abstract as they progress. The written component will culminate with a final written report. This report will be compared to various smaller writing samples collected over the course to measure any increase in mathematical understanding.

The second course, Introduction to Real Analysis, is a content course. In courses where a certain amount of content must be covered, writing prompts are used instead of a long-term project. Introduction to Real Analysis is taught using a problem-based learning method, where students are provided with a sequential list of problems to be solved. Students are required to present solutions in class, and students are prompted at certain points to write about their understanding of fundamental concepts. Oral presentations and writing allow students to express their ideas, and gives the instructor data about student progress. For example, students give their own definitions of a convergent sequence, and then are shown the standard definition. Students investigate the differences between their definitions and the standard definition as well as confront the necessity of rigor.