An Evaluation of Portfolios Used as Assessment in Mathematics Courses

M. E. (Murphy) Waggoner

Simpson College

How do we know whether a specific writing assignment in a mathematics course meets the desired learning goals or if the students consider the writing as just a hoop through which to jump? The purpose of this study was to collect information from the students and their work on a specific writing assignment used in two different mathematical subjects over three semesters. The data was used to evaluate how useful the writing assignment was to the students and to make decisions about future use of the assignment.

I have required portfolios and reflective essays in three different classes. In each of these classes the students had to produce mathematical writing throughout the semester. At the end of the semester they chose the work that best illustrated their successes and failures and submitted that work as evidence in support of the statements made in a reflective essay. The specific goals of the portfolio and reflective essay were to help my students improve their mathematical writing and critical thinking skills, retain the information learned in the course, take pride in their work, find value in self-assessment and reflective writing, develop their own method of self-assessment, and understand the purpose and nature of the course.

The portfolios were used in Math 265 - Introduction to Advanced Mathematics (a bridge course which focused on proof-writing) in Fall 1999 and Fall 2002 and in Math 116 - Mathematics for Elementary School Teachers (a content course for pre-service elementary teachers) in Spring 2000. In each course the students produced an average of 50 pieces of mathematical writing (proofs in paragraph form for Math 265 and detailed problem solutions in paragraph form for Math 116). Some of the writings were from specific assignments and some were chosen by the students from a "Big List" to help them fill out their collection of writings. In many cases, the students were allowed to revise substandard solutions or proofs.

The reflective essay in Fall 1999 required the students to choose 10 writings and to explain how those writings illustrated both a breadth and depth of knowledge of the material covered in the course. The reflective essays in Spring 2000 and Fall 2002 required answers to 4 specific questions such as, "Describe a topic from this course on which you have made the most progress this semester. Explain how your understanding of this topic has improved."

To assess the learning goals of the portfolio and reflective essay, qualitative and quantitative data was collected from a variety of sources: anonymous comments and ratings from students on the end-of-semester course evaluations, a questionnaire distributed to students after the course was over, and the content of the reflective essays.

The assessment revealed that the students found the portfolio and the reflective essay useful tools for reviewing and synthesizing the contents of the course and for reflecting on their accomplishments. They considered the writing an essential part of the course and valued the experience of writing the reflective essay, but there were mixed feelings about using reflection in other classes or except when required. The students felt that writing in other disciplines did not prepare them adequately for mathematical writing. The style of writing in the reflective essay was of a different nature than the style of writing the students did during the semester, and the quality of the reflective writing was not as strong as the mathematical writing.

I plan to use portfolios and reflective essays in the future in these two subjects and will expand to other subjects. I will continue to modify the questions asked in the reflective essay to make the writing of it more useful to the students as a review tool. To help the students improve their expository writing skills, I will incorporate more reflective writing during the semester.