ERIC Identifier: ED434802
Publication Date: 1998-01-00
Author: Koca, S. Asli - Lee, Hea-Jin
Source: ERIC Clearinghouse for Science Mathematics and Environmental Education Columbus OH.
Portfolio Assessment in Mathematics Education. ERIC Digest.
The ongoing reform of mathematics instruction creates a need to refine student assessment practices. Columba & Dolgos (1995) claim that evaluating student computational skills by traditional methods cannot provide enough information related to the component of the overall evaluative process needed in mathematics. Current standardized tests seem like to measure performance on rote mathematical tasks instead of creating environments for students to reason, communicate, and problem solve.
In regard to measuring students' performance, NCTM (1989) states that "to demonstrate real growth in mathematical power, students need to demonstrate their ability to do major pieces of work that are more elaborate and time consuming than short exercises portfolios are some examples of more instructional and assessment activities" (p.36) in "Assessment Standards for School Mathematics." Like NCTM (1989), portfolio assessment is supported by many educators, because portfolio is considered as a collection of student work representing their mathematical power, a showcase for a student work or a place where many types of assignments, projects, reports, and writing can be collected (Columba & Dolgos, 1995). The idea of portfolio is close enough to satisfy educators' belief that assessment is most effective when it becomes an integral part of instruction.
THE TYPES OF THE PORTFOLIO ASSESSMENT
* Showcase: This type of portfolio focuses on the student's best and most representative work. This type of portfolio is similar to an artist's portfolio where a variety of work is selected to reflect breadth of talent. Therefore, in this portfolio the student selects what he or she thinks is representative work. This folder is most often seen at open houses and parent visitations (Columba & Dolgos, 1995, p. 174-175).
* Teacher-Student Portfolio: This type of portfolio is often called the "working portfolio" or a "working folder". This is an interactive teacher-student portfolio that aids in communication between teacher and student. The teacher and student conference to add or delete within the content of the portfolio (Columba & Dolgos, 1995, p. 175).
*T eacher Alternative Assessment Portfolio: All the items in this type of portfolio are scored, rated, ranked, or evaluated. Teachers can keep individual student portfolios that are solely for the teacher's use as an assessment tool. This is a focused type of portfolio and is a model of the holistic approach to assessment (Columba & Dolgos, 1995, p. 175).
FOCUS AND CONTENT OF MATHEMATICS PORTFOLIOS
SUGGESTED ITEMS TO CONSIDER FOR MATHEMATICS PORTFOLIOS
*A report of group project.
*Work from another subject area.
*Problems posed by student.
*A book review.
*Excerpts from a student's daily journal.
*A table of contents.
*Draft, revised, and final versions of student work on a complex mathematical problem.
*A description by the teacher of a student activity that displayed understanding of a mathematical concept.
*Newspaper and magazine articles.
*A letter from the student to the reader of the portfolio, explaining each item.
*Audio tapes of student-teacher interview.
*A photo or sketch made by student of student's work with manipulatives.
*Papers that show the student's correction of errors or misconceptions.
*Notes from an interview by the teacher or another student.
*Sample journal entries.
*Work in the student's primary language.
*Videotapes of student's work.
*A mathematical autobiography.
THE ADVANTAGES OF PORTFOLIO ASSESSMENT
THE DISADVANTAGES OF PORTFOLIO ASSESSMENT
AGENCIES AND WEBSITES HAVING INFORMATION ON PORTFOLIO ASSESSMENT
National Council of Teachers of Mathematics (NCTM)
National Council on Measurement in Education (NCME)
National Center for Research on Evaluation, Standards, and Student Testing (CRESST)
ERIC Clearinghouse on Assessment and Evaluation (ERIC/TM)
Portfolio News (Portfolio Assessment Clearinghouse)
ERIC Clearinghouse for Science, Mathematics and Environmental Education
Eisenhower National Clearinghouse for Mathematics and Science Education (ENC)
The portfolio assessment including open-ended questions can aid teachers in observing how students process mathematics information and also help differentiate the skill levels of individual students. However, the downside is that the use of portfolio assessment will require many teachers to face the difficult task of changing their teaching style. Great care must be used in proving the reliability, validity, and consistency of evaluating grades when using the portfolio assessment.
Brosnan, P.A. and Hartog, M.D. (1993). "Approaching standards for mathematics assessment." (ERIC Document Reproduction Service No. ED 359 069)
Columba, L., and Dolgos, K.A. (1995). Portfolio assessment in mathematics. "Reading Improvement," 32 (3), 174-176.
Gilman, D.A., Andrew, R. and Rafferty, C.D. (1995). Making assessment a meaningful part of instruction. "NASSP Bulletin," 79 (573), 20-24.
Johnson, Judi Mathis (1994). Portfolio assessment in mathematics: Lessons from the field. "Computing Teacher." v21 n6 p22-23.
Hayes, B. and Kretschmann, K.J. (1993). "Portfolio assessment: An annotated bibliography of selected resources." (ERIC Document Reproduction Service No. ED 362 731)
Koretz, Daniel (1994). "The evolution of a portfolio program: The impact and quality of the Vermont Portfolio Program in its second year (1992-1993)." (ERIC Document Reproduction Service No. ED 379 301)
Midkiff, R.B. and Thomasson, R.D. (1993). "A practical approach to using learning styles in math instruction." Springfield, IL: Thomas Books.
NCTM. (1995). "Assessment Standards For School Mathematics." Reston, VA: Author.
Owings, C.A., and Follo, E.(1992). "Effect of portfolio assessment on students' attitudes and goal setting abilities in mathematics." Michigan.
Stenmark, J.K. (1991). "Mathematics assessment: Myths, models, good questions and practical suggestions." (ERIC Document Reproduction Service No. ED 345 943)
Smyser, S.(Ed.) "Encouraging reflection through portfolios. proceedings of the national conference on linking liberal arts and teacher education (San Diego, California, October 6-7, 1994)." (ERIC Document Reproduction Service No. ED 390 817 )
Wolfe, Edward W (1996). "Student reflection in portfolio assessment." (ERIC Document Reproduction Service No. ED 396 004)
OTHER PORTFOLIO INFORMATION AVAILABLE ON THE WORLD WIDE WEB
Student Portfolios: Classroom Uses
Student Portfolios: Administrative Uses