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
According to Columba & Dolgos (1995), there are basically three types of portfolios to consider
for classroom use.
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).
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
Some of the
main goals of portfolios are to see "student thinking, student's growth over
time, mathematical connections, student views of themselves as mathematicians,
and the problem solving process" (Stenmark, 1991, p.37). A variety of items can
be included in a mathematical portfolio in order to achieve these goals.
SUGGESTED ITEMS TO CONSIDER FOR MATHEMATICS
*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
*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
*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
Because of the
limitation of traditional assessment tests, many educators have been
experimenting with alternative forms of assessment, and many have described the
advantages of portfolio assessments. According to Owings and Follo(1992), the
portfolio assessment can help students understand their strengths and
weaknesses. They also believe that students are more able to link successes and
failures to performance and may also facilitate goal setting through portfolio
assessment. Gilman, Andrew and Rafferty (1995, p.22) and Midkiff and Thomasson
(1993) have also identified several advantages of portfolios. According to them,
portfolios can be used to evaluate both products and process, and they allow the
integration of learning and assessment. Learning based on portfolio assessment
can be more student-directed, and since evaluation is not based on single
scores, instruction based on learning styles is more easily evaluated. Moreover,
Gilman et al, (1995) claim that portfolios provide more information about
student progress and encourage students to be responsible of their own learning.
Therefore, students feel as they take bigger roles in the learning and the
assessment processes. Portfolios also help students develop skills necessary for
life-long learning. On the other hand, portfolios reduce the teacher's daily
burden of grading papers. In sum, portfolios enable to assess global
understanding and thinking skills with a multidimensional form of evaluation.
THE DISADVANTAGES OF PORTFOLIO ASSESSMENT
results in using portfolio assessments are positive, some educators found
disadvantages of using portfolios. In Koretz's (1994) study teachers indicated
some concerns about the use of portfolios. Mostly they mentioned that portfolio
assessment imposes substantial burdens on them such as time demands of planing
and administering problems. Moreover, it is harder to ensure that portfolios are
accurately recorded and scored students' performance; evaluation is more
subjective than traditional testing, and reliability and validity can be
questionable. Also, maintaining portfolios can be problematic and
time-consuming. Finally, deciding the content of portfolios can be harder than
other assessment techniques.
AGENCIES AND WEBSITES HAVING INFORMATION ON PORTFOLIO ASSESSMENT
Council of Teachers of Mathematics (NCTM)
Council on Measurement in Education (NCME)
Center for Research on Evaluation, Standards, and Student Testing (CRESST)
Clearinghouse on Assessment and Evaluation (ERIC/TM)
The findings of the research conducted by Wolfe
(1996) show that "through the use of large-scale portfolio assessment, students
can realize educational outcomes that are not afforded in an educational system
that focuses on traditional goals such as acquiring content knowledge and
performing well on standardized multiple-choice tests. Students were able to
reflect on and formulate statements about their personal beliefs and values,
their understandings of themselves as learners and writers, their abilities and
skills as writers, and their goals and aspirations" (p. 12). Moreover, the
conclusion drawn from the National Conference on Linking Liberal Arts and
Teacher Education (San Diego, California, October 6-7, 1994) was that portfolios
are a valuable tool for demonstrating through authentic evidence that the
professional skills necessary for teaching have been mastered, that many methods
of portfolio use are valuable, and that further research in this area is
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.
Asturias, H. (1994). Implementing the assessment
standards for school mathematics: using students portfolios to assess
mathematical understanding. "Mathematics Teacher," 87(9), 698-701.
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
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:
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)
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