Mathematics Professional Series|
Alternative Assessment Geometry
A portfolio is a representative sample of a student's work that is collected over a period of time. Portfolios tell a story about a student's activities in mathematics. Their focus is on problem solving, thinking and understanding, written communication, mathematical connections, and students' views of themselves as learners of mathematics.
A portfolio is not just a folder of a student's work. The pieces of work placed in a portfolio have more significance than other work a student has done. They are chosen as illustrations of a student's best work at a particular point in time. Thus, each item in a portfolio should be dated and placed in order to chronicle student progress. The range of items selected shows a student's intellectual growth in mathematics over time.
Portfolios can be used to assess a student's performance on a range of mathematical tasks during the school year. To do this, the portfolio should reflect the range of instructional goals and related tasks. An assessment portfolio can be created by the teacher and student working together. Students should collect all their work for a two- or three-week period in a work portfolio. A periodic review of the work portfolio provides a basis for selecting items that will go into the assessment portfolio. The teacher can assist students with the review but should not direct the process. The actual selection of the items by the students tells the teacher what pieces of work the students think are significant. The student may wish to include a sheet in the portfolio that tells why each item was selected. Student-selected items help the teacher to understand the students' views of themselves as developing "mathematicians."
Balancing a Portfolio
The selection of work samples for a portfolio should be done with an eye toward presenting a balanced portrait of a student's achievements. Students and their teachers should seek samples that illustrate growth in understanding in each of the following:
Other important curriculum considerations for portfolio samples are:
- Problem-solving skills
- Reasoning and critical thinking skills
- Communication skills
- Mathematical connections
- Statements on mathematical disposition such as motivation, curiosity, and self-confidence
- Group skills in working with others
- Use of technological tools
Sample Portfolio Topics
The following examples illustrate topics that are appropriate for inclusion in a geometry student's portfolio.
- A solution to a difficult or nonroutine problem that shows originality of thought
- A written report of an individual project or investigation
- Examples of problems or conjectures formulated by the student
- Responses to open-ended questions or challenging homework problems
- Excerpts from a journal
- Mathematical artwork
- A student's contribution to a group report
- A photo or sketch of physical models or manipulatives to illustrate a mathematical idea
- Teacher-completed checklists showing mathematical growth
- A mathematical autobiography
- An applied use of mathematics in another discipline
- An explanation by the student of each item in the portfolio and why it was included
- A table of contents
Ideally, the criteria of establishing and assessing a portfolio is known by both the teacher and the students. It is these criteria that form the basis for the assessment comments the teacher makes on the work in the portfolio. In creating a portfolio, the student then follows the criteria established by the teacher. Work is selected to represent progress toward the key goals of instruction.
The assessment criteria for establishing a portfolio can be organized into categories that align with the curriculum goals you are implementing. These criteria help to guide the teacher in making holistic judgments about students' work. They are also useful in keeping the teacher's assessments of different students consistent.
Assessment criteria categories may include, but not be limited to, problem solving, language, reasoning, real-world applications, use of different mathematical representations or models, and technology.
For more information on performance assessment and other types of alternative assessment, see "Alternative Assessment in the Mathematics Classroom," one of the booklets in the Glencoe Mathematics Professional Series.