The attached pages come from a short handbook designed to give primary grade teachers some ideas on how to begin using portfolios in math for very young students. The author contends that the primary use for portfolios is to assist students to take control of their own learning. Students assemble their portfolios to tell a story about who they are mathematically. Students should be in control of their portfolios, and self-assessment should be emphasized. (The author, however, also points out that there might be other audiences and purposes for the portfolios that might have to be addressed.) The author provides ideas for tasks that students could do to generate material for the portfolio, provides some very practical suggestions for getting started, gives ideas for activities to encourage student self-reflection, discusses student-led conferences, and includes an entire portfolio for a second grade student.

• Portfolio Tips
• Tips for Child Portfolios
• Setting Student Standards
• Guide For Judging Portfolios

"Portfolio Guidelines in Primary Math," 1994
Leon Paulson
Multnomah County ESD
P.O. Box 301039
Portland, OR 97230
(503) 255-1842

Building a portfolio involves a wide variety of classroom activities. The more variety, the better. It is important to expose students to many kinds of activities so that they have a wide choice of things to put into their portfolios.

• Have students collect all math work in a folder. Periodically (maybe once a week) ask them to look through the folder and select pieces for their portfolio. Have them write why they selected the piece. Accept any reason as valid, but encourage them gradually to become more thoughtful in their reasons. "I liked it," "It shows what I know," "It was fun," "Shows symmetry" are all good reasons. The key is to get them to make a habit of judging their own work.

• Encourage students to talk about how they solve math problems. Form small groups so that they can talk to each other. This will make it easier for them to learn to write about how they solve the problems. (Research shows that students encouraged to talk about the problem they're solving do better than those who don't talk.)

• Give children concrete things to talk about and reflect on. Don't ask them to reflect on everything they have done over the year. Ask ;them to look at two specific examples of their work (say one from early in the year and one from later) and ask them what specific differences they notice. Allow them to discover how much they have learned. Celebrate! Ask them to write about their portfolios.

• Encourage students to write about their portfolios as much as possible. Use any special event as an excuse for writing. Parent night, an anticipated visit by the school principal, a visit from another class, a special guest.

• Encourage the students to present their portfolios. A student-led conference is a wonderful opportunity. Put them in charge of setting up and conducting the presentation.

Portfolios offer several opportunities to view standards in a new way. A recent, and exciting development in portfolio assessment is student-negotiated standards. In student-negotiated standards, students take a leading role in setting personal standards that they use to guide their own progress. Here are some ways that you can encourage students to set standards.

• Distribute some examples of math papers done for another (maybe last year's) class. Ask students to look at the papers and decide which are the better papers. Encourage them to figure out, to discover what constitutes good math work. Then have each student select one or more characteristic to work on in their own papers. Help them build a rubric or checklist to keep track of their own progress.

• Teach the students to assess work using a set of progress guidelines. Don't worry that their "scores" agree with yours, but do work for them to make consistent judgments so that they can see their own growth. Encourage students to talk to you and to each other about what constitutes good math problem solving - help them discover that doing math well involves much more than merely finding the right answer.

• Have students interview adults, especially adults with technical training to find out what real mathematicians do. Have the class build a list of things mathematicians do. Have students look for examples in their portfolios that correspond to the items on the list.

This is a relatively new area and there are few guidelines in education. Negotiated standards have been successful in industry, especially in the work of W. Edwards Deming. For an example of student-negotiated standards in a writing portfolio, see Paulson, Paulson & Frazier (in press).

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An Outstanding Portfolio

An outstanding portfolio is a coherent story of the student as a reflective learner where all the parts of the portfolio bear a clear relationship to each other and to a central purpose. There is an awareness of the perspectives of other stakeholders, and the student's self-assessment has been enhanced by this knowledge. A reviewer can look at the portfolio and easily understand how the judgments about the learner came to be made and the degree to which different stakeholders would agree. When reviewing the portfolio, outsiders get the feeling they really know the person whose achievement is depicted there, and have a fair understanding of how the learning came about.

An On-Track Portfolio

An on-track portfolio is in the process of becoming a story of the student as an independent learner. There are relationships between one part of the portfolio and another. There is evidence of student ownership. The learner has a personal investment in selecting and explaining the content. It is possible to distinguish other stakeholders' goals from the student's or to recognize instances when they overlap. The portfolio may be created for others to assess, but there is also evidence of self-assessment. The student's voice is always audible.

An Emerging Portfolio

In an emerging portfolio there is a sense of intentionally controlling some of the student's choices. Students may not be able to verbalize the reasons, even as they reflect on their choices, but the reviewer may be able to recognize a relationship between some exhibits or infer the reasons. Or, there may be evidence that the student had some insight into the teacher's purposes. While evidence of self-reflection adds information to the presentation, at this point in the development of the portfolio there is insufficient information or organization to characterize the portfolio as either a story of learning or a portrait of the learner.

An Off-track portfolio

An off-track portfolio is simply a container of student work or assessments, without an attempt on the part of the learner to provide organization. There is no attempt by the learner to make a coherent statement about what learning has taken place. The child's understanding of the task is minimal, the portfolio is about "collecting what the teacher asks for." For the student, the portfolio was built by following instructions. Self-reflective statements, if present, add little to clarify organization or explain learning. Based on "A Guide for Judging Portfolios" by F. L. and Pearl R. Paulson. (Available from the author.)

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