Intent Students review and document their mathematical activity and learning during the course of the unit. Their product is an opportunity for assessing what they have learned and what they believe is important in their learning (see “About Portfolios” in the Overview to the Interactive Mathematics Program).

Mathematics Students review their work on all the mathematical topics of the unit, with an emphasis on In-Out tables, proof, and integer arithmetic. Other ideas, such as functions and the distributive property, are approached more informally at this stage and are not specifically addressed. This metacognitive activity is an important mathematical task in itself, in that mathematics learned in school has a quality distinct from the natural mathematical activity that emerges from interaction with real problems, or at least problems that are real to students. The distinction involves learning the agreed-upon conventions, notation, and terminology for referring to particular ideas that the formal study of mathematics requires.

Progression Students are formally introduced to the notion of a portfolio and the particular expectations for the Patterns portfolio. They review their materials and begin to compile their portfolios as they write their cover letters.

Approximate Time 20 minutes for introduction 30 minutes for activity (at home or in class)

Classroom Organization Whole-class introduction, then individuals

Doing the Activity Prior to this day, emphasize the need for students to bring all their work from the unit to school. For some students, having to assemble a portfolio can become a reminder for the need to maintain some organization of their materials. Disorganization can be an early indicator of students who may find less success in school. You might invite students who are particularly disorganized to visit with you privately to help them organize their materials from the unit, possibly into a three-ring notebook, and then draw out particular activities for their portfolios. Such private time will give you an opportunity to make a personal connection with students as well as support them in getting off to a good start in your class. Before students begin work on their portfolios, you may want to ask what they recall about portfolios from the discussion at the beginning of the unit. What is the purpose of a portfolio? What would be good items to include in a portfolio? After this brief review of portfolios in general, ask students to read Patterns Portfolio carefully. You may then wish to lead a general review discussion of the unit before students begin assembling their portfolios, or you may prefer to let students work in groups or on their own. The primary goal of this first IMP portfolio is that students have some success becoming aware of and completing each of the three phases: “Cover Letter,” “Compiling Papers,” and “Personal Growth.” The writing of cover letters and the selection of portfolio materials are intertwined activities. Students should probably at least begin their general review of the unit before selecting portfolio materials, but they will need to make certain selections in order to complete the cover letter. You might suggest two possible orders for work on the portfolios. Students could (1) identify papers to include, (2) write their cover letters, and (3) write their personal growth statements. Or they might (1) write their cover letters only through the point of describing the central ideas of the unit, (2) identify papers to include, (3) complete the cover letters by explaining their choices, and (4) write their personal growth statements. As students review the unit and their work, they should think about both the mathematical content of the unit and the quality of their writing. Suggest that they choose work that conveys the essence of the unit as well as work that illustrates their expertise in solving and writing about problems. Have students complete the Patterns portfolio for homework. Ask that they bring the portfolios back tomorrow with the cover letter as the first item. You might also mention that they will be able to refer to their portfolios when they work on unit assessments.

Discussing and Debriefing the Activity You might have students share their portfolios as part of the closing activity to the unit, the Unit Reflection, by reading cover letters and/or personal growth statements as a class or in small groups, sharing portfolios among group members, or having a class conversation about what was learned during the unit. The portfolio is a very personal product for many students, something they may take a great deal of pride in. Public recognition of the thoughtfulness that students invested in creating their portfolios will add to the classroom learning environment and to students’ connection to that environment.

Key Question What are portfolios? What should go into them?