Varied and appropriate ways to demonstrate mathematical power

The following are strategies for providing students with varied and appropriate ways to demonstrate their mathematical power, from the NCTM Assessment Standards for School Mathematics (1993, working draft) and the National Research Council's Measuring What Counts (1993):

• Use different formats and modes of response - e.g., interviews, long-term projects, journals, illustrations, and models.

• Evaluate all aspects of performance - e.g., individual and group projects; open-ended and structured tasks; self-, peer, and teacher assessment; attitudes; and thinking processes.

• Provide sufficient space, time, and tools - e.g., calculators and manipulatives - for students to exhibit optimal work.

• Communicate problems effectively - e.g., by using bilingual techniques or appropriate visuals - and recognize how students' command of language affects mathematical expression.

• Provide accommodations to students with special needs during both instruction and assessment.

• Include multiple points of entry and exit on assessments.

• Recognize varying degrees of mathematical sophistication in responses.

• Be sensitive to differences in background that might affect results - e.g., the individual student's understanding of the context of a problem or task.

• Involve students in setting criteria for performance evaluation.

• Encourage students to participate in high-quality opportunities to learn the material that will be assessed.

• Whenever possible, provide opportunities for students to make assessment choices - e.g., format, mode of response, task, criteria.

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