informs instructional decision making and ultimately, how it propels learning. When a teacher uses problems that elicit multiple levels or types of correct answers, instruction and assessment become a seamless process. Problems with multiple levels of responses provide the opportunity to document a student's initial level of performance while allowing or encouraging the student to adopt more mature perspectives. At the same time, the teacher receives a wide range of responses from the class, which, when ordered by sophistication, provide a picture of the manner in which the students' knowledge develops, and gives the teacher a basis for making instructional decisions.
Finally, the kinds of problems we develop for classroom use and the manner in which we interpret student thinking communicate what we believe about learning mathematics with understanding, about individual differences, about what constitutes good teaching, about the nature of mathematics, and about the individual construction of knowledge. Providing students the flexibility to move around in a mathematical territory and teachers the flexibility to interpret student thinking from a variety of perspectives will provide a more realistic conception of mathematical ability.
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Publication information: Book title: Assessment of Authentic Performance in School Mathematics. Contributors: Richard Lesh - Editor, Susan J. Lamon - Editor. Publisher: AAAS Press. Place of publication: Washington, DC. Publication year: 1992. Page number: 341.