Principles and Standards for School Mathematics (NCTM 2000) proposes that mathematics instruction provide opportunities for students to engage in mathematical inquiry and in meaningmaking through discourse. Mathematics teachers are encouraged to build on student discoveries in designing subsequent instruction. Natural consequences of using an inquiry-based approach to teaching include the emergence of unexpected mathematical results and the articulation of novel and different strategies by students. Anticipating the potential for such occurrences, Professional Standards for Teaching Mathematics (NCTM 1991) urges all teachers to remain flexible and responsive to student ideas in their instruction: Help students make connections among various solutions, tie student ideas to important mathematical structures, and extend student inquiry by posing questions and tasks that challenge their initial interpretations of problems or their false generalizations.
Azita Manouchehri, Manouchehri.email@example.com, is a professor of mathematics education in the School of Teaching and Learning, College of Education and Human Ecology, Ohio State University, Columbus, OH 43210-1172.