The "'Standards'-like" Role of Teachers' Mathematical Knowledge in Responding to Unanticipated Student Observations. First Draft

Recent research explaining the influence of teacher knowledge and beliefs on instruction tends to illustrate what teachers cannot do by describing their limited beliefs about mathematics or gaps in mathematics knowledge. Those studies illustrating what teachers can do tend to focus on one teacher. This paper describes what nine secondary level mathematics teachers--who are unusual in their exceptional backgrounds in mathematics and commitment to the "Professional Standards for Teaching Mathematics"--can do. By identifying patterns in these teachers' strategies for responding to unanticipated student observations (conveyed through errors, difficulties, and alternative problem solving approaches), a conceptualization of teacher knowledge use is proposed that is based in mathematics problem solving strategies. The teachers' beliefs are related to these strategies and their intentions to implement certain aspects of the "Standards" in their teaching. The implications for the mathematics instruction of prospective teachers and for other areas of teacher preparation are discussed. Appendixes contain the teacher interview protocol and a description of teaching episodes. (Contains 4 tables and 29 references.) (Author/SLD)