EXAMINING HOW BELIEFS SHAPE INSTRUCTION: CASE STUDIES OF TEACHING ASSISTANTS IN A 'REFORM' CALCULUS COURSE

Natasha M. Speer

University of California, Berkeley

nmspeer@socrates.berkeley.edu

Mathematics educational reform calls for increased emphases on conceptual understanding and communication of mathematics. Such reform often calls for new teaching practices, different from those that the teachers themselves experienced or were taught. Research has documented the significant influence that teachers' beliefs have on their practice (Cooney & Shealy, 1997; Thompson, 1992). This body of research has established the role that beliefs play in shaping how practices such as problem solving and sense-making are carried out in classrooms. It has not, however, analyzed the influence of beliefs on the moment-to-moment decisions that teachers make in their classrooms.

This study examines how graduate student teaching assistants' (TAs') beliefs about teaching, learning and the nature of mathematics shapes their interactions with calculus students as they implement reform-oriented discussion sections. The sections were designed so that TAs facilitate discussions and assist students working in collaborative small groups to solve challenging problems. Course materials are designed with the intention that TAs' interactions with students will focus on sense-making and conceptual understanding.

Fine-grained analyses of videotaped classes and interview transcripts are used to examine how TAs’ beliefs influence their moment-to-moment decisions about asking questions and offering assistance. Different degrees to which each TA emphasize sense-making and conceptual understanding of the mathematical ideas are traced to different beliefs held by each TA.

Reference

Cooney, T. J., & Shealy, B. E. (1997). On Understanding the Structure of Teachers' Beliefs and Their Relationship to Change. In E. Fennema, & B. Scott Nelson (Ed.), Mathematics Teachers in Transition (pp. 87-109). Mahwah, NJ: Lawrence Erlbaum Associates.

Thompson, A. G. (1992). Teachers' Beliefs and Conceptions: A Synthesis of the Research. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 127-146). NY: Macmillan.