Assessing Teaching Practices of Secondary Mathematics Student Teachers: An Exploratory Cross Case Analysis of Voluntary Field Experiences (1) (Section III: Course and Professor Level of Assessment of Innovation‪)‬

Current reform efforts to improve the quality of mathematics teacher education include recommended changes in standards from multiple sources such as professional organizations (National Council for Teachers of Mathematics, NCTM, 2000; National Council for Accreditation of Teacher Education, NCATE, 2002). Moreover, researchers (von Glasserfeld, 1987; Glaser, 1988) note that recent reforms support a constructivist framework concerning assumptions about knowledge, learning, and teaching that promote students' deeper understandings of concepts and the relationships of concepts as opposed to memorization of isolated information. According to O'Brien and Korth (1991), learning outcomes are viewed as a result of the ways that students process and interact with information, leading to an interactive view of teaching. Interactive instruction engages students in problem solving, modeling, and constructively building conceptual understanding in student-centered classrooms. In addition, the standards advocate promoting excellence for all students irrespective of their gender, race, social, cultural and economic backgrounds (Kennedy, 1991). The kind of teaching supported by the standards requires a more active, inquiry-based process where students are at the center of instruction with the teacher as an organizer, challenger, and facilitator of student achievement (Bigelow, 1990). However, despite the general acceptance of a constructivist active learning approach to reforming teacher practices nationally, researchers have found that teaching practice continues to be viewed as knowledge transmission from teachers to students by telling followed by practice (Smith III, 1996). To mitigate this outcome, the Pre-service Secondary Mathematics Teacher Education Program at Florida International University (FIU) was revised to incorporate the six principles from the National Council of Teachers of Mathematics (2000) shown in Table 1, emphasizing early field experiences with teachers who modeled constructivist teaching and learning. The curriculum approach provided opportunities for the pre-service teachers to experiment with abstract concepts, objects, and relationships, and pursue conceptual understandings (Jiang, McClintock, & O'Brien, 2003; Jiang, Manouchehri, & Enderson, 2002; McClintock & Jiang, 1997; Jiang & McClintock, 1997). In addition, modeling in mathematics is emphasized in the courses of the mathematics education program as recommended by Dossey, Giordano, McCrone, & Weir (2002). In the courses, the FIU faculty designed field experiences to help pre-service teachers understand the nature of teaching by observing and interacting with mentor teachers, reflect upon learning and teaching, and prepare for student teaching. Pre-service teachers were invited to participate in after class workshops that featured guest experts from other universities, schools, and/or professional associations on topics such as modeling, technology and learning, and integrating mathematics, science, and technology in the classroom.