Assessing Teaching Practices of Secondary Mathematics Student Teachers: An Exploratory Cross Case Analysis of Voluntary Field Experiences1

Teacher Education Quarterly, Summer 2005 by McClintock, Edwin, O'Brien, George, Jiang, Zhonghong

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, inquirybased 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.

Analyses of the impact of reform-based teaching practices in FIU's program have been previously reported (Jiang, O'Brien, & McClintock, 2003; Mendez, O'Brien, McClintock, & Jiang, 2003; Jiang, O'Brien, & McClintock, 2002). However, the impact of the field experiences per se has not been assessed. The purpose of this study was to determine if field experiences can change pre-service teachers' views about teaching from knowledge transmission to a more interactive constructivist perspective. The following question was posed: Do pre-service teachers with a significant amount of optional supplemental field experiences use reformed-based practices more compared to those who do not?

Method

The naturalistic paradigm (Moschkovich & Brenner, 2000; Erlandson, Harris, Skipper, & Allen, 1993) was used for the investigation. This paradigm combines the linear structure of the traditional research design (i.e., define the research question, design the study, collect the data, and analyze the data) with a more circular qualitative research process.

Participants

In the spring semester of 2003, seventeen pre-service mathematics teachers enrolled for student teaching. Classroom observations were conducted every week during the semester. Each student teacher was observed five times by the authors. Detailed field notes were taken for each observation. In addition to the observations, each student teacher agreed to be videotaped during three other class lessons. The purpose of the videotaping was to secure a record of the lessons for in-depth analysis (Lesh & Lehrer, 2000).

In depth case study analyses were conducted for a sample of four of the seventeen student teachers enrolled in the spring and summer of 2003 : Lisa, Debbie, Victor, and Jay. [Note: Pseudonyms are used to protect their anonymity.] They had the highest GPAs and strongest academic mathematics backgrounds (considering the depth of mathematics courses completed and grades in these courses) of all the student teachers in the cohort. Two of the student teachers, Lisa and Victor, had participated in the voluntary experiences in the Partnership in Academic Communities (PAC) program during their junior and senior years. They were the only student teachers in the group of 17 with these extensive voluntary experiences. While Victor completed his student teacher internship in the PAC program, the other three participants completed their student teaching at local public schools. The student teachers were placed with the best available cooperating teachers during the semester. Because the four participants were similar in terms of their academic performance, the researchers focused on the possible differences among them due to the differences in their volunteer experiences.