Preservice Elementary Teachers: Building Portfolios around Students' Writings
Pokay, Patricia, Tayeh, Carla, Teaching Children Mathematics
Traditionally, college mathematics courses have rarely asked students to write or to reflect on their learning, concentrating instead on textbook exercises and problem sets in a lecture format. The intent of this study was to model the use of portfolio assessment in a college mathematics course for preservice teachers while focusing on the contributions of the students' writing in the mathematics classroom. In the study, portfolios were the vehicle for organizing the students' writings.
The release of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) spurred a reform movement that calls for instructional practices to shift from "teaching by telling," memorizing rules, and relying on follow-the-example exercises to emphasizing open-ended problems, written and oral communication, active engagement, and mathematical connections. Evaluation is redefined as an integral part of teaching and of improving instruction. The inability of past assessment measures to reflect students' understanding of mathematical concepts and procedures has led to a push toward alternative assessments in mathematics, including open-ended questions, projects, self-evaluation and peer evaluation, performance assessment, observation, interviews, and portfolios (Clarke, Clarke, and Lovitt 1990; NCTM 1989; Stenmark 1989). Implementing the Curriculum and Evaluation Standards will require that teachers be receptive to these alternative approaches to teaching and to assessing students' learning. The reform movement focuses on learning and teaching K-12 mathematics, and the education of preservice teachers affords an ideal place for intervention. If future teachers are to implement these recommendations in K-12 classrooms, they first need to see these practices modeled during their training.
A growing body of evidence suggests that writing in the mathematics classroom facilitates learning and serves to improve communication between student and teacher (Azzolino 1990; Geeslin 1977; Johnson 1983; McIntosh 1991; Mett 1987; Miller 1991; Nahrgang and Petersen 1986). Writing is a unique tool in mathematics classrooms because it allows students to record, reflect on, and modify their ideas about mathematics. In this way, it helps to clarify relationships and make connections among concepts (Emig 1977; Rose 1989, 1991). This type of reflection and modification is important in developing thinking and reasoning skills, skills the Curriculum and Evaluation Standards has articulated as being important in mathematics. An argument can be made that writing is even more important in a mathematics classroom for preservice elementary teachers (Burton 1985; White and Dunn 1989). Ideally, these students should learn the mathematics content while reflecting on themselves as learners of mathematics and as classroom teachers.
This goal of encouraging preservice elementary teachers to reflect on the mathematics and on the learning process prompted the initial use of portfolios built around students' writings. Portfolios help students develop the ability to assess their own work as well as help them visualize the learning that has taken place during the semester (Wolf 1989). Most studies on student portfolios have, however, focused on elementary and secondary classrooms or have been found in college courses in the arts and humanities. The focus of this study was on using portfolios with preservice elementary teachers to encourage them to reflect on themselves as learners of mathematics and to begin to reassess their role as a classroom teacher.
The purpose of this article is to share what was learned about using portfolios and writing with preservice teachers. Specifically, the procedure that was used and information about what was learned from student self-evaluations about the students and teaching will be presented.
To explore the use of mathematics portfolios with preservice elementary teachers, a geometry class was chosen that is required of all elementary education students majoring or minoring in mathematics and that is usually taken during the sophomore or junior year. …