Using performance assessment to engage preservice teachers in mathematical discourse

School Science and Mathematics, Feb 1999 by Thompson, Denisse R

This article describes one mathematics educator's inclusion of an oral performance assessment into mathematics methods courses for preservice teachers at both the elementary and middle school levels. The nature of the assessment is described, issues related to implementation are discussed, and reflections about the assessment from the instructor and the students are shared.

The Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 1989, hereafter referred to as Standards) discusses the changing nature of student assessment. The Standards encourage the use of materials such as calculators, computers, and manipulatives, while incorporating "multiple assessment techniques, including written, oral, and demonstration formats" (p. 191). These ideas are extended in the Assessment Standards for School Mathematics (NCTM, 1995), which calls for the use of "multiple and complex assessment tools" (p. 29), including oral demonstrations, and recommends that assessment contribute to students' learning of mathematics. Both documents strongly recommend the use of evaluation techniques that assess what students know as well as what they do not know.

Although these recommendations are focused mainly on K-12 classrooms, they are equally applicable to content-specific pedagogical courses for preservice teachers. As the Professional Standards for Teaching Mathematics (NCTM, 1991) indicate, "teachers are influenced by the teaching they see and experience" (p. 124). The experiences from their years in K-12 classrooms may not be experiences that align with the reform movement in mathematics education. Hence, it becomes essential that content-specific methods courses provide opportunities influencing preservice teachers' perceptions of teaching and learning mathematics in the current era of reform. Additionally, changes in instructional techniques and pedagogical strategies need to be accompanied by changes in assessment. If classroom teachers are expected to use multiple assessment techniques with their students, then educators must model the use of multiple assessment techniques in mathematics methods courses (Adams, 1996).

The recommendations for greater use of alternative forms of assessment date to at least the 1940s (Lambdin, 1993). As Lambdin noted, a number of problems have hindered the implementation of alternative assessments in the past: difficulty in the design of assessments; difficulty in organizing, summarizing, and reporting nontest data; the time-intensive nature of many alternative assessments; and the tradition of written tests. Others have noted concerns about validity, reliability of scoring, and generalizability to other tasks (Herman, Aschbacher, & Winters,1992) or teachers' lack of confidence in providing solutions, concern about fairness in grading, and lack of resources to help develop more open and extended items (Cooney, Badger, & Wilson,1993). Despite the perceived problems, the current educational climate suggests optimism. Lambdin noted the broad-based support of the NCTM Standards and teachers' ownership in the documents, the national concern over students' ability to solve problems, and the impact of new technologies as reasons the current recommendations may have a greater chance of implementation.

As alternatives to traditional written exams are developed and used, it is important to remember that a major reason for broadening assessment practice is "the value that the diversification has as a tool for the improvement of our teaching and the students' mathematics learning" (Stenmark, 1991, p. 3). Good assessment tasks require students to communicate about mathematics and give their best performance (Cooney et al., 1993), permit teachers to learn what students know and students to learn what teachers value (NCTM, 1995), and provide information to impact classroom instruction and decision-making (Herman et al.,1992; Wolf & Reardon, 1996). A number of assessment alternatives have been described in the literature, including journals, open-ended problems, portfolios, interviews, observations, and performance assessments (Berenson & Carter, 1995; Huinker, 1993; Long & Ben-Hur, 1991; Stenmark, 1991).

This article describes one specific type of performance assessment, an oral interview exam, used in mathematics methods courses for preservice teachers at both the elementary and middle school levels. The nature of the oral exam is described, issues related to implementation are discussed, and reflections about the assessment from the instructor and the students are shared.

The Nature of the Mathematics Methods Courses

At the University of South Florida, preservice elementary teachers take two mathematics methods courses. The first, a three-semester credit course, focuses on prenumber concepts, place value, and operations with numbers, including whole numbers, fractions, and decimals. The second, a two-semester credit course, focuses on geometry, measurement, statistics, and probability. The content is based on increasing teachers' knowledge base in content and pedagogy relative to the elementary standards in the NCTM Standards and Florida's Curriculum Framework for Mathematics (State of Florida, 1996).