Classroom Vignette: An Alternative-Assessment Tool
Walen, Sharon B., Hirstein, James, Teaching Children Mathematics
How can the upper-elementary or middle-grades teacher create a safe forum for students to discuss mathematics and mathematics attitudes while simultaneously evaluating their progress and achievement? The classroom vignette is an effective communication-enhancing tool for teachers that has grown in popularity since being used extensively in the NCTM's Professional Standards for Teaching Mathematics (1991).
Teachers have the responsibility to move mathematics assessment beyond its traditional limiting notions of grading to a broader notion, as described in the working draft of the Assessment Standards for School Mathematics (NCTM 1993, 5):
Assessment occurs at the intersection of the important mathematics that is taught with how it is taught, what is learned, and how it is learned. It is a dynamic process that continuously yields information about student progress toward the achievement of mathematical power.... The process of gathering evidence in order to make inferences about student learning communicates to students and all of those concerned with their learning what is valued in mathematics and how students are progressing toward specific goals. Assessment also enhances mathematics learning when there is a shared understanding of the learning goals and of the methods used for demonstrating progress toward those goals.
A crucial issue for those involved in mathematics-education reform is the expansion of assessment strategies to guide students as they examine their individual roles in mathematical learning, extend their ability, communicate mathematically, express their world view in relationship to the classroom, and, as specifically addressed in this article, self-evaluate their own concepts and principles in today's classroom.
Vignettes: An Assessment Resource
Constructivist theories suggest that the importance of environment and communication be stressed in mathematics learning (vonGlasserfeld 1990) and that attention be focused on helping students to become risktakers (McLeod 1991; Walen 1993). Using classroom vignettes - experiences expressed in narrative or dialogue form - presents opportunities both to assist students' development and to assess their progress in attaining classroom expectations aligned with the reform movement. Vignette activities open a window on students' perceptions of mathematics and classroom roles.
Two Sample Vignettes
The vignettes discussed here focus on fifth- and sixth-grade students' discussions on perspectives of group interactions and knowledge of order of operations. These students freely interpreted, translated, and expanded the direction of their talk to areas of importance to them. The vignettes let students respond in an assessment situation by using the framework of their own experience and did not require them to have a specific correct response to a question. Additionally, work in small groups allowed teachers the freedom to listen and note discussions.
The rule vignette
The rule vignette allowed students to examine a portion of a group discussion. This vignette, by design, is free of specific mathematical content. Students were to address the broader issue of what it means to do mathematics rather than issues surrounding a specific rule. This particular vignette was chosen after listening to and assessing students' perspectives.
Students in a mathematics class discuss how to start their homework:
Kelly: I think I remember how to do it, but I'm not sure. We can figure this out.
Pat: Sure we can figure it out ... but how will we know if we get it right?
Gerry: Let's just ask the teacher what the rule is. Math has a lot of rules and you have to use the right rule.
Kelly: No, don't ask for help yet, we can figure this out.
Pat: I get sick of spending so much time listening to you try to figure things out and I really want to know how to do it right.
Gerry: This takes too long; let's just ask for the rule. …