Academic journal article Learning Disability Quarterly

Enhancing Student Achievement on Performance Assessments in Mathematics

Academic journal article Learning Disability Quarterly

Enhancing Student Achievement on Performance Assessments in Mathematics

Article excerpt

Abstract. This article is part of a program of iterative research involving students with learning disabilities in reform mathematics classrooms at the intermediate grade levels. The study reports the findings from a larger, yearlong case study focusing on ways to improve problem solving through classwide performance assessment tasks and ad hoc tutoring for students with learning disabilities. The purpose of these interventions was to enhance a student's deeper understanding of mathematics and to develop the kind of strategic knowledge needed to solve complex problems. A quantitative analysis of the results indicate that these two interventions led to demonstrable differences over time and when compared to a limited number of students with learning disabilities who did not receive this kind of instruction. Qualitative analyses of student performance show two distinct trends in the improvement of the students in the intervention group. Findings from this study have implications for special educators interested in mathematical problem-solving instruction, as well as policymakers who are interested in performance assessment.

The difficulties with traditional, norm-referenced tests as measures of student achievement in disciplines such as mathematics are well documented. These tests, on which students typically select answers from multiple-choice options, tend to stress isolated facts, definitions, and procedures (Darling-Hammond, 1990; Linn, 1993; Smith 1991; Stiggins, 1997; Wilson, 1992). More importantly, educators such as Romberg (1995) argue that norm-referenced tests and other objective assessments are anathema to mathematical reform by perpetuating the focus among teachers, administrators, and policymakers on basic skills that are usually presented in a linear, fragmented fashion. In order to promote deeper levels of curricular and pedagogical reform, Romberg and others recommend substantive changes in the ways we assess mathematical understanding.

Alternative forms of assessments such as portfolios, performance tasks, observations, and student interviews offer a variety of avenues for documenting substantive mathematical understanding, while at the same time supporting and reinforcing changes in classroom instruction (Kulm, 1990; Resnick & Resnick, 1992; Romberg, 1995). Performance assessment tasks generally require students to: (a) solve a complex problem(s), and (b) communicate how they derived their answer(s) or justify why their answer(s) is correct. Examples of successful answers to performance assessment tasks in mathematics include the use of pictures, tables, charts, and/or words to explain thinking (e.g., Lesh & Lamon, 1992; Romberg, 1992; Webb, 1993).

Writing about one's mathematical understanding presents intriguing possibilities for math educators. Writing is seen not only as a means to communicate knowledge, but also as a vehicle for learning (Connolly, 1989; King, 1982; McMillen, 1986; Yinger, 1985). Writing about mathematical concepts or solutions to problems can help students critically examine, organize, and refine their understanding (Burns, 1995). In this regard, writing can be an important vehicle for enhancing a student's deeper understanding of important mathematical ideas and of ways of engaging in mathematical inquiry (see Morocco, this issue).

In fact, performance assessments can be a vehicle for helping students with learning disabilities: (a) improve their strategic knowledge, (b) allow for substantive interactions with peers in small-group settings, and (c) facilitate teacher-guided discussions (or constructive conversations, as Morocco describes them) in the classroom. This latter issue of classroom discussions that involve students with learning disabilities is particularly important. Current models of classroom mathematics discussions are daunting for many practitioners because they require a considerable amount of content and pedagogical knowledge, with few, if any, models for how to engage students with learning disabilities in these contexts (Ball, 1993; Ball & Rundquist, 1993; Cobb & Bauersfeld, 1995; Lampert, 1997). …

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