Academic journal article School Psychology Review

An Exploratory Validation of Curriculum-Based Mathematical Word Problem-Solving Tasks as Indicators of Mathematics Proficiency for Third Graders

Academic journal article School Psychology Review

An Exploratory Validation of Curriculum-Based Mathematical Word Problem-Solving Tasks as Indicators of Mathematics Proficiency for Third Graders

Article excerpt

Abstract. This study evaluated the validity of curriculum-based word problem-solving measures as indicators of proficiency in mathematics with a sample of 77 children in third grade. In the winter and spring of third grade, children completed a battery of general achievement tests in mathematics in addition to curriculum-based problem-solving and computation assessments. Specifically, the study investigated the reliability and concurrent and predictive validity of the word problem-solving measures through correlation and regression analysis. Results supported the adequacy of the word problem-solving measures as useful indicators of mathematics proficiency for third graders.

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The 2001 reauthorization of the Elementary and Secondary Education Act, No Child Left Behind (NCLB) requires that all students be assessed in reading and mathematics in Grades 3 through 8. This reflects the federal government's commitment to and reinforcement of state accountability systems in measuring educational outcomes for all students. NCLB comes at the heels of national and statewide school reform movements toward challenging academic standards for all students. An important implication of the standards-based reforms is that complex higher order thinking and problem solving are integral to learning (Chatterji, 2002; National Research Council, 2001; Nolet & McLaughlin, 2000).

Traditionally, research on reading has received far more interest than research on mathematics. Yet, about 5% to 8% of school age children are mathematically disabled (Geary, 2004) and are as disabled as those with significant reading problems (Bartel, 1990). Results of international and national assessments of mathematics achievement indicate that U.S. students may learn to execute rote procedures, but fail to perform adequately on mathematical problem-solving tasks (e.g., Beaton et al., 1996; Hiebert & Carpenter, 1992). In light of such performance, the Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000) called for mathematics instruction and assessment to focus more on conceptual understanding than procedural knowledge or rule-driven computation. This change has forced educators to look critically at the way instruction is designed, delivered, assessed, and monitored.

Although assessing student learning in mathematics is important, direct measures of this process are rare. Formative assessment tools (i.e., items sampled from the students' curriculum), however, can be used regularly to gather data on students' ongoing academic performance with the ultimate goal of using the data to inform instructional decisions. A system of assessment procedures that has an extensive research base, is technically adequate, and provides information about student learning is curriculum-based measurement (CBM; Deno, 1985; Fuchs & Deno, 1991; Fuchs, Fuchs, & Courey, 2005; Shinn, 1998). CBM systematically samples items from the curriculum content domain to produce outcome measures that are sensitive to growth (Fuchs & Deno, 1991). Data from CBM provide teachers with information about student progress and indicate whether changes to instruction or curriculum modifications are necessary (Fuchs et al., 2005; Fuchs, Fuchs, Hamlett, & Stecker, 1991; Whinnery & Fuchs, 1992).

The majority of research on CBM in mathematics has focused almost exclusively on computational skills with elementary school students. Empirical support for CBM involving conceptual understanding is limited to a few studies. For example, Fuchs et al. (1994) investigated the technical adequacy of CBM concepts and applications assessments administered to 140 second- through fourth-grade students. The CBM conceptual (e.g., finding patterns in a list of numbers) and application (e.g., reading the temperature from a picture of a thermometer) tasks were administered weekly for 20 weeks in general education classrooms. …

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