Academic journal article Learning Disability Quarterly

Identification and Remediation of Systematic Error Patterns in Subtraction

Academic journal article Learning Disability Quarterly

Identification and Remediation of Systematic Error Patterns in Subtraction

Article excerpt

Abstract. The present study investigated 90 elementary teachers' ability to identify two systematic error patterns in subtraction and then prescribe an instructional focus. Presented with two sets of 20 completed subtraction problems comprised of basic facts, computation, and word problems representative of two students' math performance, participants were asked to examine each incorrect subtraction problem and describe the errors. Participants were subsequently asked which type of error they would address first during math instruction to correct students' misconceptions. An analysis of the data indicated teachers were able to describe specific error patterns. However, they did not base their instructional focus on the error patterns identified, and more than half of the teachers chose to address basic subtraction facts first during instruction regardless of error type. Limitations of the study and implications for practice are discussed.


According to the Goals 2000: Educate America Act (PL 103-227), a high level of mathematics achievement for all students is a national priority. According to the National Research Council (2002), all students can and should achieve proficiency in mathematics. Additionally, mathematical skills are fundamental for individuals seeking occupational and educational advancement. Without proficiency in mathematics, students will likely experience difficulty completing other more advanced branches of mathematics (e.g., algebra) and be unprepared for many occupations. Mathematics education should enable students to understand and apply mathematical concepts. With this emphasis on conceptual understanding and higher-order problem-solving skills, teachers must not ignore computation.

Knowledge of basic computation skills cannot be separated from the overall conceptual understanding and forms the foundation for mathematical thinking (Wu, 1999). The National Council of Teachers of Mathematics (NCTM; 2000) emphasizes computation over overall performance in mathematics. According to the NCTM (2000), it is critical for students to know the basic number facts for addition, subtraction, multiplication, and division. Students' fluency and accuracy in methods of computation are equally important. The National Research Council (2002) further articulates the importance of computation by listing computation as the second of five main strands in mathematics. Yet, many students do not learn the basic mathematics skills required for success.

Even more troubling is the mathematics performance of students with learning disabilities (LD). Students with LD experience difficulties learning math, with problems surfacing early and continuing throughout their education (Bottge, 1999; Mercer & Miller, 1992). Deficiencies in mathematics performance are not limited to basic skills. Higher-order thinking skills such as problem solving are also a major challenge for these students (Jitendra, DiPipi, & Perron-Jones, 2002). The average mathematical performance of 16- and 17-year-old students with LD is approximately at the fifth-grade level (Cawley & Miller, 1989). Furthermore, students with LD have documented deficits in the areas of (a) basic facts, (b) subtraction, (c) solving word problems, (d) acquiring concepts, and (e) problem solving (e.g., Garnett, 1992; Miller, Stawser, & Mercer, 1996; Montague & Brooks, 1993).

Many students who are not proficient in the basic mathematics skills demonstrate numerous mathematics misconceptions (Marchand-Martella, Slocum, & Martella, 2004). For example, subtracting the smaller number from the larger number regardless of position is a common misconception not just among low-performing students or students with disabilities (Resnick & Omanson, 1987). When students make errors and formulate mathematical misconceptions, teachers should recognize the errors, prescribe an appropriate instructional focus, and implement an effective and efficient reteaching plan. …

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