Academic journal article Exceptional Children

Fourth-Grade Culturally and Linguistically Diverse Exceptional Students' Concepts of Number Line

Academic journal article Exceptional Children

Fourth-Grade Culturally and Linguistically Diverse Exceptional Students' Concepts of Number Line

Article excerpt

Prior research has indicated that CLD students with disabilities demonstrate less than adequate academic progress in content areas, as well as experiencing general language difficulties (Smith, 1995). In the area of mathematics, performance deficiencies are most commonly observed when CLD students with disabilities are required to comprehend and solve word problems, where language problems combine with difficulties with arithmetic computation to result in far below average levels of performance (Secada, 1991). During problem-solving activities, semantic differences in terminology can confuse CLD students with disabilities (Churton, Cranston-Gingras, & Blair, 1998). Further, the emphasis within a culture toward schooling and mathematics in particular also influences children's mathematical success.

Cummins (1984) distinguished between two levels of language proficiency, Basic Interpersonal Communication Skills (BICS) and Cognitive Academic Language Proficiency (CALP). His research indicates that students could be proficient in BICS, but deficient in CALP, which has a profound impact on their school performance. The distinction between BICS and CALP is important, for it affects how academics are taught. Further, it makes even more important the question raised by educators about how to ensure that the language of mathematics is effectively taught and communicated to CLD students when they do not have the necessary English language proficiency to understand mathematics.

Understanding the numeration system and the relation of number to quantity is one of the basic foundations of mathematics. It has been proposed that by the age of 31/2 years, children have a fairly well developed understanding of the relative position of numbers and can connect number to quantity (cardinality) for as high as they can count (Wynn, 1992). For SLD, however, this concept often does not develop at the expected age, or the development is in some way incomplete due to a lack of the prerequisites of classification, conservation of number, one-toone correspondence, visual clustering, and sequence (Sharma, 1990).

Difficulties in understanding numeration and the relation to quantity are compounded for culturally and linguistically different students who are in need of special education. These students have difficulty connecting language to actions, memory, and concepts (Torres-Raborn, 1995). In the context of learning number concepts, they experience difficulty acquiring the concepts and recognizing where to apply them based on the problem at hand.

Problem-solving is even more challenging. Research has indicated that young SLD show deficient levels of performance, but can improve considerably when provided schema-based instruction (Jitendra & Hoff, 1996) and instruction in self-monitoring strategies (Case, Harris, & Graham, 1992). Explanations for initial poor performance have included (a) developmental factors in the way the students conceptualized the experimental situation (Bednarz & Garnier, 1993), (b) differences in cognitive ability and style that interact with the instructional context (Zentall & Ferkis, 1993), and (c) shutdown of cognitive resources without attempting to solve the problem (Montague & Applegate, 1993). However, these findings do not speak directly to the challenges for students who also are CLD.

Limited research on mathematical problem-solving has been conducted with CLD students. Leon (1993) found that bilingual students with disabilities experienced similar difficulties dealing with extraneous information in word problems in both Spanish and English, but were successful in solving word problems without extraneous information in both languages. Secada (1991) observed consistency in first-grade Hispanic students' ability to solve, change, and compare types of word problems in both languages.

Research has looked at numeration and computational abilities within the context of cardinality, but has not considered counting within a measurement context. …

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