National Mathematics Standards
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The NCTM standards have undergone review and revision since 1989, headed by The Commission on the Future of the Standards, a process that resulted in the 2000 Principles and Standards for School Mathematics (NCTM). The writing group appointed by the commission circulated a discussion draft of the revised standards in 1998, and equity was one of nineteen issues raised during this input period. How can the document better address the needs of special student populations? Basically the issue concerned whether either curriculum or instruction should vary to meet the differing needs of various groups of students. Should we be concerned with meeting individual needs? In response, the equity section of the new standards document (pages 12 to 14), defined equal access to high-quality curriculum and instruction for all students as "reasonable and appropriate accommodations [should] be made as needed to promote access and attainment for all students," not identical instruction. "Some students may need further assistance to meet high mathematics expectations," such as "increased time to complete assignments or oral rather than written assignments." They "may need additional resources such as after-school programs, peer mentoring, or cross-age tutoring." What was not stated is revealing: these students have access rights to the curriculum and many are served with Individualized Education Programs (IEP) or "504" plans that require accommodations and collaboration with other educators.
In response to criticism of the earlier standards, another document, A Research Companion to NCTM's Standards, was published in 2003. This support document mentioned students with disabilities in only a few paragraphs in its entire 413 pages. In the chapter on implications of cognitive research, Siegler included a section on individual differences where he described three types of mathematics students: good, not-so-good, and perfectionists. The "not-so-good" type is slower, less accurate, uses less advanced strategies, and performs poorer on tests. In the last two paragraphs Siegler cited Geary's (1994) term "mathematical disabilities" as describing about 6 percent of students. This group is described as similar to the not-so-good group, but their problems are a result of a combination of limited background knowledge, limited processing capacity (working memory), and limited conceptual understanding. According to Siegler, these difficulties "need to be addressed," but he cited none of the research on mathematics instruction for students with disabilities. Other authors in this edited work briefly addressed specific concerns for students with disabilities such as an over-reliance on prescriptive methods rather than formative assessment, equity issues for large-scale assessment (Wilson & Kenney, 2003), and providing an opportunity to learn that takes into account prior knowledge and student engagement needs (Hiebert, 2003).
The NCTM documents collectively seem to have drawn a line, a parameter that excludes any detailed discussion of students with special needs with the exception of those with gifts. The emphasis in the research document is on the fidelity of classroom instruction with what the new standards are recommending. The authors of the 1989 standards found that teachers were not actually changing their traditional instructional methods. The current document clearly identifies the most important factor in learning as the opportunity to learn and regards any individual differences as the result of poor teaching.
Math Instruction for Students with Learning Problems, by Susan P. Gurganus, is a field-tested and research-based approach to mathematics instruction for students with learning problems. It is designed to build the confidence and competence of pre-service and in-service teachers (Pre-K-12). Field-testing over a three-year period showed the approaches in this text resulted in significantly improved teacher candidate attitudes about mathematics, increased mathematics content understanding, and professional-level skills in mathematics assessment and instruction.