National Mathematics Standards
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Leadership in reorienting reform efforts to focus on curriculum, instruction, and assessment standards for mathematics was provided by the National Council of Teachers of Mathematics (NCTM) in 1986 when it established the Commission on Standards for School Mathematics and involved all constituent groups in the development of national standards (Romberg, 1993). The Curriculum and Evaluation Standards for School Mathematics were published in 1989, the Professional Teaching Standards in 1991, and Assessment Standards for School Mathematics in 1995. The driving vision statement for the standards was "All students need to learn more, and often different, mathematics and...instruction in mathematics must be significantly revised" (NCTM, 1989, p. 1).
The 1989 curriculum standards were organized into four sections, matching the four planning groups: K-4, 5-8, 9-12, and evaluation. Each of the three grade-level spans included processes as the first four standards: problem solving, communication, reasoning, and connections. Nine or ten curricular areas followed within each span. The evaluation standards included three related to general principles of assessment, seven on student assessment, and four concerned with program evaluation. Since 1989, most states have revised their curriculum frameworks to reflect the NCTM standards.
Criticism of the standards and their development process was immediate. The standards were developed primarily through expert opinion and consensus, rather than research review. The product, therefore, was plagued by vague constructs, pedagogical dogma, and idealistic goals. The curriculum standards were criticized for being, on the one hand, an idealistic vision for promoting conversations about mathematics education while, on the other, attempting to establish clear expectations for student achievement by the end of each grade-level span.
Special educators cited the complete absence of references to students with disabilities, especially egregious given the increasing diversity of the K-12 student population in the 1990s (Hofmeister, 1993; Mercer, Harris, & Miller, 1993). They also questioned the fundamental process of directing change by standard setting rather than through validated, replicable, and affordable educational interventions that have been demonstrated to work with specific students. Also of concern was the emphasis on broad-based thinking skills rather than domain-specific ones. Further, they challenged the rigid adherence to an extreme constructivist paradigm where students invent their own knowledge and spend little time practicing routine skills, where teachers pose open-ended problems and provide opportunities to explore and converse, but don't directly instruct.
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.
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