Students With Disabilities and Their Mathematics Instruction Book Report

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Individuals with Disabilities Education Act (IDEA) governs how the U.S. states offer special education services to children with disabilities. It addresses the educational needs of the children with disabilities from birth to age 21, and involves more than a dozen specific categories of disability. Congress has reauthorized and amended IDEA several times, most recently in December 2004. Although historically, students with disabilities have not had the same access to the general education curriculum as their peers, IDEA has changed the access and accountability requirements for special education students immeasurably (NCTM, 2011).

The challenges for meeting the needs of students with disabilities and ensuring their mathematical proficiency, confront teachers of mathematics every day. Teachers must use the results of all assessments, formative and summative, to identify the students whose learning problems have gone unrecognized, and monitor the progress of all students. Regardless of the level or method of assessment used, teachers must focus on gauging students' conceptual understandings, critical thinking and ability to solve problems, not just acquiring skills. As a crucial component of planning and instruction, assessment measures the breadth and depth of learning, and identifies misconceptions that may influence students' thinking. But assessment is more than item analysis, proficiency levels and making Adequate Yearly Process (AYP) (NCTM, 2011). It's also the monitoring, affective and expressive qualities of student engagement. One important role of assessment is communicating and interpreting results with and for parents and others. Assessments should not be done to students; rather assessments are for students and should be used to guide and enhance their learning. Every student must have access, every day, to a mathematics teaching and learning environment, and related experiences that meets their needs, challenges them and for which they are accountable. Every parent and teacher must get away from the sort of impulsive reaction of thinking that children who struggle need to be considered for special education, rather than taking the time to determine their actual needs, and forge an intervention path. The schools and the government must find a way for teachers of mathematics and special education to truly and regularly collaborate in areas related to learning, instruction and assessment, mathematics content and related pedagogy, to be considered as special education students (NCTM, 2011).

Chapter 2

Despite the seemingly endless dialogue that some refer to as the 'math wars,' some agreement exists about what the goals of school mathematics should be. According to 'Adding it up: Helping children learn mathematics by Kilpatrick Swafford and Findell in 2001, and 'Foundations for Success: The final report of the National Mathematics Advisory Panel by the U.S. Department of Education in 2008, mathematics instruction should foster mathematical proficiency. This proficiency includes: conceptual understanding, procedural fluency e.g. fluency with basic computational skills, strategic and adaptive mathematical thinking like problem solving and logical reasoning, and a productive disposition like the beliefs and confidence necessary to use mathematics effectively in everyday life, even as it changes constantly and rapidly (NCTM, 2011).

Because experts use a variety of strategies, including automatic or semiautomatic rules and reasoning processes, we should define number combination proficiency or mastery broadly as including any efficient strategy not narrowly as a fact retriever.

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Thus, students should be encouraged, not discouraged from flexibly using a variety of strategies. Teachers should patiently help children construct number sense and not prematurely drill facts. That is, teachers should encourage the invention, sharing and refinement of informal strategies. Children typically adopt more efficient strategies as their number sense expands, or when a real need to do so surfaces e.g. in determining an outcome of rolling dice in an interesting game. To promote meaningful memorization or mastery of basic combinations (combination fluency), teachers should focus on encouraging children to look for patterns and relations; to use these discoveries to construct reasoning strategies; and to share, justify and discuss their strategies (NCTM, 2011).

Helping children with learning or behavioral difficulties achieve mathematical proficiency and adaptive expertise will require an approach different from and more sophisticated than the traditional direct instruction and drill method. It will require purposeful, meaningful and inquire-based instruction that promotes all aspects of mathematical proficiency in an integrated manner. Planning and implementing such instruction will require considerable time, effort and knowledge from teachers, but significantly greater student development will reward their investment (NCTM, 2011).

Chapter 3

To truly embrace the vision and promise of the Principles and Standards for School Mathematics, one must revitalize mathematics programs and rethink teaching and learning for the benefit of all students. Some researchers in special education express doubt that proposed methods and trials associated with reform mathematics are appropriate for students with learning abilities or those at risk. For example, special educations have long been recommended using a set of procedures to reduce ambiguity when teaching mathematics (NCTM, 2011). Believing that multiple approaches to solving problems can lead to confusion, researchers view alternative strategies and invented algorithms, a common approach as reform-based mathematics instruction, is problematic for low achievers. These researchers see one simple set of rules as the best approach to teaching these students. Research on attempts to achieve inclusion for special education students, particularly, students with learning disabilities, also suggest that general education teachers have a hard time accommodating such students' needs. Researchers have typically tried inclusion in settings where general education teachers used traditional pedagogy and curricular materials. One view is that traditional pedagogy is, in some sense, responsible for the difficulties that low achievers experience; and that with curricula and pedagogy that emphasize levels of both content and pedagogical reform, many students who formerly struggled in traditional mathematics instruction will thrive (NCTM, 2011).

To guide the efforts in improving learning of individuals experiencing difficulties in mathematics, Bottge's model of key lock method can be examined. The model is based on theories of cognition, emphasizes the NTCM (2000) Equity Principle; and considers learner, contextual and task variables essential to an adequate description of teaching and learning mathematics. For significant learning to occur, the six teeth of the instruction key (meaningful, explicit, informal, (de)situational, social and teacher specific), must fit a pin of the learning lock (engagement, foundations, intuitions, transfer, cultural supports and student specific). Without attention to the interplay of these variables, students may never have the opportunity to see mathematics as a subject of worth, a subject of connections, a subject that they.....

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