Effective Mathematics Instruction for Students With Moderate and Severe Disabilities: A Review of the Literature
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Educational programs for students with moderate and severe disabilities (MSD) have undergone drastic changes since the mandate for access to the general curriculum was provided by Individuals With Disabilities Education Act. Since then, educators have struggled to find methods to use to promote optimal learning, including in the area of mathematics. The purpose of this systematic literature review was to provide an update on research related to teaching mathematics to students with MSD published from 2005 to 2017. Results from the included studies indicated that mathematics research has started to diversify in the skills that are being taught to this population. In addition to skills taught, current research has continued to inform the field on some promising methods that can be used to teach a broader range of mathematics skills. Emerging strategies that were identified included the use of concrete representations, anchored instruction, and instructional technology. Suggestions for future research are discussed.Keywords:
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This assumption that how teachers teach mathematics is fundamentally connected with how they learned it underlies the first standard of the “Standards for the Professional Development of Teachers of Mathematics.” This standard, Experiencing Good Mathematics Teaching, focuses on the role of the college and university mathematics professors in the process of reforming school mathematics teaching. It is essential that mathematics teacher educators invite and encourage college-level mathematics faculty to join them in implementing the teaching standards. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Standards for Teaching Mathematics (1991) present a new vision of school mathematics. Mathematics courses and programs of study in colleges and universities should share in this vision.
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Based on the new request of mathematics curriculum reform of the foundation education to the accomplishment of mathematics teachers in middle school,based on the present situation investigation and the analysis of colleges and universities mathematics education curriculum,and the innovation from a new high perspective point of view to the high mathematics education curriculum content,the paper has constructed a system of courses of mathematics education in normal universities,which adopt the reform of mathematics foundation education.The specific measures of mathematics teacher career development include: 1)to change the separation between higher education and the foundation education;2)to optimize the curriculum system of mathematics and the applied mathematics of the specialized teachers;3)to renew professional education of curriculum content mathematics and applied mathematics;4)to realize many kinds of teaching methods nimble to use;5)to perfect the appraisal system of mathematics and applied mathematics professional education curriculum.And carry on the reform and the practice in course structure,content and curriculum teaching and so on,to realize closely the integration of mathematics education in normal universities and with the new mathematics curriculum in the foundation education.
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Members of the National Council of Teachers of Mathematics can be proud of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). Not only has the Standards document set the course for improving mathematics education, but it has been imitated by virtually every other content-oriented teachers' organization. Thus, as well as recasting mathematics education, the NCTM has led the way toward recasting education generally. However, professional educators have an obligation to reconsider and reflect on the Standards themselves and any other recommendations made by responsible educators and organizations.
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If one accepts the year 1957 as the beginning of the “modern mathematics” era for the elementary school and high school mathematics programs, then we are now more than half way through the second decade of the “revolution” in mathematics education. In 1967 a number of speakers at meetings of the National Council of Teachers of Mathematics expressed the view that the first decade of the mathematics curriculum reform movement was devoted to developing worthwhile mathematics content, and since that phase of curriculum reform had been accomplished with great success, the second decade should be devoted to the pedagogical issues of how this content can be taught successfully to children. Although many mathematics educators may be satisfied with the mathematics content of the present programs, an increasing number of educators are raising serious questions about these mathematics curriculums.
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The history of mathematics can play a positive role in teaching of mathematics, however, there is evidence that it is rarely addressed in teaching. This is, in part, some teachers lack good Quality of History of Mathematics. In this paper, we will distinguish QHM of mathematics teachers to include three elements: recognition of history of mathematics, knowledge about history of mathematics and the ability to utilize history of mathematics in teaching. We will discuss appropriate measures that can be taken to improve QHM among teachers. “The history of mathematics and mathematics education” is a hot topic of international educational research in mathematics. The educational value of history of mathematics has being increasingly highlighted. The mathematics curriculum standard in China emphasizes the history of mathematics, aiming at introducing the history of mathematics into mathematics classroom teaching. However, in the practice of teaching, the phenomenon of “high evaluation, low use” with the history of mathematics exists generally. Previous research showed: The key reason was that teachers’ quality of history of mathematics (QHM) is relatively low (Li, 2005). This paper focuses on characterizing QHM of mathematics teachers and offers strategies for improving it. Connotation of the QHM of Mathematics Teachers The QHM is an important part of mathematics teachers’ professionalism. It is also an important vehicle for grounding teachers’ understanding of mathematics and its structure. The QHM of mathematics teachers is different from the purely theoretical disciplinary knowledge of mathematical historians in that for teachers the QHM includes three elements: recognition of history of mathematics, knowledge about history of mathematics, and the ability to utilize history of mathematics in teaching. This paper discusses the relevance of QHM for middle school mathematics teachers.
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Introduction The Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 1989) was issued to reflect what should be of value and to promote reform in mathematics education. The Professional Standards for Teaching Mathematics (NCTM, 1991) envisioned teachers as the primary agents for implementing the Curriculum Standards. In response, the Curriculum Standards have been incorporated into mathematics methods courses to prepare teachers to assume their roles as agents of change. However, success depends on the value that preservice teachers assign to the Standards and trends in these valuations remain unexamined. Since its publication, the Curriculum Standards (hereafter referred to as the Standards), have had a highly visible impact on mathematics education. Besides being incorporated into mathematics methods courses, they have influenced K-12 curricula, and methods of assessment, as as professional development programs (Ferrini-Mundy, 1996; Findell, 1996; Research Advisory Committee, 1998). In addition, publishers have aligned school mathematics textbooks with the Standards, although sometimes merely as addons (Battista, 1999; Chandler & Brosnan, 1994). The Standards have spawned numerous articles pointing to a myriad of effects they would have on schools and students (Crosswhite, Dossey & Frey, 1989; Lindquist, Dossey & Mullis, 1995; Loveless, 1997; Research Advisory Committee, 1990) and have been recently updated by the Principles and Standards for School Mathematics (NCTM, 2000). Despite the visibility of reform in these contexts, other manifestations of reform are less obvious. It is difficult to determine to what degree teachers have implemented the NCTM's vision of how mathematics should be taught in the classroom. Widespread awareness or acceptance of reform was not the case in 1993, when a survey (Weiss, 1994) was conducted of 6000 teachers in grades 1-12. Only 56% of high school teachers and less than 28% of elementary teachers were well aware of the Standards. Also, when teachers from the elementary and high school levels were asked how important: instructional strategies suggested by the Standards were to effective instruction, they valued some strategies but rejected others. The Standards called for a vision of mathematics teaching that encourages active student participation and problem solving. It fostered a vision in which students would be given opportunities to pose their own problems that involve everyday situations and have opportunity to read, write, and discuss meaningful mathematics. Students would be exposed to a variety of computation techniques, such as using paper and pencil, using calculators, and performing mental computation both exact and approximate. Ultimately, this style of teaching would encourage students to construct their own knowledge. However, this vision is in conflict with both the way many preservice teachers learned mathematics and their conceptions of mathematics teaching (Frykholm, 1996; NCTM, 1991; Schram & Wilcox, 1988). All too often, they have been exposed to a style of mathematics teaching in which students are discouraged from being anything other than passive receptors of knowledge -- a style preoccupied with paper and pencil computation which emphasizes memorization of facts, rules, and formulas along with a diet of routine problems often lacking in meaning. The Professional Standards (NCTM, 1991) acknowledged this conflict and recommends that preservice teachers be provided with opportunities to examine and revise their conceptions about mathematics teaching. Examination of their conceptions, before they take methods courses, might form a baseline for comparison and a compass for needed revisions. Preservice educators could benefit in knowing the initial value their students assign to the Standards, as as trends in these evaluations. …
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In the early 1980's, the National Commission on Excellence in Education responded to the call for reform in the teaching and learning of mathematics. In particular, the Commission developed a document addressing the consensus that all students need to learn more, and often different, mathematics and that instruction in mathematics must be significantly revised. In a response to these calls for mathematics education reform, the National Council of Teachers of Mathematics (NCTM) developed its Curriculum and Evaluation Standards (1989) with a two-fold purpose: 1) to create a coherent vision of what it means to be mathematically literate in a world that relies on calculators and computers, and 2) to create a set of standards to guide the revisions of school mathematics curriculum.
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Affording more opportunities to engage students in thinking and communicating mathematically and integrating technology into mathematics education are clear trends in curricular reform. Recent recommendations emphasize adopting a more active, process-oriented approach to mathematics learning and teaching. The Mathematical Sciences Education Board's document Reshaping School Mathematics (1990) emphasizes that a person engaged in mathematics gathers, discovers, creates, and expresses facts and ideas about patterns. The National Council of Teachers of Mathematics in its Curriculum and Evaluation Standards for School Mathematics (1989) advocates mathematics teaching through activities that encourage students to explore mathematics, to gather evidence and make conjectures, and to reason and communicate mathematically as they discuss and write about ideas that use the language of mathematics. This vision of the classroom specifies a mathematics curriculum in which students are “doing and investigating” mathematics rather than just “knowing” mathematics.
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