Designing Mathematics or Science Curriculum Programs A Guide for Using Mathematics and Science Education Standards (1999) / Chapter Skim
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Introduction
Introduction
Pages 1-16
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3 Reaching strategies and the classroom assessments associ ate(1 with the use of instructional materials are also part of the program but will not be discussed in this report per se.) All of the components of a curriculum program together are often referred to as the "intended curriculum" of a school (listrict and may (1iffer from what is implemented by the teacher the "implemented curriculum" and what is learned by the students the "achieved curriculum." This report does not deal with implemented or achieved curricula but monitoring both can provi(le (listricts with important (lata to guide their process anti results.)
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By contrast, this report emphasizes the importance of defining and coordinating curricula across the entire 13-year span based on standards in use by local school districts as a way to improve the quality of education. It describes the components of coherent curriculum programs based on mathematics or science standards or both and a process for (resigning such programs.
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There may be a number of reasons that the science assessment performance of the fourth-grade students in the United States was relatively high compared to those of students in other countries, including the fact many other countries do not include formal science instruction in the early grades; however education analysts found it most startling that achievement appears to decline over time in the United States relative to other countries. Whatever the cause, it appears to be cumulative, contributing to the decrease in U.S.
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~; Complex information (information involving the integration of bits of simple information; examples include differentiating, comparing, contrasting, synthesizing; specific examples are understanding how increased external pressure raises boiling point of liquids, how fire is a part of the life cycle of pine trees) (Robitaille et al., 1993~.
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The TIMSS achievement data suggest that the toll this takes on student learning is great and greater as the curricula advance through the grades. A number of practices in curriculum design and implementation appear to contribute to the lack of coherence and challenge in mathematics and science curricula in the United States.
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Instead, as students are exposed to an annual cycle of repeating what was previously taught, they lose motivation as well as are denied access to higher level con cepts, procedures, and problems. Students who are slower to gain skills early are especially hard hit by this practice because the impact of (lenie access to new concepts begins so early and accumulates over time, causing these students to fall farther anti farther behind.
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Several major curriculum development projects have produced complete K-6 programs based on a matrix that assigns four modules per grade level. Even when these programs are based on a wellthought-out development of concepts, processes, and skills over the six or seven elementary grades, schools, school (listricts, anti states often "mix and match" the modules as they see fit.
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Also, the instructional materials selection process often does not include attention to multi-grade coherence and articulation. The curriculum program should guide the selection of instructional materials to ensure that the entire set provides the coherence needed to ensure the development of concepts and skills within a given grade level, from one gra(le level to the next, from one year to the next, anti from elementary school to middle school to high school.
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10. Since the release of these documents, state educational agencies and local school districts have been developing their own content standards as a foundation of their efforts to improve the quality of educational opportunities for their students in K-12 mathematics and science (Council of Chief State School Officers [CCSSO]
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These standards include · consistency across Aid elements of the science program and across the K-12 continuum; · quality in the program of studies; · coordination with mathematics; · quality resources; equitable opportunities for achievement; and collaboration within the school community to support a quality program. Specifically, the narrative for the second standard calls for "district-wide goals and expectations for student achievement, as well as the curriculum frameworks, [which]
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Therefore, while a coherent curriculum program wall usually contain fewer topics than an incoherent program, the topics will be richer and lead to greater depth and persistence of understanding. ~ OU~E FOR FIG it If a deep understanding is to be achieved, content must be presented to students at an age when they have a readiness for it, are capable of un(lerstanding it, and can see the relationships between the ideas to which they are being expose(1 presently anti those to which they were expose(1 previously (Schoenfeld, Smith & Arcavi, 19931.
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Use of a variety of tools, such as calculators, computers, measurement equipment, and computational recording devices, can increase the likelihood that students with past gaps in experience, particularly computational gaps, wfl} not be denied access to new material while being encouraged to gain procedural fluency with past material. Students at all levels of preparation solve problems in their own unique ways and can contribute significant insights to a cIass's mathematical activity.
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Some ideas and procedures are more fundamental than others because they are the foundation for ideas that wait be taught, have rich explanatory power, and relate to everyday experiences (NRC, 1996b; NRC, 19931. Mathematics and science curriculum programs should focus on providing students with the opportunity to learn a limited number of fundamental ideas well rather than presenting them with a long list of random, unconnected information (Schoenfeld, Smith & Arcavi, 19931.
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In systemic reform, goals, standards, instructional materials, teaching practices, professional development opportunities, and assessment practices all are aligned with one another. In systemic reform, educational agencies adopt policies for the establishment and alignment of high-quality programs in curricula, teaching, assess ment, professional development, and systems of support (Smith & O'Day, 1991; O'Day & Smith, 19931.
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As school districts develop curriculum programs, they need to be as thorough in their consideration of and communication about the instructional approaches of teachers as they are in their consideration of and communication about mathematics anti science content. Instructional approaches that wait lead / ~ Professional :~' | Development ~E~- Learning Em,, ~ (Assessment)
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