CHAPTER 2
STANDARDS FOR MATHEMATICS, SCIENCE, AND TECHNOLOGY EDUCATION

The term “standards” conveys different meanings to different people. For many members of the general public and for the education policy community, “standards” focus on outcomes and imply “a mechanism by which to hold schools accountable for what students learn” (Raizen, 1998, p. 73). In such cases, specific levels of performance relative to standards are defined, and assessments are designed to measure student progress toward attaining those standards. Assessment results may then be used as part of an accountability system, as a professional development tool to provide feedback to teachers, or to inform policy decisions. Ravitch (1995, p. 13) points out that policy makers and others also use “opportunity-to-learn, or school delivery, standards” in regard to “the availability of programs, staff, and other resources that schools, districts, and states provide so that students are able to meet challenging content and performance standards.”

To many educators, a “standard” is a statement describing what a person should know or be able to do. That use of “standard” is often called a “content standard.” In Testing, Teaching, and Learning (National Research Council [NRC], 1999f) a content standard is defined as setting “expectations for learning for all students.” The National Council of Teachers of Mathematics (NCTM, 1989), the National Research Council (NRC, 1996), and International Technology Education Association (ITEA, 2000) use the word standard in a broader sense, including not just content



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Investigating the Influence of Standards: A Framework for Research in Mathematics, Science, and Technology Education CHAPTER 2 STANDARDS FOR MATHEMATICS, SCIENCE, AND TECHNOLOGY EDUCATION The term “standards” conveys different meanings to different people. For many members of the general public and for the education policy community, “standards” focus on outcomes and imply “a mechanism by which to hold schools accountable for what students learn” (Raizen, 1998, p. 73). In such cases, specific levels of performance relative to standards are defined, and assessments are designed to measure student progress toward attaining those standards. Assessment results may then be used as part of an accountability system, as a professional development tool to provide feedback to teachers, or to inform policy decisions. Ravitch (1995, p. 13) points out that policy makers and others also use “opportunity-to-learn, or school delivery, standards” in regard to “the availability of programs, staff, and other resources that schools, districts, and states provide so that students are able to meet challenging content and performance standards.” To many educators, a “standard” is a statement describing what a person should know or be able to do. That use of “standard” is often called a “content standard.” In Testing, Teaching, and Learning (National Research Council [NRC], 1999f) a content standard is defined as setting “expectations for learning for all students.” The National Council of Teachers of Mathematics (NCTM, 1989), the National Research Council (NRC, 1996), and International Technology Education Association (ITEA, 2000) use the word standard in a broader sense, including not just content

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Investigating the Influence of Standards: A Framework for Research in Mathematics, Science, and Technology Education standards, but also standards for teaching, assessment, and professional development as well as other standards to support their enactment. THE CONTEXT IN WHICH STANDARDS EVOLVED For mathematics and science education, several reform periods occurred during the first half of the twentieth century, as educators attempted to improve education for an ever-widening school audience (Hurd, 1960; NCTM, 1970). Then, in 1957, the Soviet Union’s launching of Sputnik captured national attention and stimulated public pressure to upgrade U.S. science and mathematics education, with particular emphasis on increasing the pool of U.S. scientists and engineers capable of surpassing the Soviet achievement (Hurd and Gallagher, 1968; Raizen, 1991). While those efforts were at least partially successful, teacher, parent, and public discomfort with some of the emerging curricula contributed to counter-reforms that followed two quite different pathways. One led “back to basics,” while the other sought more socially relevant instructional approaches (Raizen, 1991; DeBoer, 1991). In 1983, A Nation at Risk declared that “…the educational foundations of our society are presently being eroded by a rising tide of mediocrity that threatens our very future as a Nation and a people” (National Commission on Excellence in Education, 1983, p. 5). The document called for higher student expectations and equitable treatment of all learners, improvement in teacher preparation and the teaching profession, leadership by educators and elected officials, and increased fiscal support from citizens. It stimulated new thinking within the U.S. mathematics and science communities about how to address changing societal needs and, consequently, about the need to prepare a mathematically and scientifically literate population for the future. Later publications— such as A Nation Prepared: Teachers for the 21st Century (Carnegie Forum on Education and the Economy, 1986)—reemphasized that

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Investigating the Influence of Standards: A Framework for Research in Mathematics, Science, and Technology Education educational reforms must provide equitable opportunities for all students. States responded in the 1980s by developing new curriculum guidelines, frameworks, standards, and testing programs (e.g., Education Commission of the States, 1983; Armstrong, Davis, Odden, and Gallagher, 1988; Davis and Armstrong, 1990). By the end of the decade, the NCTM Standards and the American Association for the Advancement of Science’s (AAAS) Science for All Americans (1989) articulated a national direction for teaching and learning in mathematics, science, and technology. President George H.W.Bush convened the first National Education Summit to discuss national educational goals with state governors (Miller, 1989). Discussions initiated at the summit transmuted into discussions about national education standards (National Governors Association [NGA], 1990; Fuhrman and Elmore, 1994), and in 1990, the National Education Goals Panel was formed. Standards were soon embraced as a way to improve education and became the consensus view among state and national policy makers, crossing partisan lines (National Council on Education Standards and Testing, 1992). “Systemic reform” was conceptualized as a strategy to align reform activities across all components of the education system, rather than pursuing isolated changes in parts of the system (Smith and O’Day, 1991; O’Day and Smith, 1993). During the 1990s, states and school districts adapted the nationally developed standards in various ways (Humphrey, Anderson, Marsh, Marder, and Shields, 1997; Council of Chief State School Officers [CCSSO], 1997). Many states initiated additional efforts aimed at improving education, and, for many reformers, the term “systemic reform” became synonymous with “standards-based reform.” The mathematics, science, and technology teaching and learning promoted by the NCTM, NRC, and ITEA standards documents reflect the reform period within which they were developed. The vision they describe represents a departure from

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Investigating the Influence of Standards: A Framework for Research in Mathematics, Science, and Technology Education common patterns of practice (Weiss, 1978, 1987; Weiss et al., 1994; Stake and Easley, 1978; Stigler and Hiebert, 1999). The nationally developed NCTM, NRC, and ITEA standards are addressed in the following sections, with emphasis on their scope, interrelationships, and commonality of vision. DEVELOPING NATIONAL STANDARDS IN MATHEMATICS In 1985, NCTM funded a group of its members—including teachers, researchers, and higher education representatives involved in mathematics teacher education—to create standards for K-12 mathematics. The resulting Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) provided classroom teachers, school mathematics coordinators, and curriculum developers with a vision and guidance for shaping content, instruction, and assessment within K-12 mathematics programs. NCTM standards called for content changes that reflected changing needs in an increasingly technological world, such as the inclusion of statistics, probability, and discrete mathematics in K-12 curricula. The document also specified standards for problem-solving, communicating, reasoning, and making connections—that is, portraying mathematics as something that is done, not just a body of material to be memorized. NCTM followed the release of curriculum standards with publication of Professional Standards for Teaching Mathematics (1991) and Assessment Standards for School Mathematics (1995). These documents emphasized that, in addition to appropriate student learning goals, appropriate teaching and assessment were critical components of an effective mathematics program. In 1995, in response to what had been learned since the publication of the first set of standards, new research in teaching and learning, and the increased sophistication and power of technology, NCTM began work on updating the mathematics standards. The new document, Principles and Standards for School Mathematics

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Investigating the Influence of Standards: A Framework for Research in Mathematics, Science, and Technology Education BOX 2–1 Basic Principles and Features of Principles and Standards for School Mathematics This document is intended to (p. 6): set forth a comprehensive and coherent set of goals for mathematics for all students from prekindergarten through grade 12 that will orient curricular, teaching, and assessment efforts during the next decades; serve as a resource for teachers, education leaders, and policymakers to use in examining and improving the quality of mathematics instructional programs; guide the development of curriculum frameworks, assessments, and instructional materials; stimulate ideas and ongoing conversations at the national, provincial or state, and local levels about how best to help students gain a deep understanding of important mathematics. The six principles for school mathematics address overarching themes (p. 11): Equity. Excellence in mathematics education requires equity—high expectations and strong support for all students. Curriculum. A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades. Teaching. Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well. Learning. Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge. Assessment. Assessment should support the learning of important mathematics and furnish useful information to both teachers and students. Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning. SOURCE: NCTM, 2000. (NCTM, 2000), under the umbrella of goals and principles, focuses on content expectations along with instruction and assessment and devotes increased attention to the vertical (pre-K-12) development of important mathematical ideas (see Box 2–1).1 1   Several publications document the development, expected applications, and dissemination of NCTM mathematics standards, and their use in developing state standards (NRC and NCTM, 1997; Romberg, 1998; Kirst and Bird, 1997; McLeod et al, 1996; Humphrey et al., 1997; CCSSO, 1997; Weiss et al., 1994).

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Investigating the Influence of Standards: A Framework for Research in Mathematics, Science, and Technology Education DEVELOPING NATIONAL STANDARDS IN SCIENCE As with the mathematics standards developed by NCTM, efforts leading to development of science standards were initiated by educators. AAAS’s Project 2061 began efforts to identify desired learning goals in the mid-1980s. As its title implies, Science for All Americans (AAAS, 1989) reflected the consensus of much of the scientific community regarding a common core of learnings for everyone in science, mathematics, and technology. Then, based on cognitive research and the expertise of teachers and teacher leaders, Benchmarks for Science Literacy (AAAS, 1993) described how those core concepts can be introduced and developed within the grade-level spans of K-12 schooling. In 1989, the National Science Teachers Association (NSTA) started its Scope, Sequence, and Coordination project, which sought to delineate a multigrade sequencing of concepts across scientific disciplines within the secondary-school curriculum (NSTA, 1992). In 1991, the NRC agreed to coordinate development of national science education standards, supported by funding from the National Science Foundation (NSF), U.S. Department of Education, National Aeronautics and Space Administration (NASA), and National Institutes of Health. The National Science Education Standards (NRC, 1996), informed by the earlier work of NCTM, AAAS, and NSTA, emerged as the central product of that collaborative effort. Again, consistent with intentions of the mathematics standards, NRC standards offered a vision of science education for all students, including what they should know, understand, and be able to do within particular K-12 grade intervals. In addition to physical, life, earth, and space science concepts, the content standards addressed science as inquiry, unifying concepts and processes (such as systems and the nature of models), science and technology, science in personal and social perspectives, and the history and nature of science. Furthermore, the document takes a systemic perspective, including standards that address science teaching,

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Investigating the Influence of Standards: A Framework for Research in Mathematics, Science, and Technology Education BOX 2–2 Basic Principles and Features of National Science Educa tion Standards Purpose (p. 17): Define scientific literacy Principles and Definitions (Chapter 2) Content Standards (Chapter 6) Provide guidance for teachers and other science educators Teaching Standards (Chapter 3) Assessment Standards (Chapter 5) Professional Development Standards (Chapter 4) Clarify the responsibility of policy makers and the community Program Standards (Chapter 7) System Standards (Chapter 8) Principles (p. 19): Science is for all students. Learning science is an active process. School science reflects the intellectual and cultural traditions that characterize the practice of contemporary science. Improving science education is part of systemic education reform. SOURCE: NRC, 1996. professional development, and assessment at classroom, district, state, and national levels, as well as standards that address the necessary components of a comprehensive school science program, and policies and resources deemed necessary from all components of the education system to attain science literacy for all students (see Box 2–2).2 2   Numerous publications document the development, intended uses, and dissemination of the National Science Education Standards (Raizen, 1998; NRC and NCTM, 1997; Bybee, 1997; Collins, 1997; NRC, 1997; Kirst and Bird, 1997; Humphrey et al, 1997; CCSSO, 1997).

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Investigating the Influence of Standards: A Framework for Research in Mathematics, Science, and Technology Education DEVELOPING STANDARDS FOR TECHNOLOGICAL LITERACY In 1994, ITEA initiated the Technology for All Americans Project, funded by NSF and NASA, to promote the study of technology and attainment of technological literacy for all citizens. The project, through release of Technology for All Americans: A Rationale and Structure for the Study of Technology (ITEA, 1996), defined what a technologically literate person should know and be able to do. The document argues that technological literacy will enable all Americans to become informed decision makers and participate fully in a technological society. It also defines the processes, knowledge, and contexts that constitute the study of technology, and describes how technology should be integrated into the K-12 curriculum. The project’s second phase led to release of Standards for Technological Literacy: Content for the Study of Technology (ITEA, 2000). That document defines technological literacy, distinguishing what all students should know and understand about technology from what they should be able to do (e.g., apply a design process to solve a technological problem). The standards, organized within four grade-level ranges, address the nature of technology; technology and society; design; abilities for a technological world; and the designed world (see Box 2–3). ITEA received third-phase funding from NSF and NASA to develop assessment, program, and professional development standards to complement and guide implementation of the technology content standards.3 COMMONALITIES ACROSS THE MATHEMATICS, SCIENCE, AND TECHNOLOGY STANDARDS The standards for mathematics, science, and technology share a number of key characteristics, starting with affirmation of the 3   Several articles describe the development of the Standards for Technological Literacy, their dissemination, and intended uses (e.g., Dugger, 2000, 2001; Wulf, 2000).

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Investigating the Influence of Standards: A Framework for Research in Mathematics, Science, and Technology Education BOX 2–3 Basic Principles and Features of Standards for Technological Literacy: Content for the Study of Technology Technology Content Standards is designed as a guide for educating students in developing technological literacy. Technological literacy is the ability to use, manage, assess, and understand technology. A technologically literate person understands, in increasingly sophisticated ways that evolve over time, what technology is, how it is created, and how it shapes society, and in turn is shaped by society. He or she will be able to hear a story about technology on television or read it in the newspaper and evaluate the information in the story intelligently, put that information in context, and form an opinion based on that information. A technologically literate person will be comfortable with and objective about technology, neither scared of it nor infatuated with it (pp. 9–10). Technology is defined as the modification of the natural environment in order to satisfy human needs and wants (p. 7). The Technology Content Standards lay out what should be learned and accomplished by each student in the study of technology at four levels (p. 13). Basic features (p. 13): It offers a common set of expectations for what students in technology laboratory-classrooms should learn. It is developmentally appropriate for students. It provides a basis for developing meaningful, relevant, and articulated curricula at the local, state, and provincial levels. It promotes content connections with other fields of study in grades K-12. SOURCE: ITEA, 2000. importance of increased expectations, opportunities, and achievement of all students, including groups largely bypassed historically, such as girls and ethnic and language minorities. All three sets of standards call on teachers to recognize the rich diversity students bring to classrooms—their linguistic backgrounds, cultures, and world views, as well as their prior knowledge and beliefs about scientific phenomena, mathematical concepts, and technological innovations—and provide opportunities for all students to learn. The nationally developed mathematics, science, and technology standards offer a vision of what literate citizens should know and be able to do within their respective subject areas, along with descriptions of the teaching practices, professional development, resources, assessment practices, and support needed to achieve

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Investigating the Influence of Standards: A Framework for Research in Mathematics, Science, and Technology Education such literacy. All three sets of standards articulate a common vision for improving student learning—a vision that emphasizes understanding of basic concepts and “big ideas” in each subject area, acquisition of useful skills, engagement in inquiry-based learning, and coherent articulation of learning opportunities across all grade levels. The standards call for instruction that actively engages students in learning and that provides all students with opportunities to learn challenging mathematics, science, and technology concepts and skills. The standards also call for students to be able to use their knowledge, skills, and understanding to make decisions and participate productively in society, as well as to solve problems and communicate their thinking and reasoning to others (NCTM, 1995, p. 11; NRC, 1996, pp. 22–23; ITEA, 2000, p. 9–10). All three sets of standards deliberately leave specific curricular decisions to state and local officials, including assignment of specific content to each grade level (NCTM, 2000, p. 7; NRC, 1996, pp. 111–112; ITEA, 2000, p. 200). The NCTM, NRC, and ITEA standards call for changes not only in what students learn, but also in how that content is taught. According to the national standards documents, teachers should have deep understanding of the science, mathematics, and technology content they teach; recognize and address common student preconceptions; design classroom experiences that actively engage students in building their understanding; emphasize the use and application of what is learned; and use assessment as an integral part of instruction. Teachers should listen carefully to students’ ideas; recognize and respond to student diversity; facilitate and encourage student discussions; model the skills and strategies of scientific inquiry, mathematical problem-solving, and technological innovation and ingenuity; and help students cultivate those skills and behaviors. In so doing, teachers should establish a classroom climate that supports learning; encourages respect for the ideas of others; and values curiosity, skepticism, and diverse viewpoints. In addition, teachers should participate in ongoing planning and

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Investigating the Influence of Standards: A Framework for Research in Mathematics, Science, and Technology Education development of mathematics, science, and technology programs in their schools and seek and promote professional-growth opportunities for themselves and their colleagues (NCTM, 1991, pp. 20–22; NRC, 1996, pp. 27–54). In short, teachers are expected to be well-versed in the content they teach and masterful in their uses of appropriate pedagogy. One group of commentators described the instructional practices advocated by the national standards this way: There is no well-defined set of techniques that will reliably produce high levels of student performance when applied in a routine manner. Rather, to teach in a manner consistent with the new vision, a teacher would not only have to be extraordinarily knowledgeable, but would also need to have a certain sort of motivation or will: the disposition to engage daily in a persistent, directed search for the combination of tasks, materials, questions, and responses that will enable her students to learn each new idea. In other words, she must be results-oriented, intently focused on what her students are actually learning rather than simply on her own routines for “covering” the curriculum. Her knowledge and skill are valuable resources, but judgment and continuous invention are required to turn these resources into effective performance. (Thompson, Spillane, and Cohen, 1994, P. 4) The NCTM, NRC, and ITEA standards embody a vision of what professionals in each subject area believe is needed to improve the teaching and learning in their respective subject areas. However, in attempts to understand the influence of these standards, it is important to consider what must happen within the education system to realize that vision. The next chapter examines the system within which that desired teaching and learning must occur and identifies key interactions among that system’s components. That analysis leads to a framework to guide investigations regarding the possible influence of nationally developed standards upon and within that system and—most critically—on classroom teaching and learning.

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