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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy Recommendations for State Policy In the sections that follow, we propose recommendations in five areas: state infrastructure, textbooks and other instructional materials, curriculum, teaching, and assessment.10 Many of these areas are highly visible to the public and so are of particular concern as reform initiatives continue. These are also areas in which the activities and interests of the states, the National Council of Teachers of Mathematics (NCTM), and the National Research Council (NRC) intersect. As the work of states in standards-based education continues, there are many ways in which they can draw on the past experiences and current initiatives of the NCTM and NRC, be supported in specific areas of work, and influence ongoing NCTM and NRC activity. The recommendations for state policy that follow are discussed in terms of these overlaps and the potential for mutual support now and in the future. The overarching recommendations are: State infrastructure Strengthen the state infrastructure for improvement in mathematics and science education with coherent, focused standards and with the policies, structures, and resources to support their achievement. Textbooks and other instructional materials Develop policies and strategies that promote the use of standards-based textbooks and other instructional materials and that build state and local capacity for selecting and using the materials appropriately. Curriculum Structure policies and support to focus districts and schools on designing science and mathematics curricula that are high-quality, well articulated, and standards-based. Teaching Create policies and practices to ensure that well qualified, highly competent teachers, whose practice is grounded in the mathematics and science standards, are in every elementary school, mathematics, and science classroom in the state. Assessment Establish testing and assessment programs consistent with the goal of high expectations for all students to learn standards-based mathematics and science. 10 The recommendations that follow use the following definitions: Content standards specify the content knowledge and skills all students will know and be able to do upon completing particular grades or courses in K-12 education; the content standards state clearly the knowledge and skills to be learned, and at what developmental level content is to be presented (CCSSO, 1996a). Curriculum framework is a document published by a state education agency or state board of education [or school district] that generally includes desired subject content or standards for a core academic subject in K-12 education. It often serves as a bridge between national professional standards and local curriculum and instructional strategies. It may refer educators to other materials and resources to support local efforts (CCSSO, 1996a). Curriculum is the way content is designed and used with students. It includes the structure, organization, balance, and presentation of the content in the classroom (NRC, 1996a). Instructional materials are the physical components of the curriculum, including textbooks, software, kits, calculators, and teachers' guides (NRC, 1996a).
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy These recommendations are interrelated. States require strong leadership for coordination in all aspects of standards-based reform. Instructional materials, especially textbooks, are the primary tools used by many teachers and seen by most parents as fundamental resources for student learning. They contribute to the curriculum, broadly defined, through their organization and delivery of content. Teachers are seen by most reformers as the central agent in promoting high-quality mathematics and science education for all students. Effective assessment can be simultaneously a tool for improving curriculum and teaching and for measuring progress toward the goal of achieving rigorous standards for all students. Together, the five overarching recommendations listed above form a whole that can best be coordinated around standards, with each piece requiring attention and action separately. The recommendations have potential value for all disciplines and could gain more support if applied across the entire system, not just in science and mathematics. Making a set of recommendations for state policy may imply that states are all alike, and this is not true indeed. From state to state, the mechanisms of governance are different, as are the responsibilities taken on at the state level. States have many vehicles for promoting improvement of education, including regulation, support, and persuasive power. States combine these in unique ways, depending on their structures, traditions, and resources. As a consequence, it has been a challenge of this report to make recommendations that are not so global as to be unattainable, but that are specific enough to be useful to most states in spite of their differences. In addition to being as specific as possible, this report includes a number of examples of how individual states and others are approaching some of the recommendations.11 In these ways, this report seeks to provide some practical guidance for state policy as states increase their efforts toward standards-based reform in mathematics and science. Recommendation 1. State Infrastructure Strengthen the state infrastructure for improvement in mathematics and science education with coherent, focused standards and with the policies, structures, and resources to support their achievement. International studies and the efforts of states to bring about systemic reform have underlined the need for a strong state infrastructure focused on improvement (Elmore, 1996; O'Day, Goertz, & Floden, 1995). This recommendation addresses the importance of focusing all elements in the system on the achievement of high-quality state standards. Policies guiding education, funding programs, and state procedures all must be coordinated and directed toward this common goal. The theme for state capacity building and indeed all of the recommendations in this report is, as stated succinctly by the National Commission on Teaching and America's Future, "get serious about standards [emphasis added]" (1996). In order to get serious about standards, states need to go beyond their statutory duties of creating their own standards, curriculum frameworks, assessment systems, etc. and include mechanisms for ongoing learning about the standards in every one of their activities. Understanding of the standards is needed by every state official as well as the many stakeholders who participate on state committees and development efforts.12 Conscious efforts to provide professional development build the capacity to fulfill the current state role as well as plan effectively for the 11 Throughout this section we have provided examples of how some states are implementing all or part of a recommendation. These were chosen not because they are exemplary per se, but because they represent interesting ways to address the issues that are raised. We do not have extensive data about the effectiveness of these strategies. 12 Note that useful materials promoting awareness and stimulating discussion of mathematics and science standards have been developed by the Annenberg/CPB Math and Science Project.
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy future. Getting serious about standards requires states to: 1-A Develop high standards for all students, through consensus, including a process for periodic review. Most states have a document, or documents, that contain state content standards for science and mathematics education. These documents tend to draw heavily on national standards (CCSSO, 1997a). They vary considerably in specificity and scope (CCSSO, 1997a), in quality (Diegmueller, 1996; Zucker, 1997) and in their ''ambitiousness" (Tirozzi, 1997). They also differ in the process used in their development. State standards that were well developed with careful attention to involvement of educators throughout the state, as well as important stakeholders like parents, business representatives, scientists and mathematicians, and community members, appear to have benefited from critical public support (Massell et al., 1997; Zucker, Shields, Adelman, & Powell, 1995). In such a consensus process, participants become a knowledgeable force of advocates, thus building the capacity of the state to improve the system for science and mathematics education. For example, North Carolina uses a process external to the state agency to build consensus around state documents. A qualified, independent organization statistically samples both educators and the lay public regarding proposed documents, soliciting input from all groups. The organization then uses feedback from this survey to validate or make recommendations for improvement of documents in a report to the State Board of Education. This process, as well as strategies such as well publicized focus groups and expert advisory committees, provides many opportunities for input and ensures that no particular special interest group has undue influence on the development of important state documents. In the development of standards, states may find the experiences of NCTM and NRC helpful, in addition to their links to the professional communities. National standards can be a reference point against which states can evaluate the degree of rigor in their own standards, including whether they have incorporated and, if so, adhered to such principles as "less is more," that is, depth of understanding is more important than breadth of coverage. The efforts of NCTM and NRC described earlier might help suggest ways to bring the forces in the state together in the dissemination, interpretation, and implementation of their own standards. 1-B Build a coherent system for mathematics and science education within the state in which every component and level of education is aligned and has a common goal: that all students will meet these high standards. One of the benefits of having a common set of standards, built through a consensus process, is that they can focus and guide action within a state. This was the intention of both NCTM and NRC, whose national standards include attention to all components of reform including content, teaching, and assessment. They go beyond statements of what students should know and be able to do; they describe the teaching, assessment, programs, professional development, and the system support needed for students to learn that content. Further, the national mathematics and science standards address all levels of the education system, seeking "vertical integration" of what students learn in the early grades with what they learn in middle and high school and with how their teachers are prepared. Both sets of national standards suggest what needs to be done in classrooms, schools, districts, states, and at the national level. States must similarly and continuously seek a "systemic" approach to science and mathematics reform, in which parts of the system work in concert with each other. Changes in one part influence adjustments in others; the common thread is the achievement of a shared set of standards (Smith & O'Day, 1991). Curriculum frameworks, funds for instructional materials, state assessments, preservice and inservice professional development programs, funding and other
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy support for Title I and special education-all can be designed or redesigned and interrelated, using the national standards as a foundation. In Texas, for example, the Statewide Systemic Initiative (SSI) worked to build coherence among programs and leverage resources by convening local and regional teams of Title I educators and administrators with other local educators and mathematics reform specialists. The SSI not only supported conversation and communication among these groups, but also funded team projects in which Title I mathematics programs were connected to standards-based, school-wide mathematics improvement efforts. Most states have devoted a great deal of effort over the past several years to "systemic change," with varying levels of success. In some cases, federally funded programs run parallel to the state's own initiatives; this may or may not influence local reform. For example, in some states, the National Science Foundation (NSF) funded state systemic initiatives are independent of and not well integrated with efforts of the state department of education. Efforts to reform professional development in a state might be significant, but the Eisenhower-funded programs might perpetuate traditional, but less effective, approaches to science and mathematics professional development. Similarly, although standards may be written for all students, Title I and special education programs within a state may not be incorporating standards ideas. However, current Title I legislation requires that districts pay attention to state standards and that states ensure that they do. States need to identify and eliminate these "discrepancies" between different programs and initiatives and replace them with common focus and vision if the states are to achieve the goal of meaningful learning for all students. 1-C Establish a long-range plan for improvement that involves the broader community as well as mathematics and science educators and provides sufficient support for local educators as they work to implement the standards. Standards-based education requires an ongoing process in which the system is not fixed "once and for all," but rather in which the quality and coherence of the system are enhanced via a common set of standards for mathematics and for science. Through the evaluation and revision process, the system's capacity to improve will increase. Students take 13 years to go through the K-12 education system, and we cannot expect to both have and fully understand the impact of standards until at least one cohort of students has experienced a new and improved educational experience. The kinds of support needed are well documented in the literature (Fullan, 1991; Loucks-Horsley et al., 1990), and are becoming better understood in evaluations of current efforts at state reform (Zucker, 1997). Standards-based education in mathematics and science is in many ways an opportunity for scientific inquiry. Studies, such as those of previous reform efforts (National Advisory Committee on Mathematical Education, [NACOME], 1975) and current international comparisons (National Center for Educational Statistics [NCES], 1996, 1997), indicate a need for initiatives that are more coherent, systemic, sustained, and based on a commonly held set of high standards for student learning. Although reports of current "systemic" initiatives indicate that steady progress is being made in implementing key components of reform (Massell et al., 1997; Zucker, 1997), it is still unknown as to whether, under what conditions, and in what configurations such initiatives are successful in increasing the science and mathematics learning of students. The long-range plan suggested by standards is based on the best knowledge available to date, but such a plan must have feedback and evaluation mechanisms at many points and at many levels to inquire into its influence and impact, and to inform its revision and midcourse adjustment. Ongoing dialogues between state reform leaders and constituents provide one form of data. Careful measures of implementation of various components of the system, such as professional development and new
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy assessment practices, provide another kind of data. Finally, data on student learning and the conditions under which they learn are needed to address such far-reaching questions as the following: Under what conditions, if any, can all students meet the standards? What are the costs of their doing so? What are the consequences of all students meeting the standards? Any long-range plan must take into account the tentative nature of the data currently available on which to base planning decisions, build in mechanisms to collect its own data, and approach the design and implementation of the initiative as an inquiry into standards-based reform. The issue of expanding the community beyond those involved in science and mathematics education is critical. Earlier we noted the importance of including the broader community in the development of standards; ongoing involvement and support are needed as well. Working closely with business and other groups such as the PTA, states need to build the awareness and commitment of the public to the directions of standards-based education. Research suggests, however, that states are not doing well in this regard. "Lack of public support and understanding of standards-based reforms remained major obstacles to the stability of standards," note Massell and associates (1997, p. 6). Better strategies are needed to garner the support of various publics for standards-based reforms. In Washington State, raising public support for standards is the primary purpose of Partnership for Learning, a non-profit organization sponsored by Washington business and community leaders. The Partnership works to increase public awareness about the state's effort to raise academic standards in the public schools. Resources made available by the Partnership include brochures, a parent's guide to academic achievement, public opinion data, a newsletter, and a web site with links to other resources around the country related to standards and assessments. Some states have maintained coalitions in mathematics and science that were initiated by the Mathematical Sciences Education Board (MSEB) in 1990, with start-up support from the Exxon Education Foundation. These have established a "self-sustaining" leadership structure. A parent organization, the National Alliance of State Science and Mathematics Coalitions (NASSMC), now supports efforts in individual states to build broad capacity for standards-based reform, bringing together the varied resources of education, science and mathematics, and the business community. These efforts and others that work to expand the community must be folded into the state infrastructure to enhance the capacity of the system. It would be irresponsible to recommend the broad and long-term changes required to implement high standards for all students without acknowledging the time and resources required at every level of the system-classroom to state house. Where resources are limited, as they are in education, there is competition for those that exist. Every content area can make a compelling case for their share and more. Certainly demands on teachers are keen, and seem to increase daily; elementary teachers are especially pressured to invest their time and energies in reform of each of the disciplines that they teach. State policy makers need to examine carefully the issue of resources for educational reform. There are no definitive estimates of what it will cost to achieve high standards for all students. However, there is reason to believe that substantial progress towards meeting that goal could be made by reallocating current resources. As noted above, our educational systems lack coherence; major programs such as Title I and the Eisenhower funds are not always well coordinated. The result can be costly duplication of effort. The report of the National Commission on Teaching and America's Future (NCTAF, 1996 ) makes a compelling case for reallocating educational dollars. The report urges rethinking of school structures and roles to increase the number of instructional staff (and thus decrease teacher/student ratios), redirecting professional development funds to eliminate ineffective one-shot workshops, and supporting more useful forms of professional development to help
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy teachers learn how to use new curriculum and assessments. It urges investment in "strategic improvements" such as teacher preparation, recruitment, licensing, and induction to eliminate the costs of replacing 30 percent of new hires in their first few years of teaching and "band-aid" approaches to staff development for those who have not learned to teach effectively. The cost analyses contained in the NCTAF report constitute a useful place to begin examining how resources are currently being used in and how they might be used differently to support standards-based reforms. Similar estimates could be made for how resources for curriculum and assessment are being used and how they might be reallocated. 1-D Ensure that state-level leadership positions in mathematics and science education exist and are filled by staff with expertise in the disciplines and in supporting change. As of 1997, only 65 percent of the states have positions at the state level in mathematics education; 80 percent have similar positions in science education. Some of these positions are funded through external sources such as Eisenhower/Title II or NSF Statewide Systemic Initiatives; such positions may not be permanent. In several states, after the retirement or resignation of an individual holding this position, there may be a considerable time lag in hiring a replacement or the position may be eliminated altogether due to budget constraints. Some of these positions include additional general responsibilities, such as technology, assessment, or professional development; others combine mathematics and science. Individuals in these positions may have a broad range of responsibilities and serve in a variety of roles: working on state policy, coordinating mathematics and science programs, overseeing the development of state curriculum frameworks, organizing for the adoption of instructional materials, developing or influencing state assessments, and giving guidance to state superintendents. In a few cases, the main responsibility of state-level mathematics or science consultants is to consult with schools by invitation only; they are not involved in state policy. Whatever the configuration of their roles, what these individuals know and can do is critical to their state's success in science and mathematics reform. Just as the current reforms call for teachers who deeply know the mathematics and science they need to teach, so too the current reforms require similar expertise in positions of leadership. Decisions about standards and curriculum frameworks, curriculum and instructional materials, teaching and professional development, and assessment design, as well as plans for implementation, hinge to a large extent on the nature of the disciplines, how they are learned, and how they are best taught. The issues differ by discipline; for example, those making decisions about mathematics need to understand the "gatekeeper" role played by algebra courses. Science decision makers need to understand the implications of the lack of science competence of elementary teachers and the importance of carefully organized systems that provide teachers with the materials they need to teach science. State leaders have to make the final decisions about what becomes state policy and procedure, what is published in state documents, and what is funded through state initiatives. They need to make important discipline-related links to programs such as Title I and Title II (the Eisenhower Professional Development Program). Without expertise in science and mathematics curricula, teaching, and programs resident in state departments of education, the decisions made may be to the detriment of the reform movement. Expertise in the disciplines is necessary but not sufficient for state-level staff, who are increasingly moving into roles of technical assistance and away from the more traditional roles of monitoring compliance with state laws and procedures. This is important for state capacity building, but it does not happen simply by changing job descriptions; many staff do not currently have the capabilities to make this change. New knowledge and skills required include
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy design of professional development, facilitation, consultation, organizational development, public relations, and change management. Specific professional development in these areas is required. Further, just as teachers must develop skills and dispositions for lifelong learning (NRC, 1996a), so, too, staff in state positions need to have the capacity to respond to new demands in appropriate, timely, and creative ways. Their knowledge, connections, and interactions with the NCTM and NRC capacity-building efforts, such as work with the Council of State Science Supervisors (CSSS) and the Association of State Supervisors of Mathematics (ASSM), can increase their understanding of issues in their content areas, and inform their policy decisions. 1-E Provide guidance and policy support to districts and schools in restructuring the use of school time to create opportunities for teachers to work together for improvement of mathematics and science education in their system. The issue of restructuring time for teachers and administrators to work together for improvement is one that is critical to the success of standards-based initiatives. International studies indicate that teachers in countries scoring higher than the U.S. on international comparisons have far fewer student contact hours than American teachers (NCES, 1996; Raizen & Britton, 1996). Hours spent without student contact are typically devoted to teachers working together on teaching materials, lesson plans, and other areas of curriculum. The literature on school improvement repeatedly validates the importance of school staff having opportunities to talk about teaching practice; observe each other's teaching; and plan, design, research, evaluate, and prepare teaching materials together (Little, 1993; Rosenholtz, 1989). Widespread experimentation is occurring in schools and districts to restructure school schedules to provide time for staff collaboration, provide release time for teachers or purchase time outside of the school day and/or year, and make better use of available time (Watts & Castle, 1993). Some states are creating policies to address this issue. For example, in the early 1990s, the Connecticut Academy for Education in Mathematics, Science and Technology (1996) supported a task force that developed a report entitled, The Case for More Time and Better Use of Time in Connecticut Schools. Recognizing that the use of time was critical to any efforts to improve mathematics and science in schools, the monograph summarized issues and recommended ways to improve the use of time for both students and teachers, by increasing actual time and using existing time in innovative ways. A year after the release of the report, a Connecticut Academy survey discovered that many schools in the state were implementing various recommendations of the task force, including block or flexible scheduling, interdisciplinary study, and programs scheduled outside of the regular school day. Many schools were creating more teacher time through reducing nonacademic duties and lengthening both the teacher's and student's school day and school year. State policies can assist local educators by providing more professional development time, supporting creative uses of in-school time (which may involve granting waivers of some state laws), and providing assistance to schools in designing and implementing alternative school schedules. Recommendation 2. Textbooks and Other Instructional Materials Develop policies and strategies that promote the use of standards-based textbooks and other instructional materials and that build state and local capacity for selecting and using the materials appropriately. Textbooks and other instructional materials are a staple in the classroom. As teaching tools, they embody the content and values to be learned by students, and so can be a significant force in helping students achieve high standards in mathematics and science. Yet, in many states,
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy textbooks and instructional materials are a "weak link" in their improvement initiatives; educators recognize their potential value, but find the availability of high-quality materials limited (Zucker, 1997). SRI's study of 25 states with NSF funding for statewide systemic initiatives indicates that: To improve student achievement, high quality textbooks (or other instructional materials, such as kit-based elementary science programs) need to be identified (or developed if necessary) and decision makers need to be well informed about them (Zucker, 1997, p. 5). Teachers use textbooks as their main curriculum guide and source of lesson plans, especially at the elementary grades (Woodward & Elliott, 1990). Research on textbooks consistently shows that they "flip from topic to topic, covering very few in the depth a beginner would need to understand, remember, and integrate the knowledge" (Tyson, 1997, p. 2). Reports of international studies, such as A Splintered Vision (Schmidt, McKnight, & Raizen, 1997), Pursuing Excellence (NCES, 1996), Characterizing Pedagogical Flow (Schmidt et al., 1996), and Changing the Subject (Black & Atkin, 1996), characterize the U.S. curriculum as one that is "a mile wide and an inch deep." The findings support the need for textbooks and other instructional materials that have fewer topics in any given year and put more emphasis on developing understanding of basic mathematical and scientific concepts and processes. States have a great deal of influence over the nature of textbooks. This is especially true in the 20 states that "adopt" a list of state-approved textbooks and bear the cost of textbooks for all students in the state (Tyson, 1997). The influence of states contributes to the "mile-wide and inch-deep" nature of textbooks. Publishers, responding to the demand of the market, include everything that adoption states require (in particular, the high-population states of California, Texas, and Florida that have restrictive state adoption procedures). The result is broad coverage of mathematics and science topics, including a vast amount of review, which then becomes the focus of instruction. This report views the influence of the states on the market for instructional materials, especially textbooks, as potentially positive. For students to achieve high standards, the materials from which they learn must be designed to promote understanding of key areas of mathematics and science. Thus, states need to demand materials that are more compatible with the standards they want their students to achieve. There are specific actions and policy shifts that can be initiated at the state level to help improve selection processes and capacity. 2-A Implement state policies that support the development of selection criteria for instructional materials based on standards and consistent with curriculum frameworks. In some states, such as those with state adoption panels, development of selection criteria occurs at the state level. In other states, selection criteria are developed at the local level. In either case, decision makers should promote the development of selection criteria that are aligned with standards and curriculum frameworks. It is important that the set of district-and state approved criteria for selection of instructional materials go beyond textbooks to include innovative print materials, kits, calculators, software, manipulatives, and other tools that enhance the opportunities for students to learn mathematics and science. "Alignment with standards" has already taken on many meanings. For example, some publishers have claimed alignment of their science textbooks with the NRC Standards by making a quick match with the list of content standards. It is essential for those selecting materials to ask the harder question: Will students gain fundamental understandings from this material? A careful analysis is required that examines how activities and information in the instructional materials connect to help students build such understandings. State-level educators need to think carefully about what it means to be "standards-based" as
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy they develop their selection criteria and/or assist districts to develop their own. Every state has well-qualified professionals ranging from classroom teachers to curriculum specialists to university faculty who have thought about the NCTM and NRC Standards. Many have experience with the large-scale curriculum development efforts funded by NSF that attended to standards in their development. This expertise should be used as states design strategies and build capacity for materials selection. Part of this capacity building is encouraging district selection committees not to "undo" states' good selection criteria, by applying outdated or restrictive criteria. As an example of state activity, Ohio's Statewide Systemic Initiative, Discovery, and the Eisenhower National Clearinghouse collaborated to review current middle grades science curricula, assessing the areas in which they align with the NRC Standards. Several sets of materials were reviewed, each by an educator familiar with the NRC Standards, using the Discovery developed Middle Level Standards Based Inventory (grades 5-9). Checked by independent reviewers and the material's developer or publisher, these summaries assist teachers, administrators, and parents in quickly accessing information about the NRC Standards and science curriculum materials. 2-B Commission evaluations of textbooks and other instructional materials by qualified professionals, and disseminate results to local adoption committees. Efforts to describe and, in some cases, evaluate instructional materials and their alignment with standards are beginning to occur in some state agencies and other state, regional, and national organizations. But robust reviews are still rare, and many selection committees do not have access to them. State departments of education can fund and then disseminate reviews that will help state and local adoption committees make informed selections. Such reviews might be done by independent evaluators, with funding from agencies such as NSF or private foundations. 2-C Implement professional development programs that help school personnel effectively select textbooks and other instructional materials and integrate them into the science and mathematics curriculum and instructional practice. Administrators and teachers are "the market" for textbooks and other instructional materials. Commercial publishers continually point out that their market analyses indicate uneven demand for "standards-based materials." Administrators and teachers influence the nature of the materials available to them; they are important members of material selection committees and they need to be prepared for these positions. According to Tyson (1997), "training" evaluators of instructional materials is critical. She recommends developing selector training models that are "standards-driven, intellectually defensible, and informed by research. A deeper and more qualitative adoption process is the single most powerful way to improve textbooks" (p. 23). As teachers and administrators become more analytical consumers of instructional materials, teachers will learn how to use them. Textbooks used wisely can complement a well-designed curriculum. Often, however, textbooks are the curriculum, and teachers use them in a lockstep fashion (Woodward & Elliott, 1990). This is sometimes due to teachers' belief systems or the culture of the school in which they teach. As observed in the Third International Mathematics and Science Study (TIMSS), experienced teachers are more likely to make judgments about which topics to develop and which to omit, in keeping with a curriculum design, while teachers with less preparation in science and mathematics, in difficult assignments and highly accountable situations, will proceed systematically from the front to the back of the textbook, covering each topic. They teach more and the students learn less (Schmidt et al., 1997). A number of efforts are under way to assist school personnel with assessing and selecting
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy instructional material aligned with standards. The NRC, for example, has held a series of conferences for curriculum developers, commercial publishers, materials adoption committees, and science educators from various levels to explore issues related to materials development, analysis, selection, and adaptation. A set of guidelines for the evaluation, selection, and adaptation of instructional materials aligned with the science standards is soon to be completed. A new NRC project, funded by the Robert W. Woodruff Foundation, will further develop these guidelines into a set of criteria for material evaluation, and design and pilot a process for doing so by teams of local educators and scientists. NCTM, as well as MSEB, is seriously considering ways to help teachers understand the nature of the materials from which they choose to teach. Recommendation 3. Curriculum Structure policies and support to focus districts and schools on designing science and mathematics curricula that are high quality, well-articulated, and standards-based. Students need well designed, comprehensive, and coordinated experiences to help them learn important mathematics and science concepts. Although the term "curriculum" has different meanings for different people, in this report we view curriculum as the way content is designed and used with students. A textbook is not the curriculum. The results of TIMSS (NCES, 1996; Schmidt et al., 1996) and other international studies (Black & Atkin, 1996) indicate the need for a more coherent curriculum for U.S. students. Changes that will bring greater coherence to the school mathematics and science curriculum include the following: vertical integration of experiences across grade levels and between elementary, middle, and high schools; coordination of mathematics and science learning, when appropriate; equitable opportunities for all students; and a well-thought-out curriculum framework that will influence selection and implementation of instructional materials. All of these changes should focus on achievement of a common set of standards. States can support these changes in several ways: 3-A Provide technical, financial, and material support to local districts for the design and implementation of programs in which all students have opportunities to meet standards for mathematics and science. Interpretation and implementation of standards call for a thoroughly conceptualized and carefully-orchestrated plan. It is not enough to create standards; support for understanding the content, changing practice, and making assessments part of learning is critical. The resources necessary to implement a standards-based curriculum may be more than those required of a more traditional program. States can provide districts with information about best practices in other districts and states so that they can, for example, develop strategies for reallocating existing funds; phase in a new program unit by unit, or grade by grade; equip materials support centers in cooperation with other districts; and create partnerships with business and industry to design, implement, and subsidize standards-based programs (National Science Resources Center [NSRC], 1997). Many states have developed curriculum frameworks that take standards one step closer to the classroom, informing teachers and administrators about the meaning of standards, and suggesting how to design and organize instructional materials and learning experiences so their students will achieve the knowledge and skills described in the standards. Some states assist or encourage districts to align specific instructional units and courses of study with standards. This encourages vertical (K-12) and horizontal (within grade level) integration of the school program for mathematics and science. Working together, teachers and administrators can trace a standard through their curriculum and ask the question: When and how will students have the opportunity
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy to develop this understanding or ability? This process can ensure that important concepts are introduced and further developed through the grades, although the courses of study may look substantially different from district to district. As an example, Michigan's state curriculum framework provides districts with specific guidance in designing their curriculum so that it is aligned with the state benchmarks and objectives. Their science framework gives several examples of how districts can construct their own elementary, middle, and high school curriculum frameworks using commercially available programs, individual units developed by the Michigan Department of Education, chapters from textbooks that have incorporated hands-on activities, teacher-developed investigations, and special projects of various kinds. Any effort to improve the curriculum through design of a framework and selection of new instructional materials should also include a plan for the implementation of the new program--a plan that addresses the long-term nature of the change process; the need to identify and coordinate the actions of a variety of players and system components; and the attention required by individual teachers and administrators, school-based teams or departments, whole schools, and districts (Fullan, 1991; Hall & Hord, 1987). Further, implementation of changes needs to be based soundly on accurate data about the needs of teachers and student learning. As noted in the discussion of long-term state policy planning, local plans must have data-driven milestones to monitor progress and trigger mid-course corrections. 3-B Base high school graduation requirements, university placement tests, and university admission requirements on standards. There are many obstacles to comprehensive change based on standards. For example, students whose K-12 curriculum emphasizes depth of study over breadth of coverage may not do well on traditional entrance or placement exams for university study. If their coursework does not resemble the courses a university requires for admission, they will not be admitted. Changing to a standards-based approach to mathematics and science education brings with it criteria for success other than completion of courses and number of years of study. States need to consider new criteria based on standards and ways to demonstrate success, such as performance assessments or portfolios, for graduating from high school. Further, they need to explore with colleges and universities alternatives to current admission requirements and placement tests, in order to dispel the disincentives that currently exist for educators to use standards as their goal for achievement. Standards-based university admissions policies are beginning to emerge. For example, the North Carolina School for Science and Mathematics produces highly qualified seniors who do not take traditional high school courses, but instead participate in rigorous, applications-based, hands-on courses in mathematics and science. The school worked with top universities across the nation to accept their students based on portfolios of their work reflecting standards. Students kept chemistry and physics lab manuals and records of their mathematics work to demonstrate what they had completed in high school. Using these sources, students consistently placed out of college courses, often receiving college credit for their work. 3-C Put in place in every school classroom new technologies that support standards-based teaching and learning of mathematics and science. Technology includes computers, calculators, and other learning tools that can help students achieve high standards in mathematics and science. Further, technological tools can help teachers enhance their strategies for instruction. Research indicates that technology can help learners understand mathematics and science concepts more deeply and effectively (Heid, 1988; Hembree & Dessart, 1986), and that
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy there are promising ways that technology can serve teachers' needs. Initiatives in every state are currently under way to address the enormous challenge of resources needed for technology. The issues of procuring equipment, wiring schools, preparing teachers, ensuring equitable access, and addressing the frequent obsolescence of both hardware and software need to be addressed as part of a plan to move schools into the 21st century. Recommendation 4. Teaching Create policies and practices to ensure that well-qualified, highly competent teachers, whose practice is grounded in the mathematics and science standards, are in every elementary school, mathematics, and science classroom in the state. The development of standards at national, state, and local levels has heightened awareness once more of the critical role of the teacher in student learning. But it is also the case that many of today's teachers are not adequately prepared or supported to perform in ways required by the standards. Further, the projection that, in the next decade, the U.S. will need to hire more than two million teachers due to increases in enrollment and replacement of teachers who retire or leave in the early years of teaching (NCTAF, 1996) demands immediate attention to preparation programs and licensing procedures. There are some promising efforts under way to improve the quality of teachers and teaching that incorporate national standards. These efforts, or initiatives similar to these, can become part of a state's strategy. The report What Matters Most: Teaching for America's Future (NCTAF, 1996) is an especially useful resource for states and others who are interested in this area. Our first three recommendations centered on teaching reflect one of its statements: "...the three-legged stool of quality assurance-teacher education program accreditation, initial teacher licensing, and advanced professional certification-is becoming more sturdy as a continuum of standards has been developed to guide teacher learning across the career" (p. 29). Related to these three stages in teachers' careers, which are addressed as well in several NRC reports (NRC, 1995a, 1996b, 1997b), we recommend that states takes steps to move in the following directions: 4-A Accredit only teacher preparation programs that reflect the recommendations of mathematics and science standards. 4-B Incorporate as a requirement for licensing that teachers demonstrate teaching practices that are based on standards and are appropriate to the particular learning situation. 4-C Support the continuing professional development of accomplished teachers through mechanisms such as the National Board for Professional Teaching Standards. The national standards have a bearing on each of these recommendations. In mathematics, the Professional Standards for Teaching Mathematics (NCTM, 1991) provide discussion about modeling good mathematics teaching, knowledge of mathematics, and developing as a teacher of mathematics. The NRC Standards include a section on "standards for professional development for teachers of science." The documents describe in detail what teachers need to know and be able to do, and the nature of teacher development programs that best develop teachers' knowledge and skills. Both sets of standards address the depth of content knowledge required for teaching at different levels of schooling-not in terms of courses, but in terms of knowledge and skills. Both also address how teachers can learn to teach their content, the characteristics of preparation programs that help them do so, and the clinical experiences needed to apply what they learn in actual classrooms and schools. Three quality control mechanisms for improving teaching currently available to states
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy draw heavily on the mathematics and science standards. Nationally, these include the National Council for Accreditation of Teacher Education (NCATE), which accredits teacher preparation programs; the Interstate New Teacher Assessment and Support Consortium (INTASC), which is developing performance-based licensure for teachers; and the National Board for Professional Teaching Standards (NBPTS), which is developing challenging performance assessments for certifying accomplished teachers (NBPTS, 1994). State and regional accreditation and licensure entities also exist. States can take advantage of these national efforts by either becoming partners with them or developing their own similar mechanisms tailored to specific state needs and/or standards. The NRC and NCTM have both learned from and contributed to the work of NCATE, INTASC, and NBPTS, and the issues these efforts are addressing. For example, an NRC colloquium for state teams centered on teacher credentialing and licensure discussed the implications of the national science standards and resulted in action plans by each participating team (NRC, 1996b). NCTM is responsible for developing the guidelines and reviewing the NCATE folio mathematics and mathematics education components. (Folios are the self-studies of the teacher preparation programs being accredited.) NRC has issued two reports on the preparation of teachers of mathematics (NRC, 1995a) and of science (NRC, 1997b). These reports address a particular concern of the NRC that states and institutions of higher education are beginning to attend to: the critical need for undergraduate mathematics and science courses to be ''standards-based" in both content and instruction. Until this occurs, teachers will not be adequately prepared to teach these disciplines. States are actively addressing these issues of quality control in teaching. For example, representatives of major teacher education institutions in Texas have developed a set of voluntary standards entitled Guidelines for the Mathematics Preparation of Elementary Teachers. These guidelines support the state's recently adopted standards-based K-12 mathematics curriculum. After development of these standards, institutions across the state applied for funding from the Texas Statewide Systemic Initiative, the Higher Education Coordinating Board, and other funding sources to develop programs to implement the standards. Across the state of Texas, future elementary teachers will receive dramatically different mathematics preparation, focusing on deep understanding of important mathematical ideas. Parallel efforts in elementary science and in secondary mathematics and science are now under way. As another example, through its Beginning Educator Support and Training (BEST) Program, Connecticut offers a variety of state-level innovations to improve the qualifications of beginning teachers and increase the likelihood that they will receive a solid foundation for sustained excellence in the classroom. During the first year of teaching, novices receive help from a school-based mentor or mentor team. Beginning teacher clinics, conducted by state-trained assessors through observation or videotape, help teachers prepare for the assessment of essential, basic teaching competencies. First and second-year teachers' abilities are assessed using the INTASC standards. Teachers develop portfolios of their work, including videotapes of specific lessons that reflect the teaching expected by new student standards, analysis of student work, and written descriptions of ways in which they adapt instruction to the needs of individual learners. Ensuring the quality of preparation programs and teachers entering the profession is one thing; assisting those already in teaching positions to help their students achieve national standards is the role of ongoing professional development. Therefore, a final recommendation related to teaching centers on this area: 4-D Fund ongoing, high-quality professional development opportunities for teachers of science and mathematics based on standards for student learning and professional teaching.
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy Professional development is a common strategy used by states to support reform in science and mathematics education. For example, it is a high priority in 18 of the 25 states receiving NSF resources for statewide systemic initiatives. Although Zucker (1997) points out that "delivering high-quality professional development is something that we as a nation know how to do," it is not always done well, nor may the nature of current professional development efforts serve the agenda of standards-based reform (Little, 1993). Research on professional development indicates that formats common to science and mathematics teacher professional development, such as training workshops and institutes, may not always be appropriate for the changes that are both broad-scale (i.e., across departments and schools) and deep (through curriculum, teaching, and assessment), as required by current reforms (Fullan & Hargreaves, 1991; Little, 1993). Rather than relying on the "expertdriven" model that takes teachers out of their schools to learn from outsiders, teachers need more opportunities that bring them together to learn in the context of their own programs, with their own students in mind (Ball, 1997; Ferrini-Mundy, 1997). Loucks-Horsley and her associates (in press) have described 15 different strategies for professional development, including professional networks, case discussions, mentoring for beginning teachers, and study groups, that can be combined in unique ways to meet the ongoing learning needs of teachers in their efforts to help students meet new and rigorous standards. Cohen and Hill (1997) have found in their research in California that professional development that is based on particular curricular materials is related strongly to student achievement. Several states, including Colorado and Michigan, have developed standards for professional development in mathematics and science as guidelines for professional development planning by local educators and external "providers." In addition to encouraging new formats for professional development, these standards emphasize professional development as part of a teachers' daily work through opportunities for joint planning, curriculum and assessment work, research, and problem solving with colleagues. They also stress the importance of tying professional development to the curriculum teachers are teaching so they can put into practice what they are learning. States are also sponsoring their own professional development programs. For example, a key component of the Arkansas Statewide Systemic Initiative is the teacher training and professional development programs that have been developed around the NCTM Standards, the NRC Standards, and the Arkansas Science and Mathematics Curriculum Frameworks. A professional development program of particular interest is the K-4 Crusade, a two-semester, standards-based course that is offered at 11 of the state's universities and is open to all K-4 teachers and administrators. Although it is not a mandatory program, the state's accreditation standards require that all teachers participate in 30 hours of professional development every year. The goal of the K-4 Crusade is to provide teachers with high-quality content, teaching strategies, critical-thinking skills, technology, and hands-on materials to strengthen their teaching practices. The belief behind the program is that high-quality professional development programs help teachers communicate curriculum materials to students more effectively and, consequently, may play a role in increasing a student's ability to learn. California provides an example of a different approach to professional development for mathematics and science reform. In that state, professional networks are sponsored by several entities, including the state, the university system, and federal programs such as the NSF-funded statewide systemic initiative. The Subject Matter Projects, which offer summer institutes and follow-up support, occur in 11 curricular areas and focus on individual teacher development. The Mathematics Renaissance and California Science Implementation Network each work with hundreds of schools and their staffs in
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy middle school mathematics and elementary school science, respectively. These networks have a broad infrastructure staffed by teacher leaders who work to build school as well as individual teacher capacity for teaching aligned with the state frameworks and national standards. Both the NCTM and NRC have had and will continue to have initiatives aimed at helping teachers learn what they need to know to better teach their students, through development of reports, and opportunities for dialogue. NCTM in particular has a standing committee focused on professional development. In addition, each of the 14 other NCTM standing committees has been charged to design a professional development strategy for the Board's consideration. Recommendation 5. Assessment Establish testing and assessment programs consistent with the goal of high expectations for all students to learn standards-based mathematics and science. Assessment is a major component of efforts to promote improved student learning in mathematics and science. There are a number of instances where assessment has been used as a driver for reformed teaching practice, for example, in the states of Connecticut and Texas. The national standards argue for aligned changes in all areas of program, practice, and policy; changes in assessment need to be coordinated with state standards and frameworks. State roles in assessment are, as in teaching, many-fold. First, for purposes of accountability, states create state assessment systems and require or encourage their use by local educators. States sometimes impose high-stakes assessments with consequences for schools and districts. Also, states can support the development or identification and use of new forms of assessment by teachers and administrators, primarily for instructional purposes. States also can encourage teacher professional development in the area of assessment. All of these roles are addressed in the following recommendations: 5-A Ensure that assessments of student learning are aligned with standards based curriculum and assessment principles. From the beginning of the standards-based reform movement, state policy makers have worked to create assessments that are aligned with their new content standards and curriculum frameworks. As with the development of standards and frameworks, progress in assessment development has been steady and incremental, although the speed of change has varied among states (Massell et al., 1997). A recent report of the Council of Chief State School Officers (1996b) indicates that, for the 1994-95 school year, 33 states had science assessments and 46 had mathematics assessments. Most assessments combined different forms of test items, with many using open-ended and response tasks. (See Figure 4 for more detail.) Gauging the alignment of new assessments with standards is a complex process (Webb, 1997). Interestingly, U.S. Department of Education Assistant Secretary for Elementary and Secondary Education Gerald Tirozzi noted that state standards as measured by states' own assessments may not be high enough (1997). According to Tirozzi, in several states, large percentages of students scored well on tests based on their state standards, while a far lower percentage did well on NAEP tests, which are perceived to be based on national standards. Although states generally are working on standards, existing state assessments may not yet be good indicators of the impact of these efforts. As in other areas of the reform movement, many of the complexities of assessment have been revealed only as attempts to develop reliable, valid, and useful measures have progressed, and these measures have been implemented, either as pilots or full-scale. The SRI study of the 25 states funded by NSF for statewide systemic initiatives notes progress, but reports a mismatch in many states between the state goals established for student learning in standards and curriculum frameworks, and
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy the content of state-mandated tests (Zucker, 1997). This is due, in part, to two difficulties in assessment development (Massell et al., 1997). The first difficulty stems from states' interests in having their assessments serve multiple purposes, in particular, both instructional improvement and accountability. This has resulted in technical problems as states have explored the promising uses of performance assessments, such as ensuring reliability and validity. In an attempt to deal with these technical issues, some states have pooled their fiscal and intellectual resources in collaboratives focused on designing and piloting performance assessments, such as the New Standards Project and the State Collaborative on Assessment and Student Standards (SCASS) initiative of the CCSSO (1997b). One strategy to address political issues centered on assessment is to adopt a "mixed assessment model," which incorporates both multiple choice and performance items and targets basic as well as higher-order skills. Thus assessment has joined standards in this recent move towards "balance" in approach to reform, which seems to be leading to more public support and achievement of some, if not all, policy objectives (Massell et al., 1997). Alignment of assessments with standards-based curriculum is a simple idea but, as noted, fraught with challenges. Our recommendation is that policy makers "stay the course" in working towards this goal, continuing to make progress, if slower than some have hoped. 5-B Develop at the state level, or encourage local districts to develop, strong accountability systems that go beyond single-measure tests. An issue that every state and district must address is how to show progress in standards-based reforms while the plan is unfolding. Gains in student learning are unlikely to be demonstrated immediately, given that assessment systems aligned with standards are under development and changes may not have occurred or stabilized in teaching practices. States should establish intermediate milestones, such as specific changes in district policies and curriculum, numbers of students enrolled in reformulated courses, and changes in teaching practices, then monitor these indicators and hold themselves accountable over time. An explicit FIGURE 4. Status of State Assessments, 1994-95 School Year For science, 33 states had assessment programs. Nineteen of these used criterion-referenced tests; the same number used norm-referenced tests (the overlap means that some states used a combination of both). Of the 25 states that used non-traditional exercises, 5 used enhanced multiple choice items; 15 used extended response or short, open-ended response items; and 7 used individual performance tests. Twenty states have set performance standards or acceptable levels of school or student performance. For mathematics, 46 states had assessment programs. Thirty-one of these used criterion-referenced tests; the same number used norm-referenced tests (the overlap means that some states used a combination of both). Of the 35 states that used nontraditional exercises, 12 used enhanced multiple choice items; 31 used extended response or short, open-ended response items; and 8 used individual performance tests. Twenty-nine states have set performance standards or acceptable levels of school or student performance. From: CCSSO (1996b). State student assessment programs data-base for the 1994-95 school year Washington, DC: Author.
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy plan with defined milestones to indicate progress can help sustain support by the public, policy makers, business, and professional educators. Kentucky provides an example of a state that has devised a new approach to statewide assessment. The Kentucky Instructional Results and Information System (KIRIS) represents a comprehensive use of performance assessments as part of the state's accountability system. Over time the state has developed an accountability index that incorporates information from student performance tasks, multiple choice items, and mathematics portfolios. As another state example, the Texas Academic Excellence Indicator System (AEIS) is a report card for schools and districts that provides a comprehensive set of indicators for school success. The accountability system provides appropriate rewards to schools and districts for high performance and equity, and sanctions for low performance and inequity, by reporting performance not only for a school or district, but also for various ethnic, gender, and socio-economic groups within the school or district. Schools must show comparable performance across all subgroups, with state-defined target performance rates raised each year to ensure growth toward equally high performance among all groups. AEIS indicators include, among others, student performance on the state assessment program and on other standardized measures, correlations between grades and performance, data on participation in advanced academic programs, and data on dropouts and attendance. This accountability system is based on the state's mandated standards-based curriculum as measured on the state assessment. Although multiple measures are critical to understanding and documenting student learning, states and districts must guard against overtesting. Burdening students, teachers, and schools with undue data collection takes away from important instructional time and attendance. 5-C Collect and use information about learning conditions and the opportunities students have to learn. With the standards movement largely directed at helping students reach ambitious learning goals, it is easy for assessment to be viewed primarily as measures of student learning. Yet teachers, principals, and local educators responsible for designing and delivering high quality science and mathematics education cannot make informed decisions without meaningful data about what actually goes on in classrooms: data on curriculum, instruction, and classroom conditions. As Martin, Blank, and Smithson (1996, p. 2) point out, "Clearly, a key ingredient to sound policy and program decisions is accurate and relevant information." A major component of the State Collaborative on Assessment and Student Standards (SCASS), a project of the CCSSO, addresses the issue that education systems are not well organized to systematically collect and report the kinds of data that are helpful for such decisions. Both national and international studies have pointed out the importance of having such data-called students' opportunity to learn-in order to interpret student test scores (Porter, Kirst, Osthoff, Smithson, & Schneider, 1993; Schmidt et al., 1996; Stigler et al., in press). The connection between student learning and the teaching, curriculum, assessment, and support that are required for it to be successful is an important theme in both the NRC and NCTM Standards. It is also key to achieving the "science and mathematics for all" vision, for without opportunities for learning, all students cannot develop the concepts and skills described in the content standards for mathematics and science. A recent report of the NRC (1997c), which commented on the proposed national test in mathematics, makes this argument also: "It will be very difficult to interpret test results meaningfully, and to make constructive use of them, without a measure of what opportunities students have had to learn the mathematics that is being tested" (p. 3). Many states have addressed the need to assess students' opportunity to learn. Some have done so through involvement with SCASS. In
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy New Jersey, state leadership has "openly embraced opportunity-to-learn standards as part of a strategic plan to improve education and address equity" (Massell et al., 1997, p. 48). 5-D Assist schools and the general community to understand and use the results of assessments and develop action plans based on results. Reflection and understanding based on observation and evidence are at the core of science and mathematics. Assessment of student progress should be based on multiple sources of evidence. State reporting systems caution against reading too much into a single score and against using assessment results for purposes that do not match those for which the assessment was designed. Public understanding and support are especially important in the area of assessment. Educators face a number of challenges in developing and maintaining public support for new assessments. In some cases, students who score well on traditional assessments have not done well on new ones, resulting in opposition to the new tests. Because test development is so technical, the strategy of involving people so as to gain their ownership and support is problematic. New laws in both Texas and California incorporate non-educator involvement in test development; it is unclear how this will influence future directions in these states and in other locations. Public relations efforts to help promote understanding of unfamiliar assessment strategies are needed (NRC, 1997c). States have an important role in providing resources, supporting, and encouraging local educators to build systems at district, school, and classroom levels to gather appropriate information from assessment for use in design and improvement of standards-based education for their students. This role can be played in different ways, from the more direct requirement for school plans based on data, to the support of professional development for teachers and administrators to learn alternative approaches to classroom assessment. At the national level, an action strategy for improving middle grades mathematics education is being developed simultaneously with the national eighth grade mathematics exam. This may prove to be an example of how assessment and a strategy for improvement can be linked. 5-E Promote teacher assessment and student self-assessment in classrooms, based on standards. Both the NRC and NCTM assessment standards make a strong case for assessment in the service of instruction. Some of the issues involved are addressed by two NRC publications, Measuring What Counts: A Conceptual Guide for Mathematics Assessment (1993a) and Measuring Up: Prototypes for Mathematics Assessment (1993b), developed with contributions from NCTM leaders. These sources establish crucial research-based connections between standards and assessment, and provide examples of new assessment exercises that can be appropriately embedded in instruction. Because new forms of assessment, measuring the new learning goals represented in the Standards, are substantially different from teachers' common practice, professional development is crucial. Not only must teachers change their practices, they must also help their students, parents, and the community understand the purposes, procedures, and benefits of such changes. To the extent that assessments drive instruction, assessments that provide authentic pictures of student learning can be important sources of both pressure and information for educators as they work to implement standards.
Representative terms from entire chapter: