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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy NCTM and the National Standards for Mathematics Education The mission statement of the National Council of Teachers of Mathematics (NCTM or the Council), developed in 1995, centers on standards: The mission of the National Council of Teachers of Mathematics is to provide vision and leadership in improving the teaching and learning of mathematics so that every student is ensured an equitable Standards-based mathematics education and every teacher of mathematics is ensured the opportunity to grow professionally. (NCTM, 1995b) The NCTM Standards evolved over several years, beginning with the 1980 report An Agenda for Action (NCTM, 1980), an important precursor to the NCTM Standards documents. A set of events and circumstances took place in the 1980s that spurred the need for standards and for national direction in mathematics education. The education directorate at the National Science Foundation (NSF) was eliminated in 1982. A Nation at Risk (National Commission on Excellence in Education, 1983) called for broad reconsideration and reform of the U.S. education system. Also, recommendations for standards and the need for national guidance for mathematics education emerged out of the Conference Board on the Mathematical Sciences, leading to the founding of the Mathematical Sciences Education Board (MSEB) in 1985 at the National Research Council (NRC). Internal work at NCTM was also pointing toward a need for direction (McLeod et al., 1996). In 1986, the NCTM Board of Directors commissioned the first of the three sets of standards, the Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989). The development of the document was funded entirely with NCTM resources. The Curriculum and Evaluation Standards for School Mathematics was conceived as a vision of ideal practice and developed by a committee of NCTM members who thought carefully about the issues on behalf of the field. The decision to produce three separate standards documents reflects the understanding of the NCTM leadership that it was important to work on all parts of the educational system. A major aspect of the development process was consensus building across the country and across all dimensions of the mathematics education community. A 1987 draft was circulated to 10,000 members of NCTM; input was sought through professional meetings, regional affiliated groups, and NCTM's internal committees. The input was seriously considered and analyzed as the Curriculum and Evaluation Standards for School Mathematics was prepared. The resulting document carried the endorsements of a large number of professional organizations, although the entire concept of "standards" was new to the field at the time, so it is difficult to know how endorsement was construed. After the document was released, activities centered on the dissemination, interpretation, and implementation. These were coordinated by an NCTM Standards Coordinating Committee that provided oversight for the Council's activities. The MSEB, chaired in the late 1980s by Shirley Hill, a past president of NCTM, was an important collaborator with the NCTM in the standards process. In particular, the publication of Everybody Counts (NRC, 1989) is often credited with effectively making the case for the need to improve mathematics education with a broad range of audiences-and thus helping to set the stage for openness to the NCTM Standards in a wider arena.
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy Dissemination Dissemination of the NCTM Curriculum and Evaluation Standards for School Mathematics has taken many different forms. The document was provided free to all NCTM individual members and sold by the organization. As of June 1997, NCTM has distributed or sold over 647,000 copies of the Standards documents.2 An executive summary of the Curriculum and Evaluation Standards for School Mathematics was prepared and distributed to members of Congress, governors, university administrators and mathematics department chairs, school principals, PTA presidents, and school board chairs. Separate flyers were prepared for parents and policy makers as well as teachers and a general audience. A public relations firm was engaged to promote the release of the document. NCTM leaders received "public relations" training. The Council produced a kit which included speaker's guide that included a video of prominent individuals, such as musician Wynton Marsalis explaining the importance of mathematics and the NCTM Standards. The NCTM cooperated with other groups in dissemination. The Association of State Supervisors of Mathematics (ASSM) undertook "Leading Mathematics Education into the 21st Century," a joint project of the ASSM, NCTM, National Council of Supervisors of Mathematics (NCSM), Council of Presidential Awardees of Mathematics, and the MSEB. The project involved five regional conferences across the country, at which NCTM leaders and standards writers made presentations about the document to the participants, who were then expected to return to their local areas as teams and do further dissemination. This project produced a comprehensive speaker's kit and led to over 50,000 documented contacts with teachers over two years. The Professional Standards for Teaching Mathematics (NCTM, 1991) and Assessment Standards for School Mathematics (NCTM, 1995a) were developed with much input from the field, and the documents were widely circulated while in draft form. About half of the funding for the Professional Standards for Teaching School Mathematics was provided by the NSF. The Assessment Standards for School Mathematics was funded with NCTM resources only. Copies of these documents have been given free to each NCTM member. Copies of all three sets of standards are currently available from NCTM. The Curriculum and Evaluation Standards for School Mathematics is available on the World Wide Web.3 In addition, the Council has produced two short publications, Making a Living, Making a Life (1996b), intended for a general audience and explaining the importance of standards-based mathematics for all children, and Mathematics: An Introduction to the NCTM Standards (1996a), intended for those in the mathematics education community to use as a starting point for discussion about standards. The NCTM curriculum standards have been in the field for eight years. Various national surveys have assessed the level of awareness among teachers about the documents. In a 1993 survey, Weiss, Matti, and Smith (1994) found that 56 percent of secondary teachers, 28 percent of teachers at the 5-8 grade level, and 18 percent of teachers at the K-4 grade level were "well aware" of the NCTM Standards. In the Third International Mathematics and Science Study (TIMSS) conducted in 1995 (National Center for Educational Statistics, 1996), results showed that at eighth grade, 95 percent of U.S. teachers claim to be either very aware or somewhat aware of current ideas about teaching and learning mathematics, which could be taken to mean familiarity with the NCTM Standards. Awareness levels appear to be increasing. 2 This count includes 335,000 copies of Curriculum and Evaluation Standards for School Mathematics, 172,000 copies of the Professional Standards for Teaching School Mathematics, and 140,000 copies of the Assessment Standards for School Mathematics. 3 Available through the Eisenhower National Clearinghouse at www.enc.org/reform/journals/ENC2280/nf_280dtocl.htm
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy Interpretation For the NCTM Standards documents to have influence in the field, it was clear that there was a need to have illustrations and examples of how the ideas of the documents could be brought to life in classrooms. The Addenda Project was initiated in 1988 to "provide teaching lessons to exemplify the Standards" (McLeod et al., 1996). NCTM's efforts to provide assistance to the field in the area of interpretation also occurred through its journals and conventions. A journal for middle school teachers, Mathematics Teaching in the Middle School, was initiated by NCTM, and the journal for elementary teachers was renamed from the Arithmetic Teacher to Teaching Children Mathematics, thus reflecting the enriched content emphasis of the NCTM Standards for elementary students. Each journal devoted a standing column to understanding the Standards, and special focus issues were produced dealing with standards topics such as data analysis or discrete mathematics. Review criteria for selection of articles for the NCTM school-level journals included alignment with the Standards. (This criterion is currently under discussion.) Sessions at the regional and annual meetings held by the Council were focused on standards themes. A cadre of NCTM leaders were trained in making standards-based presentations. While NCTM initiated the types of interpretation activities appropriate for a large professional reorganization, other entities were again part of the process. The MSEB produced On the Shoulders of Giants (Steen, 1990) and Measuring Up (NRC, 1993b) to help teachers understand and think about assessment in ways consistent with the NCTM Standards. On the Shoulders of Giants provided a new way for mathematics educators to think deeply about content issues raised in the NCTM Standards. Measuring Up offered insights and examples of assessment tools that are aligned with the NCTM Standards. Textbook publishers chose to incorporate standards ideas in a variety of ways. Beginning in 1991, the NSF funded several major curriculum development projects at the elementary, middle and secondary levels in mathematics that were to be standards-based. As these projects are just now nearing completion, the field will soon have a set of examples of curricular interpretations of the NCTM Standards. As of 1996, forty states had content standards for mathematics based on their interpretations of the NCTM Standards and many are aligning assessment programs with these standards (Council of Chief State School Officers, 1996a, 1997a). Since 1990, the frameworks used in the National Assessment of Educational Progress (NAEP) have been adjusted to reflect elements of the NCTM Standards, including emphasis on "mathematical power," "reasoning," and ''communication" (Reese, Miller, Mazzeo, & Dossey, 1997). A by-product of these various interpretations of standards is that the field has more specific examples of what standards-based practice might mean. Mathematicians, in particular, are now becoming increasingly aware of the role that the Standards can play and are taking special interest in the revision of the NCTM Standards. Implementation The NCTM is not positioned to "implement the Standards." Rather, the role of the organization is to provide leadership in thinking about implementation, to serve as an organizational focus and catalyst for the ideas of others, and to facilitate interaction between members in their attempts at implementation. Prior to the release of the NCTM Standards, each major committee of the Council was charged to present a set of possible projects or initiatives that would promote implementation of the Standards. The NCTM Board selected several of these options and supported the development of plans that were then carried out by NCTM members through their home institutions, with funding from a variety of sources. These initiatives included a project to develop
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy secondary teachers' understanding of discrete mathematics,4 one of the new content areas introduced by the Standards. A project on number sense5 helped teachers develop number sense in their students. A geometry project6 produced materials to help teachers reflect on the geometry in their curriculum. The Research Catalyst Conferences7 were designed to bring new researchers together with mentors to design lines of research around standards-specific topic areas. Each of the more than 200 NCTM-affiliated groups was asked by the NCTM Regional Services Committee to prepare a plan indicating what they were doing in their group to move the Standards forward. These plans were shared and discussed at the regional caucuses and delegate assembly during the annual NCTM meeting. The Mathematics Education Trust--NCTM's foundation-funded small projects designed and submitted by teachers to facilitate implementation by individual members. At each regional NCTM meeting, a President's reception was held for affiliated group leaders from that region. Those leaders were asked to share their progress towards implementation. Implementation activities have also been connected to other organizations. Over the years, NCTM has worked closely with ASSM and with the NCSM on linking initiatives to promote understanding of the NCTM Standards. The NCTM instituted a yearly publisher's conference where presentations on the Standards were given and opportunities were provided for discussion between NCTM representatives and publishing editors. The NCTM used its involvement in the folio review for teacher preparation of the National Council for Accreditation of Teacher Education (NCATE) to ensure that the review documents and process were consistent with the NCTM Standards. However, studies have found that while teachers believe they are implementing standards, independent assessments of their lessons do not reveal standards-based practice (Cohen, 1990). For example, in the U.S. sample of videotaped teachers from the Third International Mathematics and Science Study (TIMSS), 75 percent of the teachers indicated that the videotaped lesson was in accord with current ideas about teaching and learning mathematics (Stigler et al., in press). Yet, analysis of those lessons along standards-like dimensions failed to show quality, as defined by the researchers. Although evidence points to awareness of and belief in the NCTM Standards, it is less clear that implementation and deep understanding are in place. Changing behaviors and practices is inherently tied to deep systemic structure. Evaluation The NCTM's Research Advisory Committee recognized very early on in the standards development process the need to plan for studies that would monitor and assess the impact of standards. An NCTM Monitoring Task Force produced a report that outlined plans for monitoring and recommended that NCTM help catalyze such work, but not necessarily play the lead role (Gawronski, Porter, & Schoen, 1989). As an early effort, NCTM commissioned a study by Weiss, The Road to Reform in Mathematics Education (1992), which reported on early awareness levels among teachers about standards. The Recognizing and Recording Reform in Mathematics (R3M) Project8 was initiated by NCTM as an effort to study sites that were engaged in substantial efforts at 4 The Discrete Mathematics Project was funded by the NSF's Teacher Enhancement Program. It was based at Boston College, under the direction of Margaret Kenney. 5 The Number Sense Project was based at Western Maryland College, with funding from the U.S. Department of Education, under the direction of Francis (Skip) Fennell. 6 The Geometry Project was based at Western Illinois University, funded by NSF, under the direction of Melfried and Judith Olson. 7 The Catalyst Conferences were funded by NSF, under the direction of Patricia Campbell at the University of Maryland. 8 The R3M Project, funded by the Exxon Education Foundation, was based at NCTM and directed by Joan Ferrini-Mundy.
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy improving their mathematics programs. The study described early efforts at mathematics education change, some of which were initiated before standards were available. The R3M findings indicated that the pedagogical elements of standards were taking hold in classrooms in more visible ways than the mathematical elements and that standards documents were used more for validation than for direction in some early implementation efforts (Ferrini-Mundy & Schram, 1997). Various organizations have studied questions of the overall effects of standards-based reform (Consortium for Policy Research in Education, 1996; Massell et al., 1997). The findings generally are that such reforms are slow to take hold in substantial ways in schools. In very specific projects that have introduced interventions in schools that might be considered standards-based, there is a trend of evidence of improved student achievement (Campbell, 1995; Cobb et al., 1991; Hiebert & Wearne, 1993; Stein & Lane, 1996; Stein, Lane, & Silver, 1996). Results of evaluations of the new NSF-funded mathematics curriculum projects, including the Interactive Mathematics Project (Webb & Dowling, 1996, 1997) and the Connected Mathematics Project (Hoover, Zawojewski, & Ridgeway, 1997), indicate strong achievement on both traditional and reformist assessment measures. The NCTM and MSEB have worked collaboratively over the years to consider the question of monitoring, although no comprehensive effort has ever been undertaken. The MSEB will be involved in a new project of the NRC's Center for Science, Mathematics, and Engineering Education, called Efficacy and Influence, that focuses on the national mathematics and science standards, and possibly those for technology, geography, and health. The first stage of this project will be to conceptualize a framework and perspective for addressing the question of how to study the effects of standards-based reform. The NRC will work with other researchers and evaluators who are studying the standards-related effort to consider how information collected annually might feed directly into improvement and revision efforts. A synthesis report will be produced in mathematics. Revision In 1994, the NCTM Board of Directors charged a Commission on the Future of the Standards to plan the review and updating of the NCTM Standards. The April 1996 report of the Commission called for a revision of the Standards documents to be released in the year 2000. The new document should preserve the main messages of the original Standards, while bringing together the "classroom" parts of the three Standards documents into a single document. A major part of the revision process involves an organized strategy for working with other professional organizations. In the initial phases of the revision process, several prominent professional organizations were invited to form "Association Review Groups." These groups have been invited by the Commission and the Writing Group leaders to respond to specific questions about the format and substance of the NCTM Standards, in an effort to obtain the field's sense of what is needed in revision. The first questions posed to the Association Review Groups were: Do the current statements of the Standards adequately communicate your view of the discipline? Do the Standards convey a sense of consistency and growth in content themes as the student moves across the grade levels? Do the Standards adequately reflect the needs of a student graduating in the 21st century and the needs of a student planning postsecondary study in a mathematics-related discipline? What suggestions can you make for blending content, teaching, and assessment? A second round of questions has focused on issues of algorithms and proof. Responses from the mathematics and mathematics education communities vary widely, and all criticisms
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Improving Student Learning in Mathematics and Science: The Role of National Standards in State Policy and suggestions will be considered seriously in the revision process. The Commission also has gathered input from NCTM members at focus groups held at regional and annual meetings. Several resource and advisory groups are being identified to support the writers and the process with specific expertise and input. The revision is a highly publicized process within the mathematics education community. The Commission has indicated that, in this version, the grades should be divided into four grade bands: Pre-K-2, 3-5, 6-8, and 9-12+. The finer grade-band divisions will allow for more specific focus on goals for students in these grades. The Writing Group faces interesting challenges in trying to preserve the main messages of the original NCTM Standards while attempting to look forward into the 21st century and seeking consensus across a field that is quite diverse in its views. The conflicts that are listed by Kirst and Bird (1996) relative to the development of content standards are especially useful for states and for national organizations to consider. Some highlights of their list include: Who must be involved in the process to feel it is inclusive? Students? Business? If you exclude groups, this will lead to charges of bias. If you include every group that is suggested, this will lead to a cumbersome and slow process. If you choose standards that achieve a broad consensus in the field, the "leading edge thinkers" will object. You will be accused of certifying "what is" rather than "what ought to be.'' If you choose a standard that achieves consensus in the field you will not be able to satisfy demands for "less is more"-consensus expands topics rather than reducing them. (Kirst & Bird, 1996, p. 31) The NCTM Standards revision marks a new phase in the standards movement. Reflection on the revision process will be important to its effectiveness. The revision provides new opportunities for a professional organization to design ways of building consensus and looking forward for the improvement of mathematics education. Perhaps of greatest significance in the NCTM story is the ground-breaking initiation of the standards movement. Not only did mathematics teachers have ready access to the NCTM Standards, but they were championed by national proponents such as Governor Roy Romer of Colorado and Senator Mark Hatfield of Oregon. The stage was set for national focus on standards.
Representative terms from entire chapter: