Introduction: Perspectives on Principles and Standards for School Mathematics

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Introduction: Perspectives on Principles and Standards for School Mathematics
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  Volume 101(6), October 2001 Joan Ferrini-MundyMichigan State UniversityGuest Co-Editor Introduction: Perspectives on  Principles and Standards forSchool Mathematics Background Welcome to a special issue of School Science and Mathematics. This issue focuses on the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics (NCTM, 2001), the latest in NCTM’s seriesof standards documents and hereafter referred to as Principles and Standards .The National Council of Teachers of Mathematics, as a professional subject-matter-based organization, broke neweducational ground with its decision in the mid-eighties to produce “standards” for school mathematics. The 1989 Curriculum and Evaluation Standards for School Mathematics were hailed at the time as a major contribution to theimprovement of school mathematics and served as a model and impetus for the production of subject-matter-basedstandards by other professional organizations and coalitions. (See October 1997 special edition of School Science and  Mathematics  for additional discussion.)NCTM’s curriculum standards, together with the subsequent Professional Standards for Teaching Mathematics (NCTM, 1991) and  Assessment Standards for School Mathematics  (NCTM, 1995), have had considerable influence in allarenas that affect mathematics education, including state and local frameworks and curricular guides, instructional materials,teacher education programs, assessments, and day-to-day classroom instruction. With this propagation of standards-basedideas into the more specific tools and practices of mathematics education has come close scrutiny and extended nationalconversation about the purposes, implementation, and effectiveness of mathematics education in the nation’s schools. Thisnational conversation about mathematics education is largely healthy and constructive and involves an expanding set of constituencies who have taken a strong interest in the improvement of mathematics teaching and learning.In the mid-nineties the NCTM began to explore the possibility of a revision, or update, of its standards documents. ACommission on the Future of the Standards was appointed in 1995, and based on their recommendation, in 1996 the NCTMBoard of Directors approved a revision process. By the spring of 1997, a writing group had been appointed and charged toestablish standards that “build on the foundation of the srcinal Standards documents; integrate the classroom portions of the Curriculum and Evaluation Standards for School Mathematics, Professional Standards for Teaching Mathematics ,and  Assessment Standards for School Mathematics ; and are organized into four grade bands: prekindergarten through grade2; grades 3-5; grades 6-8; and grades 9-12.” Writing Group members included Jeane Joyner, Angela Andrews, Douglas H.Clements, Alfinio Flores, Carol Midgett, Judith Roitman, Barbara Reys, Francis (Skip) Fennell, Catherine M. Fueglein,Melinda Hamilton, Melissa Manzano-Aleman, Susan Jo Russell, Philip Wagreich, Jean Carpenter, Sheila Gorg, W. GaryMartin, Edward A. Silver, Mary Bouck, Jean Howard, Diana Lambdin, Carol Malloy, James Sandefur, Alan Schoenfeld,Sue Eddins, M. Kathleen Heid, Millie Johnson, Ron Lancaster, Alfred Manaster, and Milton Norman. Joan Ferrini-Mundyserved as the chair of this group.The resulting document, together with the web-based “e-Standards,” have now been available for more than a year.NCTM distributed copies to all of its individual members, and in addition, more than 45,000 copies of the book have beensold. One intention for this special edition of School Science and Mathematics  is to take stock and look ahead, throughdiscussion from a variety of standpoints about standards and their role in mathematics education.One of the questions posed in the call for manuscripts for this special edition was,   “How might Principles and Standards , or elements of the process used in its development, be helpful in moderating and giving focus for substan-  School Science and Mathematics 278  Introduction tive conversations across constituencies with different perspectives?” It is possible that a major contribution of Prin-ciples and Standards , ultimately, might be the process used in its development and the architecture it provides forsystematic discussion and debate about mathematics education issues.NCTM established an elaborate process of calling for input and advice from the mathematical sciences field, throughthe organization of “Association Review Groups” (ARGs) representing mathematics and mathematics education profes-sional societies, and sought the advice of the ARGs over the several years of development of the new standards document(Ferrini-Mundy, 2000). We learned that the re-formulation of standards in the late nineties would be a challenging process,in that 10 years of experience with the 1989 standards had given the field the opportunity to develop rather strong andvaried positions about the perceived messages of the 1989 standards and also about the effectiveness of their implementa-tion and impact. Thus the Writing Group was faced with the challenge of creating a document that would, as we werecharged to do, build on the foundations of the srcinal standards, and at the same time take into account the lively debatesand implementation difficulties ongoing in the field by addressing them in rational and well-grounded ways. Principles and Standards  is replete with references to research, and the theoretical perspectives, methodologies, and findings of researchwere integral to the development process (see Ferrini-Mundy & Martin, 2001).The extensive input from the field influenced strongly the points and areas we addressed. For example, the introduc-tion of “principles” – explanations of the perspectives guiding the development of the document and proposed as centralguiding views of school mathematics – occurred in part because of a sense that, without explicit articulation of the underly-ing assumptions, readers of standards create individual interpretations of the intentions of the documents that in some casesare more extreme and ideological than intended by the writers. Input from the field, coupled with the experience and judgments of the Writing Group, led to such decisions as eliminating the discrete mathematics standard and instead integrat-ing the big ideas of discrete mathematics into the other standards; renaming the “Reasoning” standard as “Reasoning andProof,” and adding a new standard, “Representation.” Principles and Standards’  focus on “computational fluency” and asomewhat complicated stance about the role of technology in mathematics learning (where we emphasized the importance of careful teacher judgment and noted that technology is not a substitute for understanding) have already generated reactionand commentary from all directions. Such decisions were made with the clear intention of generating conversation aboutthese points in the field and giving focus, language, and structure for those conversations.Hyman Bass, an eminent mathematician and current president of the American Mathematical Society, has said,I personally think the NCTM has achieved a great deal, and I think that the new PSSM document is an extraordinaryachievement that has been well informed by the advice that was sought from other professional communities. TheNCTM has made serious and bona fide efforts to ground its policy documents in whatever research is available and insolicited advice from other professional communities. I think that a sensible and constructive way to make improve-ments is to improve the way the NCTM functions. We can’t invent solutions to these educational problems that ignorethe professional community of teachers. The rhetoric of mathematicians who publicly protest every single fault anddetail in everything the NCTM does is simply not doing the work that’s going to move us forward. The NCTM hasdemonstrated that it can productively accommodate constructively rendered criticism. (Bass, 2001, p. 314)In that respect, the articles appearing in this special edition represent a way in which standards can serve as a frame andbasis for mathematics education improvement efforts and for discussion about them. We invite your reaction to these piecesand your continued submissions and commentary about Principles and Standards . Overview of This Special Edition The call for papers for this issue was crafted to help “focus on the potential role of Principles and Standards  ininfluencing the course of school mathematics education in the new century. The issue will invite commentary about how theengagement of the wider mathematical sciences community can be sustained and productively directed in efforts to improveschool mathematics for all students.” In particular, through the papers in this issue, we explore the role of standards, ingeneral, and Principles and Standards,  in particular, within the broader context of standards-based reforms and currentissues and directions affecting school mathematics. Several questions proposed in the call for manuscripts have been takenup by the authors of these papers.In their discussion of how the state of North Carolina has been engaged in a concerted and long-term effort to advancestandards-based education, Jeane Joyner and George Bright address, from a policy perspective, how the mathematical goals  Volume 101(6), October 2001 279  Introduction proposed in Principles and Standards  are likely to advance the mathematical preparation of all students. Their discussionof how to involve a range of players in the continual improvement of mathematics education is a reminder of the complexand systemic nature of mathematics education and, in particular, how crucial it is for all the pieces (curriculum, teachereducation, assessment, and policy) to fit together. A key setting in which all students’ mathematical experiences areinfluenced is in high stakes assessments. Mary Lindquist has contributed an enlightening historical perspective about therole of standards documents in influential assessment efforts, both national and international.We asked for submissions to discuss “What emerging areas of mathematics are highlighted in  Principles and Stan-dards  that are especially necessary for all students in a technological age?” Ideas related to this are discussed by Eric Hart,Brian Keller, and W. Gary Martin in their piece about NCTM’s Illuminations project and also in the interviews of mathema-ticians and Writing Group members Alfred Manaster and Judy Roitman, composed by Mark Olson and Dawn Berk. Thearticle by Kimberly Harris, Robin Marcus, Karen McLaren, and James T. Fey also includes some particular mathematicalexamples and issues emerging within the context of standards-based curriculum development.A major concern of the developers of standards, as well as mathematicians and teacher educators, is the problem of themathematical demands standards-based improvements will place on teachers. Questions about teacher preparation andprofessional development become challenging in a context of the new mathematical and technological propositions in Principles and Standards . The papers by Hart, Keller, and Martin, as well as the discussion about teacher education byKaren Graham and Francis (Skip) Fennell, look at such teacher preparation and support issues.A vexing and long-standing problem for educational reformers in all areas is the question of whether the proposedimprovements actually have been implemented and whether they make a difference. The standards movement is no excep-tion to the ongoing challenge of generating processes and programs of research and inquiry to enable reformers to continueto improve and adjust their recommendations. In their article about NCTM’s Standards Impact Research Group, W. GaryMartin and Dawn Berk address such issues.We recognize that the particular recommendations, examples, and language of any standards document will invitecritique, disagreement, and debate. Nonetheless, we offer this special edition as evidence that the “big picture” of standards– the processes involved in their development, the projects evolving from them, and their availability as a reference – hasenormous promise for the ongoing improvement of mathematics teaching and learning in this country. These papers,collectively, suggest that the goal of enabling all students to learn mathematics with meaning, so they can use mathematicsas productive citizens and in their work, is within reach in this standards-based era. References Bass, H. (2001). Interview with Allyn Jackson.  Notices of the AMS, 48  (3), 312-315.Ferrini-Mundy J. (2000). Principles and Standards for School Mathematics : A guide for mathematicians.  Notices of the AMS  , 47  (8), 868-876.Ferrini-Mundy J., & Martin W.G. (2001). Using research in policy development: The case of the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics. Manuscript in preparation . National Council of Teachers of Mathematics. (1989).  Curriculum and evaluation standards for school mathematics. Reston, VA: Author.National Council of Teachers of Mathematics. (1991). Professional teaching standards for school mathematics .Reston, VA: Author.National Council of Teachers of Mathematics. (1995).  Assessment standards for school mathematics . Reston, VA:Author.National Council of Teachers of Mathematics. (2001). Principles and standards for school mathematics . Reston, VA:Author.  Editors’ Note: Correspondence concerning this article should be addressed to Joan Ferrini-Mundy, MichiganState University, 211 N. Kedzie, East Lansing MI 48824. Electronic mail may be sent via Internet to
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