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ED463139.Pdf DOCUMENT RESUME ED 463 139 SE 065 416 AUTHOR Addington, Susan; Clemens, Herbert; Howe, Roger; Saul, Mark TITLE Four Reactions to "Principles and Standards for School Mathematics." PUB DATE 2000-10-00 NOTE 10p. PUB TYPE Journal Articles (080) JOURNAL CIT Notices of the AMS; v47 n9 pp1072-1079 Oct 2000 EDRS PRICE MF01/PC01 Plus Postage. DESCRIPTORS Elementary Secondary Education; *Mathematics Curriculum; *Mathematics Instruction; *National Standards IDENTIFIERS *National Council of Teachers of Mathematics ABSTRACT This essay presents four reactions to the National Council of Teachers of Mathematics (NCTM) "Principles and Standards for School Mathematics" (PSSM) .The four respondents include three university mathematics professors and one teacher. The first author describes the publication as refreshingly free of mathematics education jargon, carefully organized, and written with significant input from mathematicians. The second author states that PSSM is a responsible, insightful, balanced, and inspiring document. The third author acknowledges the strengths of the document but argues that there is too much emphasis on curriculum and insufficient emphasis on teacher training. The final author imagines the document being read 100 years after its publication and concludes that it is an important, if flawed, document, particularly in the area of geometry.(MM) Reproductions supplied by EDRS are the best that can be made from the original document. Four Reactions to "Principals and Standards for School Mathematics." Susan Addington Herbert Clemens Roger Howe Mark Saul U.S. DEPARTMENT OF EDUCATION PERMISSION TO REPRODUCE AND Office of Educational Research and Improvement DISSEMINATE THIS MATERIAL HAS BEEN EDUCATIONAL RESOURCES GRANTED BY INFORMATION CENTER (ERIC) LI This document has been reproduced as received from the person or organization S. Addington originating it. 1:1 Minor changes have been made to improve reproduction quality. TO THE EDUCATIONAL RESOURCES Points of view or opinions stated in this INFORMATION CENTER (ERIC) document do not necessarily represent official OERI position or policy. 1 2 BEST COPY AVAILABLE Four Reactions to Principles and Standards for School Mathematics Susan Addington, Herbert Clemens, Roger Howe, and Mark Saul In April 2000 the National Council of Teachers of Mathematics (NCTM).,published Principles and Standards for School Mathematics (PSSM). This document is an updated and unified version of the school mathematics standards issued by the NCTM over several years starting in 1989. The Notices invited four individuals to write short pieces describing their reactions to Principles and Standards, these pieces appear below. The Notices has published two other pieces about PSSM: a news item, "Updated NCTM Standards Released", June/July 2000, pages 683-684; and an article, "Principles and Standards for School Mathematics: A Guide for Math- ematicians", by Joan Ferrini-Mundy, September 2000, pages 868-876. Allyn Jackson Susan Addington standards and every school district chooses its own curricula (sometimes several). Do the updated NCTM standards provide a good The U.S. has some current urgent problems. blueprint for reforming K-12 mathematics edu- Politicians, noticing that citizens now care about cation in the United States? education, have instituted quick fixes such as high- Yes. But reforming K-12 mathematics education stakes standardized tests, with budgets cut, prin- in the U.S. is like turning the Titanic around with cipals fired, and students failed if they do not a canoe paddle or perhaps like herding a million measure up. Most large states are suffering dire cats. teacher shortages, especially in urban schools; Despite the lack of national directives, the U.S. mathematics is one of the subjects suffering the K-12 educational system is amazingly uniform most. Most of the population thinks that learning and deeply set in its ways. The Third International mathematics is learning terms and practicing pro- Mathematics and Science Study documented how cedures, as do most elementary school teachers mathematics teaching in the U.S. is overwhelmingly and some middle and high school teachers. Even "a mile wide and an inch deep," covering dozens if a consensus were reached about what to teach of topics superficially. In a 1999 book, Stigler and and how, it takes time for teachers to learn new Hiebertl characterized U.S. mathematics teaching material and adjust to new teaching methods. as "learning terms and practicing procedures." I Three times through a lesson is a good rule of have found this to be accurate in most of the class- thumb for mastering a new teaching technique; for rooms I have visited, despite some notable excep- most K-12 teachers this means three years. And tions. districts, for the most part, have not accepted the fact that teachers need time every day to discuss On the other hand, the long history in the United and reflect on teaching and mathematics with their States of local control of schools and Americans' colleagues. general distrust of directives from the federal gov- So how could a bunch of mathematics teachers ernment mean that every state has its own get all these cats on the same track and steer the Susan Addington is associate professor of mathematics at oceanliner of U.S. education away from the ice- California State University, San Bernadino. Her e-mail bergs? address is [email protected]. In fact, the 1989 NCTM Standards were the first 1James W Stigler and James Hiebert, The Teaching Gap: such set of subject-matter standards developed by Best Ideas from the World's Teachers for Improving Ed- a professional organization; standards in other ucation in the Classroom, Free Press, 1999. subjects soon followed. The NCTM standards were 1072 NOTICES OF THE AMS VOLUME 47, NUMBER 9 very influential on state departments of educa- tion, school districts, grant agencies, and textbook How To Obtain Principles and Standards publishers. These organizations appreciated the Principles and Standards for School Mathematics is avail- fact that a knowledgeable group had organized the able on the World Wide Web, on paper, and on CD-ROM. subject and laid out general recommendations. In The Web versionisavailableathttp :// the absence of any federal standards, it became vir- standards.nctm.org/.A PDF version may be tually mandatory for textbook publishers to claim purchased onlineathttp://www.nctm.org/ that their books adhered to the NCTM standards, standards/.Paper and CD-ROM versions may be despite the fact that some of the books were the ordered on the Web athttp://www.nctm.org/ same old thing with cosmetic changes. Many (prob- standards/buyonl i ne/or by telephone at 800- ably not most) teachers began to rethink their 253-7566 (from overseas, 1-703-620-9840, extension 2601). teaching methods, and many districts tried new The postal address for orders is: curricula. National Council of Teachers of Mathematics "Math wars" and backlashes notwithstanding, I 1906 Association Drive expect the NCTM standards will continue to serve Reston, VA 20191-9988 as national guidelines. Since we may never have a national curriculum, this is the closest we will get The book (#719) is $45 (NCTM members $36), the CD- to national standards. The NCTM is a respected pro- ROM (#736) is $30 (members $24), and the PDF fessional organization, and it has done a careful version is $30 (members $24). Those purchasing job on the Standards. paper copies of the document can also request a free CD- The updated version of the Standards, released ROM. For orders under $50 there is a shipping and han- this year under the title Principles and Standards dling charge of $7. Discounts are available on larger or- for School Mathematics, was written with significant ders; consult the NCTM for further details. input from mathematicians; this was not the case A. J. with the 1989 Standards. Stung by misunder- standings of recommendations such as "decreased same material and more is on the Web; eventually attention to problems by type" and accusations of the Web version will include a search engine, more removing calculation and proof from the curricu- E-examples, video clips, and other supporting ma- lum, the NCTM has bent over backwards to be clear terial. The Web version is especially convenient for about its recommendations, supporting them with novices in mathematics education: one does not explicit research citations, sample problems, have to invest the time or money to order a paper vignettes of lessons, and samples of student work. copy. Principles and Standards is intended to be read Chapter 8, "Working Together to Achieve the Vi- by many different groups: mathematics teachers sion", outlines what must be done and by whom and supervisors, local and state educational ad- to successfully reform mathematics education. ministrators, mathematicians, politicians, parents, Much of the vitriol in the "math wars" that broke and business and community leaders. out in the 1990s comes from deeply held beliefs The document is refreshingly free of mathe- about mathematics education: that traditional Eu- matics education jargon. The writing is nonpedan- clidean geometry is the best, or the worst, way to tic and readable by any interested, educated per- teach mathematical reasoning; that paper-and- son. Readers will find little gems of mathematics pencil calculation is the key to, or a major imped- lessons, such as the young child who discovers, iment to, understanding numbers; that calcula- using a calculator, that one cannot ever get to 100 tors should not be used until paper-and-pencil by counting by 3s, then uses other mathematical arithmetic has been mastered or that they should props to explain why. replace paper-and-pencil arithmetic. Mathematics The graphic design is clean and restful to the education research does not give definitive an- eye. Unlike in many K-12 mathematics textbooks, swers to these questions, and many thoughtful there are no extraneous elements. In addition to teachers would agree with parts of each opinion.
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