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Print ED385436.TIF DOCUMENT RESUME ED 385 436 SE 056 572 AUTHOR Lacampagne, Carole B., Ed.; And Others TITLE The Algebra Initiative Colloquium. Volume 1: Plenary and Reactor Papers. INSTITUTION Office of Educational Research and Improvement (ED), Washington, DC. REPORT NO ISBN-0-16-048075-2 PUB DATE May 95 NOTE 157p.; For volume 2, see SE 056 573. AVAILABLE FROM U.S. Government Printing Office, Superintendent of Documents, Mail Stop: SSOP, Washington, DC 20402-9328. PUB TYPE Collected Works Conference Proceedings (021) Viewpoints (Opinion/Position Papers, Essays, ete.) (120) EDRS PRICE MF01/PC07 Plus Postage. DESCRIPTORS *Algebra; Conference Proceedings; *Educational Change; Elementary Secondary Education; Higher Education; *Mathematics Curriculum; Mathematics Education; *Mathematics Instruction; Teacher Education IDENTIFIERS *Reform Efforts ABSTRACT This volume contains the plenary or reactor papers presented at a conference on reform in algebra held in Leesburg, Virginia, December 9-12, 1993. Papers included are: (I) "Introduction" (C. B. Lacampagne); (2) "Summary" (C. E. Lacampagne); (3) "Recommendations" (C. B. Lacampagne); (4) "The D'velopment of Algebra and Algebra Education" (V. J. Katz); (5) "Long-Term Algebra Reform: Democratizing Access to Big Ideas" (J. J. Kaput); (6) "Algebra in the K-12 Curriculum" (G. Burrill);(7) "What Is the Appropriate K-12 Algebra Experience for Various Students?" (J. Fey); (8) "Algebra at the College Level" (M. Artin);(9) "Algebra Initiative" (V. Pless); (10) "Algebra and the Technical Workforce" (H. Pollak); (11) "Reshaping Algebra to Serve the Evolving Needs of the Technical Workforce" (S. Garfunkel); (12) "A Cognitive Perspective in the Mathematical Preparation of Teachers: The Case of Algebra" (A. G. Thompson & P. W. Thompson);(13) "Preparing Teachers to Teach Algebra for All: Preliminary Musings and Questions" (M. Enneking); and (14) "Algebra for All: Dumbing Down or Summing Up?" (L. A. Steen). Appendices include the conference agenda; Conceptual Framework for the Algebra Initiative of the National Institute on Student Achievement, Curriculum, and Assessment; and a participant list.(MKR) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. *********************************************************************** Initiative Colloquium U.S. INIEARTMENT or EIRTCaTiold roof/ Educational Ratan sad Imilowornoni EDUCATIONAL RESOURCES INFORATATTON CENTER1E11a 414cumoni MF Ylnl 111.0140CSO ocow44 from 11,11 001 Or 41.1114bOn 0,11.441ing O Mn.' cOlnilii ha.* NM mad* 14 *wen 14uttoo *W IYY C PoulltolvrOW Y OP11.011111411114 tonnes:Mr meal do not nocesanly HipesentONKNI OEM potthon Of galley I.' -S 1)(1),Irtnill of l'Aucillion ( Resvilruil Wuxi11111w0v(111(11 BEST COPY AVAILABLE The Algebra Initiative Colloquium Volume 1 Papers presented at a conference on reform in algebra December 9-12, 1993 Edited by Carole B. Lacampagne William Blair Jim Kaput U.S. Department of Education Office of Educational Research and Improvement National Institute on Student Achievement, Curriculum, and Assessment 3 U.S. Department of Educattin Richard W. Riley Secretary Office of Educational Research and Improvement Sharon P. Robinson Assistant Secretary National Institute on Student Achievement, Curriculum, and Assessment Joseph Conaty Acting Director May 1995 Ordering Information Copies of this publication are available from the Government Printing Office. For further information, call their Order Desk at 202-512-1800. th: h. the l S Oqernmeni Priming (Nike Sup,ffillnulent oi 11, lllll Stop Stith'. W.vhinrion, IX- :nue .112)( ISBN 0-16-L48075-2 4 _ -ur Contents Introduction Carole B. Lacampagne 1 Summary Carole B. Lacampagne 3 Recommendations Carole B. Lacampagne 9 The Development of Algebra and Algebra Education Victor J. Katz 15 Long-Term Algebra Reform: Democratizing Access to Big Ideas James J. Kaput 33 Algebra in the K-12 Curriculum ;ail Burrill 53 What Is the Appropriate K-12 Algebra Experience for Various Students? James Fey 61 Algebra at the College Level Michael Artin 65 Algebra Initiative Vera Pless 79 Algebra and the Technical Workforce Henry Pollak 83 Reshaping Algebra to Serve the Evolving Needs of the Technical Workforce Solomon Garfunkel 93 A Cognitive Perspective on the Mathematical Preparation of Teachers: The Case of Algebra Alba G. Thompson and Patrick W. Thompson 95 iii L-LrUni/ Preparing Teachers to Teach Algebra for All: Preliminary Musings and Questions Marjorie Enneking 117 Algebra for All: Dumbing Down or Summing Up? Lynn Arthur Steen 121 Appendices Appendix A Agenda 143 Appendix B Conceptual Framework for the Algebra Initiative of the National Institute on Student Achievement, Curriculum, and Assessment 147 Appendix C Participant List 153 iv Introduction Carole B. Lacampagne This publication contains plenary and reactor papers presented at the Algebra Initiative Colloquium held on December 9-12, 1993, in Leesburg, Virginia (see the agenda, appendix A). It also contains a summary and recommendations from the working groups. The Algebra Initiative Colloquium, sponsored by the U.S. Department of Education's Office of Educational Research and Improvement, addressed specific issues in the algebra curriculum and its teaching and learning. Algebra was chosen from among the many subject areas of mathematics because it is the language of mathematics; algebra is central to the continued learning of mathematics at all levels. Moreover, although several groups are already at work on the reform of algebra, there has been little dialog bridging educational levels. The Algebra Initiative Colloquium fostered such dialog (see the Conceptual Framework for the Algebra Initiative of the National Institute on Student Achievement, Curriculum, and Assessment, appendix B). Fifty-one distinguished algebra teachers, mathematics education researchers, algebraists, and mathematics experts from federal agencies attended the Colloquium (see Participant List, appendix C). In addition to hearing and discussing the plenary and reactor addresses, participants were assigned to one of four working groups to debate the issues and, where possible, to come up, with a set of recommendations. The working groups and their foci are listed below: Working Group 1: Creating an appropriate algebra experience for all grades K-12 students; Working Group 2: Educating teachers, including K-8 teachers, to provide these algebra experiences; Working Group 3: Reshaping algebra to serve the evolving needs of the technical work force; and Working Group 4: Renewing algebra at the college level to serve the future mathematician, scientist, and engineer. Prior to the Colloquium, working group participants wrote short papers on their group's focus area and shared papers within the working group, thus getting a head start 1 on Colloquium deliberations. These papers, revised after the Colloquium, together with recommendations from each working group, appear in the companion publication, The Algebra Initiative Colloquium, Volume 2. A short document for teachers and policymakers was prepared on the basis of recommendations from the Colloquium. This document, Algebra for All: A Lever, not a Wedge, will soon be available through the National Institute on Student Achievement, Curriculum, and Assessment. Summary Carole B. Lacampagne Sponsored by the U.S. Department of Education, The Algebra Initiative Colloquium generated a number of questions, concerns, and recommendations to promote the reform in algebra across the educational gamut, K through 16. According to Lynn Steen, "The major theme of this conference is very simple: Algebra is broken but nonetheless essential." From this premise, several subthemes/questions/concerns emerged that might be considered in setting an algebra agenda. These include: Algebra, the new civil right; The chasm that separates K-12 and 13-16 algebra education; A new algebra curriculum and pedagogy for preservice teachers and support and practice for current teachers; Algebra for the technical work force; The story line of algebra; and The brick wall. Algebra, The New Civil Right As Robert Moses so eloquently put it,'"Algebra is the new civil right." Working Group 1 (Creating an appropriate algebra experience for all grades K-12 students) calls algebra "... the academic passport for passage into virtually every avenue of the job market and every street of schooling." Moreover, since students from non-Asian minority groups are less likely to have obtained this passport than others, algebra becomes an equity issue. Working Group 1 recommended that all students have significant experiences in algebra before the end of grade 8 and that these experiences be the equivalent of current ninth-grade algebra. They also recommended that these experiences be strands that flow through K-8 mathematics. Algebra for all is a bold statement. As keynote speaker Victor Katz pointed out, algebra has a history of being an elitist subject meant for the education of future priests or leaders. Many of the story problems found in current high school algebra texts date back to antiquity and are artificial, not real-life problems. If wo are to implement algebra for all, we must overcome this longstanding elitist tradition. A question that plagued Colloquium participants was, "How do we insure that 'algebra for all' is not 'dumbing down' algebra?" The mathematical community as well as parents of college-bound students will and should demand sound preparation in algebra
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