The Algebra Initiative Colloquium. Volume 2: Working Group Papers. INSTITUTION Office of Tducational R H and Improvement (ED), Washington, DC
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DOCUMENT RESUME ED 385 437 SE 056 573 AUTHOR taco:pare, Carole B., Ed.; And Other. TITLE The Algebra Initiative Colloquium. Volume 2: Working Group Papers. INSTITUTION Office of tducational R h and Improvement (ED), Washington, DC. REPORT NO ISBN-0-16-048075-2 PUB DATE May 95 NOTE 231p.; For volume 1, see SE 056 572. 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, etc.) (120) EDRS PRICE MfO1 /PC10 Plua 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 presents recommendations from four working groups at a conference on reform in algebra held in Leesburg, Virginia, December 9-12, 1993. Working Group 1: Cresting an Appropriate Algebra Eiperience for All Grades K-12 Students produced the following papers: (1) "Report" (A. H. Schoenfeld): (2) "Five Questions About Algebra Reform (and a thought experiment)" (D. Chazi.n);(3) "Algebra and the Democratic Imperative" tR. B. Davis); (4) "Realism(s) for Learning Algebra" (R. Hall); (5) "Algebra, Ths New Civil Right" (B. Moses); (6) "Issues Surrounding Algebra" (E. Phillips): (7) "Is Thinking About 'Algebra' a Misdirection?" (A. H. Schoenfeld); and (8) "Thoughts Preceding the Algebra Colloquium" (2. Oilskin). Working Group 2: Educating Teachers, Including K-3 Teachers, to Provide These Algebra Experiences produced: (1) "Report" (A. Buccino); (2) "Educating Teachers to Provide Appropriate Algebra Experiences: Practicing Elementary and Secondary Teachers --Part of the Problem or Part of the Solution?" (C. Gifford-Banwart); (3) "Educating Teachers for Algebra" (A. Buccino):(4) "Experience, Abstraction, and 'Algebra for All': Some Thoughts on Situations, Algebra, and Feminist Research" (S. K. Daearin); (5) "Educating Teachers, Including 8-8 Teachers, to Provide Appropriate Algebra Experiences" (N. D. Fisher); (6) "On the Learning and Teaching of Linear Algebra" (G. Hared); and (7) "Algebra: The Next Public Stand for the Vision of Mathematics for All Students" (H. S. Kepner, Jr.). Working Group 3: Reshaping Algebra to Serve the Evolving Needs of the Technical Workforce produced: (1) "Report" (S. Forman);(2) "Algebra, Jobs, and Motivation" (P. Davis); (3) "To Strengthen Technical Education Systematically" (J. G. Greeno); (4) "Thoughts About Reshaping Algebra to Serve the Evolving Needs of a Technical Workforce" (R. Lash);(5) "Algebra for the Technical Workforce of the 21st Century" (P. D. McCraw);(6) "Some Thoughts on Algebra for the Evolving Work Force" (T. A. Romberg 6 M. Spence); and (7) "Algebra: A Vision for the Future" (S. S. Wood). Working Group 4: Renewing Algebra at the College Level to Serve the Future Mathematician, Scientist, and Engineer produced: (1) "Report" (J. Gillian); (2) "Some Thoughts on Teaching Undergraduate Algebra" (W. D. Blair); (3) "Toward One Meaning for Algebra" (A. Cuoco); (4) "Some Thoughts on Abstract Algebra" (S. Montgomery); and (5) "Suggestions for the Teaching of Algebra" (W. Y. Velez). Appendices include the conference agenda; Conceptual Framework for the Algebra Initiative of the National Institute on Student Achievement, Curriculum, and A t; and s participant list.(KKR) r _ A V4010110 LLD DEPARTMENT OF EDUCATION Cada a Educamead Reseamb and Imparreden1 EDUCATIONAL RESOURCES INFORMATION CENTER If RCI is extolled has been ceRrocluced ea 011.00 11001 the Demon 01 organdsbon Ofdpnalma 11. 0 Minor cloves have bee This ID on peat raonadvan00 quaNY Ponta al !odor acamOnsetsksd in MA Fact. mini do not nacnaway Norman, °Masi OFRI PC4111011W coney -ur LI L/ The Algebra Initiative Colloquium Volume 2 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 LI L/ U.S. Department of Education 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, cell their Order Desk at 202-512-1800. I +.r wilt bt ilk, S Inemmeril !kin Img 1 Mils rI I1n xxxlik. Simi Stop Still!). W.r.Innyinx IX' 211.111.191."X ISBN 0-16-048075-2 4 LI L/ Contents Introduction Carole B. Lacampagne 1 Summary Carole B. Lacampagne 3 Working Group 1: Creating an Appropriate Algebra Experience for All Grades K-12 Students 9 Report cf Working Group 1 Alan H. Schoenfeld 11 Five Questions About Algebra Reform (and a thought experiment) Daniel Chazan 19 Algebra and he Democratic Imperative Robert B. Davis 27 Realism(s) for Learning Algebra Rogers Hall 33 Algebra, The New Civil Right Bob Moses 53 Issues Surrounding Algebra Elizabeth Phillips 69 Is Thinking About "Algebra" a Misdirection? Alan H. Schoenfeld 83 Thoughts Preceding the Algebra Colloquium Zalman Usiskin 87 Working Group 2: Educating Teachers, Including K-8 Teachers, to Provide These Algebra Experiences 93 Report of Working Group 2 Alphonse Buccina 95 iii r- , Educating Teachers to Provide Appropriate Algebra Experiences: Practicing Elementary and Secondary TeachersPart of the Problem or Part of the Solution? Clare Gifford -Ban wart 113 Educating Teachers for Algebra Alphonse Buccino 117 Experience, Abstraction, and "Algebra for All:" Some Thoughts on Situations, Algebra, and Feminist Research Suzanne K. Damarin 127 Educating Teachers, Including K-8 Teachers, to Provide Appropriate Algebra Experiences Naomi D. Fisher 137 On the Learning and Teaching of Linear Algebra Guershon Hare! 141 Algebra: The Next Public.Stand for the Vision of Mathematics for All Students Henry S. Kepner, Jr. 151 Working Group 3: Reshaping Algebra to Serve the Evolving Needs of the Technical Workforce 155 Report of Working Group 3 Susan Forman 157 Algebra, Jobs. and Motivation Paul Davis 159 To Strengthen Technical Education Systemically James G. Greeno 161 Thoughts About Reshaping Algebra to Serve the Evolving Needs of a Technical Workforce Richard Lesh 165 Algebra for the Technical Workforce cif the 21st Century Patrick Dale McCray 173 Some Thoughts on Algebra for the Evolving Work Force Thomas A. Romberg and Mary Spence 177 iv Algebra: A Vision for the Future Susan S. Wood 193 Working Group 4: Renewing Algebra at the College Level to Serve the Future Mathematician, Scientist, and Engineer 197 Report of Working Group 4 Joseph Gallian 199 Some Thoughts on Teaching Undergraduate Algebra William D. Blair 203 Toward One Meaning for Algebra Al Cuoco 207 Some Thoughts on Abstract Algebra Susan Montgomery 219 Suggestions for the Teaching of Algebra William Yslas Velez 223 Appendices Appendix A Agenda 233 Appendix B Conceptual Framework for the Algebra Initiative of the National Institute on Student Achievement, Curriculum, and Assessment 237 Appendix C Participant List 243 V Introduction Carole B. Lacampagne Sponsored by the U.S. Department of Education's Office of Educational Research and Improvement, the Algebra Initiative Colloquium was held December 9-12, 1993, in Leesburg, Virginia (see the Agenda, appendix Al. The Colloquium addressed specific issues in the algebra curriculum and its teaching and learning. Algebra was chosen from among the many subject areas of mathematics because algebra is the language of mathematics; it 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 List of Participants, appendix CI.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 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)e evolving needs of the tech workforce; and Working Group 4:Renew'ng 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 on Colloquium deliberations. These papers, revised after the Colloquium, together with 1 0 recommendations from each working group and a summary of Colloquium discussions appear in this volume. Plenary and reactor papers appear in the companion publication, The Algebra Initiative Colloquium, Volume I. A short document for teachers and policymakers was prepared on the basis of