The Algebra Initiative Colloquium

Papers presented at a conference on reform in algebra, December 9-12, 1993

Carole Lacampagne | 1995 | PDF

Vol. 1

eric.ed.gov 

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: (1) "Introduction" (C. B. Lacampagne); (2) "Summary" (C. B. Lacampagne); (3) "Recommendations" (C. B. Lacampagne); (4) "The Development 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.

Vol. 2

eric.ed.gov

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: Creating an Appropriate Algebra Experience 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. Chazan); (3) "Algebra and the Democratic Imperative" (R. B. Davis); (4) "Realism(s) for Learning Algebra" (R. Hall); (5) "Algebra, The 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" (Z. Usiskin). Working Group 2: Educating Teachers, Including K-8 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. Damarin); (5) "Educating Teachers, Including K-8 Teachers, to Provide Appropriate Algebra Experiences" (N. D. Fisher); (6) "On the Learning and Teaching of Linear Algebra" (G. Harel); 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. Lesh); (5) "Algebra for the Technical Workforce of the 21st Century" (P. D. McCray); (6) "Some Thoughts on Algebra for the Evolving Work Force" (T. A. Romberg & 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. Gallian); (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 Assessment; and a participant list.

The Nature and Role of Algebra in the K-14 Curriculum

Proceedings of a National Symposium
(Compass Series)
National Council of Teachers of Mathematics, Mathematical Sciences Education Board, National Research Council

National Academies Press | 1998 | 206 páginas

on-line: nap.edu

Methods of effectively teaching algebraic thinking in elementary schools as well as secondary schools is the topic of the following 19 papers. Papers include: (1) "Transforming Algebra from an Engine of Inequity to an Engine of Mathematical Power by 'Algebrafying' the K-12 Curriculum" (J. Kaput); (2) "Developing a Coherent and Focused K-12 Algebra Curriculum" (E. Phillips); (3) "Enhancing Algebraic Reasoning with Technology" (G. Akst); (4) "Algebra for Everyone? With or Without Technology?" (M. Norman); (5) "How Might Technology Enhance Algebraic Reasoning?" (R. Zbiek); (6) "What Do We Know about K-14 Students' Learning of Algebra?" (J. Confrey); (7) "Algebra: What All Students Can Learn" (S. Williams and D. Molina); (8) "Improving K-14 Algebra Instruction: A Discussion of Teachers' Responsibilities and Students' Opportunities" (B. Moore-Harris); (9) "Capturing Patterns and Functions: Variables and Joint Variation" (G. Lappan); (10) "Functions and Relations: A Unifying Theme for School Algebra in Grades 9-12" (C. Hirsch); (11) "Middle School Algebra from a Modeling Perspective" (G. Kleiman); (12) "Why Modeling Matters" (L. Godbold); (13) "Modeling: Changing the Mathematics Experience in Postsecondary Classrooms" (R. Dance); (14) "Algebraic Structure in the Mathematics of Elementary-School Children" (C. Tierney); (15) "Structure in School Algebra (Middle School)" (M. van Reeuwijk); (16) "The Role of Algebraic Structure in the Mathematics Curriculum of Grades 11-14" (G. Foley); (17) "Language and Representation in Algebra: A View from the Middle" (R. Billstein); (18) "Teaching Algebra: Lessons Learned by a Curriculum Developer" (D. Resek); and (19) "The Nature and Role of Algebra: Language and Representation" (D. Hughes Hallett). (ASK)

Bringing Out the Algebraic Character of Arithmetic: From Children’s Ideas to Classroom Practic

Analucia Dias Schliemann, David William Carraher, Barbara M. Brizuela,

Lawrence Erlbaum | 2006 | 144 páginas | pdf | 1,37 Mb

Versão draft

on-line: earlyalgebra.terc.edu

Referência em MathEdu

Bringing Out the Algebraic Character of Arithmetic contributes to a growing body of research relevant to efforts to make algebra an integral part of early mathematics instruction, an area of studies that has come to be known as Early Algebra. It provides both a rationale for promoting algebraic reasoning in the elementary school curriculum and empirical data to support it.

The authors regard Early Algebra not as accelerated instruction but as an approach to existing topics in the early mathematics curriculum that highlights their algebraic character. Each chapter shows young learners engaged in mathematics tasks where there has been a shift away from computations on specific amounts toward thinking about relations and functional dependencies. The authors show how young learners attempt to work with mathematical generalizations before they have learned formal algebraic notation.

The book, suitable as a text in undergraduate or graduate mathematics education courses, includes a CD-ROM with additional text and video footage on how students reason about addition and subtraction as functions; on how students understand multiplication when it is presented as a function; and on how children use notations in algebraic problems involving fractions. These three videopapers (written text with embedded video footage) present relevant discussions that help identify students' mathematical reasoning. The printed text in the book includes transcriptions of the video episodes in the CD-ROM.

Bringing Out the Algebraic Character of Arithmetic is aimed at researchers, practitioners, curriculum developers, policy makers and graduate students across the mathematics education community who wish to understand how young learners deal with algebra before they have learned about algebraic notation.

Contents: Preface: Rethinking Early Mathematics Education. Interpreting Research About Learning Algebra. Part I: Interview Studies. Young Children's Understanding of Equivalences. Can Young Students Solve Equations? Part II: Classroom Studies. Addition Operations as Functions. From Quantities to Ratio, Functions, and Algebraic Notation. On Children's Written Notation to Solve Problems. Discussion.