The Ideas of Algebra, K-12 (1988 NCTM Yearbook)

Contents

Preface

Part 1: Algebra: Ideas and Issues

1. Reshaping School Algebra: Why and How? by Peggy A. House (University of Minnesota, Minneapolis, Minnesota)
2. Conceptions of School Algebra and Uses of Variables by Zalman Usiskin (University of Chicago, Chicago, Illinois)
3. Children's Difficulties in Beginning Algebra by Lesley R. Booth (James Cook University of North Queensland, Townsville, Queensland, Australia)
4. Teaching Algebraic Expressions in a Meaningful Way by Louise Chalouh (Protestant School Board of Greater Montreal, Montreal, Quebec, Canada) and Nicolas Herscovics (Concordia University, Montreal, Quebec, Canada)
5. Difficulties Students Have With the Function Concept by Zvia Markovits (Weizmann Institute of Science, Rehovot, Israel), Bat Sheva Eylon (Weizmann Institute of Science, Rehovot, Israel), and Maxim Bruckheimer (Weizmann Institute of Science, Rehovot, Israel)

Part 2: Readiness for Algebraic Concepts

6. Establishing Fundamental Concepts Through Numerical Problem Solving by Franklin Demana (Ohio State University, Columbus, Ohio) and Joan Leitzel (Ohio State University, Columbus, Ohio)
7. Algebraic Instruction for the Younger Child by Frances M. Thompson (Texas Woman's University, Denton, Texas)
8. Proportionality and the Development of Prealgebra Understandings by Thomas R. Post (University of Minnesota, Minneapolis, Minnesota), Merlyn J. Behr (Northern Illinois University, DeKalb, Illinois), and Richard Lesh (WICAT Systems and Northwestern University, Evanston, Illinois)

Part 3: Equations and Expressions in Algebra

9. Two Different Approaches Among Algebra Learners by Carolyn Kieran (Université du Québec a Montréal, Montreal, Quebec, Canada)
10. An Integration of Equation-Solving Methods Into a Developmental Learning Sequence by John E. Bernard (West Georgia College, Carrollton, Georgia) and Martin P. Cohen (University of Pittsburgh, Pittsburgh, Pennsylvania)
11. Polynomials in the School Curriculum by Theodore Eisenberg (Ben-Gurion University, Beer Sheva, Israel) and Tommy Dreyfus (Center for Technological Education, Holon, Israel)

Part 4: Problem Solving in Algebra

12. Teaching Elementary Algebra With a Word Problem by Harold L. Schoen (University of Iowa, Iowa City, Iowa)
13. From Words to Algebra: Mending Misconceptions by Jack Lochhead (University of Massachusetts, Amherst, Massachusetts) and José P. Mestre (University of Massachusetts, Amherst, Massachusetts)
14. Developing Algebraic Representation Using Diagrams by Martin A. Simon (Mount Holyoke College, South Hadley, Massachusetts) and Virginia C. Stimpson (Mercer Island High School, Mercer Island, Washington)

Part 5: Using Computers and Calculators to Learn Algebra

15. Technology and Algebra by John W. McConnell (Glenview South High School, Glenview, Illinois)
16. Computer Software for Algebra: What Should It Be? by Harley Flanders (University of Michigan, Ann Arbor, Michigan)
17. Programming Finite Group Structures to Learn Algebraic Concepts by Richard J. Shumway (Ohio State University, Columbus, Ohio)
18. Relating Functions to Their Graphs by James Saunders (Upper St. Clair High School, Upper St. Clair, Pennsylvania) and John DeBlassio (Upper St. Clair High School, Upper St. Clair, Pennsylvania)
19. Computer Lessons in Algebra by Patricia Fraze (Huron High School, Ann Arbor Michigan)
20. Computer-Calculated Roots of Polynomials by Alfinio Flores (Centro de Investigación en Matemátcas, Guanajusto, Mexico)
21. Computer-Generated Tables: Tools for Concept Development in Elementary School by M. Kathleen Heid (Pennsylvania State University, University Park, Pennsylvania) and Dan Kunkle (Mercersburg Academy, Mercersburg, Pennsylvania)
22. Using Spreadsheets in Algebra Instruction by Bruce R. Maxim (University of Michigan—Dearborn, Dearborn, Michigan) and Roger F. Verhey (University of Michigan—Dearborn, Dearborn, Michigan)
23. Using Computer Graphing Software Packages in Algebra Instruction by Joyce S. Friske (Oklahoma State University, Stillwater, Oklahoma)
24. Logarithms, Calculators, and Teaching Intermediate Algebra by Betty J. Krist (University College, Buffalo, New York)

Part 6: Algebra Teaching Ideas

25. Factoring Twins as a Teaching Tool by Lee H. Minor (Western Carolina University, Cullowhee, North Carolina)
26. An Algebra Class Unveils Models of Linear Equations in Three Variables by Deborah Davies (University School of Nashville, Nashville, Tennessee)
27. Common Mistakes in Algebra by June Marquis (Fairfax County Public Schools, Alexandria, Virginia)
28. Using Polynomials to Amaze by Catherine Herr Mulligan (Bishop Fenwick High School, Middletown, Ohio)
29. Teaching Absolute Value Spirally by Alex Friedlander (Weizmann Institute of Science, Rehovot, Isreal)
30. Which One Doesn't Belong? by David J. Glatzer (West Orange Public Schools, West Orange, New Jersey)
31. Integrating Statistical Applications in the Learning of Algebra Through Problem Solving by Carolyn A. Maher (Rutgers University, New Brunswick, New Jersey), John P. Pace (Essex County College, Newark, New Jersey), and John Pancari (St. Joseph High School, Hammonton, New Jersey)
32. Input-Output Modifications to Basic Graphs: A Method of Graphing Functions by John St. Thaeler (Weber State College)
33. Making Algebra Homework More Effective by Gregory Holdan (Mount Lebanon School District, Pittsburgh, Pennsylvania)
34. Algebra Problems for Classroom Use by Terry Goodman (Central Missouri State University, Warrensburg, Missouri) and Martin P. Cohen (University of Pittsburgh, Pittsburgh, Pennsylvania)

Cite

APA 7

Coxford, A. F., & Shulte, A. P. (Eds.). (1988). The ideas of algebra k-12. National Council of Teachers of Mathematics.