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53
A Philosophy and Framework
References
Alligood, Bob (Ed.~. Improving Mathematics, Science, and Computer
Education in Florida: A Comprehensive Plan. Tallahasse: Florida
Education and Industry Coalition, 1989.
American Association for the Advancement of Science. Science for
All Americans. Washington, D.C.: American Association for the
Advancement of Science, 1989.
Bangert-Drowns, R.; Kulik, J.A.; and Kulik, Chen C, "Effectiveness of
Computer-Based Education in Secondary Schools." Journal of
Computer-Based Education, 12:3 (Summer 1985), 59-68.
Becker, H.J. "The Importance of a Methodology that Maximizes
Falsifiability: Its Applicability to Research about LOGO."
Educational Researcher, 16:5 ( 1987), 1 1- 16.
Bell, Max S. "Microcomputer-Based Courses for School Geometry." In
Izaok Wirszup and Robert Streit (Eds.). Developments in School
Mathematics Education Around the World. Reston, Va.: National
Council of Teachers of Mathematics, 1987, 604-622.
Benezet, L.P. "The Story of an Experiment." Teaching of Arithmetic, 24
( 1 935), 8-9; 25; ( 1 936), 1 .
Board on Mathematical Sciences. Mathematical Sciences: A Unifying
and Dynamic Resource. Washington, D.C.: National Academy
Press, 1986.
Brown, J.S., and Burton, R.R. "Diagnostic Models for Procedural Bugs in
Basic Mathematical Skills." Cognitive Science, 2 (1 978), 155-192.
Brown, Stephen, and Walter, Marion. The Art of Problem Posing.
Philadelphia, Pa.: The Franklin Institute Press, 1983.
Bruner, Jerome S. On Knowing: Essays for the Left Hand. Cambridge,
Mass.: Belknap Press, 1964.
Burton, Leone. "Mathematical Thinking: The Struggle for Meaning."
Journal for Research in Mathematics Education, 15:4 (January
1 984), 35-49
Campbell, Patricia F. "Young Children's Concept of Measure." In Leslie
P. Steffe (Ed.). Transforming Early Childhood Mathematics
Education. Hillsdale, N.J.: Lawrence Erlbaum Associates, 1989.
Campione, Joseph C.; Brown, Ann L.; and Connell, Michael L.
"Metacognition: On the Importance of Understanding What You
are Doing." In Randall 1. Charles and Edward A. Silver (Eds.). The
Teaching and Assessing of Mathematical Problem Solving. Reston,
Va.: National Council of Teachers of Mathematics, 1988, 93-114.
Carpenter, Thomas. P.; Moser, J; and Romberg, Thomas A. (Eds.).
Addition & Subtraction: A Cognitive Perspective. Hillsdale, N.J.:
Lawrence Erlbaum Associates, 1982.
Carpenter, Thomas P.; Lindquist, Mary M.; Matthews, W.; and Silver,
Edward A. "Results of the Third NAEP Mathematics Assessment:
Secondary School." Mathematics Teacher, 76:9 (December 1983),
652-659.

OCR for page 53

54
Reshaping School Mathematics
Chambers, Donald L. A Guide to Curriculum Planning in
Mathematics. Madison: Wisconsin Department of Public Instruction,
1 986.
Charles, Randall 1., and Silver, Edward A. (Eds.~. The Teaching and
Assessing of Mathematical Problem Solving. Reston, Va.: Natior~al
Council of Teachers of Mathematics, 1988.
Clement, J. "Quantitative Problem Solving Processes in Children."
Ed.D. Dissertation, University of Massachusetts, Amherst, May 1977.
Clement, J.; Lockhead, J.; and Monk, G. "Translation Difficulties in
Learning Mathematics." American Mathematical Monthly, 88
(1 979), 4,
Collins, A.; Brown, J.S.; and Newman, S. "The New Apprenticeship:
Teaching Students the Craft of Reading, Writing, and
Mathematics." In D. Klahr (Ed.~. Cognition and Instruction: Issues
and Agendas. Hillsdale, NiJ.: Lawrence Erlbaum Associates, 1989.
Conference Board of the Mathematical Sciences. "The Mathematical
Sciences Curriculum K-12: What Is Still Fundamental and What Is
Not." In Educating Americans for the 21st Century: Source
Materials. National Science Board Commission on Precollege
Education in Mathematics, Science, and Technology. Washington,
D.C.: National Science Foundation, 1983, 1-23.
Crosswhite, F. Joe; Dossey, John A.; Swafford, Jane O.; McKnight,
Curtis C.; Cooney, Thomas J.; Downs, Floyd L.; Grouws, Douglas A.;
and Weinzweig, All. Second International Mathematics Study:
Detailed Report for the United States. Champaign, 111.: Stipes
Publishing Company, 1986.
Davis, Robert B. Learning Mathematics: The Cognitive Science
Approach to Mathematics Education. Norwood, N.J.: Ablex
Publishing, 1984.
Denham, Walter F., and O'Malley, Edward T. (Eds.~. Mathematics
Framework for California Public Schools, Kindergarten Through
Grade Twelve. Sacramento, Calif: California State Department of
Education, 1985.
Dessart, Donald J., and Suydam, Marilyn N. Classroom Ideas from
Research on Secondary School Mathematics. Reston, Va.: National
Council of Teachers of Mathematics, 1983.
Dossey, John A.; Mullis, Ina V.S.; Lindquist, Mary M.; and Chambers,
Donald L. The Mathematics Report Card: Are We Measuring Up?
Trends and Achievement Based on the 1986 National Assessment
of Educational Progress (NAEP). Princeton, N.J.: Educational Testing
Service, 1988.
Dugdale, Sharon. "Green Globs: A Microcomputer Application for
Graphing of Equations." Mathematics Teacher, 75:3 (March 1982),
208-2 1 4.
Easley, J., and Easley, E. "Ichinensei: The Introduction to Quantity in a
Japanese Elementary School." Technical Report, University of
Illinois, 1982.
Enloe, W., and Lewin, P. "The Cooperative Spirit ir~ Japanese Primary
Education." Educational Forum, 51:3 (Spring 1987), 233-247.
Erlwanger, S.H. "Case Studies of Children's Conceptions of
Mathematics." Ph.D. Dissertation, University of Illinois, Champaign
Urbana, 1974.

OCR for page 53

55
A Philosophy and Framework
Fawcett, Harold P. The Nature of Proof. Thirteenth NCTM Yearbook.
New York: Columbia University Teacher's College, Bureau of
Publications, 1938.
Fey, James T. "Mathematics Teaching Today: Perspectives From Three
National Surveys." Mathematics Teacher, 72:7 (October 1979), 490-
504.
Fey, James T. (Ed.~. Computing and Mathematics: The Impact on
Secondary School Curricula. Reston, Va.: National Council of
Teachers of Mathematics, 1984.
Fuson, Karen C.; Stigler, James W.; and Bartsch, Karen. "Grade
Placement of Addition and Subtraction Topics in Japan, Mainland
China, the Soviet Union, Taiwan, and the United States." Journal for
Research in Mathematics Education, 19 (November 1988), 449-456.
Gelman, R., and Gallistal, C. The Child's Understanding of Number.
Cambridge, Mass.: Harvard University Press, 1978.
Ginsburg, H.P. Children's Arithmetic: How They Learn It & How You
Teach It. New York: Van Nostrand Reinhold, 1977.
Ginsburg, H.P. (Ed.~. The Development of Mathematical Thinking. New
York: Academic Press, 1983.
Grouws, Douglas A.; Cooney, Thomas J.; and Jones, Douglas (Eds.~.
Perspectives on Research on Effective Mathematics Teaching.
Reston, Va.: National Council of Teachers of Mathematics, 1988.
Hansen, Viggo P. (Ed.~. Computers in Mathematics Education. 1984
NCTM Yearbook. Reston, Va.: National Council of Teachers of
Mathematics, 1984.
Hatano, G. "Learning to Add and Subtract: A Japanese Perspective."
In T. Carpenter, J. Moser, and T. Romberg (Eds). Addition &
Subtraction: A Cognitive Perspective. Hillsdale, N.J.: Lawrence
Erlbaum Associates, 1982.
Held, M.K. "Resequencing Skills and Concepts in Applied Calculus
Using the Computer as a Tool." Journal for Research in
Mathematics Education, 19:1 (January 1988), 3-25.
Held, M.K., and Kunkle, D. "Computer Generated Tables: Tools for
Concept Development in Elementary Algebra." In The Ideas of
Algebra, K-12. 1988 NCTM Yearbook. Reston, Va.: National Council
of Teachers of Mathematics, 1988, 170-177.
Hembree, R., and Dessart, D. "Effects of Hand-held Calculators in
Precollege Mathematics Education: A Meta-analysis." Journal for
Research in Mathematics Education, 17:2 (1986), 83-89.
Hiebert, J. (Ed.~. Conceptual and Procedural Know/edge: The Case
of Mathematics Hillsdale, N.J.: Lawrence Erlbaum Associates, 1986.
Howson, Geoffrey, and Kahane, J.-P. (Ecis.~. The Influence of
Computers and Informatics on Mathematics and Its Teaching.
Interrogational Commission on Mathematical Instruction Study Series.
Cambridge, Mass.: Cambridge University Press, 1986.
Johnston, William B., and Packer, Arnold ~E. (Eds.~. Workforce 2000:
Work and Workers for the Twenly-First Century. Indianapolis, Ind.
Hudson Institute, 1987.
Krulik, Stephen (Ed.~. Problem Solving in School Mathematics. 1980
NCTM Yearbook. Reston, Va.: National Council of Teachers of
Mathematics, 1980.

OCR for page 53

56
Reshaping School Mathematics
Lapointe, Archie E., Mead, Nancy A.; and Phillips, Gary W. A World of
Differences: An International Assessment of Science and
Mathematics. Princeton, N.J.: Educational Testing Service, 1989.
Love, Jean; Smith, Steve; and Butler, Michael. "Problem Solving as
Everyday Practice." In Randall 1. Charles and Edward A. Silver
(Eds.~. The Teaching and Assessing of Mathematical Problem
Solving. Reston, Va.: National Council of Teachers of Mathematics,
1988, 61-81.
Lesh, Richard. "The Evolution of Problem Representations in the
Presence of Powerful Conceptual Amplifiers." In C. Janvier (Ed.~.
Problems of Representation in the Teaching and Learning of
Mathematics. Hillsdale, N.J.: Lawrence Erlbaum Associates, 1987,
1 97-206.
Linn, Marcia C. (add. "Establishing a Research Base for Science
Education: Challenges, Trends and Recommendations." Report of
a National Conference held January 16-19, 1986, University of
California, Berkeley, May 1986.
Mason, J.; Burton, L.; and Stacey, K. Thinking Mathematically.
Reading, Mass.: Addison-Wesley, 1982.
Mathematical Sciences Education Board, National Research Council.
The Teacher of Mathematics: Issues for Today and Tomorrow.
Washington, D.C. National Academy Press, 1987.
Maurer, Stephen B. "New Knowledge About Errors and New Views
About Learners: What They Mean to Educators and More
Educators Would Like to Know." In A. Schoenfeld (Ed.), Cognitive
Science and Mathematics Education. Hillsdale, N.J .: Lawrence
Erlbaum Associates, 1987, 165- 187.
McKnight, Curlis C.; Crosswhite, F. Joe; Dossey, John A.; Kiter, Edward;
Swafford, Jane O.; Travers, Kenneth J.; and Cooney, Thomas J. The
Underachieving Curriculum: Assessing U.S. School Mathematics
from an International Perspective. Champaign, 111.: Stipes Publishing
Company, 1987.
Mestre, Jose. "Why Should Mathematics and Science Teachers Be
Interested in Cognitive Research Findings?" Academic
Connections, The College Board (1987), 3-5, 8-11.
National Council of Teachers of Mathematics. Curriculum and
Evaluation Standards for School Mathematics. Reston, Va.:
National Council of Teachers of Mathematics, 1989.
National Research Council: Committee on Research in Mathematics,
Science, and Technology Education. Mathematics, Science, and
Technology Education: A Research Agenda. Washington, D.C.:
National Academy Press, 1985.
National Research Council. Everybody Counts: A Report to the
Nation on the Future of Mathematics Education. Washington, D,C.:
National Academy Press, 1989.
Noddings, Nell "Preparing Teachers to Teach Mathematical Problem
Solving." In Randall 1. Charles and Edward A. Silver (Eds.~. The
Teaching and Assessing of Mathematical Problem Solving. Reston,
Va.: National Council of Teachers of Mathematics, 1988, 244-258.
Oaxaca, Jaime, and Reynolds, Ann W. Changing America: The New
Face of Science and Engineering. Washington, D.C.: Task Force on
Women, Minorities, and the Handicapped in Science and
Technology, September 1988.

OCR for page 53

57
A Philosophy and Framework
Office of Technology Assessment. Educating Scientists and Engineers,
Grade School to Grad School. Washington, D.C.: Office of
Technology Assessment, 1988.
Palmiter, J.R. "The Impact of a Computer Algebra System on College
Calculus." Dissertation, Ohio State University, November 1986.
Papert, Seymour. Mindstorms: Children, Computers, and Powerful
Ideas. New York: Basic Books, 1980.
Papert, Seymour. "Information Technology and Education: Computer
Criticism vs. Technocentric Thinking." Educational Researcher, 16:1
(1 987).
Pea, Roy D. "Cognitive Technologies for Mathematics Education," In
Alan H. Schoenfeld (Ed.~. Cognitive Science and Mathematics
Education. Hillsdale, N.J.: Lawrence Erlbaum Associates, 1987a, 89-
122.
Pea, Roy D. "The Aims of Software Criticism: Reply to Professor Papert."
Educational Researcher, 16:5 (1 987b), 4-8.
Peterson, P.L. "Teaching for Higher-order Thinking in Mathematics: The
Challenge for the Next Decade." In Douglas A. Grouws, Thomas J.
Cooney, and Douglas Jones (Eds.~. Perspectives on Research on
Effective Mathematics Teaching, Volume 7. Reston, Va.: National
Council of Teachers of Mathematics, 1988, 2-26.
Peterson, P.L., and Carpenter, T.L. (Eds.~. "Learning Through Instruction:
The Study of Students' Thinking During Instruction in Mathematics."
A Special Issue of the Educational Psychologist, 1989.
Piaget, J. Ou va L'education? International Commission on the
Development of Education, UNESCO (1948~. English Translation.
New York: Grossman, 1973.
Piaget, J. The Construction of Reality in the Child. New York: Basic
Books, 1954.
Polya, G. How to Solve It. Princeton, N.J.: Princeton University Press,
1 945.
Resnick, Lauren B. "Task Analysis in Instructional Design: Some Cases
from Mathematics." In D. Klahr (Ed.). Cognition and Instruction:
Issues and Agendas. Hillsdale, N.J.: Lawrence Erlbaum Associates,
1976, 51-80.
Resnick, Lauren B. "Mathematics and Science Learning: A New
Conception." Science, 220 (April 29, 1983), 477-478.
Resnick, Lauren B. Education and Learning to Think. Committee on
Mathematics, Science, and Technology Education, Commission on
Behavioral and Social Sciences and Education, National Research
Council. Washington, D.C.: National Academy Press, 1987.
Resnick, Lauren B. "Treating Mathematics as an III-Structured
Discipline." In Randall 1. Charles and Edward A. Silver (Eds.). The
Teaching and Assessing of Mathematical Problem Solving. Reston,
Va.: National Council of Teachers of Mathematics, 1988, 32-60.
Reusser, Kurt. "Problem-Solving Beyond the Logic of Things: Textual
and Contextual Effects on Understanding and Solving Word
Problems." Paper presented at the annual meeting of the
American Educational Research Association, San Francisco, Calif.,
April 1986.

OCR for page 53

58
Reshaping School Mathematics
Rheinboldt, Werner C. Future Directions in Computational
Mathematics, Algorithms, and Scientific Software. Philadelphia,
Pa.: Society for Industrial and Applied Mathematics, 1985.
Rhoads, C. "Organization of Microcomputer Instruction in Secondary
Mathematics Education." Dissertation, University of Maryland, 1986.
Romberg, Thomas A. "Policy Implications of the Three R's of
Mathematics Education: Revolution, Reform, and Research." Paper
presented at the annual meeting of the American Educational
Research Association, New Orleans, La., April 1988.
Romberg, Thomas A., and Carpenter, Thomas P. "Research on
Teaching and Learning Mathematics: Two Disciplines of Scientific
Inquiry." In M.C. Wittrock (Ed.~. Handbook of Research on
Teaching, Third Edition. New York: Macmillan, 1986, 850-873.
Schoen, Harold L. (Ed.~. Estimation and Mental Computation. 1986
NCTM Yearbook. Reston, Va.: National Council of Teachers of
Mathematics, 1986.
Schoenfeld, Alan H. Mathematical Problem Solving. New York:
Academic Press, 1985.
Schoenfeld, Alan H. (Edit. Cognitive Science and Mathematics
Education. Hillsdale, N.J.: Lawrence Erlbaum Associates, 1987.
Schoenfeld, Alan H. "Mathematics, Technology, and Higher-order
Thinking." In R. Nickerson (Ed.~. Technology in Education in 2020:
Thinking About the Non-too-distant Future. Hillsdale, N.J.: Lawrence
Erlbaum Associates, 1 988a.
Schoenfeld, Alan H. "Problem Solving in Contexts." In Randall 1.
Charles and Edward A. Silver (Eds.~. The recycling and Assessing of
Mathematical Problem Solving. Reston, Va.: National (council of
Teachers of Mathematics, 1 988b.
Schwartz, Judah L., and Yerushalmy, Michal. "Using Microcomputers
to Restore Invention to the Learning of Mathematics." In Izaok
Wirszup and Robert Streit (Eds.~. Developments in School
Mathematics Around the World. Reston, Va.: National Council of
Teachers of Mathematics, 1987, 623-636.
Shavelson, Richard J.; Webb, Noreen M.; Stasz, Cathleen; and
McArthur, David. "Teaching Mathematical Problem Solving: Insights
from Teachers and Tutors." In Randall 1. Charles and Edward A.
Silver (Eds.~. The Teaching and Assessing of Mathematical Problem
Solving. Reston, Va.: National Council of Teachers of Mathematics,
1 988, 203-23 1 .
Silver, Edward A. Teaching and Learning Mathematical Problem
Solving: Multiple Research perspectives. Hillsdale, N.J.: Lawrence
Erlbaum Associates, 1985.
Smith, David A.; Porter, Gerald J.; Leinbach, L. Carl; and Wenger,
Ronald H. (Eds.~. Computers and Mathematics: The Use of
Computers in Undergraduate Instruction. MAA Notes No. 9.
Washington, D.C.: Mathematical Association of America, 1988.
Steen, Lynn Arlhur. "The Science of Patterns." Science, 240 (April 29,
1988), 61 1-616.
Steffe, L.P.; van Glasersfeld, E.; Richards, J.; and Cobb, P. Children's
Counting Types: Philosophy, Theory, and Application. New York:
Praeger, 1983.

OCR for page 53

59
A Philosophy and Framework
Stevenson, Harold W.; Lee, S-Y; and Stigler, J.W. "Mathematics
Achievement of Chinese, Japanese, and American Children."
Science, 231 (February 14, 1986), 693-699.
Stigler, James W., and Perry, Michelle. "Cross-Cultural Studies of
Mathematics Teaching and Learning: Recent Findings and New
Directions." In Douglas A. Grouws, Thomas Cooney, and Douglas
Jones (Eds.~. Perspectives on Research on Effective Mathematics
Teaching. Reston, Va.: National Council of Teachers of
Mathematics, 1988, 194-223.
Suydam, Marilyn. "An Overview of Research Computers in
Mathematics Education, K-12." Mathematics Education Digest, No.
1. ERIC Clearinghouse for Science, Mathematics, and
Environmental Education. Columbus: Ohio State University, 1986.
Swifl, Jim. "Exploring Data with a Microcomputer." In Viggo P. I lansen
(Ed.). Computers in Mathematics Education. Reston, Va.: National
Council of Teachers of Mathematics, 1984, 107-1 17.
Walker, Decker F. "LOGO Needs Research: A Response to Papert's
Paper." Educational Researcher, 16:5 (1987), 9-1 1 .
Wearne, Diana, and Hiebert, James. "A Cognitive Approach to
Meaningful Mathematics Instruction: Testing a Local Theory Using
Decimal Numbers." Journal for Research in Mathematics
Education, 19 (November 1988), 371-384.
Wilt, Herbert S. "The Disk with the College Education." American
Mathematical Monthly, 89 (1982), 4-8.
Yerushalmy, Michal; Chazan, Daniel; and Gordon, Myles. Guided
Inquiry and Technology: A Year Long Study of Children and
Teachers Using the Geometric Supposers. Technical Report TR88-6.,
Cambridge, Mass.: Educational Technology Center, 1987.
Zorn, Paul. "Computing in Undergraduate Mathematics." Notices of
the American Mathematical Society, 34 (October 1987), 91 7-923.

OCR for page 53