Herbst P. G. (1999)
On proof, the logic of practice of geometry teaching and the two-column proof format

Proof Newsletter Janvier/Fevrier 1999.

References

© Patricio Herbst

  

Balacheff N. (1987). Processus de preuve et situations de validation [Processes of proof and situations of validation]. Educational Studies in Mathematics, 18, 147-176.
Balacheff N. (1991). Construction et analyse d'une situation didactique: Le cas de "la somme des angles d'un triangle" [Construction and analysis of a didactic situation: The case of "the sum of the angles of a triangle"]. Journal fur Matematikkdidaktikk, 12, 199-264.
Bennett A., Cuthbert D., Fawcett H., Hartung M., Havighurst R., Jablonower J., Kotinsky R., & Thayer V. T. (1938). Mathematics in general education: A report of the Committee on the function of mathematics in general education for the Commission on Secondary School Curriculum. New York: Appleton
Betz W. (1930). The transfer of training, with particular reference to geometry. In W. D. Reeve (Ed.), The National Council of teachers of Mathematics Fifth Yearbook: The teaching of geometry (pp. 149-198). New York: Bureau of Publications of Teachers College, Columbia University.
Betz W. (1936). The reorganization of secondary education: A study of present problems and trends, with particular reference to mathematics. In W. D. Reeve (Ed.), The National Council of Teachers of Mathematics Eleventh Yearbook: The place of mathematics in modern education (pp. 22-135). New York: Bureau of Publications of Teachers College, Columbia University.
Carson G. (1913). Essays on mathematical education. London: Ginn.
Caveing M. (1990). Platon, Aristote et les hypotheses des mathematiciens [Plato, Aristotle, and the hypotheses of mathematicians]. In J.-F. Mattei (Ed.), La naissance de la raison en Grece: Actes du congres de NiceæMai 1987 (pp. 119-128). Paris: Presses Universitaires de France.
Clemens S., O'Daffer P., Cooney T., & Dossey J. (1994). Geometry. Menlo Park, CA: Addison-Wesley.
Fawcett H. (1938). The nature of proof&emdash;The National Council of Teachers of Mathematics Thirtheenth Yearbook. New York: Bureau of Publications of Teachers College, Columbia University.
Gugle M. (1926). Revision of college preparatory mathematics. The Mathematics Teacher, 14, 321-328.
Heilbron J. L. (1998). Geometry civilized: History, culture, and technique. Oxford: Clarendon Press.
Herbst P. (1998). What works as proof in the mathematics class. Unpublished doctoral dissertation, The University of Georgia, Athens.
Hilbert D. (1971). Foundations of geometry. (L. Unger, Trans., P. Bernays, Rev.). La Salle, IL: Open Court. (Original work published in 1899)
Hofstadter R. (1962). Anti-intellectualism in American life. New York: Vintage.
Judd C. H. (1928). The fallacy of treating school subjects as "tool subjects." In J. Clarke & W. Reeve (Eds.), The National Council of Teachers of Mathematics Third Yearbook: Selected topics in the teaching of mathematics (pp. 1-10). New York: Bureau of publications of Teachers College, Columbia University.
Kilpatrick J. (1997). Confronting reform. The American Mathematical Monthly, 104, 955-962
Kilpatrick, W. H. et al. (1920). The problem of mathematics in secondary education. A report of the commission on the reorganization of secondary education, appointed by the National Education Association. Bureau of Education Bulletin 1920(1), 1-24.
Kliebard H. (1986). The struggle for the American curriculum 1893-1958. Boston: Routledge & Kegan Paul.
Kolesnik W. (1958). Mental discipline in modern education. Madison, WI: The University of Wisconsin Press.
Lakatos I. (1976). Proofs and refutations: The logic of mathematical discovery (J. Worrall & E. Zahar, Eds.). Cambridge: Cambridge University Press.
Legendre A.-M. (1848). Elements of geometry and trigonometry (D. Brewster, Trans.; C. Davies, Rev. and Ed.). New York: Barnes.
Moore E. H. (1926). On the foundations of mathematics. In C. Austin, H. English, W. Betz, W. Eells, & F. Touton (Eds.), A general survey of progress in the last twenty-five years: First Yearbook. (pp. 32-57). Washington, DC: National Council of Teachers of Mathematics. (Original speech delivered in 1902)
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics. (1998). Principles and standards for School Mathematics: Discussion Draft Standards 2000. On-line at www.nctm.org.
National Education Association. (1894). Report of the Committee of Ten on Secondary School Studies with the reports of the conferences arranged by the committees. New York: American Book Company.
Nightingale A. F. et al. (1899). Report of the Committee of College Entrance Requirements. In Journal of Proceedings and Addresses of the Thirty-eight annual meeting (pp. 633-817). Chicago: NEA.
Osborne A. & Crosswhite F. J. (1970). Forces and issues related to curriculum and instruction, 7-12. In A. Coxford (Ed.), A history of mathematics education in the United States and Canada&emdash;The thirty-second yearbook. Washington, DC: NCTM.
Pickett H. C. (1938). An analysis of proofs and solutions of exercises used in plane geometry tests. New York: Bureau of publications of Teachers College, Columbia University.
Quast W. G. (1968). Geometry in the high schools of the United States: An historical analysis from 1890 to 1966. Unpublished doctoral dissertation. Rutgers&emdash;The State University of New Jersey, New Brunswick.
Ross K. (1998). Doing and proving: The place of algorithms and proofs in school mathematics. American Mathematical Monthly 105, 252-255.
Rosskopf M. (1953). Transfer of training. In H. Fehr (Ed.), The learning of mathematics: Its theory and practice&emdash;The twenty-first yearbook. Washington, DC: NCTM.
Rubinstein R., Craine T., & Butts T. (1995). Integrated mathematics 2. Evanston, IL: McDougal Littell.
Sanders A. (1901). Elements of plane and solid geometry. New York: American Book Company.
Schlauch W. S. (1930). The analytic method in the teaching of geometry. In W. D. Reeve (Ed.), The National Council of teachers of Mathematics Fifth Yearbook: The teaching of geometry (pp. 134-144). New York: Bureau of Publications of Teachers College, Columbia University.
Schoenfeld A. (1988). When good teaching leads to bad results: The disasters of "well-taught" mathematics courses. Educational Psychologist 23(2), 145-166.
Schoenfeld A. (1991). On mathematics and sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In J. Voss, D. Perkins, & J. Segal (Eds.), Informal reasoning and education (pp. 311-343). Hillsdale, NJ: Erlbaum.
Schultze A. (1912). The teaching of mathematics in secondary schools. New York: Macmillan.
Sekiguchi Y. (1991). An investigation on proofs and refutations in the mathematics classroom. Unpublished doctoral dissertation, The University of Georgia, Athens.
Skovsmose O. (1992). Democratic competence and reflective knowing in mathematics. For the Learning of Mathematics, 12(2), 2-11.
Stanic G. M. A. (1986). The growing crisis in mathematics education in the early twentieth century. Journal for Research in Mathematics Education, 17, 190-205.
Thorndike E. L. (1924). Mental discipline in high school studies. Journal of Educational Psychology, 15, 1-22, 83-98.
Thurston W. (1995). On proof and progress in mathematics. For the Learning of Mathematics, 15(1), 29-37.
Touton F. C. (1924). Solving geometric originals. New York: Teachers College, Columbia University.
Upton C. B. (1930). The use of indirect proof in geometry and in life. In W. D. Reeve (Ed.), The National Council of teachers of Mathematics Fifth Yearbook: The teaching of geometry (pp. 102-133). New York: Bureau of Publications of Teachers College, Columbia University.
Usiskin Z., Hirschhorn D., Coxford A., Highstone V., Lewellen H., Oppong N., DiBianca R. & Maeir M. (1997). The University of Chicago School Mathematics Project: Geometry. (2nd ed.). Glenview, IL: Scott Foresman.
Vygotsky L. (1986). Thought and language (Alex Kozulin, Trans. & Ed.). Cambridge, MA: MIT Press. (Original work published in 1934)
Wertsch J. V. (1991). Voices of the mind: A sociocultural approach to mediated action. Cambridge, MA: Harvard University Press.
Wu H. S. (1997). The mathematics education reform: Why you should be concerned and what you can do. The American Mathematical Monthly 104, 946-954.
Young J. W. (1906). The teaching of mathematics in the elementary and the secondary school. New York: Longmans, Green & Co.