Alibert, D. (1988). Codidactic system in the course of mathematics: How to introduce it. In A. Borbàs (Ed.), Proceedings of the Twelfth International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 109-116). Veszprém, Hungary: Ferenc Genzwein, OOK.
Arsac, G. Chapiron, G., Colonna, A., Germain, G., Guichard, Y. & Mante, M. (1992), Initiation au Raisonnement Déductif au Collège. Presses Universitaires de Lyon.
Arsac,
G., N. Balacheff, & M. Mante, (1992),
Teacher's Role and Reproducibility of Didactical Situations. Educational
Studies in Mathematics. Vol.
23, pp. 5-29.
Balacheff, N. (1991). The benefits and limits of social interaction: The case of mathematical proof. In A. Bishop, S. Mellin-Olson & J. van Doormolen (Eds.), Mathematical knowledge: Its growth through teaching (pp. 175-192). Boston: Kluwer Academic.
Bell, A. (1976). A study of pupils’ proof-explanations in mathematical situations. Educational Studies in Mathematics, 7, 23-40.
Braconne, A. & Dionne, J. (1987). Secondary school students' and teachers' understanding of demonstration in geometry. In Proceedings of the Eleventh Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 109-116). Montreal.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page R-1
To Beginning of Section | To End of Section
Chazan, D. (1993). High school geometry students’
justification for their views of empirical evidence and mathematical proof. Educational
Studies in Mathematics, 24, 359-387.
Cockcroft,
W. H. (1982). Mathematics Counts: Report
of The Committee of Enquiry Into The Teaching of Mathematics In Schools.
London: Her Majesty's Stationery Office.
de Villiers, M. (1992). Children's acceptance of theorems
in geometry. Poster presented at
The Sixteenth Annual Conference of the International Group for the Psychology
of Mathematics Education, Durham NH.
English, L. (1996). Children's reasoning in solving novel
problems of deduction. In L. Puig
& A. Gutiérrez, (Eds.), Proceedings
of the Twentieth Annual Conference of the International Group for the
Psychology of Mathematics Education, (Vol. 4, pp. 49-56). Lisbon.
Fawcett, H. P. (1938). The nature of proof: a description and evaluation of certain procedures
used in a senior high school to develop an understanding of the nature of
proof. (NCTM yearbook 1938) New
York: Teachers' College, Columbia University.
Finlow-Bates, K. (1994). First year mathematics students'
notions of the role of informal proofs and examples. In J. da Ponte & J. Matos,
(Eds.), Proceedings of the
Eighteenth Annual Conference of the International Group for the Psychology of
Mathematics Education, (Vol. 2, pp. 334-351). Lisbon.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page R-2
To Beginning of Section | To End of Section
Fischbein, E. (1982). Intuition and Proof. For the Learning of Mathematics, 3(2), 9-18.
Graves, B. & Zack, V. (1996). Discourse in an inquiry math elementary classroom and the collaborative construction of an elegant algebraic expression. In L. Puig & A Gutiérrez,(Eds.), Proceedings of the Twentieth Annual Conference of the International Group for the Psychology of Mathematics Education, (Vol. 3, pp. 27-34). Valencia, Spain.
Graves, B. & Zack, V. (1997). Collaborative mathematical reasoning in an inquiry classroom. In E. Pehkonnen (Ed.) Proceedings of the Twentieth-first Annual Conference of the International Group for the Psychology of Mathematics Education, (Vol. 3, pp. 17-24
). Lahti, Finland.
Hanna, G. (1983). Rigorous
proof in mathematics education. Toronto:
OISE Press.
Healy, L. & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 369-428.
Henle, M. (1962). On the relation between logic and thinking. Psychological Review, 69,366-378.
Kieren, T., Gordon Calvert, L., Reid, D. & Simmt, E. (1995) An Enactivist Research Approach to Mathematical Activity: Understanding, Reasoning and Beliefs. Presented at the Annual Meeting of the American Educational Research Association, San Francisco.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page R-3
To Beginning of Section | To End of Section
Kieren, T., Gordon-Calvert, L., Reid, D. & Simmt, E. (1996) Occasioning: Learning in the interaction. Presented at the Annual Meeting of the American Educational Research Association, New York.
Lakatos, I. (1976). Proofs and Refutations. Princeton, NJ: Princeton University Press.
Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1) 29-63.
Maher, C. & Martino, A. (1996). The development of the idea of mathematical proof: a 5 year case study. Journal for Research in Mathematics Education, 27(2), pp. 194-214.
Maturana, H. & Varela, F. (1992). The Tree of Knowledge: The biological roots of human understanding. Boston: Shambhala.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston VA: Author.
National
Council of Teachers of Mathematics. (1991). Professional Standards for
Teaching Mathematics. Reston, VA: Author.
Pólya, G. (1968). Mathematics and plausible reasoning (2nd ed.). Princeton, NJ: Princeton University Press.
Reid, D. (1992). Mathematical induction: An epistemological study with consequences for teaching. Unpublished master’s thesis, Concordia University, Department of Mathematics and Statistics.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page R-4
To Beginning of Section | To End of Section
Reid, D. (1993). Pre-formal, formal, and formulaic proving. Proceedings of the 1993 Annual Meeting of the Canadian Mathematics Education Study Group, Toronto.
Reid, D. (1994a) Classroom Discourse. In Applying the NCTM Standards in Alberta Eds. A. Olson & D. Reid. Edmonton: Centre for Mathematics, Science and Technology Education.
Reid, D. (1994b). "Why 4?": Explanations in mathematical problem solving. Presented at the Annual Meeting of the Canadian Society for the Study of Education. Calgary.
Reid, D. (1995a). The need to prove. Unpublished doctoral dissertation, University of Alberta, Department of Secondary Education.
Reid, D. (1995b). Mechanical deduction and related aspects of students proving in problem solving. Presented at the Annual Meeting of the Canadian Society for the Study of Education. Montréal.
Reid, D. (1995c). Proving to explain. In L. Meira & D Carraher, (Eds.), Proceedings of the Nineteenth Annual Conference of the International Group for the Psychology of Mathematics Education, (Vol.3, pp. 137-143). Recife, Brazil.
Reid, D. (1996). Enactivism as a methodology. In L. Puig & A Gutiérrez,(Eds.), Proceedings of the Twentieth Annual Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp. 203-210). Valencia, Spain.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page R-5
To Beginning of Section | To End of Section
Schoenfeld,
A. (1988). When good teaching leads to bad results: The disasters of
"well taught" mathematics courses. Education
Psychologist, 23(2), 145-166.
Sekiguchi
Y. (1991). An investigation on proofs and refutations in the mathematics
classroom. Ed. D. Dissertation, The University of Georgia. University
Microfilms 9124336. Ann Arbor, MI.
Senk, S. (1985, September). How well do students write geometry proofs? Mathematics Teacher, pp. 448-456.
Shanny, B. & Erlich A. (1992) Conviction and understanding in proofs. Paper presented at ICME-7, Topic Group 6; The theory and practice of proof.
Stiff, L. (1999). Developing mathematical reasoning in grades K-12: 1999 Yearbook. Reston, VA: National Council of Teachers of Mathematics.
Tymoczko, T. (Ed.), (1986). New directions in the philosophy of mathematics: An anthology.
Boston: Birkhäuser.
Varela, F., Thompson, E., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge MA: MIT Press.
Wason, P. C. (1966). Reasoning. In B. M. Foss (Ed.), New
horizons in psychology. Harmondsworth: Penguin.
Zack, V. (1995) Algebraic thinking in the upper elementary school: The role of collaboration in making meaning of "generalization". In L. Meira & D Carraher, (Eds.), Proceedings of the Nineteenth Annual
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page R-6
To Beginning of Section | To End of Section
Conference of the International Group for the Psychology of Mathematics Education, (Vol.2, pp. 106-113). Recife, Brazil.
Zack, V. (1997). “You have to prove us wrong”: Proof at the elementary school level. In Erkki Pehkonnen (Ed.) Proceedings of the Twentieth-first Annual Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp. 291-298). Lahti, Finland.
The
Psychology of Students' Reasoning in School Mathematics
David A Reid
Page R-7
To Beginning of Section | To End of Section