Preuve, la bibliographie de J à Z
A   I

 

J

    Jahnke, H. N. (2007). Proof and hypotheses. ZDM. The International Journal on Mathematics Education, 39(1-2), 79-86.
    Jahnke, H. N. (2008) Theorems that admit exceptions, including a remark on Toulmin ZDM The International Journal on Mathematics Education 40/3, 363-371
Jones K. (1997) Student-Teachers' Conceptions of Mathematical Proof. Mathematics Education Review 9, 23 - 32
    Jones K. (2000) The Student Experience of Mathematical Proof at University Level. International Journal of Mathematical Education in Science and Technology 31(1) 53-60.

 

 

Jones K. (2000) : Providing a Foundation for Deductive Reasoning: Students' Interpretations when Using Dynamic Geometry Software and Their Evolving Mathematical Explanations. Educational Studies in Mathematics, Vol. 44, Issues 1&2, Keith Jones, Ángel Gutiérrez Maria Alessandra Mariotti (eds.) 55-85

K

    Kaiser, Mark J. (1993): Demonstrating Proof by Contrapositive and Contradiction through Physical Analogs School Science and Mathematics, vol. 93 n7 p. 369-72

Keskessa B. (1992) Preuves et résolutions de problèmes de lieux géométriques. Thèse. Grenoble : Université Joseph Fourier.

Keskessa B. (1994) Preuve et plan de signification : une hypothèse.Recherches en didactique des mathématiques. 14(3) 357-392.

King I. L. (1973) A formative development of elementary school unit on proof. Journal for Research in Mathematics Education 4, 57-63.

Kleiner I., Movshovitz-Hadar N. (1990) Aspects of the Pluralistic Nature of Mathematics. Interchange 21(1) 28-37.

Kleiner I., Movshovitz-Hadar N. (1997) Proof: A many-splendored thing. The mathematical intelligencer 19 (3) 16-26

    Klymchuk, S.(2004) Counter-Examples in Calculus. Maths Press, New Zealand, 116 p. ISBN: 0-476-01215-5.
  Klymchuk, S. (2005) Counter-examples in teaching/learning of Calculus: Students' performance. The New Zealand Mathematics Magazine. ISSN: 0549-0510. Vol 42, No 1, pp. 31-38.
    Knipping K. (2008) A method for revealing structures of argumentations in classroom proving processes ZDM The International Journal on Mathematics Education 40/3, 427-441

Knuth E. J., Elliott R. (1998) Characterizing students's understandings of mathematical proof. Mathematics Teacher. 91(8) 714-717

    Knuth E. J. (2002) Secondary school mathematics teachers' conceptions of proof. Journal for research in mathematics education 33(5) 379-405
    Knuth E. (2002) Teachers' Conceptions of Proof in the Context of Secondary School Mathematics Journal of Mathematics Teacher Education 5 (1) pp. 61-88

Koedinger K. R., Anderson J. R. (1993) Effective use of intelligent software in high school math classrooms. Artificial Intelligence in Education. Edimburg.

Koedinger K. R. (1998) Conjecturing and argumentation in high school geometry students. In Lehrer, R. and Chazan D. (eds.) New Directions in the Teaching and Learning of Geometry.  Hillsdale: NJ: Lawrence Erlbaum Associates.

    Komatzu K. (2008) Defining the concept of action proof in school mathematics. Tsukuba Journal of Educational Studies in Mathematics. 26, 29-38 [Text in Japanese]

Konior J. (1972) Essai de détermination des causes d'échec des élèves dans la recherche de démonstrations. Educational Studies in Mathematics 4, 466-483.

Koseki K. (ed.) (1987) Zukei no ronsho shido [Teaching of proof in geometry]. Tokyo: Meiji Tosho. (in Japanese)

Krummheuer G. (1995) The ethnography of argumentation. In: Cobb. P., Bauersfeld H. (eds.) The emergence of mathematical meaning: interaction in the classroom culture. Hillsdale, NJ: Erlbaum.

    Krummheuer G. (2000) Mathematics learning in narrative classroom cultures: studies of argumentation in primary mathematics education [1]. For the Learning of Mathematics. 20(1) 22-32

Kumagai K. (1998) The justification process in a fifth grade mathematics classroom: From a social interactionist perspective. Reports of Mathematical Education (Journal of Japan Society of Mathematical Education (80) Supplementary Issue 70, 3-38 (in Japanese).

Kunimoto K. (1995) A study on a conception of proof of junior high school students.  Journal of JASME: Research in Mathematics Education 1, 117-124. (in Japanese)

Kunimune S. (1987) The study on development of understanding about the significance of demonstrations in learning geometrical figures. Reports of Mathematical Education. Journal of Japan Society of Mathematical Education (69) Supplementary Issue 47-48, 3-23 (in Japanese).

Kunimune S., Kumakura H. (1996) A study on levels of students' understanding of literal expressions.  Reports of Mathematical Education. Journal of Japan Society of Mathematical Education (78) Supplementary Issue 65-66, 35-55 (in Japanese).

L

    Laborde C. (2000) : Dynamic Geometry Environments as a Source of Rich Learning Contexts for the Complex Activity of Proving. Educational Studies in Mathematics, Vol. 44, Issues 1&2, Keith Jones, Ángel Gutiérrez Maria Alessandra Mariotti (eds.) 151-161
    Lagrange J.B. (à paraître) Curriculum, classroom practices and tool design in the learning of functions through technology-aided experimental approaches.
International Journal of Computers for Mathematical Learning, Kluwer

Lampert M. (1990) When the Problem Is Not the Question and the Solution Is Not the Answer. American Educational Research Journal 27(1) 29-63

Lampert M. (1992). Practices and problems in teaching authentic mathematics. In F. Oser, A. Dick, and J.L. Patry (Eds.) Effective and responsible teaching: the new synthesis. San Francisco: Jossey Bass.

    Lannin, J., Barker, D., Townsend B. (2007) How students view the general nature of their errors Educational Studies in Mathematics 66/1, 43-59
  Largeault J. (1992) Intuitionisme et théorie de la démonstration. Paris : Vrin.

Lars C. J. (1974) Structural and linguistic variables that constribute to difficulty in the judgement of simple verbal deductive arguments. Educational Studies in Mathematics 5,493-505.

    Larsen S. & Zandieh M. (2008) Proofs and refutations in the undergraduate mathematics classroom Educational Studies in Mathematics 67/3, 205-216

Legrand M. (1988) Genèse et étude sommaire d'une situation co-didactique: le débat scientifique en situation d'enseignement. In : Laborde C. (ed.) Premier colloque franco allemand de didactique des mathématiques et de l'informatique. Grenoble : La Pensée Sauvage.

Legrand M. (1990) Rationalité et démonstration mathématique, le rapport de la classe à une communauté scientifique. Recherches en didactique des mathématiques. 9(3) 365-406.

    Legrand M. (1996) Débat scientifique en cours de mathématiques et spécificité de l'analyse. in : L'enseignement des mathématiques : des repères entre savoirs, programmes et pratiques (pp.171-192). Pont-à-Mousson : Topiques éditions

Leron U. (1983) Structuring mathematical proofs. American Mathematical Monthly 90, 174-185.

Leron U. (1985) A direct approach to indirect proofs. Educational Studies in Mathematics 16(3) 321-325.

Leron U. (1985) Heuristic presentation: The role of structuring. For the Learning of Mathematics 5(3) 7-13.

Lerouge A. (1992) Représentation cartésienne, rationalité mathématique et rationalité du quotidien chez des élèves de collége. Thèse. Montpellier : Université de Montpellier.

    Lerouge A. (2000) La notion de cadre de rationalité. A propos de la droite au collège. Recherches en didactique des mathématiques 20 (2) 171-208

Lester F. K. (1975). Developmental aspects of children's ability to understand mathematical proof.Journal for Research in Mathematics Education Jan., 14-25

    Lin Fou-Lai (2002) Designing activities for understanding procing. Fou Lai Lin (ed.) 2002 International Conference on Mathematics - "Understanding proving and proving to understand". Taipei: NSC and NTNU (pp.108-142)
    Lin F.-L. & Yang K-L (2007) The Reading Comprehension of Geometric Proofs: The Contribution of Knowledge and Reasoning International Journal of Science and Mathematics Education, 5/4, 729-754
    Lithner J. (2008) A research framework for creative and imitative reasoning Educational Studies in Mathematics 67/3, 255-276
    Livingston E. (1999) Cultures of Proving. Social Studies of Science 29, 867-888

Lopes A. J. (1998) Gestión de interacciones y producción de conocimiento matemático en un dia a dia lakatosiano. Uno, Revista de Didáctica de la matemáticas 16, 25-37

    Lynch M. P. (1998) Truth in context. Cambridge, MA: The MIT Press.
  Luengo V., Balacheff N. (1998) Contraintes informatiques et environnements d'apprentissage de la démonstration en géométrie. Sciences et techniques éducatives 5(1) 15-45.

 

Luengo V. (2001) Aider le raisonnement déductif sans imposer un modèle : le micromonde Cabri-Euclide. Barbin E., Duval R., Giorgiutti I., Houdebine J., Laborde C. (eds.) Produire et lire des textes de démonstration. Paris : Ellipse. 225-240

M

MacKernan J. (1996) What's the point of proof? Mathematics Teaching 155, 14-20

Maher C. A., Martino A. M. (1996) The development of the Idea of Mathematical Proof: A 5-year Case Study. Journal for Research in Mathematics Education. 27(2) 194-214.

Maher C. A., Martino A. M. (1996) Young children invent method of proof: The gang of four. In: Steffe L., Nesher P., Cobb P., Goldin G., Greer B. (eds.) Theories of Mathematical Learning. (pp. 431-447) Mahwah, New Jersey: Lawrence Erlbaum Associates, Publishers

    Maher C. (1998) Can teachers help children make convincing arguments? A glipms into the process. Séries Relexões em Educação Matemática. Universidade Santa Úrsula. Brasil.
    Maher C. (1998) Professores podem ajudar seus alunos a construir argumentos convicentes? um breve exame deste processo. Séries Relexões em Educação Matemática. Universidade Santa Úrsula. Brasil.
    Malafosse D. (2002) Pertinence des notions de cadre de rationalité et de registre sémiotique en didactique de la physique. Recherches en didactique des mathématiques 22(1) 31-76

Malara N. A., Gherpelli L. (1997) Argumentazione e dimostrazione in aritmetica nel trienno di escuela media. L'educazione Matematica Anno XVIII - Serie V, 2(2) 82-102.

    Mancuso P. (2000) Mathematical explanation. In Grosholz E., Breger H. (eds.) The Growth of Mathematical Knowledge. Dordrecht: Kluwer Academic Publishers.

Man-Keung Siu (1993) Proof and Pedagogy in Ancient China: Examples from Liu Hui's Commentary on Jiu Zhang Suan Shu.Educational Studies in Mathematics 24(4) 345-357.

    Man-Keung Siu (2001) Mathématiques = démonstration ? Bulletin de l'Association des Professeurs de Mathématiques de l'Enseignement Public. 434, 374-386
    Manin Y. I. (1971) How convincing is a proof? (reprint from "A course on mathematical logic"). The Mathematics Intelligencer 2(1) 17-18

Margolinas C. (1993) De l'importance du vrai et du faux dans la classe de mathématiques. Grenoble : La Pensée Sauvage.

    Mariotti, M. A. and Balacheff, N. (2008) Introduction to the special issue on didactical and epistemological perspectives on mathematical proof ZDM The International Journal on Mathematics Education 40/3, 341-344
    Markel, William D. (1994): The Role of Proof in Mathematics Education School Science and Mathematics, vol. 94, n6 p. 291-95
    Marrades R., Gutiérrez Á. (2000) : Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, Vol. 44, Issues 1&2, Keith Jones, Ángel Gutiérrez Maria Alessandra Mariotti (eds.) 87-125
    Mariotti M. A. (1998) Introduzione alla dimostrazione all'inizio della scuola secondaria superiore. L'insegnamento della matematica e delle scienze integrate. 21B(3) 209-252
    Mariotti M. A. (2000) : Introduction to Proof: The Mediation of a Dynamic Software Environment. Educational Studies in Mathematics, Vol. 44, Issues 1&2, Keith Jones, Ángel Gutiérrez Maria Alessandra Mariotti (eds.) 25-53
    Mariotti A. (2001) Justifying and proving in the Cabri environment. International Journal of Computers for Mathematical Learning 6(3) 283-317.
  Mariotti, M.A. (2005) Proof and proving in Algebra, Proceedings of the 1st Conference of the Greek Ass. for research in mathematics education
(GARME) - (Athens 9-11 Dec. 2005) .
    Martin, T.S., Soucy McCrone, S.M., Wallace Bower, M.L., Dindyal, J. (2005) The interplay of teacher and student actions in the teaching and learning of geometric proof. Educational Studies in mathematics, vol. 60 (1), p. 95-124.

Martin W. G., Harel G. (1989) Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education 20(1) 41-51.

    Martino A. M., Maher C. (1999) Teacher questioning to promote justification and generalization in mathematics: what research practice has taught us. Journal of mathematical behavior 18 (1) 53-78.
    Martínez J. C. (2000) Demostració automàtica. Butletín de la Societat Catalana de Matemàtiques 15 (1) 55-70.
   

McClure J. E. (2000) Start where they are: Geometry as an introduction to proof. The American Mathematical Monthly 107(1) 44-52

    McCrone S. S. (2005) The development of mathematical discussions: an investigation in a fifth-grade classroom. Mathematical Thinking and Learning 7 (2) 111-134

Mesquita A. L. (1989) Sur une situation d'éveil à la déduction en géométrie. Educational Studies in Mathematics 20, 55-57.

Mesquita A. L.(1989) L'influence des aspects figuratifs dans l'argumentation des élèves en géométrie. Thèse. Strasbourg : Université Louis Pasteur.

Miyazaki M. (1992) Students'activity in order to show the generality of a conjecture: How does one student use a generic example to make an explanation? Reports of Mathematical Education. Journal of Japan Society of Mathematical Education (74) Supplementary Issue 57, 3-19 (in Japanese).

    Miyazaki M. (2000) Levels of proof in lower secondary school mathematics. Educational Studies in Mathematics 41(1) 47-68.
    Mogetta C. (1998) Il passaggio dall'argomentazione matematica alla dimostrazione in situaione di problem solving: elementi di rottura e di continuità cognitiva. L'insegnamento della matematica e delle scienze integrate. 21B(5) 429-460.

Motte M. (1971) En marge de l'apprentissage de la déduction. Educational Studies in Mathematics 4(2)

Moore R. C. (1994) Making the transition to formal proof. Educational Studies in Mathematics 27, 249-266.

Movshovitz-Hadar N. (1988) Stimulating Presentation of theorems followed by responsive proofs. For the Learning in Mathematics 8(2) 12-19.

Movshovitz-Hadar N. (1988) School mathematics theorems, an endless source of surprise. For the Learning of Mathematics 8 (3) 34-40.

  Movshovitz-Hadar N., Hadass R. (1988) Preservice education of math teachers using paradoxes. Educational Studies in Mathematics 21 (3) 265-287.

 

Mudali, Vimolan (2004). Modeling of real-world problems is often the starting point for proof. In Henn, H-W & Blum, W. (Eds.) Proceedings of the ICMI study 14: Applications and Modelling in Mathematics Education, 187-192, University of Dortmund, Germany.

N

    Najjar R. (2005) La démonstration euclidienne. Petit X 67, 7-11

Neubrand M. (1989) Remarks on the acceptance of proofs: the case of some recently tackled major theorems. For The Learning Of Mathematics 9 (3) 2-6.

    Neumann B. H. (1979) Proofs. The Mathematics Intelligencer 2(1) 18-19
    Netz R. (1998) Greek mathematical diagrams: their use and their meaning. For the Learning of Mathematics 18(3) 33-39
  Netz R. (1999) The Shaping of deduction in Greek mathematics: A study in cognitive history. Cambridge University Press.

Noirfalise R. (1993) Contribution à l'étude de la démonstration. Etude de régularités dans les modalités de fonctionnement du savoir mathématique dans les divers chapitres de géométrie d'un manuel de sixième. Recherches en didactique des mathématiques. 13(3) 229-256.

Noirfalise R. (1998) Une étude sur le maniement d'énoncés dans une démonstration. Petit X 46, 5-17.

    Nunokawa K. (1996) Applying Lakatos' Theory to the Theory of Mathematical Problem Solving. Educational Studies in Mathematics 31, 269-293.

Nunn T. (1925) The sequence of theorems in school geometry. Mathematics Teacher 18, 321-332

O

O'Brien T. C. (1972) Logical thinking in adolescents. Educational Studies in Mathematics 4(4) 401-428.

    Oehrtman M. & Lawson A. E. (2008) Connecting Science and Mathematics: The Nature of Proof and Disproof in Science and Mathematics International Journal of Science and Mathematics Education, 6/2, 377-403
    Orus Baguena (1992) Le raisonnement des élèves dans la relation didactique. Thèse. Bordeaux: Université de Nordeaux 1.

Otte M. (1980) On the Question of the Developement of Theoritical Concepts. Communication and Cognition 1(13) 63-76.

Otte M. (1990) Intuition and formalism in mathematical proof. Interchange 21(1) 59-64.

Otte M. (1994) intuition and logic in mathematics. In : Robitaille D. F., Wheeler D. H., Kieran C. (eds.) Selected lectures from the 7th International Congress in Mathematical Education (pp.271-284) Sainte-Foy : Les Presses de l'Université Laval.

Otte M. (1994) Mathematical knowledge and the problem of proof. Educational Studies in Mathematics 26(4) 299-321.

P

Pastre D. (1978) Observation du mathématicien : aide à l'enseignement et à la démonstration automatique de théorèmes. Educational Studies in Mathematics 9(4) 461-502.

    Pedemonte B. (2002) Etude didactique et cognitive des rapports de l'argumentation et de la démonstration dans l'apprentissage des mathématiques, Thèse de l'Université Joseph Fourier, Grenoble I.
  Pedemonte B. (2005) Quelques outils pour l'analyse cognitive du rapport entre argumentation et démonstration, Recherche en Didactique des Mathématiques Vol. 25, n° 3 pp. 313-348
    Pedemonte B. (2007) How can the relationship between argumentation and proof be analysed? Educational Studies in Mathematics 66/1, 23-41
    Pedemonte, B. (2008) Argumentation and algebraic proof ZDM The International Journal on Mathematics Education 40/3, 385-400
    Perry Carrasco P., Camargo Uribe L., Samper de Caicedo C., Rojas Morales C. (2006) Actividad Demostrativa en la formacion inicial del profesor de matemáticas, Universidad Pedagógica Nacional, Bogotá Colombia.
    Pinto M., Tall D. (2002) : Building fomal mathematics on visual imagery: a case study and a theory. For the Learning of Mathematics 22(1) 2-10
    Perry P. (1999) Algunos aspectos de la prueba en la clase de matemáticas. Revista EMA 5(1) 91-96.

Pickett H. C. (1938) An analysis of proofs and solutions of exercises used in plane geometry tests. New York: Teachers college, Columbia University.

Porteous K. (1990) What do children really believe? Educational Studies In Mathematics 21(6) 589-598

Prince A. A. (1998) Prove it! Mathematics Teacher. 91(8) 726-728

Py D. (1990)Reconnaissance de plan pour l'aide à la démonstration dans un tuteur intelligent de la géométrie. Thèse. Rennes : Université de Rennes 1.

Py D. (1994) Reconnaissance de plan pour la modélisation de l'élève. Le projet MENTONIEZH. Recherches en didactique des mathématiques 14(1/2) 113-138.

Py D. (1996) Aide à la démonstration en géométrie : le projet Mentoniezh.Sciences et Techniques Educatives 3(2) 227-256.

Py D., El Gass B. (1992) Expérimentation du tutoriel Mentoniezh en classe de quatrième. Petit X 30, 63-72.

Py D., Nicolas P. (1990) MENTONIEZH: A geometry ITS for figure drawing and proof setting. Artificial Intelligence in Education 1(3) 41-55.
  Py D. (2001) Environnements Interactifs d'Apprentissage et démonstration en géométrie. Habilitation. Université de Rennes 1.
    Py D. (2001) La démonstration dans les EIAO de géométrie. Barbin E., Duval R., Giorgiutti I., Houdebine J., Laborde C. (eds.) Produire et lire des textes de démonstration. Paris : Ellipse. 215-224

 

 

Py D. (2001) Le logiciel Mentoniezh. Barbin E., Duval R., Giorgiutti I., Houdebine J., Laborde C. (eds.) Produire et lire des textes de démonstration. Paris : Ellipse. 249-254

Q

Quast W. G. (1968) Geometry in the high schools of the United States: An historical analysis from 1890 to 1966. Ed. D. Dissertation, Rutgers-The State University of New Jersey. University Microfilms 68-9162. Ann Arbor, MI.

R

Radford L. (1985) Interprétation d'énoncés implicatifs et traitement logique. Thèse. Strasbourg : Université Louis Pasteur.

Radford L. (1995) La enseñanza de la demostración; aspectos teóricos y prácticos. Educación Matemática 6(3) 21-36.

    Raman M. (2003) Key Ideas: What are they and how can they help us understand how people view proof? Educational Studies in Mathematics 52(3), 319-325

Recio T. (1999) Tratamiento automático de la información geométrica. Uno, revista de Didáctica de las matemáticas 20, 63-72.

    Recio A. M., Godino J. D. (2001) Institutional and personal meanings of mathematical proof, Educational Studies in Mathematics 48 (1), pp. 83-99

Redmond C., Federici M. P., Platte D. M. (1998) Proof by contradiction and the electoral college. Mathematics Teacher. 91(8) 655-658

Reid D. A. (1998) Sharing ideas about teaching proving. Mathematics Teacher. 91(8) 704-706

    Reid D. A. (2001) Conjectures and refutations in Grade 5 Mathematics. Journal for Research in Mathematics Education 33(1) 5-29
    Reid D. A.; Robert R. (2004) Adult learners' criteria for explanations Zentralblatt für Didaktik der Mathematik 36(5) pp. 140-149
    Reiss K., Renkl A. (2002) Learning to Prove: The Idea of Heuristic Examples Zentralblatt für Didaktik der Mathematik 34 (1) pp. 29-35
    Reiss, M. K., Heinze, A., Renkl, A.and Groß, C. (2008) Reasoning and proof in geometry: effects of a learning environment based on heuristic worked-out examples ZDM The International Journal on Mathematics Education 40/3, 455-467

Retzer K. A. (1984) Proofs with visible inference schemes. School Science and Mathematics 84(5) 367-376.

Retzer K. A. (1984) Inferential logic in geometry. School Science and Mathematics 84(4) 277-284.

Reynolds J. (1967) The Development of the Concept of Proof in Grammar School Pupils. PhD Thesis. University of Nottingham.

    Richards E. (1892) Old and new methods in elementary geometry. Educational Review, 3, 31-39.
  Richard P. (2000) Diagnostic sur la structure et la qualité de preuves inadmissibles. Séminaire de Didactique des mathématiques. Grenoble : laboratoire Leibniz.
    Richard, P. R. (2004). L’inférence figurale : un pas de raisonnement discursivo-graphique. Educational Studies in Mathematics, 57, 229–263.
  Richard P. R. (2004) Raisonnement et stratégies de preuve dans l'enseignement des mathématiques Bernes: Peter Lang (Collection de la Société Suisse pour la Recherche en Education, Vol. 125)

Roberge J. J. (1970) A study of children's ability to reason with basic principles of deductive reasoning. American Educational Research Journal 7, 583-596.

Roberge J. J. (1972) Recent research on the development of children's comprehension of deductive reasoning schemes. School Science and Mathematics 72, 197-200.

Roberge J. J. (1975) Development of comprehension of logical connectives in symbolic or verbal form. Educational Studies in Mathematics 6(2) 207-212.

    Robert A. (2003) Un point de vue sur les spécificités du travail géométrique des élèves à partir de la quatrième : l'organisation des connaissances en niveaux de conceptualisation. Petit x, 63, 7-29
    Rodd M. M. (2000) On mathematical warrants: Proof does not always warrant, and a warrant may be other than proof. Mathematical Thinking and Learning 2(3) 221-244.
    Roditi E. (2004) Le théorème de l'angle inscrit au collège: analyse d'une séance d'introduction. Petit X 66, 18-48

Ross K. A. (1998) Doing and Proving: The place of Algorithms and Proof in School Mathematics American Mathematical Monthly , 252-255.

    Rossi H. (1995) When is the best proof not the best proof? CBMS Issues in Mathematics Education (American Mathematical Society). 5, 31-53.
    Rossari C. (2000) Connecteurs et relations de discours : des liens entre cognition et signification. Presses Universitaires de Nancy.
    Ruthven K. (2002) Barbin, E., Duval, R., Giorgiutti, I., Houdebine, J. and Laborde, C. (Eds.), Produire et lire des textes de démonstration, Paris: Ellipses, 2001 Educational Studies in Mathematics 51(1-2), 145-147

Ryan J. (1928) Two methods of teaching geometry: syllabus vs. textbook. Mathematics Teacher 21, 31-36

S

    Sackur C., Assude T., Maurel M., Drouhard J.-P., Paquelier Y. (2005) L'expérience de la nécessité épistémique. Recherches en didactique des mathématiques 25(1) 57-90

Sáenz-Ludlow (1998) Procesos inferenciales en el pensamiento matematicó de Miguel. Revista EMA. 4(1) 3-15.

Sanchez P. (1992) Analyse cognitive de quelques démonstrations du théorème de Pythagore. Strasbourg: IREM de Strasbourg.

Schoenfeld A. (1985) Mathematical Problem solving. Orlando : Academic Press.

Schoenfeld A. (1989) Exploration of students' mathematical beliefs and behavior. Journal of Research in Mathematics Education 20(4) 338-355.

Schoenfeld A. (1991) On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In: Voss J. F., Perkins D. N., Segal J. W. (eds.) Informal Reasoning and Education (pp. 311-343). Hillsdale, N.J.: Lawrence Erlbaum.

    Schramm R. (1988) How to develop the students' capacity for dealing with problems of proof? Zentralblatt für Didaktik des Mathematik. 88/3 104-107.

Schumann H., de Villiers M. D. (1993) Continuous variation of geometric figures: interactive theorem finding and problems in proving. Pythagoras 31, 9-20.

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.

Sekiguchi Y. (1999) Cognitive structures underlying conceptions of mathematical proof. Tsukuba Journal of Educational Studies in Mathematics 18, 45-56.

Selden J., Selden A. (1995) Unpacking the logic of mathematical statements. Educational Studies in Mathematics 29, 123-151.

    Selden A., Selden J. (2003) Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for research in mathematics education 34(1) 4-36

Senk S. (1985) How well to students write proofs ? Mathematics teacher  78(6) 448-456.

Senk S. (1989) Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education 20, 209-321.

Sémadéni Z. (1984) Action proofs in primary mathematics teaching and in teacher training. For the learning of mathematics 4(1) 32-4.

    Sfard A. (2000) Steering discourse between metaphors and rigor: using focal analysis to investigate the emergence of mathematical objects. Journal for Research in Mathematics Education 31(3) 296-327
    Sharon S. McCrone and Tami S. Martin (2004) Assessing High School Students’ Understanding of Geometric Proof Canadian Journal of Science, Mathematics & Technology Education 4 (2)

Shimizu Y. (1997) A mode of thought in J. W. A. Young's theory of the disciplinary value of the study of mathematics: as succeeded by H. P. Fawcett in "The nature of proof". Tsukuba Journal Of Educational Studies in Mathematics 16, 39-48 (en japonais)

Shimizu Y. (1998) The influence of "supposed others" in the social process of making a mathematical definition. Tsukuba Journal of Educational Studies in Mathematics Education 17, 195-204.

Shumway R. J. (1974) Negative instances in mathematical concepts acquisition : transfer effects between the concepts of commutativity and associativity. Journal of Research in Mathematics Education 5(1) 197-211.

    Shutts G. (1892) Old and new methods in geometry. Educational Review. 3, 264-266.

Shinzato T. (1995)  Student's perception of similarity among geometric proof problems. Journal of JASME: Research in Mathematics Education 1, 125-131. (in Japanese)

Silver J. A. (1998) Can computers be used to teach proof? Mathematics Teacher. 91(8) 660-663

    Simon M. A. (1996) Beyond inductive and deductive reasoning: the search for a sense of knowing. Educational Studies in Mathematics 30(2) 197-210.

Simon A. (2001) Premier pas : un outil d'apprentissage et de révélation des erreurs. Barbin E., Duval R., Giorgiutti I., Houdebine J., Laborde C. (eds.) Produire et lire des textes de démonstration. Paris : Ellipse. 241-248

    Siu, M-K. (2008) Proof as a practice of mathematical pursuit in a cultural, socio-political and intellectual context ZDM The International Journal on Mathematics Education 40/3, 355-361

Siwek H. (1973) Logique formelle et raisonnement des élèves dans l'enseignement mathématique.Educational Studies in Mathematics 5, 23-37.

Smith E. P., Henderson K. B. (1959) Proof. In: Fawcett H., Hach A., Junge C., Syer H., van Engen H., Jones P. (Eds.) The growth of mathematical ideas K-12. Twenty-fourth yearbook. (pp. 111-181). Washington, DC: NCTM.

Smith R. (1940) Three major difficulties in the learning of demonstrative geometry. Part I : Analysis of errors. Mathematics Teacher 33, 99-134.

Smith R. (1940) Three major difficulties in the learning of demonstrative geometry. Part II : Description and evaluation of methods used to remedy errors. Mathematics Teacher 33, 150-178.

    Solomon Y. (2006) Deficit or difference? The role of Students' epistemologies of mathematics in their interactions with poof, Educational Studies in Mathematics Vol 61 n. 3, pp. 373-393

Solow D. (1984) Reading, writing and doing mathematical proofs. Book 1 : Proof technics for geometry.

Soulé-Beck I. (1994) Quelques aspects linguistiques de la cohérence tectuelle dans un chapitre de manuel scolaire de géométrie. Thèse. Université de Metz.

Sowder L., Harel G. (1998) Types of students' justifications. Mathematics Teacher. 91(8) 670-675

    Sowder L., Harel G. (2003) Case Studies of Mathematics Majors' Proof Understanding, Production, and Appreciation Canadian Journal of Science, Mathematics and Technology Education 3(2)

Steen L. (1999) Twenty questions about mathematical reasoning. In Stiff L., Curcio F. (eds.) Developing mathematical reasoning in grades K-12 (pp. 270-285). Reston, VA: NCTM.

Stein M. (1984) Beweisen. Bad Salzderfurth : Verlag Franzecker.

  Stylianides, G.J., Stylianides, A.J., & Philippou, G. N. (2007). Preservice teachers’ knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education, 10(3), 145-166.
  Stylianides, A. J. (2007) Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38, 289-321.
    Stylianides, A. J. (2007) The notion of proof in the context of elementary School Mathematics Educational Studies in Mathematics Vol. 65 (1) pp. 1-20
  Stylianides, A. J., Stylianides, G. J., & Philippou, G. N. (2004). Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contexts. Educational Studies in Mathematics, 55, 133-162.
 
Stylianides, G. J. (2007). Investigating the guidance offered to teachers in curriculum materials: The case of proof in mathematics. International Journal of Science and Mathematics Education 6, 191-215.
    Stylianides G. J. (2008) An analytic framework of reasoning-and-proving (part 1) For the learning of mathematics 28/1, 9-16
    Stylianides G. J. (2008) Investigating the Guidance Offered to Teachers in Curriculum Materials: The Case of Proof in Mathematics International Journal of Science and Mathematics Education 6/1, 191-215
    Stylianides G. J., Stylianides A. J. (2008) Proof in school mathematics: insight from psychological research into students' ability for deductive reasoning. Mathematical thinking and learning. 10 (2) 103-133

Sträßer R. (1996) Students' Constructions and Proof in a Computer Environment &emdash; Problems and Potentials of a Modelling Experience. In: Laborde J.-M. (ed.) Intelligent Learning Environments: The Case of Geometry (pp.203-217). Berlin: Springer-Verlag.

    Stroup P. (1926) When is a proof not a proof. Mathematics Teacher 19, 499-505

Szombathelyi A., Szarvas T. (1998) Ideas for developing students' reasoning: a hungarian perspective. Mathematics Teacher. 91(8) 677-681

T

Tall D. (1989) The nature of Mathematical Proof. Mathematics Teaching 128, 28-32.

    Tall D. (2002) Differing modes of proof and belief in mathematics. Fou Lai Lin (ed.) 2002 International Conference on Mathematics - "Understanding proving and proving to understand". Taipei: NSC and NTNU (pp.91-107)
    Tall, D. (2006) A Theory of Mathematical Growth through Embodiment, Symbolism and Proof, Annales de didactique et de sciences cognitives, IREM de Strasburg (ed.) Vol. 11, p. 195-215
    Tall D. (2006) A Theory of Mathematical Growth through Embodiment, Symbolism and Proof, Annales de didactique et de science cognitives IREM Strasburg, Vol. 11, p. 195-215
    Tanguay D. (2002) Analyse des problèmes de géométrie et apprentissage de la preuve au secondaire Canadian Journal of Science, Mathematics and Technology Education 2(3)
    Thomas-Van Dieren F. (2001) Rédiger la synthèse d'une activité, apprendre à démontrer. Barbin E., Duval R., Giorgiutti I., Houdebine J., Laborde C. (eds.) Produire et lire des textes de démonstration. Paris : Ellipse. 161-182
    Thurston, William P. (1995): On Proof and Progress in Mathematics For the Learning of Mathematics, vol. 15 n1 p. 29-37
    Touton F. C. (1919) Solving geometric originals. Contributions to Education No 146, 1924. New York: Teachers college, Columbia University.

Tsoumpélis L. (2005) Aspects théoriques et méthodologiques dela didactique des sciences physiques. Explication et causalité dans les situations didactiques. Recherches en didactique des mathématiques 25(2) 187-246

U

Uhlig F. (2002) The Role of Proof in Comprehending and Teaching Elementary Linear Algebra Educational studies in mathematics Volume 50, Issue 3, pp. 335-346

V

Vadcard L. (1999) La validation en géométrie avec Cabri-géomètre : mesures exploratoires et mesures probatoires. Petit X 50, 5-21

Van Dormolen J. (1977) Learning to understand what giving a proof really means. Educational Studies in Mathematics 8(1) 17-34.

    Van Schalkwijk L., Bergen T., Van Roou A. (2001) Learning to prove by investigation: A promising approach in Dutch secondary education. Educational Studies in Mathematics 43(3) 293-311.

Vinner S. (1976) The Naive Concept of Definition in Mathematics. Educational Studies in Mathematics 4 (7) 413-429.

Vollrath H.-J. (1994) On the appreciation of theorems by students and teachers. In : Robitaille D. F., Wheeler D. H., Kieran C. (eds.) Selected lectures from the 7th International Congress in Mathematical Education (pp.353-365) Sainte-Foy : Les Presses de l'Université Laval.

W

    Watson J. M. (2001) Longitudinal Development of Inferential Reasoning by School Students, Educational Studies in Mathematics 47 (3)pp. 337-372
    Weber K. (2001) Student difficulty in constructing proofs: The need for strategic knowledge, Educational Studies in Mathematics 48 (1), pp. 101-119
    Weber K. (2001) Student difficulty in constructing proofs: The need for strategic knowledge, Educational Studies in Mathematics 48 (1), pp. 101-119
    Weber, K. (2002). Beyond proving and explaining: proofs that justify the use of definitions and axiomatic structures and proofs that illustrate technique. For the Learning of Mathematics, 22 (3), 14-17.
    Weber K. (2004). Traditional instruction in advanced mathematics courses: A case study of one professor's lectures and proofs in an introductory real analysis course. Journal of Mathematical Behavior, 23(2), 115-133.
    Weber K. and Alcock L. (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56, 209-234.
    Weber K. and Alcock L. (2005). Using warranted implications to understand and validate proofs. For the Learning of Mathematics, 25(1), 34-38.

Wertheimer R. (1990) The geometry proof tutor : an intelligent computer-based tutor in the classroom. Mathematics Teacher April, 308-317.

Wheeler D. (1990) Aspects of mathematical proof. Interchange 21(1) 1-5.

Williams E. (1980) An Investigation of Senior High School Student's Understanding of the Nature of Mathematical Proof. Journal for Research in Mathematics Education 11, 165-166.

Winicki-Landman G. (1998) On proofs and their perfomances as works of art. Mathematics Teacher. 91(8) 722-725

Winsløw C. (1998) A linguistic approach to the justification problem in mathematics education. For the Learning of Mathematics 18(1) 10-16.

Wittmann E. C., Müller G. (1990) When is a proof a proof ? Bulletin de la Socitété Mathématique Belge 1, 15-40

    Wood T. (1999) Creating a context for arguments in the mathematics class. Journal for Research in Mathematics Education 30(2) 171-191.
    Watson J. M., Moritz J. B. (2001), Development of reasoning associated with pictographs: Representing, interpreting, and predicting, Educational Studies in Mathematics 48 (1) pp. 47-81

Watson J. M. (2002) Inferential reasoning and the influence of cognitive conflict Educational Studies in Mathematics 51(3), 225-256

X

Y

    Yackel E., Cobb P. (1996) Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. Journal for Research in Mathematics Education 27(4) 458-477.
    Yang K-L & Lin F.-L. (2008) A model of reading comprehension of geometry proof Educational Studies in Mathematics 67/1, 59-76
    Yu Jing (2002) Understanding a proof. Fou Lai Lin (ed.) 2002 International Conference on Mathematics - "Understanding proving and proving to understand". Taipei: NSC and NTNU (pp.143-147)

Z

    Zaslavsky O., Shir K. (2005) Student's conception of a mathematical definition. Journal for research in mathematics education. 36 (4) 317-3
    Zaslavsky O. (2005) Seizing the Opportunity to Create Uncertainty in Learning Mathematics Educational Studies in Mathematics Vol. 60 n° 3 pp. 297-321
    Zazkis R., Liljedahl, P. & Chernoff E. J (2008) The role of examples in forming and refuting generalizations ZDM The International Journal on Mathematics Education 40, 131-141
    Zazkis R. & Chernoff E. J (2008) What makes a counterexample exemplary? Educational Studies in Mathematics 68/3, 195-208
    Zazkis R. & Chernoff E. J (2008) What makes a counterexample exemplary? Educational Studies in Mathematics 68/3, 195-208
    Zbiek R. M. (1992). Understanding of function, proof and mathematical modelling in the presence of mathematical computing tools: Prospective secondary school mathematics teachers and their strategies and connections. Ph D thesis. Penn State University, Graduate School. USA

Anonyme

(1972) Problèmes de la pensée logique dans l'enseignement des mathématiques. Educational Studies in Mathematics 4, 491-500.

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