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PageCollaborative Group for Research in Mathematics Education
This project concerned students' conceptions of proof, particularly in undergraduate mathematics.
Topics we worked on included:
We have provided some examples of hypertext (structured) proofs:
We also worked with Dr Elfrida Ralha, Department of Mathematics, University of Minho, Portugal
Publications
Jones, K. (2000), The Student Experience of Mathematical Proof at University
Level. International Journal of Mathematical Education, 31(1),
53-60. ISSN: 0020-739X
Click here for full article in pdf format.
Jones, K. (1998), Mathematics Graduates' Conceptions of Mathematical Proof.
In: D Holton (Ed), On the Teaching and Learning of Mathematics at University
Level: pre-proceedings of the ICMI study. Singapore: National Institute of
Education, 161-164.
Click here for
full article in pdf format.
Jones, K. (1997), Student Teachers' Conceptions of Mathematical Proof.
Mathematics Education Review, 9, 21-32.
Click here for
full article in pdf format.
Davis, G. and Jones, K. (1996), The Psychology of Experimental Mathematics.
In: L. Puig and A. Gutiérrez (Eds), Proceedings of the 20th Conference of
the International Group for the Psychology of Mathematics Education.
University of Valencia, Spain, Volume 1, 149 [extended abstract].
Click here for
full article in pdf format.
Conference Presentations
ICMI study 11 on the Teaching and Learning of Mathematics at University Level, Singapore, 1998
20th Conference of the International Group for the Psychology of Mathematics Education (PME20), University of Valencia, Spain, 1996.
Related CRME Projects
The
School-University Transition in Mathematics
The project was supported by a British Council 'Treaty of Windsor' Grant.
The
Metacognitive Behaviour of Mathematics Undergraduates when Solving Calculus
Problems
This project was supported by ESRC research award R00429524142
Psychology of Experimental Mathematics
Indicative Bibliography
(also see the online proof newsletter)
Ag Almouloud S. (1992) Aide logicielle à la résolution de problèmes avec preuve : des séquences didactiques pour l'enseignement de la démonstration. Recherches en didactique des mathématiques. 12(2/3) 271-318.
Agassi J. (1980) On Mathematics Education : the Lakatosian Revolution. For the Learning of Mathematics, 1, 27-31.
Alibert D., Thomas M. (1991) Research on Mathematical Proof. In: Tall D. (ed.) Advanced Mathematical Thinking. (pp. 215-230). Dordrecht: The Netherlands: Kluwer Academic Publishers.
Anderson J. A. (1994) The Answer is not the Solution - Inequalities and Proof in Undergraduate Mathematics. International Journal of Mathematics Education in Science and Technology, 25, 655-663.
Anderson J. R. (1983) Acquisition of Proof Skills in Geometry. In : Carbonnel J. G., Michalski R., Mitchell T. (eds.) Machine Learrning: An Artificial Intelligence Approach ( pp.191-219). Palo Alto, CA : Tioga.
Antibi A. (1988) Etude sur l'enseignement de méthodes de démonstration. Enseignement de la notion de limite : reflexions, propositions. Thèse d'état. Toulouse : Université Paul Sabatier.
Antibi A. (1993) Qualche considerzione sulla dimostrazione. L'Educazione Matematica, 3(4) 135-140.
Arsac G. (1987) L'origine de la démonstration : essai d'épistémologie didactique. Recherches en didactique des mathématiques, 8(3) 267-312.
Arsac G. (1988) Les recherches actuelles sur l'apprentissage de la démonstration et les phénomènes de validation en France. Recherches en didactique des mathématiques. 9(3) 247-280.
Arsac G., Chapiron G., Colonna A., Germain G., Guichard Y., Mante M. (1992) Initiation au raisonnement déductif au collège. Lyon : Presses Universitaires de Lyon.
Arsac G., Mantes M. (1997) Situations d'initiation au raisonnement déductif. Educational Studies in Mathematics 33, 21-43.
Avital S., Hansen R.T. (1976) Mathematical Induction in the Classroom. Educational Studies in Mathematics 7, 399-411.
Baguena O. (1992) Le raisonnement des élèves dans la relation didactique. Thèse. Bordeaux: Université de Nordeaux 1.
Balacheff N. (1978) Une étude à l'aide de graphes, de démonstrations mathématiques formulées par des élèves. Educational Studies in Mathematics. 11(1) 91-111.
Balacheff N. (1982) Preuve et démonstration en mathématiques au collège. Recherches en didactique des mathématiques. 3(3) 261-304.
Balacheff N. (1987) Processus de preuves et situations de validation. Educational Studies in Mathematics. 18(2) 147-176.
Balacheff N. (1987) Cognitive versus situational analysis of problem-solving behaviors. For the learning of mathematics 6(3) 10-12
Balacheff N. (1988) Etude des processus de preuve chez des élèves de Collège. Thèse. Grenoble : Université Joseph Fourier.
Balacheff N. (1988) Aspects of proof in pupils' practice of school mathematics. In: Pimm D. (ed.) Mathematics, Teachers and Children (pp.316-230). London : Hodder and Stoughton.
Balacheff N. (1991) Treatment of refutations : aspects of the complexity of a constructivist approach of mathematics learning. In : Von Glasersfeld E. (ed.) Radical constructivism in Mathematics Education (pp.89-110). Dordrecht : Kluwer Academic Publisher.
Balacheff N. (1991) Benefits and limits of social interaction: The case of teaching mathematical proof. In : Bishop A., Mellin-Olsen S., Van Dormolen J. (eds.) Mathematical knowledge : Its growth through teaching (pp. 175-192). Dordrecht : Kluwer Academic Publisher.
Balacheff N., Laborde C. (1985) Langage symbolique et preuves dans l'enseignement mathématique : une approche socio-cognitive. In : Mugny G. (ed.) Psychologie sociale du développement cognitif (pp.203-224). Berne : Ed. P. Lang.
Barbeau E. (1990) Three faces of proof. Interchange 21(1) 24-27.
Barbin E. (1988) La démonstration mathématique : significations épistémologiques et questions didactiques. Bulletin APMEP 366, 591-620.
Barbin E. (1994) Quelles conceptions épistémologiques de la démonstration pour quels apprentissages ? Repères IREM 12, 93-113.
Barbin E. (1995) La démonstration aura-t-elle encore une place dans l'enseignement des mathématiques ? Bulletin APMEP 397, 368-385.
Barnard T. (1995) The Impact of "Meaning" on Students' Ability to Negate Statements. PME XIX (vol.2, pp.3-10). Recife, Brazil.
Bartolini Bussi M., Pergola M. (1996) History in the Mathematics Classroom: Linkages and Kinematic Geometry. In: Jahnke H. N., Knoche N., Otte M. (hrsg.) Geschichte der Mathematik in der Lehre. Goettingen: Vandenhoeck & Ruprecht.
Barwise J., Etchemendy J. (1991) Visual Information and Valid reasoning. In: Zimmermann W., Cunningham S. (eds.) Visualization in Teaching and Learning Mathematics (Notes Series, Vol. 19, pp. 9-24). Providence, RI: MAA.
Bkouche R. (1996) De la démonstration en géométrie. In: Gagatsis A., Rogers L. (eds) Didactics and History of Mathematics (pp.269-316). Thessalonikis, Université Aristote.
Bkouche R. (1996) La place du numérique dans la construction de la géométrie. In: Gagatsis A., Rogers L. (eds) Didactics and History of Mathematics (pp.317-352). Thessalonikis, Université Aristote.
Blum W., Kirsch A. (1991) Preformal proving: examples and reflections. Educational Studies in Mathematics 22(2) 183-203.
Boero P., Chiappini G., Garuti R., Sibilla A. (1995) Towards Statements and Proof in Elementary Arithmetics. PME XIX (vol.3, pp.129-136). Recife, Brazil.
Chayé J. (1971) Apprentissage de la déduction.Educational Studies in Mathematics 4(2)
Chazan D. (1993) High School geometry Student's Justification for their Views of Empirical Evidence and Mathematical Proof. Educational studies in Mathematics 24(4) 359-387.
Chouraqui E., Inghilterra C. (1996) A Model of Case-BAsed Reasoning for Solving Problems of Geometry ina Tutoring System. In: Laborde J.-M. (ed.) Intelligent Learning Environments: The Case of Geometry (pp.1-16). Berlin: Springer-Verlag.
Coe R., Ruthven K. (1994) Proof Practice and Constructs. British Educational Research Journal 20, 41-53.
Coppé S. (1997) Etude des processus de vérification mis en oeuvre par les élèves de première S. Bulletin de l'APMEP 411, 471-484.
Coppé S., Arsac G., Guichard Y. (1996) Vérifications en devoir surveillé. Repères 22, 13-32.
Daconto E. (1996) Sul come intendere la dimostrazione. La matematica e la sua didattica 2, 153-165
Davis Ph. J. (1993) Visual Theorems.Educational studies in Mathematics 24(4) 333-344.
de Villiers M. D. (1990) The role and function of proof in mathematics. Pythagoras 24, 17-24.
de Villiers M. D. (1991) Pupils' need for conviction and explanation within the context of geometry. Pythagoras 26,18-27.
de Villiers M. D. (1995) An alternative introduction to proof in dynamic geometry. Micromath 11(1) 14-19.
Dhombres J. (1993) Is one Proof Enough? Travels With a Mathematician of the Baroque Period. Educational studies in Mathematics 24(4) 401-419.
Dreyfus T., Hadas N. (1996) Proof as answer to the question why. Zentralblatt für Didaktik der Mathematik 28 (1) 1-5.
Duval R. (1991) Structure du raisonnement déductif et apprentissage de la démonstration. Educational Studies in Mathematics, 22(3) 233-261.
Duval R. (1992) Argumenter, démontrer, expliquer : continuité ou rupture cognitive. Petit X 31, 37-61.
Duval R., Egret M.-A. (1993) Introduction à la démonstration et apprentissage du raisonnement déductif. Repère-IREM 12, 114-140.
Epp S. (1994) The role of proof in problem solving. In: Schoenfeld A. (ed.) Mathematical thinking and problem solving (pp.257-269). Hilsdale, NJ: Erlbaum.
Epstein, D. et al (1997) Proof by contradiction. MATHEDU Archives.
Fawcett H. P. (1938). The Nature of Proof. NCTM Year Book. New York : Columbia University Teachers College.
Fishbein E. (1982) Intuition and Proof. For the Learning of Mathematics, 3(2) 9-18 et 24.
Galbraith P. L. (1981) Aspects of proving: A clinical investigation of process. Educational Studies in Mathematics, 12, 1-28.
Gaud D., Guichard J.-P. (1984) Apprentissage de la démonstration. Petit x 4, 5-25.
Gras R., Giorgiutti I. (1996) Computer Aided Proofs in School Geometry. In: Laborde J.-M. (ed.) Intelligent Learning Environments: The Case of Geometry, (pp.63-81). Berlin: Springer-Verlag.
Guin D. (1996) A Cognitive Analysis of Geometry Proof Focused on Intelligent Tutoring Systems. In: Laborde J.-M. (ed.) Intelligent Learning Environments: The Case of Geometry, (pp.82-93). Berlin: Springer-Verlag.
Hanna G. (1995) Review of M. Detlefsen (ed.) Proof and Knowledge in Mathematics. Educational Studies in Mathematics, 28(1) 87-90.
Hanna G. (1996) The role of proof in mathematics education. Joetsu Journal of Mathematics Education, 11, 155-168. (In Japanese)
Hanna G. (1990) Some pedagogical aspects of proof. Interchange, 21(1) 6-13.
Hanna G. (1991) Mathematical proof. In: Tall D. (ed.) Advanced Mathematical Thinking. Kluwer, Dordrecht.
Hanna G. (1989) More than formal proof. For the Learning of Mathematics, 9(1), 20-25.
Hanna G., Jahnke N. (1996) Proof and Proving. In: Bishop A. et al (eds.) (pp.877-908). International Handbook of Mathematics Education. Dordrecht: Kluwer Academic Publishers.
Hanna, G. & Jahnke (Eds.) (1993) Aspects of proof. Educational Studies in Mathematics, 24(4).
Hanna G., Jahnke N. (1993) Proof and Application. Educational studies in Mathematics, 24(4) 421-438.
Hazzan O., Leron U. (1996) Students' use and misuse of mathematical theorems: The case of Lagrange's theorem. For the Learing of Mathematics, 16(1) 23-26.
Hersh R. (1993) Proving is Convincing and Explaining. Educational Studies in Mathematics, 24(4) 389-399.
Jones, K. (2000), The Student Experience of Mathematical Proof at University Level. International Journal of Mathematical Education, 31(1), 53-60.
Jones, K. (1997), Student-Teachers' Conceptions of Mathematical Proof. Mathematics Education Review, 9, 23 - 32
Keskessa B. (1994) Preuve et plan de signification : une hypothèse. Recherches en Didactique des Mathématiques. 14(3) 357-392
Kleiner I., Movshovitz-Hadar N. (1997) Proof: A many-splendored thing. The mathematical intelligencer, 19(3) 16-26
Lamport, L. (1995) How to write a proof. American Math Monthly, 102(7), 600-608
Leron, U. (1983) Structuring Mathematical Proofs.Amer. Math. Monthly, 90, 174-185.
Leron, U. (1985) Heuristic Presentations: The role of structuring. For the Learning of Mathematics, 5(3), 7-13.
Leron U. (1985) A direct approach to indirect proofs. Educational Studies in Mathematics 16(3) 321-325.
Lovett, M.C. & Anderson, J.R. (1994) Effects of solving related proofs on memory and transfer in geometry problem solving. J of Experimental Psychology: Learning, Memory, and Cognition, 20(2), 366-378
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. (in press) Young Children Inventing Method of Proof: The gang of four. In: Steffe L., Nesher P., Cobb P., Goldin G., Greer B. (eds.) Theories of Mathematical Learning. Hillsdale, NJ: Erlbaum.
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.
Marafioti Garnica A. V. (1996) fascination for the technical, decline of the critical: a study on the rigorous proof in the training of mathematics teachers. In: Gagatsis A., Rogers L. (eds) Didactics and History of Mathematics (pp.161-192). Thessalonikis, Université Aristote.
Mariotti M. A. (1997) Justifying and Proving: Figural and Conceptual Aspects. in: Hejny M., Novotna J. (eds.) Proceedings of the European Conference on Mathematical Education (pp.21-26). Prague: Prometheus Publishing House.
Mariotti M. A. (1997) Justifying and Proving: Figural and Conceptual Aspects. (revised and extended version).
Martin W. G., Harel G. (1989) Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education 20(1) 41-51.
Mesquita A. L. (1989) Sur une situation d'éveil à la déduction en géométrie. Educational Studies in Mathematics 20, 55-57.
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.
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.
Otte M. (1994) Mathematical knowledge and the problem of proof. Educational Studies in Mathematics 26(4) 299-321.
Otte M. (1990) Intuition and formalism in mathematical proof. Interchange 21(1) 59-64.
Reid D. (1995) Proving to Explain. PME XIX (vol.3, pp.137-144). Recife, Brazil.
South, N. et al (1997) Irrationality of sqrt(2). MATHEDU Archives.
Thurston, W.P. (1994) On proof and progress in mathematics. Bull Amer Math Soc, 30(2) 161-177
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