La lettre de la Preuve


ISSN 1292-8763

Printemps 2003



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  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
  Knuth E. J. (2002) Secondary school mathematics teachers' conceptions of proof. Journal for research in mathematics education 33(5) 379-405
  Knuth, E. J. (2002), Teachers' conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education 5, 61-88.
  Hewitt D. (2002) La arbitrario y lo necessario: educación de la consciencia. Revista EMA 7(3) 310-343
  Samper C., Leguizamón, Camargo L. (2002) La construcción de conceptos: une actividad importante para desarollar razonamiento en geometría. Revista EMA 7(3) 293-309
  Leung A., Lopez-Real F. (2002) Theorem, Justification and acquisition in dynamic geometry: a case of proof by contradiction. International Journal of Computers for Mathematical Learning 7(2) 145-165


Observation and design in mathematical proof

Willi Dörfler

Institut für Mathematik, Universität Klagenfurt, Austria

Empirical and perceptive observation becomes a decisive part of mathematical reasoning, of devising and understanding proofs and mathematical arguments. Mathematical reasoning in this view is not so much the handling of abstract ideas in one's mind but the observation of the effects of one's manipulations of diagrams. The mathematical ideas rather reside in the invention of diagrams and of their fruitful manipulations, transformations, compositions.
From diagrammatic reasoning derives also the absolute reliability and security of mathematics, its so-called logical necessity. This differentiates observation of diagrams also from empirical observation in the natural sciences.
Finally, it should be emphasized that diagrammatic reasoning is very much different from algorithmic calculations. Though it is rule based it needs creativity and inventiveness like composing music.

To

Argumentation and proof

Group 4 to the CERME 3 conference

Vom Hofe R., Knipping C.,
Mariotti M. A., Pedemonte B

During CERME 3 Conference the topics proposed in the Working Group 4 "Argumentation and Proof", were the following:

1) Forms and uses of logical and mathematical reasoning from a didactical point of view. This topic was about logical, historical and epistemological aspects, related to the nature of mathematical argumentation and proof (Papers concerning this topic: V. Durand Guerrier, B. Pedemonte, D. A. Reid, O. Yevdokimov)
2) Argumentation and proof in class - comparing different classroom contexts. This topic concerned different classroom contexts of student construction of proof and arguments (Papers concerning this topic: N. Douek, C. Knipping, A. Scimone)
3) Students explanations, proof competence and experiences with proofs. This topic dealed with cognitive and epistemological aspects, concerning the processes of production of conjectures and construction of proofs (Papers concerning this topic: A. Heinze & K. Reiss, D. Küchemann & C. Hoyles, C. Misailidou & J. Williams, K. Nordstroem)
4) Empirical thinking and epistemological obstacles in argumentation and proof. This topic was about mathematical aspects of reality-related thinking, empirical reasoning, and epistemological obstacles for student's arguing and proving (Papers concerning this topic: J. P. van Bendegem, W. Blum, R. vom Hofe).

The full-text versions of these papers are given below (PDF):

Blum, W. : On the role of "grundvorstellungen" for reality-related proofs.
Reid, . A. : Forms and uses of abduction.
Douek, N. : From oral towritten texts in grade I and the approach to argumentation: the role of social interaction and task context.
Durand-Guerrier, V. : Logic and mathematical reasoning from a didactical point of view
Heinze, A. & Reiss, K. : Reasoning and proof: methodological knowledge as a component of proof competence.
Knipping, C. : Argumentation structures in classroom proving situations.
Küchemann, D. & Hoyles, C. : The quality of students' explanations on a non-standard geometry item.
Misailidou, C. & Williams J. : Children's arguments in discussion of a "difficult" ratio problem: the role of a pictorial representation.
Nordstroem, k. : Swedish university entrants' experiences about and attitudes to proof and proving.
Pedemonte, B. : What kind of proof can be constructed following an abductive argumentation?
Scimone, A. : An educational experimentation on Goldbach's conjecture.
van Bendegem, J. P. : Proofs and arguments - The special case of mathematics.
vom Hofe R. : Epistemological problems with the limit concept - a case study on communication and argumentation within a computer-based learning environment.
Yevdokimov, O. : The place and significance of the problems for proof in learning mathematics.

The Teaching of Proof

D. Loewenberg Ball, C. Hoyles,
H. Niels Jahnke (chair), N. Movshovitz-Hadar

Paper presented at the last International Congress of Mathematicians in Beijing

This panel draws on research of the teaching of mathematical proof, conducted in five countries at different levels of schooling. With a shared view of proof as essential to the teaching and learning of mathematics, the authors present results of studies that explore the challenges for teachers in helping students learn to reason in disciplined ways about mathematical claims.

This paper was presented at the last International Congress of Mathematicians in Beijing
The reference is the following: LI Tsatsien (ed.), Proceedings of the International Congress of Mathematicians, Beijing 2002, August 20-28, Vol. III: Invited Lectures, 907 - 920.

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Math Forum Internet News

Universita di Pisa

Editeur : Maria-Alessandra Mariotti
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La lettre de la Preuve


ISSN 1292-8763