Abstract
Geometry is a school subject, but also and primarily geometry is a mathematical domain. As mathematics educators we are interested in geometry from both points of view. That is the reason why a first discussion is devoted to highlighting some characteristics of geometry as a mathematical domain.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Baulac Y., Bellemain, F. & Laborde, J.M. (1988). Cabri-géomètre, un logiciel d’aide c l‘enseignement de la géométrie, logiciel et manuel d’utilisation, Paris: Cedic-Nathan.
Colmez, F. (1984). La représentation plane en perspective cavalière des objets de l’espace, un problème de géométrie; essai d’ingénierie didactique en classe de première S. In Acte du Colloque inter IREM de Géométrie, Ed. IREM Marseille.
Eisenberg, T. & Dreyfus, T. (1991). On reluctance to visualize in mathematics. In Zimmerman, W. and Cunningham, S. (eds.) (1991) Visualization in Teaching and Learning Mathematics, Math. Ass. of America, MAA Notes, 19.
Ferrari, P.L. & Bondesan M.G. (1991). The active comparison of strategies in problem-solving: an exploration study, Proceedings of the Fifteenth PME Conference, Assisi (Italy).
Fischbein, E. (1963). Conceptele figurale, Ed. Acad. Rep. Pop. Romine.
Fischbein, E. (to appear). The theory of figural concepts, to appear in Educational Studies in Mathemetics.
Freudental H. (1973). Mathematics as an educational task, Dordrecht: Reidel.
Gaulin, C. (1985). The need for emphasizing various graphical representations of 3-dimensional shapes and relations, Proceedings of the Ninth Intern. Conf. Psychology of Mathematical Education, Utrecht, pp. 53–71.
Gonseth, F (1974). Les mathematiques et la réalité, Paris: Presses Universitaire de France.
Grize, J.B. (1964). Remarques sur la structure de la géométrie élémentaire. In: Etude d’épistémologie génétique XVIII, L’épistémologie de l’espace, Paris.
Hersckovitz, R. (1989). Visualization in geometry. Two sides of the coin, Focus on learning problems in mathematics, 111.
Hersckovitz, R.(1990). Psychological aspects of learning geometry. In Kilpatric J. Nesher P. (eds.), Mathematics and cognition, Cambridge Univ. Press.
Hershkovitz, R. (1987). The acquisition of concepts and misconcepts in basic geometry-or when ,a little learning is a dangerous thing”. In: Novak, J.D. (ed.), Proceedings of the Second International Seminar Miconceptions and Educational Strategies in Science and Mathematics, vol. 3, pp. 238–251, NY, Ithaca, Cornell Univ.
Hirabayashi, I. (1987). Some notes on geometrical terminology in mathematics education. In Geometry Working Group Report from the Xth PME Conference.
Horowitz, M.J. (1978). Image formation and cognition, New York: Appelton-Century-Crafts.
Mariotti, M.A. (1989). Mental images: some problems related to the development of solids, Actes de la 13e Conference Int. PME, Paris.
Mariotti, M.A. (1991). Age variant and invariant elements in the solution of unfolding problems. Proceedings XV PME Conference, Assisi.
Mariotti, M.A. (1992). Geometrical reasoning as a dialectic between the fígural and the conceptual aspect, Topologie structurale/Structural topology, n. 18
Mariotti, M. A. (1992) The dialectical process between figures and definition in social interaction in the classroom, Proceedings of the Second Italian-German Bilateral Symposium on Didactics of Mathematics (to appear).
Mariotti, M.A. (1992). Immagini e concetti in geometria, L’Insegnamento della Matematica e delle Scienze Integrate, 159.
Osta, I. (1988). L’ordinateur comme outil d’aide à l’enseignement. Une sequence didactique pour l’enseignement du repérage dans l’espace é l’aide de logiciels graphiques, Thèse, Université Joseph Fournier, Grenoble.
Parzysz, B. (1991). Representation of space and students conceptions at High School level, Educational Studies in Mathematics, V. 22, 575–593.
Parzysz, B.(1988). Knowing vs seeing. Problems of the plane representation of space geometry figures, Educational Studies in Mathematics, V. 19, 266–299.
Piaget, J. and Inhelder, B. (1966). L’image mentale chez l’enfant. Paris: Presses Universitaire de France. (It. trans. L’immagine mentale nel bambino. Firenze, 1974)
Piaget, J. and Inhelder, B. (1947). La representation de l‘esapace chez l’enfant. Paris: Presses Universitaire de France. (It. trans. La rappresentazione dello spazio nela bambino, Firenze, 1976)
Vinner, S. and Herschkovitz, R. (1983). On concept formation in geometry, ZDM 931, 20–25.
Vinner, S. and Cunningham, S. (eds.) (1991). Visualization in teaching and learning mathematics, MAA notes, 19.
Programmi per la scuola primaria, DPR 122. 1985.
Programmi per la scuola media, DPR 92. 1979.
Piani di studio della scuola Secondaria Superiore. (1991). Le proposte della commisione Brocca. Annali della Pubblica Istruzione. Studi e documenti, vol. 56, 59–60, Roma.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mariotti, M.A. (1995). Images and Concepts in Geometrical Reasoning. In: Sutherland, R., Mason, J. (eds) Exploiting Mental Imagery with Computers in Mathematics Education. NATO ASI Series, vol 138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57771-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-57771-0_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-63350-8
Online ISBN: 978-3-642-57771-0
eBook Packages: Springer Book Archive