Saper vedere in matematica alla luce della ricerca in didattica. Visualizzare in geometria come problema didattico

 Access to full text

 Full (PDF)

 Full (DjVu)

1. ALEXANDROV, A.D. (1994), Geometry as an element of culture, in Selected lectures from the 7th International Congress on Mathematical Education: Québec, 17-23 August 1992, Presses de l'Université Laval. 
2. ARCAVI, A., & HADAS, N. (2000), Computer mediated learning: an example of an approach, International Journal of Computers for Mathematical learning, 5(1), 2000, 25-45. 
3. ARZARELLO, F., OLIVERO, F., PAOLA, D. & ROBUTTI, O. (2002), A cognitive analysis of dragging practises in Cabri environments, Zentralblatt für Didaktik der Mathematik, 43, n. 3, 66-72. 
4. AUDIBERT, G. (1986), L'enseignement de la géométrie de l'espace, Bullettin APMEP, n. 355, 501-526. 
5. BISHOP, A. (1979), Visualizing and mathematics in a pre-technological culture, Educational Studies in Mathematics, 10, 135-146. 
6. BISHOP, A. (1983), Space and geometry, in Lesh, R., Landau, M. (Eds.) Acquisition of Mathematics concept and processes, New York: Academic Press, 176-203. MR740369
7. BISHOP, A. (1989), Review of research on mathematics education, Focus on learning problems in mathematics, 11.1, 7-15. MR1187045
8. BOTTAZZINI, U. (2001), I geometri italiani e i Grundlagen der Geometrie di Hilbert, Bollettino dell'Unione Matematica Italiana, s. 8, 4-B, 545-570. MR1859422
9. CLEMENTS, D.H., BATTISTA, M.T. (1992), Geometry and spatial reasoning, in Grouws, D.A. (Ed.) Handbook of reasearch on mathematics teaching and learning, New York: Macmillan Pub. Co. MR111591
10. CLEMENTS, D.H., SARAMA, J., YELLAND, N.J. & GLASS, B. (2008), Learning and teaching geometry with computers in the elementary and middle school, in M.K. Heid & G. Blum (Eds.), Research on Technology and the Teaching and Learning of Mathematics: Research syntheses. vol. 1, IAP, 109-154. 
11. CURRIE, P., PEGG, J. (1998), Investigating students understanding of the relationships among quadrilaterals, in C. Kanes, M. Goos and E. Warren (Eds.), Teaching Mathematics in New Times, Proceedings of the Annual Conference of the Mathematics Education Research Group of Australia, 1, 177-184. 
12. DE VILLIERS, M. (1994), The role and function of a hierarchical classification of quadrilaterals, For the Learning of Mathematics, 14(1), 11-18. 
13. DENIS, M. (1991), Image & Cognition, Harvester Wheatsheaf (Trad. inglese di Denis, M. Image et cognition, Paris : Presses Universitaires de France, 1989), Ney York: Harvester-Weatcheaf. 
14. DUVAL, R. (2006), A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics, Educational Studies in Mathematics, 61 (1-2), 103-131. 
15. EISENBERG, T., DREYFUS, T. (1991), On reluctance to visualize in mathematics, in Zimmermann, W. & Cunnigham, S. (Eds.), Visualization in teaching and learning mathematics, MAA Notes, N. 19, 25-38. 
16. EREZ, M., YERUSHALMY, M. (2006), ``If you can turn a rectangle into a square, you can turn a square into a rectangle'': young students' experience the dragging tool, International Journal of Computers for Mathematical Learning, 11(3), 271-299. 
17. FINKE, R.A. (1989), Principles of Mental Imagery, Cambridge: The MIT Press (MA). 
18. FISCHBEIN, E. (1993), The theory of figural concepts, Educational Studies24 (2), 139-162. 
19. FREUDENTAL, H. (1973), Mathematics as an educational task, Dodrecht: Reidel. MR462822
20. FUJITA, T., JONES, K. (2007), Learners' understanding of the definitions and hierarchical classification of quadrilaterals: towards a theoretical framing, Research in Mathematics Education, 9 (1-2), 3-20. 
21. GUTIÉRREZ, A. (1996), Visualization in 3-dimensional geometry: In search of a framework, in Proceedings of PME, 18.1, 3-20. 
22. HADAMARD, J. (1954), The psychology of invention in the mathematical field, New York: Dover. Zbl0056.00101MR11665
23. HEALY, L., HOYLES, C. (1996), Seeing, doing and expressing: An evaluation of task sequences for supporting algebraic thinking, in Proceedings of PME, 18.3, 3-67. 
24. HERSCKOVITZ, R. (1989), Visualization in geometry. Two sides of the coin, Focus on learning problems in mathematics, 11, n. 1, 61-76. 
25. HOELZ, R. (1996), How does ``dragging'' affect the learning of geometry, International Journal of Computer for Mathematical Learning, 1.2, 169-87. 
26. HOLLEBRANDS, K., LABORDE, C., & STRAESSER, R. (2007), The learning of geometry with technology at the secondary level, in Research on technology in the learning and teaching of mathematics: Syntheses and perspectives, Greenwich, CT:Information Age Publishing, 155-205. 
27. HOUDEMENT, C., KUZNIAK, A. (1999), Un exemple de cadre conceptuel pour l'étude de l'enseignement de la géométrie en formation des maîtres, Educational Studies in Mathematics, 40 (3), 283-312. 
28. JACKIW, N. (2001), The Geometers Sketchpad (version 4.0) [Computer software], Emeryville. 
29. KRUTETSKII, V.A. (1976), The Psychology of Mathematical Abilities in Schoolchildren, Chicago: University of Chicago Press. 
30. KUZNIAK, A. (2013) Teaching and Learning Geometry and Beyond, in CERME 8 Proceedings, 33-49. 
31. LABORDE, C. (1988), L'enseignement de la géométrie en tant que terrain d'exploration de phénomène didactiques, Recherche en Didactique des Mathématiques, 9, n. 3, 337-364. 
32. LABORDE, C. (2000), Dynamic geometry environments as a source of rich learning contexts for the complex activity of proving, Educational Studies in Mathematics, 44 (1-2), 151-161. 
33. LABORDE, C. (2005), Robust and Soft Constructions, Proceedings of the 10th Asian Technology Conference in Mathematics, Korea, National University of Education, 22-35. 
34. LABORDE, J.M., STRAESSER, R. (1990), Cabri-Géomètre: A microworld of geometry for guided discovery learning, Zentralblatt für Didaktik der Mathematik, 22 (5), 171-177. 
35. LEUNG, A., BACCAGLINI-FRANK, A., MARIOTTI, M.A. (2013), Discernment of invariants in dynamic geometry environments, Educational Studies in Mathematics, 84.3, 439-460. 
36. LOPEZ-REAL, F., LEUNG, A. (2006), Dragging as a conceptual tool in dynamic geometry, International Journal of Mathematical Education in Science and Technology, 37 (6), 665-679. 
37. MARIOTTI, M.A. (1992), Immagini e concetti in geometria, L'Insegnamento della Matematica e delle Scienze Integrate, 15 (9), 863-885. 
38. MARIOTTI, M.A. (2005), La Geometria in classe, Bologna: Pitagora Editrice, 2005 
39. MARIOTTI, M.A., FISCHBEIN, E., (1997), Defining in classroom activities, Educational Studies in Mathematics, 34, 219-248. 
40. MARUCCI, F.S. (1995), Le immagini mentali: teorie e processi, Roma: La Nuova Italia Scientifica. 
41. MASSIRONI, M. (1995), Il ``fisico'' e il ``fenomenico'' nelle immagini mentali, in F.S. Marucci, Le immagini mentali, Roma: NIS, 45-78. 
42. MOATES, D.R., SCHUMACHER, G.M. (1983), Psicologia dei processi cognitivi, Bologna: Il Mulino (Trad. da: An Introduction to cognitive psychology, Belmont, 1980). 
43. MONAGHAN, F. (2000), What difference does it make? Children views of the difference between some quadrilaterals, Educational Studies in Mathematics, 42(2), 179-196. 
44. NEISSER, U. (1981), Conoscenza e realtà, Bologna: Il Mulino (Trad. da: Cognition and reality: Principles and implications of cognitive psychology. New York: WH Freeman/Times Books/Henry Holt & Co., 1976). 
45. PARZYSZ, B. (1988), Knowing vs seeing. Problems of the plane representation of space geometry figures, Educational Studies in Mathematics, 19, 266-299. 
46. PARZYSZ, B. (1991), Representation of space and students' conceptions at High School level, Educational Studies in Mathematics, 22, 575-593. 
47. PIAGET, J., INHELDER, B. (1947), La représentation de l'espace chez l'enfant, Paris : Presses Universitaire de France. 
48. POINCARÉ, H. (1902), La science et l'hypothèse, Paris : Flammarion. 
49. PÓLYA, G. (1967), Come risolvere i problemi di Matematica, Milano: Feltrinelli. (Trad. da: How to solve it, Princeton (New Jersey): Princeton Univ. Press, 1945). MR2183670
50. PRESMEG, N. C. (1986), Visualization in high school mathematics, For the Learning of Mathematics, 6 (3), 42-46. 
51. PRESMEG, N.C. (1997a), A semiotic framework for linking cultural practice and classroom mathematics, in J. Dossey, J. Swafford, M. Parmantie and A. Dossey (Eds.), Proceedings of the 19th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, vol. 1, ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Columbus, Ohio, 151-156. 
52. PRESMEG, N.C. (1997b), Generalization using imagery in mathematics, in L.D. English (Ed.), Mathematical reasoning: Analogies, metaphors and images, Mahwah, NJ, USA: Lawrence Erlbaum, 299-312. MR1730463
53. PRESMEG, N.C. (2006), Research on visualization in learning and teaching mathematics, in Handbook of research on the psychology of mathematics education, 205-235. 
54. RADFORD, L. (2006), Tre tradizioni semiotiche: Saussure, Peirce e Vygotskij, Rassegna, 29, 34-39. 
55. RUTHVEN, K., HENNESSY, S., & DEANEY, R. (2008), Constructions of dynamic geometry: A study of the interpretative flexibility of educational software in classroom practice, Computers & Education, 51(1), 297-317. 
56. STRAESSER, R. (2001), Cabri-géomètre: does dynamic geometry software (DGS) change geometry and its teaching and learning?, International Journal of Computers for Mathematical Learning, 6, 319-333. 
57. VINNER, S., HERSHKOWITZ, R. (1983), On concept formation in geometry, Zentralblatt für Didaktik der Mathematik, 83 (1), 20-25. 
58. VINNER, S. (1991), The role of definitions in the teaching and learning of mathematics, in D.O. Tall (Ed.) Advanced Mathematical Thinking, Dordrecht: Kluwer Academic Publishers, 65-81. MR1145739DOI10.1007/0-306-47203-1