Teaching and learning geometry with technology

Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future

Volumn , Issue , 2006, Pages 275-304

  Laborde, Colette ^a   Kynigos, Chronis ^b   Hollebrands, Karen ^c   Strässer, Rudolf ^d,e  

^a UNIV GRENOBLE ALPES   (France)

^b UNIVERSITY OF ATHENS   (Greece)

^c NORTH CAROLINA STATE UNIVERSITY   (United States)

^d JUSTUS LIEBIG UNIVERSITY   (Germany)

^e LULEÅ UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547781266     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (138)

1. Abelson, H., & DiSessa, A. (1981). Turtle geometry: The computer as a medium for exploring mathematics. Cambridge, MA, USA: MIT Press.
2. Arcavi, A., & Hadas, N. (2000). Computer mediated learning. An example of an approach. International Journal of Computer for Mathematical Learning, 5(1), 25-45.
3. Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7(3), 245-274.
4. Arzarello, F. (2000). Inside and outside: Spaces, times and language in proof production. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th PME International Conference, 1, 23-38.
5. Arzarello, F., Micheletti, C., Olivero, F., & Robutti, O. (1998). Dragging in Cabri and modalities of transition from conjectures to proofs in geometry. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd PME International Conference, 2, 32-39.
6. Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practices in Cabri environments. Zentralblatt für Didaktik der Mathematik, 34(3), 66-72.
7. Assude, T. (2005). Time management in the work economy of a class: A case study: Integration of Cabri in primary school mathematics teaching. Educational Studies in Mathematics, 59(1-3), 183-203.
8. Balacheff, N. (1993). Artificial intelligence and real teaching. In C. Keitel & K. Ruthven (Eds.), Learning through computers: Mathematics education and technology (pp. 131-158). Berlin, Germany: Springer Verlag.
9. Bartolini Bussi, M. G. (1998). Verbal interaction in mathematics classroom: A Vygotskian analysis. In H. Steinbring et al. (Eds.), Language and communication in mathematics classroom. (pp. 65-84). Reston, USA: NCTM.
10. Bellemain, F., & Capponi, B. (1992). Spécificité de l'organisation d'une séquence d'enseignement lors de l'utilisation de l'ordinateur. Educational Studies in Mathematics, 23(1), 59-97.
11. Berthelot, R., & Salin, M.-H. (1998). The role of pupils' spatial knowledge in the elementary teaching of geometry. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century (pp. 71-77). Dordrecht, The Netherlands: Kluwer.
12. Boychev, P. (1999). Elica [Computer program]. Sofia, Bulgaria: University of Sofia.
13. Brock, C., Cappo, M., Carmon, N., Erdös, A., Kamay, Y., Kaplan, D., et al. (2003). Geometry Inventor (v. 3.04) [Computer Program]. San Francisco, CA, USA: Riverdeep.
14. Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht, The Netherlands: Kluwer.
15. Chazan, D. (1993). High school geometry students' justifications for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24(4), 359-387.
16. Clements, D., & Battista, M. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). New York, USA: MacMillan.
17. Clements, D., & Battista, M. (1994). Computer environments for learning geometry. Journal of Educational Computing Research, 10(2), 173-197.
18. Clements, D. H., & Sarama, J. (1995). Design of a Logo environment for elementary geometry. Journal of Mathematical Behavior, 14, 381-398.
19. Clements, D., & Sarama, J. (1997). Research on Logo: A decade of progress. Computers in the Schools, 14(1-2), 9-46.
20. De Villiers, M. (1991). Pupils' needs for conviction and explanation within the context of geometry. In F. Furinghetti (Ed.), Proceedings of the 15th PME International Conference, 1, 255-262.
21. diSessa, A. (1997). Open toolsets: New ends and new means in learning mathematics and science with computers. In E. Pehkonen (Ed.), Proceedings of the 21st PME International Conference, 1, 47-62.
22. diSessa, A. (2000). Changing minds, computers, learning and literacy. Cambridge, MA, USA: MIT Press.
23. diSessa, A., & Lay, E. (1986). Boxer [Computer program]. Berkeley, CA, USA: University of Berkeley.
24. Dubinsky, E. (2000). Meaning and formalism in mathematics. International Journal of Computers for Mathematical Learning, 5, 211-240.
25. Duval, R. (1988). Pour une approche cognitive des problèmes de géométrie en termes de congruences. Annales de Didactique et de Sciences Cognitives, 1, 57-74. Strasbourg, France: IREM et Université Louis Pasteur.
26. Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century (pp. 37-52). Dordrecht, The Netherlands: Kluwer.
27. Duval, R. (2000). Basic issues for research in mathematics education. In T. Nakahara & M. Koyama (Eds.), Procedings of the 24th PME International Conference, 1, 55-69.
28. Edwards, L. D. (1988). Children's learning in a transformation geometry microworld. In A. Borbás (Ed.), Proceedings of the 12th PME International Conference, 1, 263-269.
29. Edwards, L. D. (1990). The role of microworlds in the contruction of conceptual entities. In G. Booker, P. Cobb, & T. N. Mendicuti (Eds.), Proceedings of the 14th PME International Conference, 2, 235-242.
30. Edwards, L. (1992). A comparison of children's learning in two interactive computer environments. Journal of Mathematical Behavior, 11, 73-81.
31. Edwards, L. D. (1994). Making sense of a mathematical microworld: A pilot study from a Logo project in Costa Rica. In J. P. Ponte & J. F. Matos (Eds.), Proceedings of the 18th PME International Conference, 2, 296-303.
32. Eisenberg, M. (1995). Creating software applications for children: Some thoughts about design. In A. diSessa, C. Hoyles, & R. Noss (Eds.), Computers and exploratory learning (pp. 175-196). Heidelberg, Germany: Springer Verlag.
33. Falcade, R., Laborde, C., & Mariotti, M. A. (2004). Towards a definition of function. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th PME International Conference, 2, 367-374.
34. Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24(2), 139-162.
35. Flanagan, K. (2001). High school students' understandings of geometric transformations in the context of a technological environment. Unpublished PhD dissertation, Pennsylvania State University, USA.
36. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, The Netherlands: Reidel.
37. Furinghetti, F., Morselli, F., & Paola, D. (2005). Interaction of modalities in Cabri. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th PME International Conference, 3, 9-16.
38. Gallou-Dumiel, E. (1989). Logo et symétrie centrale. In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the 13th PME International Conference, 2, 3-10.
39. Goldenberg, E. P., & Cuoco, A. (1998). What is dynamic geometry? In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 351-368). Mahwah, NJ, USA: Lawrence Erlbaum.
40. Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3(3), 195-227.
41. Hadas, N., Hershkowitz, R., & Schwarz, B. (2000). The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Educational Studies in Mathematics, 44(1-3), 127-150.
42. Hanna, G. (1998). Proof as explanation in geometry. Focus on Learning Problems in Mathematics, 20(2-3), 4-13.
43. Harvey, B. (2005). USB Logo [Computer program]. Berkeley, CA, USA: University of California at Berkeley.
44. Healy, L. (2000). Identifying and explaining geometrical relationship: Interactions with robust and soft Cabri constructions. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th PME International Conference, 1, 103-117.
45. Hilbert, D., & Cohn Vossen, S. (1952). Geometry and the imagination. New York, USA: Chelsea Publishing. (translation by P. Nemenyi of Anschauliche Geometrie. Berlin, Germany: SpringerVerlag, 1932).
46. Hillel, J., Kieran, C., & Gurtner, J. (1989). Solving structured geometric tasks on the computer: The role of feedback in generating strategies. Educational Studies in Mathematics, 20, 1-39.
47. Holland, G. (2002). GEOLOG [Computer program]. Giessen, Germany: University of Giessen.
48. Hollebrands, K. (2002). The role of a dynamic software program for geometry in high school students developing understandings of geometric transformations. In D. Mewborn (Ed.), Proceedings of the 24th PME-NA Annual Meeting, 695-706.
49. Hollebrands, K. (2003). High school students' understandings of geometric transformations in the context of a technological environment. Journal of Mathematical Behavior, 22(1), 55-72.
50. Hölzl, R. (1996). How does 'dragging' affect the learning of geometry. International Journal of Computers for Mathematical Learning, 1, 169-187.
51. Hölzl, R. (2001). Using dynamic geometry software to add contrast to geometric situations - A case study. International Journal of Computers for Mathematical Learning, 6(1), 63-86.
52. Hoyles, C. (1995). Exploratory software, exploratory cultures? In A. di Sessa, C. Hoyles, R. Noss, & L. Edwards (Eds.), Computers and exploratory learning (pp. 199-219). Berlin, Germany: Springer Verlag.
53. Hoyles, C. (1998). A culture of proving in school mathematics. In D. Tinsley & D. Johnson (Eds.), Information and communication technologies in school mathematics (pp. 169-181). London, UK: Chapman and Hall.
54. Hoyles, C., & Noss, R. (1987). Seeing what matters: Developing an understanding of the concept of parallelogram through a Logo microworld. In J. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11th PME International Conference, 2, 17-24.
55. Hoyles, C., & Noss, R. (1988). Formalising intuitive descriptions in a parallelogram microworld. In A. Borbás (Ed.), Proceedings of the 12th PME International Conference, 2, 449-456.
56. Hoyles, C., & Noss, R. (2003). Digital technologies in mathematics education In A. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second international handbook of mathematics education (1, pp. 323-350). Dordrecht, The Netherlands: Kluwer.
57. Hoyles, C., Noss, R., & Sutherland, R. (1989). A Logo-based microworld for ratio and proportion. In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the 13th PME International Conference, 2, 115-122.
58. Hoyles, C., Noss, R., & Sutherland, R. (1991). Evaluating a computer based microworld: What do pupils learn and why? In F. Furinghetti (Ed.), Proceedings of the 15th PME International Conference, 2, 197-204.
59. Hoyles, C., & Sutherland, R. (1990). Pupil collaboration and teaching interventions in the Logo environment. Journal für Mathematik-Didaktik, 4, 324-343.
60. Jackiw, N. (1991). The Geometer's Sketchpad [Computer program]. Berkeley, CA, USA: Key Curriculum Press.
61. Jahn, A.-P. (2000). New tools, new attitudes to knowledge: The case of geometric loci and transformations in dynamic geometry environment. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th PME International Conference, 1, 91-102.
62. Jahn, A.-P. (2002). "Locus" and "Trace" in Cabri-géomètre: Relationships between geometric and functional aspects in a study of transformations. Zentralblatt für Didaktik der Mathematik, 34(3), 78-84.
63. Jones, K. (1996). Coming to know about dependency within a dynamic geometry environment. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th PME International Conference, 3, 145-151.
64. Jones, K. (1998). Deductive and intuitive approaches to solving geometrical problems. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century (pp. 78-83). Dordrecht, The Netherlands: Kluwer.
65. 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, 44(1-2), 55-85.
66. Jones, K. (2002). Research on the use of dynamic geometry software: Implications for the classroom. MicroMath, 18(3).
67. Kadunz, G. (2002). Macros and modules in geometry. Zentralblatt für Didaktik der Mathematik, 34(3), 73-77.
68. Kadunz, G., Kautschitsch, H. (1993). THALES - Software zur experimentellen Geometrie [Computer program]. Stuttgart, Germany: Ernst Klett Schulbuchverlag.
69. Kafai, Y., & Resnick, M. (Eds.). (1996). Constructionism in practice. Designing, thinking and learning in a digital world. Mahwah, NJ, USA: Lawrence Erlbaum.
70. Kakihana, K., Shimizu, K., & Nohda, N. (1996). From measurement to conjecture and proof in geometry problem. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th PME International Conference, 3, 161-168.
71. Kalas, I. (2001). Imagine Logo [Computer program]. Cambridge, UK: Logotron.
72. Kieran, C. (1986). Logo and the notion of angle among fourth and sixth grade children. In C. Hoyles & L. Burton (Eds.), Proceedings of the 10th PME International Conference, 99-104.
73. Kordaki, M., & Potari, D. (2002). The effect on area measurement tools on students' strategies: The role of a computer microworld. International Journal of Computers for Mathematical Learning, 7(1), 65-100.
74. Kynigos, C. (1988). Constructing bridges from intrinsic to cartesian geometry. In A. Borbás (Ed.), Proceedings of the 12th PME International Conference, 2, 449-456.
75. Kynigos, C. (1989). Intrinsic versus Euclidean geometry: Is the distinction important to children learning with the turtle? In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the 13th PME International Conference, 2, 194-201.
76. Kynigos, C. (1991). Can children use the turtle metaphor to extend their learning to non-intrinsic geometry? In F. Furinghetti (Ed.), Proceedings of the 15th PME International Conference, 2, 269-276.
77. Kynigos, C. (2001). E-slate turtleworlds [Computer program]. Athens, Greece: Educational Technology Lab, School of Philosophy, PPP Faculty, Department of Education, University of Athens and Patra, Greece: Research Academic Computer Technology Institute.
78. Kynigos, C. (2002). Generating cultures for mathematical microworld development in a multi-organisational context. Journal of Educational Computing Research, 27(1-2), 185-211.
79. Kynigos, C. (2004). Black and white box approach to user empowerment with component computing. Interactive Learning Environments, 12(1-2), 27-71.
80. Kynigos, C., & Argyris, M. (2004). Teacher beliefs and practices formed during an innovation with computer-based exploratory mathematics in the classroom. Teachers and Teaching: Theory and Practice, 10(3), 247-273.
81. Kynigos, C., & Psycharis, G. (2003). 13 year olds' meanings around intrinsic curves with a medium for symbolic expression and dynamic manipulation. In N. Paterman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 3, 165-172.
82. Laborde, C. (1998). Relationship between the spatial and the theoretical in geometry: The role of computer dynamic representations in problem solving. In D. Tinsley & D. Johnson (Eds.), Information and communication technologies in school mathematics (pp. 183-194). London, UK: Chapman & Hall.
83. Laborde C. (2001). Integration of technology in the design of geometry tasks with Cabri-geometry. International Journal of Computers for Mathematical Learning, 6, 283-317.
84. Laborde, C. (2003). Technology used as a tool for mediating knowledge in the teaching of mathematics: The case of Cabri-geometry. In W.-C. Yang, S. C. Chu, T. de Alwis, & M. G. Lee (Eds.), Proceedings of the 8th Asian Technology Conference in Mathematics (1, pp. 23-38). Hsinchu, Taiwan ROC: Chung Hua University.
85. Laborde, J.-M. (1999). Some issues raised by the development of implemented dynamic geometry as with Cabri-geometry. In H. Brönnimann (Ed.), Proceedings of the 15th European Workshop on Computational Geometry (pp. 7-19). Sophia Antipolis, France: INRIA.
86. Laborde, J.-M., Baulac Y., & Bellemain, F. (1988). Cabri-géomètre I [Computer program]. Grenoble, France: University Joseph Fourier.
87. Laborde J.-M., & Bellemain, F. (1995) Cabri-géomètre II and Cabri-géomètre II plus [Computer programs]. Dallas, USA: Texas Instruments and Grenoble, France: Cabrilog.
88. Lagrange, J.-B. (1999). Complex calculators in the classroom: Theoretical and practical reflections on teaching pre-calculus. International Journal of Computers for Mathematical Learning, 4, 51-81.
89. Lagrange, J.-B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and math education: A multidimensional overview of recent research and innovation. In J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second international handbook of mathematics education (pp. 237-270). Dordrecht, The Netherlands: Kluwer.
90. Leron, U., & Hazzan, O. (1998). Computers and applied constructivism. In D. Tinsley & D. C. Johnson (Eds.), Information and communications technologies in school mathematics (pp. 195-203). IFIP, London, UK: Chapman and Hall.
91. Leung, A. (2003). Dynamic geometry and the theory of variation. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 3, 197-204.
92. Leung, A., & Lopez-Real, F. (2000). An analysis of students' explorations and constructions using Cabri geometry. In M. A. Clements, H. Tairab, & W. K. Yoong (Eds.), Science, mathematics and technical education in the 20th and 21st centuries (pp. 144-154). Brunei: Universiti Brunei Darussalam.
93. 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, 145-165.
94. Magina, S., & Hoyles, C. (1991). Developing a map of children's conception of angle. In F. Furinghetti (Ed.), Proceedings of the 15th PME International Conference, 2, 358-465.
95. Mariotti, M. A. (1995). Images and concepts in geometrical reasoning. In R. Sutherland & J. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 97-116). Berlin, Germany: Springer Verlag.
96. Mariotti, M. A. (2000). Introduction to proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, 44(1-2), 25-53.
97. Mariotti, M. A. (2001). Influence of technologies advances on students' mathematics learning. In L. English, M. G. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (pp. 695-723). Mahwah, NJ, USA: Lawrence Erlbaum.
98. Mariotti, M. A., & Bartolini Bussi, M. G. (1998). From drawing to construction: Teachers mediation within the Cabri environment. In A. Olivier and K. Newstead (Eds.), Proceedings of the 22nd PME International Conference, 1, 180-95.
99. Mariotti, M. A., Laborde, C., & Falcade, R., (2003). Function and graph in a DGS environment. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 3, 237-244.
100. Marrades, R., & Gutiérrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44(1-2), 87-125.
101. Mason, J. (1992). Geometric tools. Micromath, 8(3), 24-27.
102. Monaghan, J. (2004). Teachers' activities in technology-based lessons. International Journal of Computers for Mathematical Learning, 9(3), 327-357.
103. Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings. Dordrecht, The Netherlands: Kluwer.
104. Noss, R., Hoyles, C., Healy, L., & Hoelzl, R. (1994). Constructing meanings for constructing: An exploratory study with Cabri-geometry. In J. P. Ponte & J. F. Matos (Eds.), Proceedings of the 18th PME International Conference, 3, 360-367.
105. Olive, J., & Lankenau, C. (1987). The effects of Logo-based learning experiences on students' nonverbal cognitive abilities. In J. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11th PME International Conference, 2, 24-31.
106. Olivero, F. (2002). The proving process within a dynamic geometry environment. Unpublished PhD dissertation, University of Bristol, Graduate School of Education, Bristol, UK.
107. Pallascio, R. (1987). Les habiletés perspectives d'objets polyhédriques. In J. Bergeron, N. Herscovics, & K. Kieran (Eds.), Proceedings of the 11th PME International Conference, 2, 39-46.
108. Papert, S. (1980). Mindstorms. Children, computers and powerful ideas. Brighton, UK: Harvester Press.
109. Papert, S. (2002). The turtle's long slow trip: Macro-educological perspectives on microworlds. Journal of Educational Computing Research, 27(1), 7-28.
110. Parmentier, C. (1989). Angles et pixels - Quelle synergie à 9 ans? In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the 13th PME International Conference, 3, 90-97.
111. Parzysz, B. (1988). Knowing vs seeing: Problems of the plane representation of space geometry figures. Educational Studies in Mathematics, 19(1), 79-92.
112. Pratt, D., & Ainley, J. (1996). Construction of meanings for geometric construction: Two contrasting cases. International Journal of Computers for Mathematical Learning, 1(3), 293-322.
113. Pratt, D., & Davison, I. (2003). Interactive whiteboards and the construction of definitions for the kite. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 4, 31-38.
114. Resnick, M. (1995). New paradigms for computing, new paradigms for thinking. In A. di Sessa, C. Hoyles, R. Noss, & L. Edwards (Eds.), Computers and exploratory learning (pp. 31-44). Berlin, Germany: Springer Verlag.
115. Rolet, C. (1996). Dessin et figure en géométrie: Analyse et conceptions de futurs enseignants dans le contexte Cabri-géomètre. Unpublished PhD dissertation, University of Lyon 1, Lyon, France.
116. Ruthven, K., Hennessy, S., & Deaney, R. (2005). Incorporating dynamic geometry systems into secondary mathematics education: Didactical perspectives and practices of teachers. In The Association of Mathematics Teachers (Ed.), Moving on with dynamic geometry (pp. 138-158). Derby, UK: The Association of Mathematics Teachers.
117. Sacristán, A. I. (2001). Students' shifting conceptions of the infinite through computer explorations of fractals and other visual models. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th PME International Conference, 4, 129-136.
118. Sánchez, E., & Sacristán, A. I. (2003). Influential aspects of dynamic geometry activities in the construction of proofs. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 4, 111-118.
119. Sarama, J., & Clements, D. (2002). Design of microworlds in mathematics and science education. Journal of Educational Computing Research, 27(1), 1-3.
120. Scally, S. P. (1987). The effects of learning Logo on ninth grade students' understanding of geometric relations. In J. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11th PME International Conference, 2, 46-53.
121. Scher, D. (2001). Students' conceptions of geometry in a dynamic geometry software environment. Unpublished PhD dissertation, New York University, New York, USA.
122. Schwartz, J., Yerushalmy, M., & Shternberg, B. (1985). The Geometric Supposer [Computer program]. Pleasantville, NY, USA: Sunburst Communication.
123. Schwartz, J., Yerushalmy, M., & Shternberg, B. (2000). The Geometric Supposer-3 [Computer program]. Israel: The Center for Educational Technology.
124. Sereno, F. (1994). A perspective on fractals for the classroom. In J. P. Ponte & J. F. Matos (Eds.), Proceedings of the 18th PME International Conference, 4, 249-256.
125. Sherin, B. (2002). Representing geometric constructions as programs: A brief exploration. International Journal of Computers for Mathematical Learning, 7, 101-115.
126. Sinclair, K., & Moon, D. (1991). The philosophy of Lisp. Communications of the ACM, 34(9), 40-47.
127. Sinclair, M. (2003). Some implications of the results of a case study for the design of pre-constructed, dynamic geometry sketches and accompanying materials. Educational Studies in Mathematics, 52(3), 289-317.
128. Silverman, B. (1999). MicroworldsPro [Computer program]. Highgate Springs, Vermont, USA: LCSI.
129. Soury-Lavergne, S. (1998). Étayage et explication dans le préceptorat distant, le cas de TéléCabri. Unpublished PhD dissertation, University Joseph Fourier, Grenoble, France.
130. Strässer, R. (1991). Dessin et figure - Géométrie et dessin technique à l'aide de l'ordinateur (Occasional paper No. 128). Bielefeld, Germany: Universität Bielefeld, Institut für Didaktik der Mathematik.
131. Strässer, R. (1992). Didaktische Perspektiven auf Werkzeug-software im Geometrie-Unterricht der Sekundarstufe I. Zentralblatt für Didaktik der Mathematik, 24(5), 197-201.
132. Strässer, R. (1996). Students' constructions and proofs in a computer environment - Problems and potentials of a modelling experience. In J.-M. Laborde (Ed.), Intelligent learning environments: The case of geometry (pp. 203-217). Berlin, Germany: Springer Verlag.
133. Strässer, R. (2002). Research on dynamic geometry software (DGS) - An introduction. Zentralblatt für Didaktik der Mathematik, 34(3), 65.
134. Talmon, V., & Yerushalmy, M. (2004). Understanding dynamic behavior: Parent-child relations in dynamic geometry environments. Educational Studies in Mathematics, 57(1), 91-119.
135. Vadcard, L. (1999). La validation en géométrie au collège avec Cabri-géomètre: Mesures exploratoires et mesures probatoires. Petit x, 50, 5-21.
136. Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology in Education, 9(3), 77-101.
137. Wilensky, U. (1999). NetLogo [Computer program]. Evanston, IL, USA: Center for Connected Learning and Computer-Based Modeling, Northwestern University.
138. Zack, V. (1988). Say it's perfect then pray it's perfect: The early strategies of learning about Logo angle. In A. Borbás (Ed.), Proceedings of the 12th PME International Conference, 2, 657-664.