:

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24

. .

. . .

. .

. .

. . .

. .

. . .

2 :

41.1

51.2

71.3

81.4

11 :

122.1

132.1.1

152.1.2

162.1.3

192.1.4

222.1.5

242.1.6

262.2

272.2.1

282.2.2

292.2.3

342.2.4

372.2.5

392.2.6

432.3

442.3.1

452.3.2

482.3.3

542.4

552.4.1

592.4.2

632.4.3

652.4.4

692.4.5

702.5

712.5.1

742.5.2

772.5.3

792.5.4

872.5.5

902.6

93 :

943.1

953.1.1

963.1.2

973.1.3

983.2

993.2.1

1013.2.2

1023.3

1053.3.1

1083.3.2

1113.4

1123.4.1

1133.4.2

1153.5

117 :

1194.1

1204.1.1

1304.1.2

1394.2

1404.2.1

1424.2.2 :

1444.2.3 :

1464.2.4 :

1484.2.5 :

1514.3

1524.3.1

1534.3.2

1544.3.3

1554.3.4

157 :

1615.1

1635.1.1 :

1675.1.2 :

1695.1.3 :

1715.1.4 :

1735.1.5 :

1755.2

1765.2.1

1775.2.2

1815.2.3

1825.3

1835.3.1

1845.3.2

1855.3.3

1865.4

192

120 4:

121 4:

122 4:

123 4:

124 4:

125 4:

126 4:

127 4:

128 4:

129 4:

133 4:

134 4: ANCOVA

135 4: ANCOVA

136 4: ANCOVA

137 4: ANCOVA

138 4: ANCOVA

13 2:

25 2:

33 2:

39 2:

40 2:

83 2:

88 2:

105 3:

108 3:

109 3:

110 3:

114 3:

120 4:

122 4:

124 4:

126 4:

128 4:

130 4:

130 4:

131 4: MANCOVA

132 4: MANCOVA

133 4:

134 4: ANOCVA

135 4: ANOCVA

136 4: ANOCVA

137 4: ANOCVA

138 4: ANOCVA

155 4:

156 4:

177 5:

179 5 (1(1)

180 5: (2(1)

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62. .

63. .

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68. .

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79.

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81.

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85.

86.

87.

88.

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92.

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95.

96.

97.

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100. ( VHGT)

101. ( )

102.

103.

104.

105.

106.

(1986) 3 1 2 . . .

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108.

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112.

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115. .

116. .

117. .

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119.

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125.

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129.

130.

131.

132.

133.

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134. .

135. .

136. .

137. .

138. .

2.5

( 1996 1997). . . .

(1990) . 1998 . . (1998) .

. . . :

139.

140.

141.

142.

143. .

2.5.1

. . . . . .

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(1998) . (1999) .

( 1925) . .

(1998) . . .

(1995) . . . . (1999) . .

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(1997) . ( ) : . ( 1999) (2006) .

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2.5.2

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.

1920 1930 . . . () () () . :

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162. .

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165.

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169.

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40 . . . 5 . .

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Aikalay, M. (1993). The use of computers for independent exploration in precalculus: Effect on attitudes. Journal of Computers in Mathematics and Science Teaching

Arzarello, F. (1998), Micheletti, C., Olivero, F., Robutti, O. Paola D. & Gallino, G.. Dragging in Cabri and modalities of transition from conjectures to proofs in geometry

Balacheff, N. & Kaput, J. (1996). Computer-based lerning environments in mathematics. Interriatiaiiai handbook of mathmatics edircatiatr (pp. 469-50 1 ). Dordrecht: Kluwer Academic Publishers.

Balacheff, N. (1998). Some questions on mathematical learning environrnents., Proceedings of lhe 21st Cotferetrce of the Iwrtwriotml Group for the Psychology of Mathematics Education

Battista, M. T. (1990). Spatial visualization and gender differences in high school geometry.Journal for Research in Mathematics Educator.

Baylor, Terry William (2002), Analysis of the interplay of factors that influenced how students used a dynamic geometry computer program to solve certain mensuration problems

Bennett, D. (1998). Exploring geometry with The Geometers SketchPad. Key Curriculum Press.

Brousseau. G. ( 1997). theory of didactical situations in mathematics: Didactique des mathematiqes, 1970-1990 (N. Balacheff, M. Cooper, R. Sutherland. & V. Warfield. Eds. & Trans). Dordrecht: Kluwer Academic Publishers.

Clements, D. H, & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and leaming: A project of the National Council of Teachers of Mathematics (pp. 420-464). New York: MacMillan Publishing Co.

Cohen, R, & Geva, E. (1987). The effects on young chiidren of learning turtle geornetry programming through the use of Logo Microworlds. Toronto: Ontario Institute for Studies in Education.

Cuoco, A. (1996), Goldenberg, E. P., & Mark, J.. Habits of mind: Anorganizing principle for mathematics curricula. Journal of Mathematical Behavior, 15, 375-402.

De Villiers M. (1997). The Role of Proof in Investigative, Computer-based Geometry: Some personal reflections..

Dev, P. C. (1998). Intrinsic motivation and the student with learning disability. Journal of Research and Development in Education, 31(2), 98-108.

Dreyfus, T. (1991). Didactic design of computer-based learning environments.

Dreyfus, T. (1994). Imagery and reasoning in mathematics and mathematics education. In D. F. Robitaille, D. H. Wheeler, & C. Kieran (Eds.), Selected lectures from the 7th International Conference on Mathematics Education (pp. 107-122). Sainte-Foy, Quebec: Les Presses de lUniversit Laval.

Finzer, W. F., & Bennett, D. (1995). From drawing to construction with The Geometers SketchPad. Mathematics Teacher, 88, 428-431. quoted from Scher, D. (2002) Students Conceptions of Geometry in a Dynamic Geometry Software Environment, New York University

Fuys, D., Geddes, D., & Tischler, R. (1988). The Van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education, Monograph Number 3. Reston, VA: National Council of Teachers of Mathematics.

Gay, D. (1998). Geometry by discovery. New York, NY: John Wiley & Sons, Inc.

Gillis. John. M (2005) An investigation of student conjections in static and dynamic geometry environments Auburn university

Goldenberg, E. P. (1991). The difference between graphing software and educational graphing software. In W. Zimmerman & S. Cunningham (Eds.), Visualization in teaching and learning mathematics (pp. 77-86). Washington, DC: Mathematical Association of America.

Goldenberg, E. P. (1998).Designing learning environments for developing understanding of geometry and space (pp. 351-367). Mahwah, NJ: Lawrence Erlbaum Associates.

Gomes, Alex Sandro, Vergnaud, Gerard (2004), On the Learning of geometric concepts using Dynamic Geometry Software

Hadas, N., & Hershkowitz, R (1999). The roIe of uncertainty in constnicting and proving in computerized environments. In O. Zasiavsky (Ed-), Proceedings of the 23rdPME Conference (Vol, 3. pp. 57-64).

Halat, Erdogan, (2003) Performance, motivation and gender with two different instructional approaches in geometry, the florida state university college of education

Hanna. G. (1998). Proof as explanation in geometry. In M. Sharma. J. Schmittau. & L. ScheI1 (Eds.). Focus on Learning Problems in Mathematics. 20). 4-13

Hodanbosi, Carol Lea, (2001) A comparison of the effects of using a dynamic geometry software program and construction tools on learner achievement

Hoffer, A. (1981). Geometry is more than proof. Mathematics Teacher, 74, 11-18.qouted in Jaguthsing Dindyal (2007), The Need for an Inclusive Framework for Students Thinking in School Geometry

Hoffer, A. (1983). Van Hiele-based research. In R. Lesh & M. Landau (Eds.), Acquisition of mathemarics concepts and processes (pp. 205-2 19). New York: Academic Press.

Hoyles, C., & Noss. R (1994). Dynamic geometry environments: What's the point? Mathematics Teacher, 8 7(9), 7 1 6-7 17.

Jackiw, N. (1994). Dynamics of a point on a line and interesting triangle behavior. [On-line]. Available: http://forum.swarthmore.edu/ epigone/geometrysoftware-dynamic.

Jones, E & Nimoo. (1995). Emergent curriculum. Washington, D.C. : NAEYC

Katherine L. Dix (1999) ,The Application of Computer Technology in the Teaching of Junior High School Geometry Elschenbroich, H. J. (1997) Dynamic Geometry Programs: Death of Proving

Laborde, C. (1993). The computer as part of the learning environment: The case of geometry. In C. Keitel & K. Ruthen (Eds.), Learning from computers: Mathematics education and technology (pp. 48-67). Germany: Springer-Verlag.

Laborde, C. & Laborde, J. M. (1995). What about a learning environment where Euclidean concepts are manipulated with a mouse? In A. A. diSessa, C. Hoyles, & R. Noss (Eds.), Computers and exploratory learning (pp. 241-262). Germany: Springer-Verlag.

Laborde, C. (1998). Visual phenomena in the teaching/learning of geometry in a computer-based environment. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century (pp. 113-121). The Netherlands: Kluwer Academic Publishers.

Liu L, Cummings R.,(2001) A learning model that simulates geometric thinking through use of PCLogo and Geometer's SketchPad, Towson university

Mavrikis M. P. (2001) Towards More Intelligent and Educational Dynamic Geometry Environments School of Artificial Intelligence Division of Informatics University of Edinburgh

Melczarek, Robert Jan, (1996), The effects of problem-solving activities using dynamic geometry computer software on readiness for self-directed learning

Memam S. B. (1998). Qualitative research and case study application in education. San Francisco, CA: Jossey-Bass Publishers.

Middleton, J. A. (1995). A study of intrinsic motivation in the mathematics classroom: A personal constructs approach. Journal for Research in Mathematics Education, 26(3), 254-279.

Mofeed Abu-Mosa (2007), Using GSP in Discovering a New Theory

Moss, Laura Jean (2000). The use of dynamic geometry software as a cognitive tool

Moyer, Todd O (2003), An investigation of The Geometer's Sketchpad and van Hiele levels

Nordstrom, Kirsti, Ph. D. Student teachers and proof student, University of Stockholm, Sweden

Olive, J. (2000). Implications of using dynamic geometry technology for teaching and learning. Paper presented at the Conference on Teaching and Learning Problems in Geometry, May 6-9, 2000, Fundao, Portugal. [On-line]. Available: http://jwilson.coe.uga.edu/olive/Portugal/ Portugal_paper.html.

Papert, S. (1980). Mindstorms: Children. computers, power ideas. New York: Basic Books. Inc.

Patricia M. (2001) Supporting Student Efforts to Learn with Understanding: An Investigation of the Use of JavaSketchpad Sketches in the Secondary Geometry Classroom Department of CurriculumTeaching and Lcaming Ontario Institutc for Studies in Education of the University of Toronto

Pegg, J., & Davey, G. (1998). Interpreting student understanding in geometry: A synthesis of two models. In R. Lehrer & D. Chazan (Eds.), Desigiing leartiing awironments for developing understanding of geometry and space (pp. 109-136). Mahwah, NJ: Lawrence Erlbaum Associates.

Pirie, S., & Kieren, T. (1994). Growth in mathernatical understanding: How can we characterize it and how can we represent it? Education study in Mathematics, 26, 1 65- 1 90.

Quaresma, Pedro (2006), Integrating Dynamic Geometry Software, Deduction Systems, and Theorem Repositories

Rita Nagy-Kondor R.N. (2004) Dynamic geometry systems in teaching geometry University of Debrecen

Scher D. (2002) Students Conceptions of Geometry in a Dynamic Geometry Software Environment New York University

Schoenfeld. A. H. (1989). Problem solvin in context(s). In R. 1. Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving, volume 3 (pp. 83-9 1). Reston VA: National Council of Teachers of Mathematics.

Stevens. James p. (2007), Intermediate statistics, Lawrence Erlbaum Associates

Subramanian, Lalitha (2005), An investigation of high school geometry students' proving and logical thinking abilities and the impact of dynamic geometry software on student performance

Towers, J. (1999). In what way do teachers'interventions interact with and occasion the grawth of students' mathematical understanding. University of British Columbia.

Usiskin, Z. (1982). Van Hiele Levels and Achievement in Secondary School Geometry. (Final report of the Cognitive Development and Achievement in Secondary, School Geometry Project.) Chicago: University of Chicago. (ERIC Document ED220288).

Van Hiele, p (1986). Structure and insight: A theory of mathematics education. FL academic Press.

Wentzel, K. R. (1997). Students motivation in middle school: The role of perceived pedagogical caring. Journal of Educational Psychology, 89(3), 411-419.

Whiteley, Walter, (2002) Teaching To See Like a Mathematician, Department of Mathematics and Statistics, York University, Toronto, Canada.

Yerushalmy, M., & Chazan, D. (1993). Overcoming visual obstacles with the aid of the Supposer. In J.L. Schwartz, M. Yerushalmy, & B. Wilson (Eds.), The Geometric Supposer: What is it a case of? (pp. 25-56). Hillsdale, NJ: Lawrence Erlbaum Associates.

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