@incollection{,
	
					
					
					CDD410C948EFB09AC642063FD431E4EF
				,
	author={{StavroulaPatsiomitou} and {University of Loannina}},
	journal={{Global Journal of Computer Science and Technology}},
	journal={{GJCST}}0975-41720975-435010.34257/gjcst,
	address={Cambridge, United States},
	publisher={Global Journals Organisation}141142
}

@incollection{b0,
	
	
		,
	title={{The functions of multiple representations}}
		,
	author={{
			SAinsworth
		}}
	
	
		,
	journal={{Computers & Education}}
		
			33
			
			,
	year={1999}
		
	

}

@incollection{b1,
	
	
		,
	title={{DeFT: A conceptual framework for learning with multiple representations}}
		,
	author={{
			SEAinsworth
		}}
	
	
		,
	journal={{Learning and Instruction}}
		
			16
			3
			
			,
	year={2006}
		
	

}

@book{b2,
	
	
		,
	title={{The effect of using the geometer's sketchpad (GSP) on Jordanian students' understanding of geometrical concepts}}
		,
	author={{
			FAlmeqdadi
		}}
		
			,
	year={2000}
		
		
			Jordon: Yarmouk University
		
	

}

@incollection{b3,
	
	
		,
	title={{Mathematical Discussion and Perspective Drawing in Primary School}}
		,
	author={{
			BartoliniBussi
		} and {
			MG
		}}
		
	
	
		,
	journal={{Educational Studies in Mathematics}}
		
			31
			
			,
	year={1996}
		
	

}

@incollection{b4,
	
	
		,
	title={{The development of geometric and spatial thinking}}
		,
	author={{
			MTBattista
		}}
	
	
		,
	booktitle={{Second Handbook of Research on Mathematics Teaching and Learning}}
				,
	editor={
			FLester
		}
		
			,
	publisher={NCTM}
			,
	year={2007}
			
		
	

}

@book{b5,
	
	
		,
	title={{}}
		,
	author={{
			VAReston
		}}
		
		
			National Council of Teachers of Mathematics
		
	

}

@incollection{b6,
	
	
		,
	title={{Conceptualizations and issues related to learning progressions, learning trajectories, and levels of sophistication}}
		,
	author={{
			MTBattista
		}}
		
	
	
		,
	journal={{The Mathematics Enthusiast}}
		
			8
			
			,
	year={2011}
		
	

}

@book{b7,
	
	
		,
	author={{
			HBauersfeld
		}}
		,
	title={{Integrating Theories for Mathematics Education. For the Learning of Mathematics}}
				
			,
	year={1992}
			12
			
		
	

}

@incollection{b8,
	
	
		,
	title={{The act of discovery}}
		,
	author={{
			JSBruner
		}}
	
	
		,
	journal={{Harvard Educational Review}}
		
			31
			
			,
	year={1961}
		
	

}

@book{b9,
	
	
		,
	title={{Toward a theory of instruction}}
		,
	author={{
			JSBruner
		}}
		
			,
	year={1966}
			,
	publisher={Belkapp Press}
			,
	address={Cambridge, Mass}
		
	

}

@book{b10,
	
	
		,
	author={{
			JSBruner
		}}
		,
	title={{Actual Minds, Possible Worlds}}
				Cambridge, Mass
		
			,
	publisher={Harvard University Press}
			,
	year={1986}
		
	

}

@book{b11,
	
	
		,
	title={{The real world and mathematics}}
		,
	author={{
			HBurkhardt
		}}
		
			,
	year={1981. 1986}
			,
	publisher={Harvard University Press}
			,
	address={Glasgow, UK: Blackie Cambridge, Mass}
		
	

}

@incollection{b12,
	
	
		,
	title={{Using knowledge of children's mathematics thinking in classroom teaching: An experimental study}}
		,
	author={{
			TPCarpenter
		} and {
			EFennema
		} and {
			PLPeterson
		} and {
			CChiang
		} and {
			MLoef
		}}
		
		
		
		
	
	
		,
	journal={{American Educational Research Journal}}
		
			26
			4
			
			,
	year={1989}
		
	

}

@book{b13,
	
	
		,
	title={{Children's mathematics: Cognitively Guided Instruction}}
		,
	author={{
			TPCarpenter
		} and {
			EFennema
		} and {
			MFranke
		} and {
			LLevi
		} and {
			SBEmpson
		}}
		
		
		
		
		
			,
	year={1999}
			,
	publisher={Heinemann}
			,
	address={Portsmouth, NH}
		
	

}

@book{b14,
	
	
		,
	author={{
			JMChoppin
		}}
		,
	title={{Spiral through recursion. Mathematics Teacher}}
				
			,
	year={1994}
			87
			
		
	

}

@book{b15,
	
	
		,
	title={{Research into practise: Constructivist learning and teaching. Arithmetic Teacher}}
		,
	author={{
			DHClement
		} and {
			MTBattista
		}}
		
		
			,
	year={1990}
			38
			
		
	

}

@book{b16,
	
	
		,
	title={{The emergence of mathematical meaning: Interaction in classroom cultures}}
		,
	editor={Cobb, P., & Bauersfeld, H.}
		
			,
	year={1995}
			,
	publisher={Erlbaum}
			,
	address={Hillsdale, NJ}
		
	

}

@incollection{b17,
	
	
		,
	title={{A constructivist alternative to the representational view of mind in mathematics education}}
		,
	author={{
			PCobb
		} and {
			EYackel
		} and {
			TWood
		}}
		
		
	
	
		,
	journal={{Journal for Research in Mathematics Education}}
		
			23
			1
			
			,
	year={1992}
		
	

}

@book{b18,
	
	
		,
	title={{}}
		,
	author={{
			ColumbiaCollege
		} and {
			University
		}}
		
		
		
	

}

@book{b19,
	
	
		,
	author={{
			AFCoxford
		} and {
			ZPUsiskin
		}}
		
		,
	title={{Geometry: A Transformation Approach}}
				
			,
	publisher={Laidlaw Brothers, Publishers}
			,
	year={1975}
		
	

}

@incollection{b20,
	
	
		,
	title={{Connecting mathematics problem solving to the real world}}
		,
	author={{
			EDe Corte
		} and {
			LVerschaffel
		} and {
			BGreer
		}}
		
		
	
	
		,
	booktitle={{Proceedings of the International Conference on Mathematics Education into the 21st Century: Mathematics for living}}
				the International Conference on Mathematics Education into the 21st Century: Mathematics for livingAmman, Jordan
		
			,
	year={2000}
			
		
		
			The National Center for Human Resource Development
		
	

}

@incollection{b21,
	
	
		,
	title={{From artifacts to instruments: A theoretical framework behind the orchestra metaphor}}
		,
	author={{
			PDrijvers
		} and {
			LTrouche
		}}
		
		
	
	
		,
	booktitle={{Research on technology and the teaching and learning of mathematics: Cases and perspectives}}
				,
	editor={
			GW KBlume & M
			Heid
		}
		
			,
	year={2008}
			2
			
		
	

}

@incollection{b22,
	
	
		,
	title={{Uses of ICT tools for CSCL: how do students make as their's own the designed environment?}}
		,
	author={{
			FDocq
		} and {
			ADaele
		}}
		
		
	
	
		,
	booktitle={{Proceedings of the First European Conference on Computer-Supported Collaborative Learning}}
				the First European Conference on Computer-Supported Collaborative LearningMaastricht, Netherlands
		
			,
	year={2001}
			
		
	

}

@incollection{b23,
	
	
		,
	title={{An exploration of the use of an Open Source software called Moodle to support a social constructionist epistemology of teaching and learning within Internet-based communities of reflective inquiry}}
		,
	author={{
			MDougiamas
		}}
		
	
	
		,
	journal={{Science and Mathematics Education Centre}}
		
		
			Curtin University of Technology
		
	
	,
	note={PhD thesis}

}

@book{b24,
	
	
		,
	title={{Sémiosis et pensée humaine}}
		,
	author={{
			RDuval
		}}
		
			,
	year={1995}
			,
	publisher={Peter Lang}
			,
	address={Berne}
		
	

}

@book{b25,
	
	
		,
	title={{Taking science to school: Learning and teaching science in grades K-8}}
		,
	author={{
			ADuschl
		} and {
			HSchweingruber
		} and {
			AShouse
		}}
		
		
		
			,
	year={2007}
			,
	publisher={National Academies Press}
			,
	address={Washington, DC}
		
	

}

@incollection{b26,
	
	
		,
	title={{The role and uses of technologies for the teaching of algebra and calculus: Ideas discussed at PME over the last 30 years}}
		,
	author={{
			FFerrara
		} and {
			DPratt
		} and {
			ORobutti
		}}
		
		
		
	
	
		,
	booktitle={{Handbook of research on the psychology of mathematics education: Past, present and future}}
				,
	editor={
			AGutierrez
			& PBoero
		}
		Rotterdam, The Netherlands; The Netherlands
		
			,
	publisher={Sense Fractovia}
			,
	year={2006. 1973}
			
		
	
	,
	note={Mathematics as an Educational Task. Dordrecht: Reidel}

}

@incollection{b27,
	
	
		,
	title={{Didactical phenomenology of mathematical structures}}
		,
	author={{
			HFreudenthal
		}}
	
	
		,
	booktitle={{Revisiting Mathematics Education: China Lectures}}
				,
	editor={
			D
		}
		Dordrecht, The Netherlands; Dordrecht
		
			,
	publisher={Kluwer Academic Publishers}
			,
	year={1983. 1991}
			595
		
	

}

@incollection{b28,
	
	
		,
	title={{Achievement results for second and third graders using the Standards-based curriculum}}
		,
	author={{
			KCFuson
		} and {
			WMCarroll
		} and {
			JVDrueck
		}}
		
		
	
	
		,
	journal={{Everyday Mathematics. Journal for Research in Mathematics Education}}
		
			31
			
			,
	year={2000}
		
	

}

@book{b29,
	
	
		,
	title={{}}
		,
	author={{
			DFuys
		} and {
			DGeddes
		} and {
			RTischler
		}}
		
		
		
			,
	year={1984}
		
	

}

@book{b30,
	
	
		,
	title={{English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele. Brooklyn: Brooklyn College. (ERIC Document Reproduction Service No. ED 287 697)}}
				
	

}

@incollection{b31,
	
	
		,
	title={{The Van Hiele model of thinking in geometry among adolescents}}
		,
	author={{
			DFuys
		} and {
			DGeddes
		} and {
			RTischler
		}}
		
		
	
	
		,
	journal={{Journal for Research in Mathematics Education : Monograph Number}}
		
			3
			,
	year={1988}
		
	

}

@incollection{b32,
	
	
		,
	title={{Descriptions and conflicts in dynamic geometry}}
		,
	author={{
			VGiraldo
		} and {
			EBelfort
		} and {
			LMCarvalho
		}}
		
		
	
	
		,
	booktitle={{Proceedings of the 28th PME International Conference}}
				,
	editor={
			MJ BHeines & A
			Fuglestad
		}
		the 28th PME International Conference
		
			,
	year={2004}
			2
			
		
	

}

@incollection{b33,
	
	
		,
	title={{Students' conceptions of congruency through the use of dynamic geometry software}}
		,
	author={{
			EVGlasersfeld
		} and {
			GGonzález
		} and {
			PHerbst
		}}
		
		
	
	
		,
	journal={{International Journal of Computers for Mathematical Learning}}
		
			14
			2
			
			,
	year={1995. 2009}
			,
	publisher={Falmer Press}
		
	
	,
	note={Radical constructivism: A way of knowing and learning}

}

@incollection{b34,
	
	
		,
	title={{Principles, Art, and Craft in Curriculum Design: The Case of Connected Geometry}}
		,
	author={{
			PGoldenberg
		}}
	
	
		,
	journal={{International Journal of Computers for Mathematical Learning}}
		
			4
			,
	year={1999}
			,
	publisher={Kluwer}
		
	

}

@incollection{b35,
	
	
		,
	title={{Reston: National Council of Teachers of Mathematics. collaborative zones of proximal development in small group problem solving}}
		,
	author={{
			GGoldin
		} and {
			Kilpatrick
		} and {
			WMartin
		} and {
			DSchifter
		}}
		
		
		
	
	
		,
	booktitle={{& National Council of Teachers of Mathematics}}
				
			,
	year={2003}
			17
			
		
	
	,
	note={A research companion to Principles and standards for school mathematics}

}

@incollection{b36,
	
	
		,
	title={{Perspectives on technology mediated learning in secondary school mathematics classrooms}}
		,
	author={{
			MGoos
		} and {
			PGalbraith
		} and {
			PRenshaw
		} and {
			VGeiger
		}}
		
		
		
	
	
		,
	journal={{Journal of Mathematical Behavior}}
		
			22
			
			,
	year={2003}
		
	

}

@incollection{b37,
	
	
		,
	title={{A dynamic approach to quadrilateral definitions}}
		,
	author={{
			RGovender
		} and {
			MDe Villiers
		}}
		
	
	
		,
	journal={{Pythagoras}}
		
			58
			
			,
	year={2004}
		
	

}

@book{b38,
	
	
		,
	title={{Constructive Evaluations of Definitions in a Sketchpad Context. Paper presented at the Association for Mathematics Education of South Africa National conference}}
		,
	author={{
			RGovender
		} and {
			MDe Villiers
		}}
		
		
		
			,
	year={2002. July 2002}
			,
	address={Durban}
		
		
			University of Natal
		
	

}

@book{b39,
	
	
		,
	title={{Creating Opportunities for Students to Reinvent Mathematics}}
		,
	author={{
			KP EGravemeijer
		}}
		
		
			,
	year={2004. July 4-11}
			,
	address={Kopenhagen, Denmark}
		
	
	,
	note={Paper presented at ICME 10}

}

@incollection{b40,
	
	
		,
	title={{On the assessment of the Van Hiele levels of reasoning}}
		,
	author={{
			AGutierrez
		} and {
			AJaime
		}}
		
		
	
	
		,
	journal={{Focus on Learning Problems in Mathematics}}
		
			20
			2/3
			
			,
	year={1998}
		
	

}

@incollection{b41,
	
	
		,
	title={{The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments}}
		,
	author={{
			NHadas
		} and {
			RHershkowitz
		} and {
			BBSchwarz
		}}
		
		
	
	
		,
	journal={{Educational Studies in Mathematics}}
		
			44
			1/2
			
			,
	year={2000}
		
	

}

@incollection{b42,
	
	
		,
	title={{Identifying the organization of writing processes}}
		,
	author={{
			JRHayes
		} and {
			LSFlower
		}}
		
	
	
		,
	booktitle={{Cognitive processes in writing}}
				,
	editor={
			LW RGregg & E
			Sternberg
		}
		Hillsdale NJ
		
			,
	publisher={Erlbaum}
			,
	year={1980}
		
	

}

@incollection{b43,
	
	
		,
	title={{Psychological aspects of learning geometry}}
		,
	author={{
			RHershkovitz
		}}
	
	
		,
	booktitle={{Mathematics and Cognition}}
				,
	editor={
			PNesher
			JKilpatrick
		}
		Cambridge
		
			,
	publisher={Cambridge University Press}
			,
	year={1990}
		
	

}

@book{b44,
	
	
		,
	author={{
			AHoffer
		}}
		,
	title={{Geometry is more than proof. Mathematics Teacher}}
				
			,
	year={1981}
			74
			
		
	

}

@incollection{b45,
	
	
		,
	title={{The role of a dynamic software program for geometry in the strategies high school mathematics students employ}}
		,
	author={{
			KHollebrands
		}}
	
	
		,
	journal={{Journal for Research in Mathematics Education}}
		
			38
			2
			
			,
	year={2007}
		
	

}

@incollection{b46,
	
	
		,
	title={{Using dynamic geometry software to teach secondary school geometry: Implications from research}}
		,
	author={{
			KFHollebrands
		} and {
			RCSmith
		}}
		
	
	
		,
	booktitle={{T}}
				
			,
	year={2009}
		
	

}

@incollection{b47,
	
	
		,
	title={{Understanding Geometry for a Changing World}}
		,
	author={{
			Craine
		}}
	
	
		,
	booktitle={{Yearbook of the NCTM}}
				
			,
	year={2009}
		
	

}

@book{b48,
	
	
		,
	title={{Reston: VA: National Council of Teachers of Mathematics}}
		,
	author={{
			Tbd)
		}}
		
	

}

@book{b49,
	
	
		,
	title={{The Geometer's Sketchpad}}
		,
	author={{
			NJackiw
		}}
		
			,
	year={1991}
		
	

}

@book{b50,
	
	
		,
	title={{}}
		,
	author={{
			CABerkeley
		}}
		
			,
	publisher={Key Curriculum Press}
		
	

}

@book{b51,
	
	
		,
	title={{Mathematics and the Aesthetic: New Approaches to an Ancient Affinity. Mechanism and Magic in the Psychology of Dynamic Geometry}}
		,
	author={{
			NJackiw
		}}
		
			,
	year={2006}
			,
	publisher={Springer Verlag}
			,
	address={Heidelberg}
		
	

}

@book{b52,
	
	
		,
	title={{Iteration and Dynamic Geometry: Beyond Common Fractals with The Geometer's Sketchpad NCTM Philadelphia Session 142}}
		,
	author={{
			NJackiw
		} and {
			NSinclair
		}}
		
		
			,
	year={2004}
		
	

}

@incollection{b53,
	
	
		,
	title={{Inquiry as a pervasive pedagogic process in mathematics education development}}
		,
	author={{
			BJaworski
		}}
		
	
	
		,
	booktitle={{Proceedings of the Third Conference of the European Society for Research in Mathematics Education}}
				the Third Conference of the European Society for Research in Mathematics EducationBellaria, Italy
		
			,
	year={2003}
		
	

}

@book{b54,
	
	
		,
	author={{
			PNJohnson-Laird
		}}
		,
	title={{Mental Models: Towards a Cognitive Science of Language, Inference, and Consciousness}}
				Cambridge; Cambridge, MA
		
			,
	publisher={Harvard University Press}
			,
	year={1983}
		
	

}

@incollection{b55,
	
	
		,
	title={{Image -metaphordiagram}}
		,
	author={{
			GKadunz
		} and {
			RSträßer
		}}
		
	
	
		,
	booktitle={{visualisation in learning mathematics Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education}}
				
			,
	year={2004}
			4
			
		
	

}

@book{b56,
	
	
		,
	title={{Critique of Pure Reason}}
		,
	author={{
			IKant
		}}
		,
	editor={Norman Kemp Smith}
		
			,
	year={1929}
			,
	publisher={Palgrave}
			,
	address={Basingstoke: Hants}
		
	

}

@incollection{b57,
	
	
		,
	title={{Notations and representations as mediators of constructive processes}}
		,
	author={{
			JKaput
		}}
	
	
		,
	booktitle={{Radical Constructivism in Mathematics Education}}
				,
	editor={
			EGlasersfeld
		}
		Netherlands
		
			,
	publisher={Kluwer Academic Publishers}
			,
	year={1991}
			
		
	

}

@incollection{b58,
	
	
		,
	title={{Representations, inscriptions, descriptions and learning: A kaleidoscope of windows}}
		,
	author={{
			JKaput
		}}
	
	
		,
	journal={{Journal of Mathematical Behavior}}
		
			17
			2
			
			,
	year={1999}
		
	

}

@incollection{b59,
	
	
		,
	title={{Technology and Mathematics Education}}
		,
	author={{
			JJKaput
		}}
	
	
		,
	booktitle={{Handbook of research on mathematics teaching and learning}}
				,
	editor={
			DAGrouws
		}
		New York
		
			,
	publisher={Macmillan}
			,
	year={1992}
			
		
	

}

@book{b60,
	
	
		,
	title={{Mathematics in Western Culture}}
		,
	author={{
			MKline
		}}
		
			,
	year={1990}
			,
	address={Penguin, London}
		
	

}

@incollection{b61,
	
	
		,
	title={{Using Learning Progressions to Inform the Design of Coherent Science Curriculum Materials}}
		,
	author={{
			JKrajcik
		} and {
			NShin
		} and {
			SYStevens
		} and {
			HShort
		}}
		
		
		
		
	
	
		,
	booktitle={{Paper presented at the Annual Meeting of the American Education Research Association}}
				San Diego, CA
		
			,
	year={2009}
		
	

}

@incollection{b62,
	
	
		,
	title={{Using Learning Progressions to Inform the Design of Coherent Science Curriculum Materials}}
		,
	author={{
			JKrajcik
		} and {
			NShin
		} and {
			SYStevens
		} and {
			HShort
		}}
		
		
		
	
	
		,
	booktitle={{Paper presented at the Annual Meeting of the American Education Research Association}}
				San Diego, CA
		
			,
	year={2009}
		
	

}

@incollection{b63,
	
	
		,
	title={{From construction to proof: explanations in dynamic geometry environment}}
		,
	author={{
			Leung
		} and {
			COr
		}}
		
	
	
		,
	booktitle={{Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education}}
				,
	editor={
			JHWoo
			HCLew
			KSPark
			DYSeo
		}
		the 31st Conference of the International Group for the Psychology of Mathematics EducationSeoul
		
			,
	publisher={PME}
			,
	year={2007}
			3
			
		
	

}

@book{b64,
	
	
		,
	title={{Mathematical, cognitive and didactic elements of the multiplicative conceptual field investigated within a Rasch assessment and measurement framework. Doctoral dissertation. University of Cape Town}}
		,
	author={{
			MCLong
		}}
		
		
			,
	year={2011. 2011}
		
	
	,
	note={The_mulitplcative_conceptual_field_investi gated_within_a_Rasch_measurement_framework_.P DF}

}

@incollection{b65,
	
	
		,
	title={{Introduction to proof: The mediation of a dynamic software environment}}
		,
	author={{
			M.-AMariotti
		}}
	
	
		,
	journal={{Educational Studies in Mathematics}}
		
			44
			1-3
			
			,
	year={2000}
		
	

}

@incollection{b66,
	
	
		,
	title={{BENOÎT MANDELBROT}}
		,
	author={{
			JuanMartinez
		}}
	
	
		,
	journal={{Third.Apex.to.fractovia}}
		
	

}

@book{b67,
	
	
		,
	title={{Facilitating whole-class discussion in secondary mathematics classrooms}}
		,
	author={{
			RHMcgraw
		}}
		
		
			,
	year={2002. 2003}
			02
			19
			,
	address={Bloomington, IN.}
		
		
			Indiana University
		
	
	,
	note={Unpublished doctoral dissertation}

}

@incollection{b68,
	
	
		,
	title={{On conceptual obstacles linked with external representation in geometry}}
		,
	author={{
			AMesquita
		}}
	
	
		,
	journal={{Journal of Mathematical Behavior}}
		
			17
			2
			
			,
	year={1998}
		
	

}

@incollection{b69,
	
	
		,
	title={{Providing the Motivation to Prove in a Dynamic Geometry Environment}}
		,
	author={{
			CMogetta
		} and {
			FOlivero
		} and {
			KJones
		}}
		
		
	
	
		,
	booktitle={{Proc. of the British Society for Research into Learning Mathematics}}
				of the British Society for Research into Learning MathematicsSt Martin's University College, Lancaster
		
			,
	year={1999. 1999}
			
		
	

}

@book{b70,
	
	
		,
	title={{National Science Education Standards}}
		
			,
	year={1996}
			,
	publisher={National Academy Press}
			,
	address={Washington, D.C}
		
		
			National Research Council
		
	

}

@incollection{b71,
	
	
		,
	title={{Knowing what students know: The science and design of educational assessment}}
	
	
		,
	booktitle={{Board on Testing and Assessment, Center for Education, Division of Behavioral and Social Sciences and Education}}
				,
	editor={
			JPelligrino
			NChudowsky
			&RGlaser
		}
		Washington, DC; Washington, DC
		
			,
	publisher={National Academy Press}
			,
	year={2001. July 12-August 2, 2010}
			74
		
		
			National Research Council
		
	
	,
	note={A framework for science education: Preliminary public draft}

}

@book{b72,
	
	
		,
	title={{Mathematische Kompetenzen von Schülerinnen und Schülern in Deutschland: Vertiefende Analysen im Rahmen von PISA-2000}}
		,
	author={{
			MNeubrand
		}}
		
			,
	year={2004}
			,
	publisher={VS -Verlag für Sozialwissenschaften}
			,
	address={Wiesbaden}
		
	

}

@book{b73,
	
	
		,
	title={{Grundlager der Erganzung des Internationalen PISA-Mathematik-Tests in der Deutschen Zusatzerhebung}}
		,
	author={{
			MNeubrand
		} and {
			RBiehler
		} and {
			ECohors-Fresenborg
		} and {
			LFlede
		} and {
			NKnoche
		} and {
			DLind
		} and {
			WLoding
		} and {
			GMoller
		} and {
			AWynands
		}}
		
		
		
		
		
		
		
		
		
		
			,
	year={2001}
		
	

}

@book{b74,
	
	
		,
	title={{Kompetencer og Uddannelsesbesk rivelse (Competencies and subject description)}}
		,
	author={{
			MNiss
		}}
		
			,
	year={1999}
		
	

}

@book{b75,
	
	
		,
	title={{}}
		,
	author={{
			Uddanneise
		}}
		
			9
			
		
	

}

@book{b76,
	
	
		,
	author={{
			MNiss
		}}
		,
	title={{Mathematical competencies and the learning of mathematics: The Danish KOM project. Third Mediterranean Conference on Mathematics Education}}
				Athens
		
			,
	year={2003}
			
		
	

}

@incollection{b77,
	
	
		,
	title={{Assessing Scientific, Reading and Mathematical Literacy -A Framework for PISA}}
	
	
		,
	journal={{OECD}}
		
			,
	year={2006. 2006}
			,
	publisher={OECD}
		
	

}

@book{b78,
	
	
		,
	title={{PISA 2012 Mathematics Framework}}
		,
	author={{
			Oecd
		}}
		
		
			,
	year={2010}
			,
	publisher={OECD Publications}
			,
	address={Paris}
		
	

}

@incollection{b79,
	
	
		,
	title={{Knowing versus seeing: problems of the plane representation of space geometry figures}}
		,
	author={{
			SOlkun
		} and {
			NBSinoplu
		} and {
			DDeryakulu
		}}
		
		
		
	
	
		,
	journal={{International Journal for Mathematics Teaching and Learning}}
		
			19
			
			,
	year={2005. 1988}
		
	
	,
	note={Educational Studies in Mathematics}

}

@book{b80,
	
	
		,
	title={{Fractals as a context of comprehension of the meaning of sequence in a Dynamic Geometry environment}}
		,
	author={{
			SPatsiomitou
		}}
		
			,
	year={2005}
		
		
			Department of Mathematics of the National and Kapodistrian University of Athens
		
	
	,
	note={Master Thesis}
	,
	note={in cooperation with the University of Cyprus}

}

@incollection{b81,
	
	
		,
	title={{Fractals as a context of comprehension of the meanings of the sequence and the limit in a Dynamic Software environment}}
		,
	author={{
			SPatsiomitou
		}}
	
	
		,
	booktitle={{Electronic Proceedings of the 8th International Conference on Technology in Mathematics Teaching (ICTMT8) in Hradec Králové (E. Milková}}
				
			,
	year={2007}
			5
			
		
	

}

@incollection{b82,
	
	
		,
	title={{Linking Visual Active Representations and the van Hiele model of geometrical thinking}}
		,
	author={{
			SPatsiomitou
		}}
		
	
	
		,
	booktitle={{Proceedings of the 13 th Asian Conference in Technology in Mathematics}}
				the 13 th Asian Conference in Technology in MathematicsBangkok, Thailand; Bangkok, Thailand
		
			,
	year={2008b. 2008c}
			
		
		
			Suan Shunanda Rajabhat University ; Suan Shunanda Rajabhat University
		
	
	,
	note={Proceedings of the 13 th Asian Conference in Technology in Mathematics}

}

@incollection{b83,
	
	
		,
	title={{Custom tools and the iteration process as the referent point for the construction of meanings in a DGS environment}}
		,
	author={{
			SPatsiomitou
		}}
		
	
	
		,
	booktitle={{Proceedings of the 13 th Asian Conference in Technology in Mathematics}}
				the 13 th Asian Conference in Technology in MathematicsBangkok, Thailand
		
			,
	year={2008d}
			
		
		
			Suan Shunanda Rajabhat University
		
	

}

@incollection{b84,
	
	
		,
	title={{The Impact of Structural Algebraic Units on Students' Algebraic Thinking in a DGS Environment}}
		,
	author={{
			SPatsiomitou
		}}
	
	
		,
	journal={{Electronic Journal of Mathematics and Technology (eJMT)}}
		
			3
			3
			
			,
	year={2009}
		
	

}

@incollection{b85,
	
	
		,
	title={{Building LVAR (Linking Visual Active Representations) modes in a DGS environment}}
		,
	author={{
			SPatsiomitou
		}}
	
	
		,
	journal={{Electronic Journal of Mathematics and Technology}}
		
			4
			1
			
			,
	year={2010a}
		
	

}

@book{b86,
	
	
		,
	title={{Learning mathematics with the Geometer's Sketchpad v4}}
		,
	author={{
			SPatsiomitou
		}}
		
			,
	year={2010b}
			,
	publisher={Kleidarithmos}
			,
	address={Athens}
		
	
	,
	note={in Greek}

}

@incollection{b87,
	
	
		,
	title={{Theoretical dragging: A nonlinguistic warrant leading to dynamic propositions}}
		,
	author={{
			SPatsiomitou
		}}
	
	
		,
	booktitle={{Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education}}
				the 35th Conference of the International Group for the Psychology of Mathematics EducationAnkara, Turkey
		
			,
	year={2011}
			1
			PME
		
	

}

@book{b88,
	
	
		,
	title={{The development of students geometrical thinking through transformational processes and interaction techniques in a DGS environemnt. Linking Visual Active Representations}}
		,
	author={{
			SPatsiomitou
		}}
		
			,
	year={2012a. December, 2012}
			,
	address={Ioannina}
		
		
			University of Ioannina
		
	
	,
	note={Unpuplished Ph.D. Thesis.}

}

@incollection{b89,
	
	
		,
	title={{A Linking Visual Representation DHLP for student's cognitive development}}
		,
	author={{
			SPatsiomitou
		}}
	
	
		,
	journal={{Global Journal Of Computer Science and Technology}}
		
			12
			6
			
			,
	year={2012b}
		
	

}

@book{b90,
	
	
		,
	title={{Students learning paths as 'dynamic encephalographs' of their cognitive development. ?nternational journal of computers & technology}}
		,
	author={{
			SPatsiomitou
		}}
		
			,
	year={2013. 18 April 2013}
			4
			
		
	

}

@incollection{b91,
	
	
		,
	title={{Developing students geometrical thinking through linking representations in a dynamic geometry environment}}
		,
	author={{
			SPatsiomitou
		} and {
			EKoleza
		}}
		
	
	
		,
	booktitle={{Proceedings of the Joint Meeting of the 32nd Conference of the International Group for the Psychology of Mathematics Education}}
				,
	editor={
			OFigueras
			ASepúlveda
		}
		the Joint Meeting of the 32nd Conference of the International Group for the Psychology of Mathematics Education
		
			,
	year={2008}
			
		
	

}

@incollection{b92,
	
	
		,
	title={{Developing geometric thinking skills through dynamic diagram transformations}}
		,
	author={{
			MichoacánMorelia
		} and {
			SPatsiomitou
		} and {
			AEmvalotis
		}}
		
		
		PME 97
	
	
		,
	booktitle={{Proceedings of MEDCONF 2009, The Sixth Mediterranean Conference on Mathematics Education}}
				MEDCONF 2009, The Sixth Mediterranean Conference on Mathematics EducationPlovdiv, Bulgaria
		
			,
	year={2009a}
			
		
	

}

@incollection{b93,
	
	
		,
	title={{Does the Building and transforming on LVAR modes impact students way of thinking}}
		,
	author={{
			SPatsiomitou
		} and {
			AEmvalotis
		}}
		
	
	
		,
	booktitle={{Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education}}
				,
	editor={
			MTzekaki
			MKaldrimidou
			CSakonidis
		}
		the 33rd Conference of the International Group for the Psychology of Mathematics EducationThessaloniki, Greece
		
			,
	publisher={PME}
			,
	year={2009b}
			4
			
		
	

}

@incollection{b94,
	
	
		,
	title={{Economy' and 'Catachrèse' in the use of custom tools in a Dynamic geometry problem-solving process}}
		,
	author={{
			SPatsiomitou
		} and {
			AEmvalotis
		}}
		
	
	
		,
	booktitle={{Electronic Proceedings of the 9th International Conference on Technology in Mathematics Teaching (ICTMT9) in}}
				Metz, France
		
			,
	year={2009c}
		
	

}

@book{b95,
	
	
		,
	title={{Composing and testing a DG research-based curriculum designed to develop students' geometrical thinking}}
		,
	author={{
			SPatsiomitou
		} and {
			AEmvalotis
		}}
		
		
		
			,
	year={2009d}
		
	

}

@incollection{b96,
	
	
		,
	title={{The development of students' geometrical thinking through Linking Visual Active Representations}}
		,
	author={{
			SPatsiomitou
		} and {
			EKoleza
		}}
		
	
	
		,
	booktitle={{Proceedings of the 5 th International Colloquium on the Didactics of Mathematics}}
				,
	editor={
			MTzanakis
			C
		}
		the 5 th International Colloquium on the Didactics of MathematicsRethymnon, Greece
		
			,
	year={2009}
			II
			
		
	

}

@incollection{b97,
	
	
		,
	title={{The development of students' geometrical thinking through a DGS reinvention process}}
		,
	author={{
			S &Patsiomitou
		} and {
			AEmvalotis
		}}
		
	
	
		,
	booktitle={{Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education}}
				,
	editor={
			MPinto
			TKawasaki
		}
		the 34th Conference of the International Group for the Psychology of Mathematics EducationBelo Horizonte. Brazil
		
			,
	publisher={PME}
			,
	year={2010a}
			4
			
		
	

}

@incollection{b98,
	
	
		,
	title={{Students' movement through van Hiele levels in a dynamic geometry guided reinvention process}}
		,
	author={{
			SPatsiomitou
		} and {
			AEmvalotis
		}}
		
	
	
		,
	journal={{Journal of Mathematics and Technology (JMT)}}
		
			3
			
			,
	year={2010b}
		
	

}

@incollection{b99,
	
	
		,
	title={{Secondary students' "dynamic reinvention of geometric proof" through the utilization of linking visual active representations}}
		,
	author={{
			SPatsiomitou
		} and {
			ABarkatsas
		} and {
			AEmvalotis
		}}
		
		
	
	
		,
	journal={{Journal of Mathematics and Technology}}
		
			5
			
			,
	year={2010}
		
	

}

@book{b100,
	
	
		,
	title={{Qualitative evaluation methods}}
		,
	author={{
			MPatton
		}}
		
			,
	year={1990}
			,
	publisher={Sage}
			,
	address={Thousand Oaks, CA}
		
	
	,
	note={2nd ed.}

}

@book{b101,
	
	
		,
	title={{Knowing what students know: The science and design of educational assessment}}
		,
	author={{
			JWPellegrino
		} and {
			NChudowsky
		} and {
			RGlaser
		}}
		
		
		
			,
	year={2001}
			,
	publisher={National Academy Press}
			,
	address={Washington, DC}
		
	

}

@book{b102,
	
	
		,
	author={{
			JPiaget
		}}
		,
	title={{The construction of reality in the child (M. Cook, Trans.)}}
				New York
		
			,
	publisher={Basic Books}
			,
	year={1937/1971}
		
	

}

@book{b103,
	
	
		,
	title={{The Essential Peirce: Selected philosophical writings}}
		,
	author={{
			CSPeirce
		}}
		,
	editor={N. Houser & C. Kloesel,}
		
			,
	year={1998. 1903d}
			,
	publisher={Indiana University Press}
			2
			
			,
	address={Bloomington}
		
	
	,
	note={The three normative sciences}

}

@book{b104,
	
	
		,
	title={{Using Dynamic Geometry to Bring the Real World into the Classroom}}
		,
	author={{
			RPierce
		} and {
			KStacey
		}}
		
		
		
			,
	year={2009}
		
	

}

@incollection{b105,
	
	
		,
	title={{Reconstructive Modelling with Dynamic Geometry Systems}}
		,
	author={{
			HSchumann
		}}
	
	
		,
	journal={{EduMath}}
		
			19
			12
			
			,
	year={2004}
		
	

}

@book{b106,
	
	
		,
	title={{Discovering geometry with a computer -using Cabri Geometre}}
		,
	author={{
			HSchumann
		} and {
			DGreen
		}}
		
		,
	editor={Studentlitteratur. Lund}
		
			,
	year={1994}
			,
	address={Sweden}
		
	

}

@incollection{b107,
	
	
		,
	title={{Characterizing interaction with visual mathematical representations}}
		,
	author={{
			KSedig
		} and {
			MSumner
		}}
		
	
	
		,
	journal={{International Journal of Computers for Mathematical Learning}}
		
			11
			
			,
	year={2006}
			,
	publisher={Springer}
		
	

}

@incollection{b108,
	
	
		,
	title={{Clearing House for Science, mathematics, and Environmental Education}}
		,
	author={{
			ASfard
		}}
		
	
	
		,
	booktitle={{Proceedings of 21 st Conference of PME-NA}}
				,
	editor={
			RSpeiser
			CMaher
			CWalter
		}
		21 st Conference of PME-NAColumbus, Ohio
		
			,
	year={2001}
			
		
	
	,
	note={Learning mathematics as developing a discourse}

}

@incollection{b109,
	
	
		,
	title={{Reconstructing mathematics pedagogy from a constructivist perspective}}
		,
	author={{
			MASimon
		}}
	
	
		,
	journal={{Journal for Research in Mathematics Education}}
		
			26
			2
			
			,
	year={1995}
		
	

}

@incollection{b110,
	
	
		,
	title={{Towards a constructivist perspective: An intervention study of mathematics teacher development}}
		,
	author={{
			MASimon
		} and {
			DShifter
		}}
		
	
	
		,
	journal={{Educational Studies in Mathematics}}
		
			22
			4
			
			,
	year={1991}
		
	

}

@book{b111,
	
	
		,
	title={{Modeling practices with The Geometer's Sketchpad. Proceedings of the ICTMA-13}}
		,
	author={{
			NSinclair
		} and {
			NJackiw
		}}
		
		
			,
	year={2007}
			,
	address={Bloomington, IL}
		
		
			Indiana University
		
	

}

@book{b112,
	
	
		,
	title={{Supporting student efforts to learn with understanding: an investigation of the use of Javasketchpad sketches in the secondary school geometry classroom. Unpublished doctoral dissertation}}
		,
	author={{
			MPSinclair
		}}
		
			,
	year={2001}
		
		
			University of Toronto, Graduate Department of Education
		
	

}

@incollection{b113,
	
	
		,
	title={{Implications of research on children's learning for standards and assessment: A proposed learning progression for matter and the atomic molecular theory}}
		,
	author={{
			R; C LSkemp
		} and {
			MWiser
		} and {
			CWAnderson
		} and {
			JKrajcik
		}}
		
		
		
	
	
		,
	booktitle={{The psychology of learning mathematics}}
				
			,
	year={1986. 2006}
			14
			
		
	
	,
	note={Harmondsworth, UK: Penguin 119. Smith,}

}

@incollection{b114,
	
	
		,
	title={{Read-thinkaloud protocols: A new data-source for formative evaluation}}
		,
	author={{
			PLSmith
		} and {
			JFWedman
		}}
		
	
	
		,
	journal={{Performance Improvement Quarterly}}
		
			1
			2
			
			,
	year={1988}
		
	

}

@book{b115,
	
	
		,
	author={{
			KStacey
		} and {
			LPSteffe
		} and {
			JEGale
		}}
		
		
		
		,
	title={{The international assessment of mathematical literacy: PISA 2012 framework and items. Paper presented at the 12th International Congress on Mathematical Education}}
				COEX, Seoul, Korea; Hillsdale, NJ
		
			,
	publisher={Lawerence Erlbaum}
			,
	year={2012. July 8-15. 1995}
		
	
	,
	note={Constructivism in education}

}

@book{b116,
	
	
		,
	author={{
			SSteketee
		}}
		,
	title={{Iteration through the math curriculum :Sketchpad 4 does it again and again NCTM Annual Meeting Session}}
				
			,
	year={2002}
			491
		
	

}

@incollection{b117,
	
	
		,
	title={{Towards a model for the development of an empirically tested learning progression}}
		,
	author={{
			SStevens
		} and {
			NShin
		} and {
			JKrajcik
		}}
		
		
		
	
	
		,
	booktitle={{Paper presented at the Learning Progressions in Science (LeaPS) Conference}}
				Iowa City, IA
		
			,
	year={2009}
		
	

}

@incollection{b118,
	
	
		,
	title={{Mathematical microworlds and intelligent computer-assisted instruction}}
		,
	author={{
			PThompson
		}}
	
	
		,
	booktitle={{Artificial intelligence and instruction: Applications and methods}}
				,
	editor={
			GKearsley
		}
		Reading
		
			,
	publisher={Addison}
			,
	year={1987}
			
		
	

}

@book{b119,
	
	
		,
	title={{The uses of argument}}
		,
	author={{
			SEToulmin
		}}
		
			,
	year={1958}
			,
	publisher={Cambridge University Press}
			,
	address={Cambridge}
		
	

}

@book{b120,
	
	
		,
	title={{Managing the complexity of the human/machine interaction in computerized learning environments: Guiding students}}
		,
	author={{
			LTrouche
		}}
		
			,
	year={2004}
		
	
	,
	note={command process through instrumental orchestrations}

}