@incollection{, B5D5D8EB5AAFF2BF41BAA197AB03A778 , author={{StavroulaPatsiomitou} and {University of Ioannina, Greece}}, journal={{Global Journal of Computer Science and Technology}}, journal={{GJCST}}0975-41720975-435010.34257/gjcst, address={Cambridge, United States}, publisher={Global Journals Organisation}1265381 } @incollection{b0, , title={{Instrumentation issues and the integration of computer technologies into secondary mathematics teaching}} , author={{ MArtigue }} , booktitle={{Proceedings of the Annual Meeting of the GDM. Potsdam}} the Annual Meeting of the GDM. Potsdam , year={2000. 2000} } @incollection{b1, , title={{Research commentary: An alternative reconceptualization of procedural and conceptual knowledge}} , author={{ AJBaroody } and { YFeil } and { ARJohnson }} , journal={{Journal for Research in Mathematics Education}} 38 2 , year={2007} } @incollection{b2, , title={{Aspects of proof in pupils' practice of school mathematics}} , author={{ NBalacheff }} , booktitle={{Mathematics, Teachers and Children}} , editor={ DPimm } London , publisher={Hodder and Soughton} , year={1988} } @incollection{b3, , title={{The development of geometric and spatial thinking}} , author={{ MTBattista }} , booktitle={{Second Handbook of Research on Mathematics Teaching and Learning}} , editor={ FLester } , year={2007} NCTM. Reston, VA: National Council of Teachers of Mathematics } @incollection{b4, , title={{Representations and cognitive objects in modern school geometry}} , author={{ MTBattista }} , booktitle={{Research on Technology and the teaching and learning of mathematics}} , editor={ GW KBlume & M Heid } Charlotte, NC , publisher={Information Age} , year={2008} 2 } @book{b5, , title={{Evaluating the Quality of Learning: the SOLO Taxonomy}} , author={{ JBiggs } and { KCollis }} , year={1982} , publisher={Academic Press} , address={New York} } @incollection{b6, , title={{Multimodal learning and the quality of intelligent behaviour}} , author={{ JBiggs } and { KCollis }} , booktitle={{Intelligence, Reconceptualization and Measurement. New Jersey. Laurence Erlbaum Assoc}} , editor={ HRowe } , year={1991} } @incollection{b7, , title={{Using technology to explore mathematical relationships: a framework for orienting mathematics courses for prospective teachers}} , author={{ &Bowers } and { Stephens }} , journal={{Journal of Mathematics Teacher Education}} 14 4 , year={2011} } @book{b8, , title={{Toward a theory of instruction}} , author={{ JSBruner }} , year={1966} , publisher={Belknap Press of Harvard University} , address={Cambridge, Mass} } @book{b9, , title={{Experimental and quasi-experimental designs for research on teaching}} , author={{ DCampbell } and { JStanley }} , editor={Gage, N.,} , year={1963} , address={Chicago, Rand McNally} , note={(ed) Handbook of Research on Teaching} } @incollection{b10, , title={{Geometric Figures from Middle to Secondary School: Mediating Theory and Practice}} , author={{ LCannizzaro } and { MMenghini }} , booktitle={{CERME 3}} , year={2003} } @incollection{b11, , title={{The development of mental representations as a problem solving}} , author={{ VCifarelli }} , journal={{Journal of Mathematical Behavior}} 17 2 , year={1998} } @incollection{b12, , title={{One theoretical perspective in undergraduate mathematics education research}} , author={{ BCzarnocha } and { EDubinsky } and { VPrabhu } and { DVidakovic }} , booktitle={{Proceedings of PME 23 , I}} PME 23 , I , year={1999} } @incollection{b13, , title={{A student's learning of geometry using the computer}} , author={{ -Koh SangChoi } and { Sook }} , journal={{Journal of Educational Research}} 92 , year={1999. 1999} } @incollection{b14, , title={{Learning trajectories in mathematics education}} , author={{ DClements } and { JSarama }} , booktitle={{Mathematical Thinking and Learning}} , year={2004} 6 } @book{b15, , title={{Logo and geometry}} , author={{ DHClements } and { MTBattista } and { Sarama }} , editor={J.} , year={2001} , address={Reston, VA} National Council of Teachers of Mathematics } @incollection{b16, , title={{Introduction: The coordination of psychological and sociological perspectives in mathematics education}} , author={{ PCobb } and { HBauersfeld }} , booktitle={{The emergence of mathematical meaning: Interaction in classroom cultures}} , editor={ PCobb & HBauersfeld } Hillsdale, NJ , publisher={Erlbaum} , year={1995} } @book{b17, , title={{The emergence of mathematical meaning: Interaction in classroom cultures}} , editor={Cobb, P., & Bauersfeld, H.} , year={1995} , publisher={Erlbaum} , address={Hillsdale, NJ} } @incollection{b18, , title={{Young childrens emotional acts while doing mathematical problem solving}} , author={{ PCobb } and { EYackel } and { TWood }} , booktitle={{Affect and mathematical problem solving: A new perspective}} , editor={ DB MMcleod & V Adams } New York , publisher={Springer-Verlag} , year={1989} } @incollection{b19, , 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} } @incollection{b20, , title={{The role and function of a hierarchical classification of quadrilaterals}} , author={{ MDe Villiers }} , booktitle={{For the Learning of Mathematics}} , year={1994} 14 } @incollection{b21, , title={{Using dynamic geometry to expand mathematics teachers' understanding of proof}} , author={{ MDe Villiers }} , journal={{International Journal of Mathematical Education in Science and Technology}} 35 , year={2004} } @incollection{b22, , title={{Teacher interventions aimed at mathematical level raising during collaborative learning}} , author={{ RDekker } and { MElshout-Mohr }} , journal={{Educational Studies in Mathematics}} 56 1 , year={2004} } @incollection{b23, , 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}} , editor={ GW KBlume & M Heid } Charlotte, NC , publisher={Information Age} , year={2008} 2 , note={Cases and perspectives} } @incollection{b24, , title={{Curriculum and teacher development: Psychological and anthropological perspectives}} , author={{ PCobb } and { EYackel } and { TWood }} , booktitle={{Integrating research on teaching and learning mathematics}} , editor={ EFennema TPCarpenter &S JLamon } , year={1991} } @book{b25, , title={{Sémiosis et pensée humaine}} , author={{ RDuval }} , year={1995} , publisher={Peter Lang} , address={Berne} } @incollection{b26, , title={{Cognitive analysis of problems of comprehension in a learning of mathematics}} , author={{ RDuval }} , journal={{Educational Studies in Mathematics}} 61 1-2 , year={March 27. 2006} } @incollection{b27, , title={{Technology and Mathematics Education: A Survey of Recent Developments and Important Problems}} , author={{ JFey }} , journal={{Educational Studies in Mathematics}} 20 , year={1989} } @book{b28, , author={{ Freudenthal }} , title={{Revisiting Mathematics Education: China Lectures}} Dordrecht , publisher={Kluwer Academic Publishers} , year={1991} } @book{b29, , author={{ HFreudenthal }} , title={{Mathematics as an Educational Task}} Reidel, Dordrecht , year={1973} } @incollection{b30, , title={{Learners' Understanding of the Definitions and Hierarchical Classification of Quadrilaterals: towards a theoretical framing}} , author={{ TFujita } and { KJones }} , journal={{Research in Mathematics Education}} 9 1&2 , year={2007} } @book{b31, , title={{Revisiting guided reinvention: icons, indexes, and symbols in the construction of mathematical objects}} , author={{ FFuringhetti } and { DPaola }} , year={2003} } @book{b32, , title={{}} , author={{ DFuys } and { DGeddes } and { RTischler }} , year={1984} } @book{b33, , 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{b34, , title={{Socially mediated metacognition: Creating collaborative zones of proximal development in small group problem solving}} , author={{ MGoos } and { PGalbraith } and { PRenshaw }} , journal={{Educational Studies in Mathematics}} 49 , year={2002} } @incollection{b35, , title={{Representations and the psychology of mathematics education}} , author={{ GGoldin } and { CJanvier }} , journal={{Journal of Mathematical Behavior}} 17 1 , year={1998} } @incollection{b36, , title={{Systems of representations and development of mathematical concepts}} , author={{ GGoldin } and { NShteingold }} , booktitle={{The roles of representation in school mathematics}} , editor={ ACucoco FCurcio } , year={2001} } @book{b37, , title={{Reston: National Council of Teachers Mathematics}} } @incollection{b38, , title={{Investigating and ordering Quadrilaterals and their analogies in space-problem fields with various aspects}} , author={{ GGraumann }} , journal={{Zentralblatt für Didaktik der Mathematik (ZDM)}} 37 3 , year={2005} } @incollection{b39, , title={{Hans Freudenthal: a mathematician on didactics and curriculum theory}} , author={{ KGravemeijer } and { JTerwel }} , journal={{Journal of Curriculum Studies}} 32 6 , year={2000} } @book{b40, , author={{ GHarel }} , title={{DNR Perspective on Mathematics Curriculum and Instruction: Focus on Proving, Part I. Zentralblatt für Didaktik der Mathematik}} , year={2008} 40 } @book{b41, , title={{Students' proof schemes: Results from exploratory studies}} , author={{ GHarel } and { LSowder }} , editor={A. Schoenfeld, J. Kaput, & E. Dubinsky} , year={1998} , publisher={American Mathematical Society} , address={Providence, RI} , note={Research in collegiate mathematics education III} } @incollection{b42, , title={{Concept formation of triangles and quadrilaterals in the second grade}} , author={{ JHasegawa }} , journal={{Educational Studies in Mathematics}} 32 , year={1997} } @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, , title={{The Geometer's Sketchpad}} , author={{ NJackiw }} , year={1991} } @book{b45, , title={{}} , author={{ CABerkeley }} , publisher={Key Curriculum Press} } @incollection{b46, , title={{Locus? and -trace? in Cabrigéomètre: relationships between geometric and functional aspects in a study of transformations}} , author={{ APJahn }} , journal={{Zentralblatt für Didaktik der Mathematik}} 34 3 , year={2002} } @book{b47, , author={{ CJanvier }} , title={{Problems of Representations in the Learning and Teaching of Mathematics}} New Jersey , publisher={Lawrence Erlbaum Associates} , year={1987} } @incollection{b48, , 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. Bellaria, Italy. Retrieved}} the Third Conference of the European Society for Research in Mathematics Education. Bellaria, Italy. Retrieved , year={2003. February 14. 2010} } @incollection{b49, , title={{Linking procedural and conceptual mathematical knowledge through CAL}} , author={{ DjKadijevich } and { LHaapasalo }} , journal={{Journal of Computer Assisted Learning}} 17 , year={2001. 2001} } @incollection{b50, , title={{Representations, inscriptions, descriptions and learning: A kaleidoscope of windows}} , author={{ JKaput }} , journal={{Journal of Mathematical Behavior}} 17 2 , year={1999} } @book{b51, , title={{The action research planner}} , author={{ SKemmis } and { RMctaggart }} , year={1982} , publisher={Deakin University Press} , address={Geelong, Victoria} } @incollection{b52, , title={{The ethnography of argumentation}} , author={{ GKrummheuer }} , booktitle={{The emergence of mathematical meaning: Interaction in classroom cultures}} , editor={ PCobb & HBauersfeld } , year={1995} } @book{b53, , title={{}} , author={{ NJHillsdale }} , publisher={Lawrence Erlbaum Associates} } @incollection{b54, , title={{Technology used as a tool for mediating knowledge in the teaching of mathematics: the case of Cabri-geometry}} , booktitle={{Plenary speech delivered at the Asian Technology Conference in Mathematics}} Taiwan , year={2003. 2003} Chung Hau University } @incollection{b55, , title={{Robust and soft constructions: two sides of the use of dynamic geometry environments}} , author={{ CLaborde }} , booktitle={{Proceedings of the 10th Asian Technology Conference in Mathematics}} the 10th Asian Technology Conference in Mathematics , year={2005} Korea National University of Education } @book{b56, , title={{The conceptual tools of Euclidean and dynamic geometry environments, Paper presented in Topic Study Group 10: Research and development in the teaching and learning of geometry}} , author={{ FJLopez-Real } and { ALeung }} , year={2004} , note={ICMI 10} } @book{b57, , title={{}} , author={{ DemarkCopenhagen }} , year={March} } @book{b58, , title={{Introduction to proof: the mediation of a dynamic software environment Educational Studies in Mathematics pp}} , author={{ Mariotti }} , year={2000} , publisher={Kluwer Academic Publishers} } @incollection{b59, , title={{Cognitive development and the structuring of geometric content}} , author={{ JLMcdonald }} , journal={{Journal for Research in Mathematics Education}} 20 1 , year={1989} } @book{b60, , title={{Qualitative research and case study applications in education}} , author={{ SBMerriam }} , year={1998} , publisher={Jossey-Bass} , address={San Francisco} } @incollection{b61, , title={{On conceptual obstacles linked with external representation in geometry}} , author={{ AMesquita }} , journal={{Journal of Mathematical Behavior}} 17 2 , year={1998} } @incollection{b62, , title={{What difference does it make? Children views of the difference between some quadrilaterals}} , author={{ FMonaghan }} , journal={{Educational Studies in Mathematics}} 42 2 , year={2000} } @incollection{b63, , title={{Mathematical knowledge and practices resulting from access to digital technologies}} , author={{ JOlive } and { KMakar } and { VHoyos } and { LKKor } and { OKosheleva } and { &RStraesser }} , booktitle={{Mathematics education and technology -Rethinking the terrain. The 17th ICMI Study}} , editor={ CHoyles & JLagrange } New York , publisher={Springer} , year={2010} } @incollection{b64, , title={{The construction of an iterative fractional scheme: The case of Joe}} , author={{ JOlive } and { LPSteffe }} , journal={{Journal of Mathematical Behavior}} 20 , year={2002} } @book{b65, , title={{From fractions to rational numbers of arithmetic: A reorganization hypothesis}} , author={{ JOlive }} , year={1999} } @incollection{b66, , title={{}} , journal={{Mathematical Thinking and Learning}} 1 4 } @incollection{b67, , title={{Students' structure for the understanding of the axis of reflective symmetry in mathematics}} , author={{ APanaoura } and { IElia } and { NStamboulides } and { PSpyrou }} , journal={{English) Acta Didactica Universitatis Comenianae. Mathematics}} 9 , year={2009} } @incollection{b68, , title={{The role of representation(s) in developing mathematical understanding}} , author={{ SPape } and { MTchoshanov }} , booktitle={{Theory into Practice}} , year={2001} 40 } @book{b69, , title={{Fractals as a context of comprehension of the meanings of the sequence and the limit in a Dynamic Computer Software environment}} , author={{ SPatsiomitou }} , year={2005} Department of Mathematics. National and Kapodistrian University of Athens (in cooperation with the University of Cyprus , note={Master Thesis} } @incollection{b70, , title={{Fractals as a context of comprehension of the meanings of the sequence and the limit in a Dynamic Computer Software environment}} , author={{ SPatsiomitou }} , booktitle={{Electronic Proceedings of the 8 th International Conference on Technology in Mathematics Teaching (ICTMT8}} , editor={ (EHradec Králové PavelMilková Prazák } , year={2007} University of Hradec Králové , note={cd-rom} } @incollection{b71, , title={{The development of students' geometrical thinking through transformational processes and interaction techniques in a dynamic geometry environment}} , author={{ SPatsiomitou }} , journal={{Issues in Informing Science and Information Technology Journal}} 5 , year={2008a} } @incollection{b72, , title={{Linking Visual Active Representations and the van Hiele model of geometrical thinking}} , author={{ SPatsiomitou }} , booktitle={{Enhancing Understanding and Constructing Knowledge in Mathematics with Technology». Proceedings of the 13th Asian Conference in Technology in Mathematics. pp 163-178. Published by Mathematics and Technology}} , editor={ W-CYang MMajewski TAlwis KKlairiree } LLC. Bangkok, Thailand , year={2008b} Suan Shunanda Rajabhat University } @incollection{b73, , title={{Building LVAR (Linking Visual Active Representations) modes in a DGS environment}} , author={{ SPatsiomitou }} , journal={{Electronic Journal of Mathematics and Technology}} 4 1 , year={2010} } @incollection{b74, , 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 Education , year={2011} 1 } @book{b75, , title={{}} , author={{ TurkeyAnkara }} PME } @incollection{b76, , title={{Developing geometric thinking skills through dynamic diagram transformations}} , author={{ SPatsiomitou } and { AEmvalotis }} , booktitle={{Proceedings of MEDCONF 2009, The Sixth Mediterranean Conference on Mathematics Education}} MEDCONF 2009, The Sixth Mediterranean Conference on Mathematics Education , year={2009a} } @book{b77, , title={{}} , author={{ BulgariaPlovdiv }} } @incollection{b78, , title={{Does the Building and transforming on LVAR modes impact students way of thinking}} , author={{ SPatsiomitou } and { AEmvalotis }} , booktitle={{Research Report in Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education}} , editor={ MTzekaki MKaldrimidou CSakonidis } , year={2009b} 4 } @book{b79, , title={{}} , author={{ GreeceThessaloniki }} , publisher={PME} } @book{b80, , title={{Composing and testing a DG research-based curriculum designed to develop students' geometrical thinking}} , author={{ SPatsiomitou } and { AEmvalotis }} , year={2009c} } @incollection{b81, , title={{The development of students' geometrical thinking through a DGS reinvention process}} , author={{ S &Patsiomitou } and { AEmvalotis }} , booktitle={{Proceedings of the 34 th Conference of the International Group for the Psychology of Mathematics Education}} , editor={ MPinto TKawasaki } the 34 th Conference of the International Group for the Psychology of Mathematics EducationBelo Horizonte. Brazil , publisher={PME} , year={2010a} 4 } @incollection{b82, , 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)}} , editor={R. M. March Aliguliyev & J. A. Jafarzade} 3 , year={2010b} } @incollection{b83, , 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 (JMT)}} , editor={R.M.Aliguliyev, Javid A. Jafarzade} 2078-0257 , year={2010} } @book{b84, , title={{Assessment in Mathematics: a developmental approach}} , author={{ JPegg }} , editor={J.M. Royer} , year={2003} } @book{b85, , title={{Advances in Cognition and Instruction}} , publisher={Information Age Publishing Inc} , address={New York} } @incollection{b86, , title={{How can the relationship between argumentation and proof be analysed ?}} , author={{ BPedemonte }} , journal={{Educational Studies in Mathematics}} 66 , year={2007} } @incollection{b87, , title={{The fundamental cycle of concept construction underlying various theoretical frameworks}} , author={{ JPegg } and { DTall }} , journal={{International Reviews on Mathematical Education (Zentralblatt für Didaktik der Mathematik)}} 37 6 , year={2005} } @book{b88, , title={{Psychogenèse et Histoire des Sciences}} , author={{ JPiaget } and { RGarcia }} , year={1983} , publisher={Flammarion} , address={Paris} } @book{b89, , title={{The Essential Peirce: Selected philosophical writings}} , author={{ CSPeirce }} , editor={N. Houser & C. Kloesel,} , year={1992} , publisher={Indiana University Press} 1 , address={Bloomington} , note={Deduction, induction, and hypothesis} } @book{b90, , author={{ JPiaget }} , title={{The construction of reality in the child (M. Cook, Trans.)}} New York , publisher={Basic Books} , year={1937/1971} } @book{b91, , title={{Les hommes et les technologies, approche cognitive des instruments contemporains}} , author={{ PRabardel }} , year={1995} , publisher={Armand Colin} , address={Paris} } @book{b92, , title={{Educating the reflective practitioner}} , author={{ DASchön }} , year={1987} , publisher={Jossey-Bass} , address={San Francisco} } @incollection{b93, , title={{Emerging knowledge structures in and with algebra}} , author={{ BSchwartz } and { RHerschkowitz } and { TDreyfus }} , booktitle={{European Research in Mathematics Education II, Proceedings of the CERME2. Praga: Charles University}} , editor={ JNovotna } , year={2001} } @incollection{b94, , 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{b95, , title={{On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin}} , author={{ ASfard }} , journal={{Educational Studies in Mathematics}} 22 1 , year={1991} } @incollection{b96, , title={{Reconstructing mathematics pedagogy from a constructivist perspective}} , author={{ MASimon }} , journal={{Journal for Research in Mathematics Education}} 26 2 , year={1995} } @incollection{b97, , title={{?Beyond inductive and deductive reasoning: the search for a sense of knowing}} , author={{ MASimon }} , journal={{Educational Studies in Mathematics}} 30 , year={1996} } @book{b98, , title={{Learning mathematics as developing a discourse}} , author={{ ASfard }} , editor={R. 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Maher, C} , year={2001} } @incollection{b99, , author={{ Walter }} , booktitle={{Proceedings of 21st Conference of PME-NA}} 21st Conference of PME-NAColumbus, Ohio } @book{b100, , author={{ RSkemp }} , title={{The psychology of learning mathematics}} UK: Penguin , publisher={Harmondsworth} , year={1986} , note={2nd ed.} } @incollection{b101, , title={{Investigating preservice teachers' understanding and strategies on a students' errors of reflective symmetry}} , author={{ JSon }} , booktitle={{Proceedings of the 30th of the International Group for the Psychology of Mathematics Education}} , editor={ JNovotna HMoraova MKratka NStehlikova } the 30th of the International Group for the Psychology of Mathematics EducationPrague , year={2006} 5 155 } @incollection{b102, , title={{Action research as an investigative approach within a computer base community of learners}} , author={{ CSteketee }} , booktitle={{Beyond the comfort zone: Proceedings of the 21st ASCILITE Conference}} , editor={ RAtkinson CMcbeath DJonas-Dwyer &RPhillips } , year={2004} } @incollection{b103, , title={{Symbolizing as a constructive activity in a computer microworld}} , author={{ LPSteffe } and { JOlive }} , journal={{Journal of Educational Computing Research}} 14 , year={1996} } @book{b104, , title={{Basics of qualitative research: Grounded theory procedures and techniques}} , author={{ AStrauss } and { JCorbin }} , year={1990} , publisher={Sage Publications, Inc} , address={Newbury Park, CA} } @incollection{b105, , title={{Van Hiele levels of geometric thought revisited}} , author={{ ATeppo }} , journal={{Mathematics Teacher}} 84 , year={1991} } @book{b106, , title={{The uses of argument}} , author={{ SEToulmin }} , year={1958} , publisher={Cambridge University Press} , address={Cambridge} } @incollection{b107, , title={{Managing the complexity of the human/machine interaction in computerized learning environments: Guiding students' command process through instrumental orchestrations}} , author={{ LTrouche }} , journal={{International Journal of Computers for Mathematical Learning}} 9 , year={2004} , publisher={Kluwer Academic Publishers} } @book{b108, , title={{Van Hiele levels and achievement in secondary school geometry. (Final report of the Cognitive Development and Achievement in Secondary School Geometry Project)}} , author={{ ZUsiskin }} , year={1982} , address={Chicago} University of Chicago. , note={ERIC Document Reproduction Service, No. ED 220 288} } @incollection{b109, , title={{Learning to understand what giving a proof really means}} , author={{ JVan Dormolen }} , journal={{Educational Studies in Mathematics}} 8 , year={1977} } @book{b110, , title={{Structure and insight: A theory of mathematics education}} , author={{ PMVan Hiele }} , year={1986} , publisher={Academic Press} , address={Orlando, Florida} } @incollection{b111, , title={{Cognition and Artifacts: a contribution to the study of thought in relation to instrumented activity}} , author={{ PVerillon } and { PRabardel }} , journal={{European Journal of Psychology of Education}} 10 1 , year={1995} } @incollection{b112, , title={{Comprehensive theory of representation for mathematics education}} , author={{ GVergnaud }} , journal={{Journal of Mathematics Behavior}} 17 2 , year={1998. March} } @incollection{b113, , title={{Teaching for abstraction: A model}} , author={{ PWhite } and { MCMitchelmore }} , journal={{Mathematical Thinking and Learning}} 12 3 , year={2010} } @book{b114, , title={{Making Sense of Transformations and Symmetry -the Heart of Geometry}} , author={{ &Whiteley } and { Moshé }} , year={2005} } @incollection{b115, , title={{The role of cognitive conflict in developing student's understanding of chance measurement}} , author={{ JMWatson } and { JBMoritz } and { EYackel } and { CRasmussen }} , booktitle={{Numeracy and beyond (Proceedings of the 24th Annual Conferenc of the Mathematics Education Research Group of Australasia}} , editor={ GLeder EPehkonen & GToerner } , year={2001. 2002} 2 , note={Beliefs and norms in the mathematics classroom. Beliefs: A hidden variable in mathematics education? (pp.} } @book{b116, , author={{ EYackel } and { PCobb }} , title={{Classroom Microcultures and Reform in Mathematics Education?, paper presented to the Annual Meeting of the}} New Orleans , publisher={American Educational Research Association} , year={1994} } @book{b117, , title={{The importance of social interactions in childrens construction of mathematical knowledge}} , author={{ EYackel } and { PCobb } and { TWood } and { GWheatley } and { GMerkel }} , editor={T. Cooney} , year={1990} , address={Reston, VA} National Council of Teachers of Mathematics , note={Teaching and learning mathematics in the 1990s} } @incollection{b118, , title={{Social and sociomathematical norms in an advanced undergraduate mathematics course}} , author={{ EYackel } and { CRasmussen } and { KKing }} , journal={{Journal of Mathematical Behavior}} 19 , year={2001} }