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<https://discovery.ucl.ac.uk/id/eprint/10020179> <http://purl.org/dc/terms/title> "From intrinsic to non-intrinsic geometry : a study of childrens understandings in logo-based microworlds."^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10020179> <http://purl.org/ontology/bibo/abstract> "The aim of the present study was to investigate the potential for children to\nuse the turtle methaphor to develop understandings of intrinsic, euclidean\nand cartesian geometrical ideas. Four aspects of the problem were\ninvestigated.\na) the nature of the schema children form when they identify with the turtle in\norder to change its state on the screen;\nb) whether it is possible for them to use the schema to gain insights into\ncertain basic geometrical principles of the cartesian geometrical system;\nc) how they might use the schema to form understandings of euclidean\ngeometry developed inductively from specific experiences;\nd) the criteria they develop for choosing between intrinsic and euclidean\nideas.\nTen 11 to 12 year - old children participated in the research, previously\nhaving had 40 to 50 hours of experience with Turtle geometry. The research\ninvolved three case - studies of pairs of children engaging in cooperative\nactivities, each case - study within a geometrical Logo microworld. The data\nincluded hard copies of everything that was said, typed and written.\nIssues a) and b) were investigated by means of the first case - study which\ninvolved three pairs of children and a microworld embedding intrinsic and\ncoordinate ideas. A model of the children's intrinsic schema and a model of\nthe coordinate schema which they formed during the study were devised. The\nanalysis shows that the two schemas remained separate in the children's\nminds with the exception of a limited number of occasions of context specific\nlinks between the two.\nIssue c) was investigated in the second case - study involving one pair of\nchildren and a microworld where the turtle was equipped with distance and\nturn measuring instruments and a facility to mark positions. The analysis\nillustrates how a turtle geometric environment of a dynamic mathematical\nnature was generated by the children, who used their intrinsic schema and\npredominantly engaged in inductive thinking. The geometrical content\navailable to the children within this environment was extended from intrinsic\nto both intrinsic and euclidean geometry.\nIssue d) was investigated by means of the third case - study involving a pair of\nchildren and a microworld where the children could choose among circle\nprocedures embedding intrinsic and/or euclidean notions in order to construct\nfigures of circle compositions. The analysis shows that the children employed\ntheir turtle schema in using both kinds of notions and did not seem to\nperceive qualitative differences between them. Their decisions on which type\nof notion to use were influenced by certain broader aspects of the\nmathematical situations generated in the study."^^<http://www.w3.org/2001/XMLSchema#string> .
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