TY  - UNPB
AV  - public
EP  - 576
A1  - Kynigos, Polychronis.
N2  - The aim of the present study was to investigate the potential for children to
use the turtle methaphor to develop understandings of intrinsic, euclidean
and cartesian geometrical ideas. Four aspects of the problem were
investigated.
a) the nature of the schema children form when they identify with the turtle in
order to change its state on the screen;
b) whether it is possible for them to use the schema to gain insights into
certain basic geometrical principles of the cartesian geometrical system;
c) how they might use the schema to form understandings of euclidean
geometry developed inductively from specific experiences;
d) the criteria they develop for choosing between intrinsic and euclidean
ideas.
Ten 11 to 12 year - old children participated in the research, previously
having had 40 to 50 hours of experience with Turtle geometry. The research
involved three case - studies of pairs of children engaging in cooperative
activities, each case - study within a geometrical Logo microworld. The data
included hard copies of everything that was said, typed and written.
Issues a) and b) were investigated by means of the first case - study which
involved three pairs of children and a microworld embedding intrinsic and
coordinate ideas. A model of the children's intrinsic schema and a model of
the coordinate schema which they formed during the study were devised. The
analysis shows that the two schemas remained separate in the children's
minds with the exception of a limited number of occasions of context specific
links between the two.
Issue c) was investigated in the second case - study involving one pair of
children and a microworld where the turtle was equipped with distance and
turn measuring instruments and a facility to mark positions. The analysis
illustrates how a turtle geometric environment of a dynamic mathematical
nature was generated by the children, who used their intrinsic schema and
predominantly engaged in inductive thinking. The geometrical content
available to the children within this environment was extended from intrinsic
to both intrinsic and euclidean geometry.
Issue d) was investigated by means of the third case - study involving a pair of
children and a microworld where the children could choose among circle
procedures embedding intrinsic and/or euclidean notions in order to construct
figures of circle compositions. The analysis shows that the children employed
their turtle schema in using both kinds of notions and did not seem to
perceive qualitative differences between them. Their decisions on which type
of notion to use were influenced by certain broader aspects of the
mathematical situations generated in the study.
PB  - Institute of Education, University of London
TI  - From intrinsic to non-intrinsic geometry : a study of childrens understandings in logo-based microworlds.
N1  - Thesis (PhD) University of London 1989..
M1  - Doctoral
ID  - discovery10020179
Y1  - 1988///
UR  - http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327074
ER  -