Summary:
The basic objective of the above work is to present the study on the
transitions from the conjecture to the proof, which was conducted by two groups
of first grade students of the high school in terms of the subject of Euclidean
geometry. We believe that these transitions are characterized by intense
argumentative activity. More specifically, two activities were formed for the
purpose mentioned before, which required the utilization of a dynamic geometry
environment. The chosen environment was Geometer’s Sketchpad, which is
considered to be a significant tool that provides technological opportunities
in the field of Geometry. The resulting data were classified on the type of the
tools- dragging, measurement and custom tools- and the type of guaranteed-
structural intuitive, inductive, deductive- that the students used to construct
their arguments which were analyzed based on Toulmin. Regarding the tools of
dragging and measurement, further classification was made as to the type of
these. (e. g.: wandering, guided etc ). Through the results, it was indicated
that during the students’ occupation with the first activity, which aimed to
the transition from the figure to the theory, while they were producing figures
they were using tools such as Sketchpad’s tools, dragging and measurement and
the evidence of their arguments (structural intuitive, inductive, deductive)
for the validation of them is directly depended on these tools. As a result,
they are depicted as non-linguistic guarantees, while their arguments as
“instrumented ones”. On the other hand, as students progress in the process of
proof, it is observed that the interaction of the students with Sketchpad
through the mouse is initially reduced and then stops and the guarantees of
their arguments arise from the theory they have been taught. Τhis fact comes to
an agreement with the existing researches which refer that the tools of these
environments influence the type of arguments utilized by the students. The
findings of the second activity which aimed to the transition from theory the
to the figure show that the students mostly use custom tools with the
appearance of the commands file and their guarantees are based less on the
theory they have been taught. This fact contradicts the existing surveys, which
indicate that these tools support the control of the logic relationships
between the properties involved.
Keywords:
Conjecture, Dynamic tools, Proof, Argument, Toulmin
