## Effects of Geometrical Construction in Computer-based Learning Environments.– The Case of Cabri-Geometry –
*Hiroko Tsuji*
`htsuji@human.tsukuba.ac.jp`
Doctoral program
**University of Tsukuba**
1-1-1 Tennodai
Japan
### Abstract
The purpose of this paper is to
consider the meaning and the effects
of the drawing figure in computer-based
learning environments. Then, we
will investigate its effects on
geometrical learning in Junior high
schools in Japan. For this study,
I refer to G. Brousseau' Ideas,
the “milieu” in particular.
Brousseau explains that the “milieu”
is a system opposing the taught
system (students) (Brousseau 1997).
This system is related to mathematical
knowledge of teaching. Brousseau
says that students adjust to the
milieu, which is one of representations
of mathematical knowledge that can
be controlled by students, although
the conditions that the milieu holds
can not be. Computer is considered
a tool setting the milieu as the
learning softwares are very much
developed in resent years (Balacheff
& Kaput 1996, etc.). The drawing
figures are a means of constructing
elements in the geometrical object.
This activity is essential to leaning
Geometry. we defined drawing figures
in computer-based environments as
follows, based in the definition
of construction and the four-steps
of problem-solving with construction
in elementary geometry; analysis,
drawing, demonstration and test
(Hayashi 1927). : The construction
in computer-based environments is
to create drawings as examples that
satisfy the conditions. In other
words, it is to create drawings
that keep the conditions even when
being moved with drag-mode on the
software such as Cabri-Geometry.
From the definition, we can be said
that the construction in computer-based
environments is a part of the milieu.
The drawing has conditions including
processes of the construction. In
the steps of demonstration and test
of the construction, students can
confirm the validity. Moreover it
gives students opportunities of
confirming their conception of the
figures. We think that this is related
to interactions between students
and the milieu proposed by Brousseau.
:
Construction, Milieu, Computer-based
leaning environment Brousseau, G.
(1997). Theory of didactical situation
in mathematics, (Edited & translated
by N. Balacheff, et al.) Kluwer.
Balacheff, N and Kaput, J. (1996).
Computer-based learning environments
in mathematics, In A. J. Bishop
et al.(eds.), International Handbook
of Mathematics Education, pp. 469-501,
Kluwer. Hayashi, T. (1927). The
Form of Elementary geometry, Kohdoh-Kan.
Pratt, D. and Ainley, J. (1997).
The construction of meanings for
geometric construction: Two contrasting
cases, International Journal of
Computers for Mathematical Learning,
1(3), 293-322, Kluwer.
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