European Research in Mathematics Education I - Fakultät für ...

European Research in Mathematics Education I: Group 2 270
COURSEWARE IN GEOMETRY
(ELEMENTARY, ANALYTIC, DIFFERENTIAL)
Sergei Rakov, V. Gorokh
Kharkov Pedagogical University, Regional Center for New Information Technologies, Bluchera street, 2, Kharkov,
Ukraine, 310168
Rakov@usa.net
Abstract: The paper deals with computer support of teaching and learning in a
geometry course for universities and a special course for high school. Four computer
packages and activities in their environments are discussed. All the discussions are
closely connected with the context of the modern textbooks by Academic A.A.
Borissenko of the National Academy of Ukraine.
Keywords: -
1. Introduction
Information technologies have changed all kinds of human activities. Mathematics is
no exception - it has become technologically dependent. The most important changes
have taken place in the process of doing mathematics - discovering new facts and their
proof. Mathematical packages offer the user a suitable environment for undertaking
computer experiments to find mathematical regularities as the first step of exploration
and then support the process of proof with the powerful opportunities of computer
algebra. No doubt that the future of mathematics is in a symbiosis of a human and
computer “thinking”. Using mathematical packages has become the inalienable
component of mathematical culture.
In mathematical education innovative trends lie in the framework of a constructivist
approach - involving students in the process of constructing their own mathematical
system which consists of mathematical knowledge and beliefs. One of the most
effective ways of realizing a constructive approach is in explorations in which students
explore open-ended problems on their own. Solving open-ended problems can be
regarded as a model of the professional mathematical work. It is therefore natural to use
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