Case Study on the Learning Process of Gifted Students in the GSP Environment
EunSung Go kes7402@hanmail.net
KyungHwa Lee khmath@knue.ac.kr
Mathematics Education Korea National University of Education South Korea
Abstract
It is widely known that gifted students put more emphasis on
compressed reasoning than ordinary students, having a stronger desire
for justification. This research is designed to find out whether such
characteristics in thinking are observed in the GSP environment, and
which role the GSP environment plays in the learning process of gifted
students. Krutetskii, V. A.(1976) observed and analyzed the
problemsolving process, behaviors, and personalities of gifted
students in mathematics over a long period of time, before reaching the
following conclusion. The gifted students tend to identify rules by
generalizing mathematical facts. Furthermore, their thinking process is
so flexible that their idea is quickly transferred from one structure
to another. They even have reversibility in thinking. Trying to come up
with easy, clear, and economical solutions, they often formalize
special mathematical concepts that are easily found in our daily lives
 though this process is carried out at a beginner level. Polya,
G(1965) explains that mathematical research is composed of
demonstrative reasoning and probable reasoning. The former is safe,
noncontroversial, and final, while the latter is adventurous,
controversial, and tentative. Polya emphasized that the process of
hypothesizing mathematically, researching and confirming the validity
of the hypothesis is very important in mathematical activities. With
regard to courses for gifted students in mathematics, such a
perspective has significant implications for identifying and developing
their potential. This research will identify the requirements of
teaching materials for gifted students by reviewing prior research and
find out how the GSP environment can contribute to meeting the
requirements. In reality, we will develop teaching materials for gifted
students in mathematics that can satisfy the requirements, comparing
their reasoning to the original goal of the materials, for analysis. In
particular, the research will study how the gifted identify the format
and structure of problems, whether logical thinking, compression in
thinking, flexibility, and reversibility are observed, and whether they
are trying to generalize mathematical concepts and develop mathematical
symbols. The ultimate purpose of this research is to identify what
potential the GSP environment can create for education for gifted
students in mathematics, through case analysis.
