• Proceedings of the Safety Management and Science Conference
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• 2011.11a
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• pp.219-224
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• 2011

The research reviews the logical approach based on the creative thoughts. The two logical approaches, including deductive convergent and inductive divergent are discussed with why-why techniques and how-how techniques. While the deductive thinking is vertical logic for interconnected hierarchical and deep domains, the inducive thinking is horizontal logic for mutually exclusive and collectively exhausted frameworks. The creative thinking comes from the reversing the logic and lessening the premise of convergent and divergent approaches.

• Journal of the Korean School Mathematics Society
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• v.16 no.3
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• pp.539-560
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• 2013

The purpose of this study was to investigate characteristics of mathematically gifted high school students' thinking in design activities using GrafEq. Eight mathematically gifted high school students, who already learned graphs of functions and inequalities necessary for design activities, were selected to work in pairs in our experiment. Results indicate that logical thinking and mathematical abstraction, intuitive and structural insights, flexible thinking, divergent thinking and originality, generalization and inductive reasoning emerged in the design activities. Nonetheless, fine-grained analysis of their mathematical activities also implies that teachers for gifted students need to emphasize both geometric and algebraic aspects of mathematical subjects, especially, algebraic expressions, and the tasks for the students are to be rich enough to provide a variety of ways to simplify the expressions.

• Journal of Gifted/Talented Education
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• v.8 no.2
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• pp.69-89
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• 1998

The purpose of this study is to develop a test which can be used in identification of the gifted students in the area of mathematics. This study was carried out for two years from 1996. Mathematical giftedness is, in this study, regarded as a result of interaction of mathematical thinking ability, mathematical creativity, mathematical task committment, background knowledge. This study presumed that mathematical thinking ability is composed of seven thinking abilities: intuitive insights, ability for information organization, ability for visualization, ability for mathematical abstraction, inferential thinking ability(both inductive and deductive thinking abilities), generalization and application ability, and reflective thinking. This study also presupposed that mathematical creativity is composed of 3 characteristics: fluency, flexibility, originality. The test for mathematical creative problem solving ability was developed for primary, middle, and high school students. The test is composed of two parts: the first part is concentrated more on divergent thinking, while the second part is more on convergent thinking. The major targets of the test were the students whose achievement level in mathematics belong to top 15~20% in each school. The goodness of the test was examined in the aspects of reliability, validity, difficulty, and discrimination power. Cronbach $\alpha$ was in the range of .60~.75, suggesting that the test is fairly reliable. The validity of the test was examined through the correlation among the test results for mathematical creative problem solving ability, I. Q., and academic achievement scores in mathematics and through the correlation between the scores in the first part and the scores in the second part of the test for mathematical creative problem solving ability. The test was found to be very difficult for the subjects. However, the discrimination power of the test was at the acceptable level.