• Journal of Educational Research in Mathematics
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• v.9 no.2
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• pp.419-438
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• 1999

This paper explored the impact of dynamic geometry software such as CabriII, GSP on student's understanding deductive justification, on the assumption that proof in school mathematics should be used in the broader, psychological sense of justification rather than in the narrow sense of deductive, formal proof. The following results have been drawn: Dynamic geometry provided positive impact on interacting between empirical justification and deductive justification, especially on understanding the necessity of deductive justification. And teacher in the computer environment played crucial role in reducing on difficulties in connecting empirical justification to deductive justification. At the beginning of the research, however, it was not the case. However, once students got intocul-de-sac in empirical justification and understood the need of deductive justification, they tried to justify deductively. Compared with current paper-and-pencil environment that many students fail to learn the basic knowledge on proof, dynamic geometry software will give more positive ffect for learning. Dynamic geometry software may promote interaction between empirical justification and edeductive justification and give a feedback to students about results of their own actions. At present, there is some very helpful computer software. However the presence of good dynamic geometry software can not be the solution in itself. Since learning on proof is a function of various factors such as curriculum organization, evaluation method, the role of teacher and student. Most of all, the meaning of proof need to be reconceptualized in the future research.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.821-840
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• 2013

Definition of geometric figure in middle school geometry seems to mere meaning of the term which could be perceived visually through its shape. However, Much research reported the low achievements of definitions of basic geometric figures. It suggested the limitation of instrumental understanding. In this research, I guided gifted middle school students to reinvent definitions of basic geometric figure by the deductive organization of its properties as Freudenthal pointed. These students understood relationally about why some geometric figure can be defined this way and how it could be defined equally via other properties. This analysis of reinventing of definitions will be a stepping stone to reflect on the pedagogical problems in teaching geometry and to search the new alternatives.

• School Mathematics
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• v.15 no.4
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• pp.667-682
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• 2013

Though teachers' lesson plays, this article analysed teachers' knowledge for mathematical teaching about mathematical definitions and their pedagogical difficulties in teaching defining. Although the participant teachers didn't transmit definitions to students and suggested possible definitions of the given geometric figure in their imaginary lessons, they didn't teach defining as deductive organization of properties of the geometric figure. They considered mathematical definition as a mere linguistic convention of a word, so they couldn't appreciate the necessity of deductive organization in teaching definitions, and the arbitrary nature of mathematical definitions. Therefore, for learning to teach definitions differently, it is necessary for teachers to reflect the gap between the everyday and mathematical definitions in teachers'education.

• Research in Mathematical Education
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• v.10 no.1 s.25
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• pp.55-70
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• 2006

The purpose of this study was to develop math creative problem solving test in order to identify the mathematically gifted on the basis of their math creative problem solving ability and evaluate the goodness of the test in terms of its reliability and validity of measuring creativity in math problem solving on the basis of fluency in producing valid solutions. Ten open math problems were developed requiring math thinking abilities such as intuitive insight, organization of information, inductive and deductive reasoning, generalization and application, and reflective thinking. The 10 open math test items were administered to 2,029 Grade 5 students who were recommended by their teachers as candidates for gifted education programs. Fluency, the number of valid solutions, in each problem was scored by math teachers. Their responses were analyzed by BIGSTEPTS based on Rasch's 1-parameter item-response model. The item analyses revealed that the problems were good in reliability, validity, difficulty, and discrimination power even when creativity was scored with the single criteria of fluency. This also confirmed that the open problems which are less-defined, less-structured and non-entrenched were good in measuring math creativity of the candidates for math gifted education programs. In addition, it discriminated applicants for two different gifted educational institutions and between male and female students as well.

• The KIPS Transactions:PartD
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• v.14D no.2
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• pp.203-210
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• 2007

Ontology can be used as a formal and demonstrative knowledgebase that can express the thinking process of human. Software Development Process is a collection of ideal practices and procedural system that is performed by mature organization with high capability. Due to complexity of process, however, Software development Process often results in obstruction of introducing and improving simple process activity. While introducing and improving software development process, application of ontology to complex software development process is more approachable by showing deductive results of relationship between ISO/IEC 15504 and CMMI. In this paper, we demonstrate a methodology that utilizes the improved process database conceptually mapping between ISO/IEC 15504 and CMMI using ontology.

• 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.

• Journal of Gifted/Talented Education
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• v.17 no.1
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• pp.1-26
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• 2007

The purpose of this study was to develop a math test for identification of the mathematically gifted on the basis of their math creative problem solving ability and to evaluate the goodness of the test. Especially, testing reliability and validity of scoring method on the basis of fluency only for evaluation of math creative problem solving ability was one of the main purposes. Ten closed math problems and 5 open math problems were developed requiring math thinking abilities such as intuitive insight, organization of information, inductive and deductive reasoning, generalization and application, and reflective thinking. The 10 closed math test items of Type I and the 5 open math test items of Type II were administered to 1,032 Grade 7 students who were recommended by their teachers as candidates for gifted education programs. Students' responses were scored by math teachers. Their responses were analyzed by BIGSTEPS and 1 parameter model of item analyses technique. The item analyses revealed that the problems were good in reliability, validity, item difficulty and item discriminating power even when creativity was scored based on the single criteria of fluency. This also confirmed that the open problems which are less-defined, less-structured and non-entrenched were good in measuring math creative problem solving ability of the candidates for math gifted education programs. In addition, it was found that the math creative problem solving tests discriminated applicants for the two different gifted educational institutions.