• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.247-282
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• 2011

In the elementary school mathematics textbooks of the 7th national curriculum, just simple construction education is provided by having students draw a circle and triangle with compasses and drawing vertical and parallel lines with a set square. The purpose of this study was to examine the mathematical thinking of sixth-grade elementary school students in the construction process in a bid to give some suggestions on elementary construction guidance. As a result of teaching the sixth graders in gifted and nongifted classes about the equal division of line segments and evaluating their mathematical thinking, the following conclusion was reached, and there are some suggestions about that education: First, the sixth graders in the gifted classes were excellent enough to do mathematical thinking such as analogical thinking, deductive thinking, developmental thinking, generalizing thinking and symbolizing thinking when they learned to divide line segments equally and were given proper advice from their teacher. Second, the students who solved the problems without any advice or hint from the teacher didn't necessarily do lots of mathematical thinking. Third, tough construction such as the equal division of line segments was elusive for the students in the nongifted class, but it's possible for them to learn how to draw a perpendicular at midpoint, quadrangle or rhombus and extend a line by using compasses, which are more enriched construction that what's required by the current curriculum. Fourth, the students in the gifted and nongifted classes schematized the problems and symbolized the components and problem-solving process of the problems when they received process of the proble. Since they the urally got to use signs to explain their construction process, construction education could provide a good opportunity for sixth-grade students to make use of signs.

• School Mathematics
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• v.15 no.3
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• pp.603-617
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• 2013

The major purpose of this article is to examine what kind of gap exists between mathematically gifted students' probability knowledge and the reality actually applying that knowledge and then analyze the cause of the gap. To attain the goal, 23 elementary mathematically gifted students at the highest level from G region were provided with problem situations internalizing a probability and expectation, and the problems are in series in which conditions change one by one. The study task is in a gaming situation where there can be the most reasonable answer mathematically, but the choice may differ by how much they consider a certain condition. To collect data, the students' individual worksheets are collected, and all the class procedures are recorded with a camcorder, and the researcher writes a class observation report. The biggest reason why the students do not make a decision solely based on their own mathematical knowledge is because of 'impracticality', one of the properties of probability, that in reality, all things are not realized according to the mathematical calculation and are impossible to be anticipated and also their own psychological disposition to 'avoid loss' about their entry fee paid. In order to provide desirable probability education, we should not be limited to having learners master probability knowledge included in the textbook by solving the problems based on algorithmic knowledge but provide them with plenty of experience to apply probabilistic inference with which they should make their own choice in diverse situations having context.

• School Mathematics
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• v.17 no.2
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• pp.273-287
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• 2015

The purpose of this study was to obtain a deeper understanding of didactic processing in the class that unified with engineering by analyzing on the types of the teacher's instumental orchestration and schematizing it as an activity system. In order to do so, a qualitative study of a 5th grade class for math-gifted students in Y elementary school with ethnography was conducted. Interviews with the students were held and various document data were collected during the participational observation of the class. The collected qualitative data were gone through the analytical induction while the instrumental orchestration of Drijvers, Boon, Doorman, Reed, & Gravemeijer as well as the secondgeneration activity theory of Engestrom were using as the frame of conceptional reference. According to the result of this study, there exist 4 types, such as 'technical demo' 'link screen board', 'detection-exploring small group' and 'explain the screen and technical demo'.

• School Mathematics
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• v.18 no.1
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• pp.85-103
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• 2016

This study was to find characteristics of argumentation derived from a discourse in a math-gifted 5 grade class, which was held for finding a Pick's formula using Geoboard function of TI-73 calculator. For the analysis, a video record of the class, transcript of its voice record, and activity paper were used as data and Toulmin's argument schemes were applied as analysis standard. As a result of the study, we found that the graphing calculator helped the students to create an experimental environment that graphing a grid-polygon and figuring out its area. Furthermore, it also provided a basic demonstration through 'data->claim' composition and reasoning activities which consisted of guarantee, warrant, backing, qualifier and refutal for justifying. The basic argumentation during the process of deriving the Pick's theorem by the numbers of boundary points and inner points was developed into a 'collective argumentation' while a teacher took a role of a conductor of the argumentation and an authorizer on the knowledge at the same time.

• School Mathematics
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• v.16 no.3
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• pp.585-611
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• 2014

The purpose of this study is to understand the decision-making behavior of a mathematics teacher in science academy of Korea by applying the framework of class analysis through the theory of goal-oriented decision-making. To this end, we selected as the participant a mathematics teacher in charge of the class of basic calculus of science high school for the gifted in the metropolitan area, and observed the teacher's lesson. Based on a questionnaire derived from previous studies, we analyzed goals, orientations and resources of the teacher. Research results show that there are certain teaching routines by analyzing the behavior patterns that appear repeatedly in the teacher's lesson. Also we understand that it can be used on goals, orientations and resources of the teacher to adequately explain his teaching routine. In the present study, in particular, it was found to have a similar but partially different routines to the teaching routines shown in the study of Schoenfeld. From these findings, We can derive the implications that the theory of goal-oriented decision making can be suitably used as analytical tool for understanding the behavior of the teacher who pursue a productive interaction in mathematics lesson in Korea.

• School Mathematics
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• v.15 no.3
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• pp.619-632
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• 2013

One area where research is especially needed is their elaboration process and how they elaborate their idea as a group in a mathematical board game re-creation project. In this research, this process was named 'Mathematical Elaboration Process'. The purpose of this research is to understand how the gifted children elaborate their idea in a small group, and which idea can be chosen for a new board game when they are exposed to a project for making new mathematical board games using the what-if-not strategy. One of the gifted children's classes was chosen in which there were twenty students, and the class was composed of four groups in an elementary school in Korea. The researcher presented a series of re-creation game projects to them during the course of five weeks. To interpret their process of elaborating, the communication of the gifted students was recorded and transcribed. Students' elaboration processes were constructed through the interaction of both the mathematical route and the non-mathematical route. In the mathematical route, there were three routes; favorable thoughts, unfavorable thoughts and a neutral route. Favorable thoughts was concluded as 'Accepting', unfavorable thoughts resulted in 'Rejecting', and finally, the neutral route lead to a 'non-mathematical route'. Mainly, in a mathematical route, the reason of accepting the rule was mathematical thinking and logical reasons. The gifted children also show four categorized non-mathematical reactions when they re-created a mathematical board game; Inconsistency, Liking, Social Proof and Authority.

• Journal of the Korean School Mathematics Society
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• v.18 no.3
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• pp.335-352
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• 2015

In this paper, we selected 145 students from engineering college students who took P University's the Scholastic Level Assessment and registered the Basic Mathematics Class among the students who achieved 4th~7th grade in the mathematics B-type of the College Scholastic Ability Test. We compared and analyzed the correlation among the chosen students' grade for the College Scholastic Ability Test, test results of the Scholastic Level Assessment and mid-term test of the Basic Mathematics Subject, type of college entrance and actual condition survey of students in order to derive optimized teaching method for general mathematics subjects which can possibly increase the students' academic ability.

• The Mathematical Education
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• v.45 no.2 s.113
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• pp.191-204
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• 2006

Computer technology has a potential to change the contents of school mathematics and the way of teaching mathematics. But in our country, the problem whether computer technology should be introduced into mathematics classroom or not was not resolved yet. As a tool, computer technology can be used by teachers who are confident of the effectiveness and who can use it skillfully and can help students to understand mathematics. The purpose of this study was to investigate the effective way to introduce and utilize computer technology based on the status quo of mathematics classroom setting. One possible way to utilize computer technology in mathematics classroom in spite of the lack of computer and the inaccessibility of useful software is using domain specific simulation software like 'Polyhedron'. 'Polyhedron', as we can guess from the name, can be used to explore regular and semi regular polyhedra and the relationship between them. Its functions are limited but it can visualize regular polyhedra, transform regular polyhedra into other polyhedra. So it is easier to operate than other dynamic geometry software like GSP. To investigate the effect of using this software in mathematics class, three classes(one in 6th grade from science education institute for the gifted, two in 7th grade) were chosen. Activities focused on the relationship between regular and semi regular polyhedra. After the class, several conclusions were drawn from the observation. First, 'Polyhedron' can be used effectively to explore the relationship between regular and semi regular polyhedra. Second, 'Polyhedron' can motivate students. Third, Students can understand the duality of polyhedra. Fourth, Students can visualize various polyhedra by reasoning. To help teachers in using technology, web sites like NCTM's illuminations and NLVM of Utah university need to be developed.

• Journal of Gifted/Talented Education
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• v.23 no.3
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• pp.355-371
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• 2013

While many research focused learners as those who excel in mathematics or science, the identification of learners with potential or demonstrated talent in visual art has also been the meaningful research topic. Since these learners exhibit high performance capability in intellectual, creative and artistic areas, they require services or programs not ordinarily provided by the schools. This research tried to clarify what high performance means when speaking of learners with outstanding talent in the visual arts based on the relevant literature. Also, this research introduced the recent trends in the field of art gifted and talented education. In order to demonstrate critical issues and find new directions in art education for gifted learners, this research conducted the survey, and this survey target group was arts high school students. Based on the survey analysis, this research conducted the semi-structured interviews with focal participants including the teachers and an artist. Interviewees generated many meaningful issues, and interview analysis reconceptualized art education for gifted learners as following. 1) Gifted education should consider learners' excellence, equity, troubles, and struggles that often go unnoticed. 2) We should reform the criteria, standards, and strategies in finding art gifted learners. 3) In order to facilitate meaningful and creative art education, higher education institutions need to change the current college entrance exam. 4) The goal of gifted art education is not only raising the world-class artists. 5) Meaningful art education for gifted learners is in interaction with the environment including group dynamics, parents influence, and teachers.

• School Mathematics
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• v.12 no.3
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• pp.353-370
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• 2010

The purpose of this study was threefold: (1) to select the components of spatial ability that could be associated with the implementation of a polycube task, embody the selected components of spatial ability as learning elements and develop the prototype of polycube teaching-learning materials applicable to gifted education, (2) to make a close analysis of the development process of the teaching-learning materials to ensure the applicability of the prototype, (3) to give some suggestions on the development of teaching-learning materials geared toward mathematically gifted classes. The findings of the study were as follows: As for the first purpose of the study, relevant literature was reviewed to make an accurate definition of spatial ability, on which there wasn't yet any clear-cut explanation, and to find out what made up spatial ability. After 13 components of spatial ability that were linked to a polycube task were selected, the prototype of teaching-learning materials for gifted education in mathematics was developed by including nine components in consideration of children's grade and level. Concerning the second purpose of the study, materials for teachers and students were separately developed based on the prototype, and the materials were modified and finalized in light of when selected students exerted their spatial ability well or didn't in case of utilizing the developed materials in class. And then the materials were finalized after being finetuned two times by regulating the learning type, sequence and degree of learning difficulty. Regarding the third purpose of the study, the polycube task performed in this study might not be generalizable, but there are seven suggestions on the development process of teaching-learning materials.