• School Mathematics
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• v.8 no.4
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• pp.379-396
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• 2006

The purpose of this study is to analyze characteristics of problem solving in mathematics for gifted students through case study on solving the mathematical problem for gifted students, and to investigate what are relationships with the cognitive and affective characteristics. To this end, this study was to analyze the characteristics on the problem solving in mathematics by using qualitative research method after it selected two students who had specific education for brilliant students. As a result, this study has shown that it had high preference for question with clear answer, high preference for individual inquiry learning, high adhesion to answer for question, and high adhesion for assignment on characteristics of process of problem solving, but there was much difference in spirit of competition. As to the characteristics of thoughts in problem solving, this study has shown that it had high grasp capacity, intuitive insight, and capacity for visualization, but there were differences in capacity for generalization and adaptability. However, both two students had low values in deductive thought. In addition, as to the home environment and cognitive and affective characteristics, they were not related to the characteristics on problem solving directly, but it has shown that it affected each other indirectly. As to the conclusion of this study, this researcher thinks that it will be valuable documentation in order to improve curriculum, development of textbooks, and teaching method for special education for the gifted students and education for secondary mathematics.

• Journal of Korean Elementary Science Education
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• v.25 no.2
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• pp.118-125
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• 2006

The purpose of the study was to research science gifted students' learning styles and perceptions on subject matter content. The data was collected from primary science and mathematics classes of a University Center for Science Gifted Education, science classes of a Metrocity Primary Gifted Education Institute, and classes of a normal school. The results of the study were that gifted students perceived the school curriculum much easier than non-gifted students did, ($X^2(4)=33.180$, p<.001), and that levels of interest in the content did not differ between the groups, but 34.6 percent of the total students responded that they found the content uninteresting. Gifted students did not see the content as being important compared to the non-gifted students, ($X^2(4)=12.443$, p<.05), and gifted students valued the methods used higher than the actual content of the textbook. The most helpful activities for their teaming that gifted students chose were projects, listening to teachers, and conducting experiments, amongst others. They also preformed 'teaming at their own speed in a mixed group'" for the study of social studies, science, and mathematics, whereas non-gifted students preformed teaming at the same speed. The two groups of science gifted students varied especially in their perceptions of most helpful activities. It is suggested that special programs for fulfilling gifted students' needs and abilities need to be developed and implemented.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.107-122
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• 2010

Mathematically gifted students' emotional changes during Mathematical Olympiad training camp were studied. The emotions of the gifted during the camp were fluctuated significantly by comparing their test scores with other camp attendants, while the morale was high at the beginning. The camp attendants were likely to overcome disappointment resulting from bad scores with putting more efforts on studying, which means their self-assessments for their mathematical talents are not affected by test results. From what characterizes the emotional changes of the gifted, we conclude as follows: First, they tend to be positive on grouping classes depending on the mathematical ability. Second, careful emotional supports and care were needed in ability grouping education. Third, it is important to let the gifted have more chances to communicate with other camp attendants. It is recommended to induce the gifted to put their focus on the learning goal. Fifth, the proper environment helps the gifted be indulged in studying mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.3
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• pp.309-330
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• 2018

The purpose of this study is to identify possibility of a mathematical problem posing ability by presenting problem posing tasks with different degrees of structure according to the study of Stoyanova and Ellerton(1996). Also, the results of this study suggest the direction of gifted elementary mathematics education to increase mathematical creativity. The research results showed that mathematical problem posing ability is likely to be a factor in identification of gifted students, and suggested directions for problem posing activities in education for mathematically gifted by investigating the characteristics of original problems. Although there are many criteria that distinguish between gifted and ordinary students, it is most desirable to utilize the measurement of fluency through the well-structured problem posing tasks in terms of efficiency, which is consistent with the findings of Jo Seokhee et al. (2007). It is possible to obtain fairly good reliability and validity in the measurement of fluency. On the other hand, the fact that the problem with depth of solving steps of 3 or more is likely to be a unique problem suggests that students should be encouraged to create multi-steps problems when teaching creative problem posing activities for the gifted. This implies that using multi-steps problems is an alternative method to identify gifted elementary students.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.339-356
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• 2010

It is important for children to develop statistical reasoning as they think through data. In particular, it is imperative to provide children instructional situations in which they are encouraged to consider variability in data because the ability to reason about variability is fundamental to the development of statistical reasoning. Many researchers argue that even highperforming mathematics students show low levels of statistical reasoning; interventions attending to pedagogical concerns about child ren's statistical reasoning are, thus, necessary. The purpose of this study was to investigate 15 gifted elementary students' various ways of understanding important statistical concepts, with particular attention given to 3 students' reasoning about data that emerged as they engaged in the process of generating and graphing data. Analysis revealed that in recognizing variability in a context involving data, mathematically gifted students did not show any difference from previous results with general students. The authors suggest that our current statistics education may not help elementary students understand variability in their development of statistical reasoning.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.131-148
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• 2016

Mathematical formal justification may be seen as a bridge towards the proof. By requiring the mathematically gifted students to prove the generalized patterned task rather than the implementation of deductive justification, may present challenges for the students. So the research questions are as follow: (1) What are the difficulties the mathematically gifted elementary students may encounter when formal justification were to be shifted into a generalized form from the given patterned challenges? (2) How should the teacher guide the mathematically gifted elementary students' process of transition to formal justification? The conclusions are as follow: (1) In order to implement a formal justification, the recognition of and attitude to justifying took an imperative role. (2) The students will be able to recall previously learned deductive experiment and the procedural steps of that experiment, if the mathematically gifted students possess adequate amount of attitude previously mentioned as the 'mathematical attitude to justify'. In addition, we developed the process of questioning to guide the elementary gifted students to formal justification.

• The Mathematical Education
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• v.58 no.4
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• pp.519-530
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• 2019

According to previous studies, meta-affect based on the interaction between cognitive and affective elements in mathematics learning activities maintains a close mechanical relationship with the learner's mathematical ability in a similar way to meta-cognition. In this study, in order to grasp these characteristics phenomenologically, small group problem-solving cases of 5th grade elementary mathematically gifted children were analyzed from a meta-affective perspective. As a result, the two types of problem-solving cases of mathematically gifted children were relatively frequent in the types of meta-affect in which cognitive element related to the cognitive characteristics of mathematically gifted children appeared first. Meta-affects were actively acted as the meta-function of evaluation and attitude types. In the case of successful problem-solving, it was largely biased by the meta-function of evaluation type. In the case of unsuccessful problem-solving, it was largely biased by the meta-function of the monitoring type. It could be seen that the cognitive and affective characteristics of mathematically gifted children appear in problem solving activities through meta-affective activities. In particular, it was found that the affective competence of the problem solver acted on problem-solving activities by meta-affect in the form of emotion or attitude. The meta-affecive characteristics of mathematically gifted children and their working principles will provide implications in terms of emotions and attitudes related to mathematics learning.

• Journal of Gifted/Talented Education
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• v.18 no.1
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• pp.79-109
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• 2008

In most curricular model for gifted children, independent study is included as an important element for developing students' study ability and producing creative production Gifted children also prefers this style of learning and they study more easily and with more fun when they learn in the learning style they prefer. This study aims to find out how gifted children in math area performs independent study and how teachers who teach them recognize independent study; survey study was used to analyze the reality of the production in relation to independent study. In result, gifted children's independent study ability was rather very low and teachers recognized the necessity of independent study but lacked understanding of the method of independent study.

• School Mathematics
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• v.15 no.2
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• pp.459-479
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• 2013

The Purpose of this study was to explore the methods of generalization and errors pattern generated by mathematically gifted students and non-gifted students in elementary school. In this research, 6 problems corresponding to the x+a, ax, ax+c, $ax^2$, $ax^2+c$, $a^x$ patterns were given to 156 students. Conclusions obtained through this study are as follows. First, both group were the best in symbolically generalizing ax pattern, whereas the number of students who generalized $a^x$ pattern symbolically was the least. Second, mathematically gifted students in elementary school were able to algebraically generalize more than 79% of in x+a, ax, ax+c, $ax^2$, $ax^2+c$, $a^x$ patterns. However, non-gifted students succeeded in algebraically generalizing more than 79% only in x+a, ax patterns. Third, students in both groups failed in finding commonness in phased numbers, so they solved problems arithmetically depending on to what extent it was increased when they failed in reaching generalization of formula. Fourth, as for the type of error that students make mistake, technical error was the highest with 10.9% among mathematically gifted students in elementary school, also technical error was the highest as 17.1% among non-gifted students. Fifth, as for the frequency of error against the types of all patterns, mathematically gifted students in elementary school marked 17.3% and non-gifted students were 31.2%, which means that a majority of mathematically gifted students in elementary school are able to do symbolic generalization to a certain degree, but many non-gifted students did not comprehend questions on patterns and failed in symbolic generalization.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.3
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• pp.523-539
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• 2013

The object of this study is to compare and analyze mathematically gifted and non-gifted elementary students in the family system and career attitude maturity, understand the characteristics of the former, and provide assistance for career education for both groups. The subjects include 145 mathematically gifted elementary students (73 fifth graders, 72 sixth graders) and 167 non-gifted students (78 fifth graders, 89 sixth graders) in G educational agencies. Materials for the experiment include amended family system test and career attitude maturity test. While t-test was conducted to solve the first research question, Pearson's correlation analysis was performed to solve the other one. The research findings were as follows: First, mathematically gifted elementary students, compared to non-gifted students, turned out to have higher rates of the family system and career attitude maturity rate and showed statistically meaningful positive relationship. Second, the lower components of the family system and career attitude maturity, there seems to be no relationship between family-flexibility and finality. However, among other components, there was a level of significance at 5% which shows statistically meaningful positive relationship. In summary, this found that the family system is able to have an effect on the career attitude maturity for both mathematically gifted elementary students and non-gifted students. Hence, it need to be considered the components of family system when the teacher guides mathematically gifted elementary students and non-gifted students associated with their career.