• Journal of Elementary Mathematics Education in Korea
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• v.24 no.1
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• pp.169-186
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• 2020

The purpose of this study is to find new material for developing teaching and learning materials for the gifted class of elementary school students by using the rotatable tangram made by modifying the traditional tangram. Rotatable tangram can be justified by gifted students through mathematical communication. However, even gifted class students have some limitations in finding and justifying triangles and rectangles of all sizes unless they go through the 'symbolization' stage at the elementary school level. Therefore, students who need an inquiry process for letters and symbols need to provide supplementary learning materials and additional questions. It is expected that the material of rotatable tangram for the development of teaching and learning materials for elementary school gifted students will contribute to the development of mathematical reasoning and mathematical communication ability.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.143-168
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• 2019

Along with the significance of algebraic thinking in elementary school, it has been recently emphasized that the properties of number and operations need to be explored in a meaningful way rather than in an implicit way. Given this, the purpose of this study was to analyze how third graders could understand the properties of operations in multiplication after they were taught such properties through a reconstructed unit of multiplication. For this purpose, the students from three classes participated in this study and they completed pre-test and post-test of the properties of operations in multiplication. The results of this study showed that in the post-test most students were able to employ the associative property, commutative property, and distributive property of multiplication in (two digits) × (one digit) and were successful in applying such properties in (two digits) × (two digits). Some students also refined their explanation by generalizing computational properties. This paper closes with some implications on how to teach computational properties in elementary mathematics.

• East Asian mathematical journal
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• v.24 no.5
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• pp.527-545
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• 2008

One of the education purpose of the section "Figures" in the eighth grade is to develop students' deductive reasoning ability, which is basic and essential for living in a democratic society. However, most or middle school students feel much more difficulty or even frustration in the study of formal arguments for geometric situations than any other mathematical fields. It is owing to the big gap between inductive reasoning in elementary school education and deductive reasoning, which is not intuitive, in middle school education. Also, it is very burden for students to describe geometric statements exactly by using various appropriate symbols. Moreover, Usage of the same symbols for angle and angle measurement or segments and segments measurement makes students more confused. Since geometric relations is mainly determined by the measurements of geometric objects, students should be able to interpret the geometric properties to the algebraic properties, and vice verse. In this paper, we first compare and contrast inductive and deductive reasoning approaches to justify geometric facts and relations in school curricula. Convincing arguments are based on experiment and experience, then are developed from inductive reasoning to deductive proofs. We introduce teaching methods to help students's understanding for deductive reasoning in the textbook by using stepwise visualization materials. It is desirable that an effective proof instruction should be able to provide teaching methods and visual materials suitable for students' intellectual level and their own intuition.

• Korean Journal of Construction Engineering and Management
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• v.11 no.4
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• pp.22-31
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• 2010

Because the estimated cost at early stage has great influence on decisions of project owner, the importance of early cost estimation is increasing. However, it depends on experience and knowledge of the estimator mainly due to shortage of information. Those tendency developed into case-based reasoning(CBR) method which solves new problems by adapting previous solution to similar past problems. The performance of CBR model is affected by attribute weight, so that its accurate determination is necessary. Previous research utilizes mathematical method or subjective judgement of estimator. In order to improve the problem of previous research, this suggests CBR schematic cost estimation method using genetic algorithm to determine attribute weight. The cost model employs nearest neighbor retrieval for selecting past case. And it estimates the cost of new cases based on cost information of extracted cases. As the result of validation for 17 testing cases, 3.57% of error rate is calculated. This rate is superior to accuracy rate proposed by AACE and the method to determine attribute weight using multiple regression analysis and feature counting. The CBR cost estimation method improve the accuracy by introducing genetic algorithm for attribute weight. Moreover, this makes user understand the problem-solving process easier than other artificial intelligence method, and find solution within short time through case retrieval algorithm.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.769-789
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• 2016

Pattern activities are useful to develop functional thinking of young students, but there has been lack of research on how to teach patterns. This study explored teaching methods of geometric patterns for developing functional thinking of elementary school students, and then analyzed the lessons in which such methods were implemented. For this, three classrooms of fourth grades in elementary schools were selected and three teachers taught geometric patterns on the basis of the same lesson plan. The lessons emphasized noticing the commonality of a given pattern, expanding the noti ce for the commonality, and representing the commonality. The results of this study showed that experience of analyzing the structure of a geometric pattern had a significant impact on how the fourth graders reasoned about the generalized rules of the given pattern and represented them in various methods. This paper closes with several implications to teach geometric patterns in a way to foster functional thinking.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.2
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• pp.205-230
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• 2015

The purpose of this study is, targeting 5th and 6th grades mathematically gifted elementary students, to analyze the effect of independent study project learning on self-directed learning ability and mathematical self-efficacy, and based on the results, examine the implications that independent study project learning has in special education for the gifted. In order to solve the study problems, 5th grade mathematically gifted elementary students(40) and 6th grade mathematically gifted elementary students(39) who had passed the selection criteria of D education institute for the gifted and had been receiving special education for the gifted were selected. The study results are as below. First, although self-directed learning ability had no significant difference at p<0.05, it statistically had some differences in averages between pre-test and post-test results. Second, although mathematical self-efficacy had no significant difference at p<0.05, it statistically had some differences in averages between pre-test and post-test results. Third, in the aspects of self-directed learning ability and mathematical self-efficacy, independent study project learning had a more positive effect on 5th grade mathematically gifted elementary students than 6th grade mathematically gifted elementary students. In addition, it had significant differences in 'the level of mathematical tasks', a sub-level of mathematical self-efficacy, and 'the openness of learning', 'the initiative of learning', and 'a sense of responsibility for learning', sub-levels of self-directed learning ability. These results imply that independent study project learning has a positive effect on self-directed learning ability and mathematical self-efficacy of mathematically gifted elementary students so that it could be meaningfully used as a teaching method for special education for the gifted at educational sites of independent study project learning.

• Journal of the Korean School Mathematics Society
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• v.12 no.3
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• pp.347-364
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• 2009

In this paper, the researchers investigated the influence of graphing calculator in learning the concept of linear function for the gifted students. Elementary students who were taking a course in enrichment mathematics at Science Education Institute for the Gifted in Mokpo National University were selected for this study. The researchers analyzed students' processes of mathematical inference and conjecture, and students' algebraic description. We found the facts that the visualization using a graphing calculator and CBL is helpful to the gifted students in understanding concepts of liner function, finding the relationship between variables, analyzing and presupposing of graph. But, using graphing calculator can be a factor that disturbs learning of students who have too much of curiosity on graphing calculator.

• The Mathematical Education
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• v.59 no.3
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• pp.217-235
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• 2020

This study examined Korean fourth-grade students' performance by gender on the Trends in International Mathematics and Science Study(TIMSS) 2011 and 2015 mathematics assessment. We first identified items which had significantly higher mean scores by gender to decide which gender did better on a certain domain(domain-level analysis). Then, we examined the content of items(item-level analysis) to understand which items lead to gender differences in mathematics achievement. Our findings showed that about 80% of the items on both assessments did not show statistically significant differences between males and females. However, there were meaningful gender differences in the other 20% items. On both assessments, females had more items with significantly higher mean scores than males on the Shapes domain, and males had more those items on the Numbers and Measurement domains and all cognitive domains(Knowing, Applying, and Reasoning). In particular, females outperformed males on items related to identifying two- and three-dimensional shapes and drawing lines and angles and identifying them. Conversely, males had higher performance than females on items related to the pre-algebraic thinking, fractions and decimals, estimation of number differences, unit of length, and measuring time, height, and volume. The effect sizes for each item ranged from .12 to .33 and the mean effect size of all items across both assessments was .20, which indicated significant gender differences but small.

• 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.

• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.179-199
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• 2007

The purpose of this study was to discover differences between mathematically gifted students (MGS) and non-gifted students (NGS) when making probability judgments. For this purpose, the following research questions were selected: 1. How do MGS differ from NGS when making probability judgments(answer correctness, answer confidence)? 2. When tackling probability problems, what effect do differences in probability judgment factors have? To solve these research questions, this study employed a survey and interview type investigation. A probability test program was developed to investigate the first research question, and the second research question was addressed by interviews regarding the Program. Analysis of collected data revealed the following results. First, both MGS and NGS justified their answers using six probability judgment factors: mathematical knowledge, use of logical reasoning, experience, phenomenon of chance, intuition, and problem understanding ability. Second, MGS produced more correct answers than NGS, and MGS also had higher confidence that answers were right. Third, in case of MGS, mathematical knowledge and logical reasoning usage were the main factors of probability judgment, but the main factors for NGS were use of logical reasoning, phenomenon of chance and intuition. From findings the following conclusions were obtained. First, MGS employ different factors from NGS when making probability judgments. This suggests that MGS may be more intellectual than NGS, because MGS could easily adopt probability subject matter, something not learnt until later in school, into their mathematical schemata. Second, probability learning could be taught earlier than the current elementary curriculum requires. Lastly, NGS need reassurance from educators that they can understand and accumulate mathematical reasoning.