• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.359-388
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• 2012

The study aims to extract the framework of sub-factors of spatial sense, to develop test instruments based on the framework to investigate the actual spatial sense ability of fourth to sixth graders in elementary school and to analyze the results. According to the framework of sub-factors of spatial sense of the study, spatial sense has two factors of spatial visualization and spatial orientation. Spatial visualization is divided into mental rotation, mental transformation and figure-ground perception while spatial orientation is categorized into direction sense, distance sense, and location sense. Based on the framework, the test instrument for spatial sense ability was developed and the test was conducted to 430 fourth to sixth students in five elementary schools in capital areas. The following conclusions were drawn from the results obtained in the study. Firstly, the higher school year gets, the more spatial sense grows. However, spatial visualization is developed much more than spatial orientation and their order is reversed with higher graders. Secondly, the most insufficient abilities among fourth to sixth elementary school students' spatial sense were mental transformation of spatial visualization and location sense of spatial orientation. Thirdly, the reasons of differences in sub-factors of spatial sense and graders seem to be from effects of students' learning experiences of spatial sense of mathematics curriculum and the complexities of test items.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.361-383
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• 2011

This study is on teaching about the areas of plane figures through open instruction, which aims to discover the pedagogical meanings and implications in the application of open methods to math classes by running the Math A & B classes regarding the areas of parallelogram, triangle, trapezoid and rhombus for fifth graders of elementary school through open instruction method and analyzing the educational process. This study led to the following results. First, it is most important to choose proper open-end questions for classes on open instruction methods. Teachers should focus on the roles of educational assistants and mediators in the communication among students. Second, teachers need to make lists of anticipated responses from students to lead them to discuss and focus on more valuable methods. Third, it is efficient to provide more individual tutoring sessions for the students of low educational level as the classes on open instruction methods are carried on. Fourth, students sometimes figured out more advanced solutions by justifying their solutions with explanations through discussions in the group sessions and regular classes. Fifth, most of students were found out to be much interested in the process of thinking and figuring out solutions through presentations and questions in classes and find it difficult to describe their thoughts.

• School Mathematics
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• v.19 no.1
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• pp.59-75
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• 2017

This study analyzed the $6^{th}$ graders' constructions about fraction operations and schemes and figured out the relationships quantitatively between operations and schemes through the written test of 432 students. The results of this study showed that most of students could do partitioning operation well, however, there were many students who had difficulties on iterating operation. There were more students who constructed partitioning operation prior to iterating operation than the opposite. The rate of students who constructed high schemes was lower than that of students who constructed low schemes according to the hierarchy of fraction schemes. Especially, there were many students who construct partitive unit fraction scheme but not partitive fraction scheme, because they could compose unit fraction but not do iterating it. And there were the high correlations between fraction operations and schemes. Given these result, this paper suggests implications about the teaching and learning of fraction.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.663-682
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• 2016

This study conducted an analysis of strategies that the 3rd to 6th grade elementary students used when they were solving problems of comparing the size of the fractions with like and unlike denominators, and unit fractions. Although there were slight differences in the students' use of strategies according to the problem types, students were found to use the 'part-whole strategy', 'transforming strategy', and 'between fractions strategy' frequently. But 'pieces strategy', 'unit fraction strategy', 'within fraction strategy', and 'equivalent fraction strategy' were not used frequently. In regard to the strategy use that is appropriate to the problem condition, it was found that students needed to use the 'unit fraction strategy', and the 'within fraction strategy', whereas there were many errors in their use of the 'between fractions strategy'. Based on the results, the study attempted to provide pedagogical implications in teaching and learning for comparing the size of the fractions.

• School Mathematics
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• v.9 no.3
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• pp.353-373
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• 2007

The purpose of this study was to provide instructional suggestions by investigating the spatial sense and spatial reasoning ability of 6th grade students. The questionnaire consisted of 20 questions, 10 for spatial visualization and 10 for spatial orientation. The number of subjects for the survey was 145. The processes through which the students solved the problems were the basis for the assessment of their spatial reasoning. The result of the survey is as follows: First, students performed better in spatial visualization than in spatial orientation. With regard to spatial visualization, they were better in transformation than in rotation. With regard to spatial orientation, students performed better in orientation sense and structure cognitive ability than in situational sense. Second, the students that weren't excellent in spatial visualization tended to answer the familiar figures without using mental images. The students who lacked spatial orientation experienced difficulties finding figures observed from the sides. Third, students had high frequency rate on the cognition and use of transformation, the development and application of visualization methods and the use of analysis and synthesis. However they had a lower rate on a systematic approach and deductive reasoning. Further detailed investigation into how students use spatial reasoning, and apply it to actual teaching practice as a device for advancing their geometric thinking is necessary.

• Education of Primary School Mathematics
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• v.19 no.3
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• pp.211-222
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• 2016

This article examines K-8 pre-service teachers' (PSTs) engagement in lesson plan modification using the eight Mathematics Teaching Practices (MTPs) in Principles to Actions, the most recent landmark publication of framework by National Council of Teachers of Mathematics (NCTM) in the U.S. The activity consisted of four phases that involved the analysis and modification of an existing lesson plan. Fifty-seven PSTs participated in the activity throughout the semester, and data from each phase was analyzed using the inductive content analysis approach. PSTs' initial conceptions of lesson planning reflected little on teaching practices (i.e., the MTPs) with more emphasis placed on the form - rather than function - of lesson elements. With the opportunity to interpret MTPs and analyze lesson plans using MTPs as an analytical lens, PSTs demonstrated various interpretations of MTPs, made efforts to incorporate MTPs into lessons, and attended to the interwoven nature of MTPs. This article also shares the challenges, conflicts, and tensions reported by PSTs during their participation of lesson plan modification; as such, the results from this study will inform the research examining the pedagogical (im)possibilities for utilizing MTPs in mathematics teacher training programs.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.113-139
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• 2013

The purpose of this study is to provide informations about cause of failures when students solve word problems by analyzing what errors students made in solving word problems and types of error and features of error according to problem solving strategy. The results of this study can be summarized as follows: First, $5^{th}$ grade students preferred the expressions, estimate and verify, finding rules in order when solving word problems. But the majority of students couldn't use simplifying. Second, the types of error encountered according to the problem solving strategy on problem based learning are as follows; In the case of 'expression', the most common error when using expression was the error of question understanding. The second most common was the error of concept principle, followed by the error of solving procedure. In 'estimate and verify' strategy, there was a low proportion of errors and students understood estimate and verify well. When students use 'drawing diagram', they made errors because they misunderstood the problems, made mistakes in calculations and in transforming key-words of data into expressions. In 'making table' strategy, there were a lot of errors in question understanding because students misunderstood the relationship between information. Finally, we suggest that problem solving ability can be developed through an analysis of error types according to the problem strategy and a correct teaching about these error types.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.89-110
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• 2004

The purpose of this study is to identify the significant characteristics shown in the field of mathematics by a gifted child, the educational curriculum for this child, and to find what has to be set in place in the areas of teacher's teaching methods and programs. The important aspect of these ideas is that one has to completely understand and know the characteristics of the gifted in order to give them the opportunity to discover their underlying talents and to develop upon those skills by giving them suitable and appropriate education for their intellectual state. This study focuses on the thoughts and behavior of a gifted male child, from his third to fifth grade, and the study shows the results and analysis of data gathered from close observation and interview, and a collection of documents gathered from the child. This study is analyzed from three different perspectives: 1. The typical life and surroundings of this gifted child, and how he was raised in this particular environment. This also shows the significant event that allowed others to recognize him as gifted. 2. Identification of how a gifted child's mind works in the field of mathematics. This attempts to analyze methods the child uses to arrive at a solution to a problem. 3. Exploration of mathematical attitude of the child. This shows the child's interest in mathematics, and the willingness to find better and more efficient ways to reach a solution. This also shows the child's ability to explain his purpose and methods of problem solving in detail, and the focus and clarity in communication of mathematics. This study will enlighten the readers with information on the importance of advanced education specifically designed for the gifted. In development of advanced education programs, it is necessary to comprehend the minds of the mathematically gifted, and furthermore, this will help in defining an appropriate teaching method and curriculum for a better equipped educational system.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.287-314
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• 2010

The algorithm is a chain of mechanical procedures, capable of solving a problem. In modern mathematics educations, the teaching algorithm is performing an important role, even though contracted than in the past. The conspicuous characteristic of current elementary mathematics textbook's manner of manipulating multiplication algorithm is exceeding converge to 'standard algorithm.' But there are many algorithm other than standard algorithm in calculating multiplication, and this diversity is important with respect to didactical dimension. In this thesis, we have reconstructed the experimental learning and teaching plan of multiplication algorithm unit by making the best use of diversity of multiplication algorithm. It's core contents are as follows. Firstly, It handled various modified algorithms in addition to standard algorithm. Secondly, It did not order children to use standard algorithm exclusively, but encouraged children to select algorithm according to his interest. As stated above, we have performed teaching experiment which is ruled by new lesson design and analysed the effects of teaching experiment. Through this study, we obtained the following results and suggestions. Firstly, the experimental learning and teaching plan was effective on understanding of the place-value principle and the distributive law. The experimental group which was learned through various modified algorithm in addition to standard algorithm displayed higher degree of understanding than the control group. Secondly, as for computational ability, the experimental group did not show better achievement than the control group. It's cause is, in my guess, that we taught the children the various modified algorithm and allowed the children to select a algorithm by preference. The experimental group was more interested in diversity of algorithm and it's application itself than correct computation. Thirdly, the lattice method was not adopted in the majority of present mathematics school textbooks, but ranked high in the children's preference. I suggest that the mathematics school textbooks which will be developed henceforth should accept the lattice method.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.179-198
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• 2011

The understanding of mathematical concepts should be backed up on a constant basis in oder to grow problem-solving skills which is one of the ultimate goals of math education. The purpose of the study was to provide readers with the information which could be considered valuably for the math educators trying both to prevent mathematical misconceptions and to develop curricular program by estimating the actual conditions and developing backgrounds of the mathematical misconceptions held by the gifted education learners. Accordingly, this study, as the first step, theoretically examined the meaning and the developing background of mathematical misconception. As the second step, this study examined the actual conditions of mathematical misconceptions held by the participant students who were enrolled in the CTY(Center for Talented Youth) program run by a university. The results showed that the percentage of the correct statements made by participant students is only 35%. The results also showed that most of the participant students belonged either to the level 2 requiring students to distinguish examples from non-examples of the mathematical concepts or the level 3 requiring students to recognize and describe the common nature of the mathematical concepts with their own expressions based on the four-level of concept formulation. The causes could be traced to the presentation of limited example, wrong preconcept, the imbalance of conceptual definition and conceptual image. Based on the estimation, this study summarized a general plan preventing the mathematical misconceptions in a math classroom.