• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.619-636
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• 2012

The main purpose of this study was to explore the process of generalization generated by mathematically gifted students. Specifically, this study probed how fourth, fifth, and sixth graders might generalize geometric patterns and represent such generalization. The subjects of this study were a total of 30 students from gifted classes of one elementary school in Korea. The results of this study showed that on the question of the launch stage, students used a lot of recursive strategies that built mainly on a few specific numbers in the given pattern in order to decide the number of successive differences. On the question of the towards a working generalization stage, however, upper graders tend to use a contextual strategy of looking for a pattern or making an equation based on the given information. The more difficult task, more students used recursive strategies or concrete strategies such as drawing or skip-counting. On the question of the towards an explicit generalization stage, students tended to describe patterns linguistically. However, upper graders used more frequently algebraic representations (symbols or formulas) than lower graders did. This tendency was consistent with regard to the question of the towards a justification stage. This result implies that mathematically gifted students use similar strategies in the process of generalizing a geometric pattern but upper graders prefer to use algebraic representations to demonstrate their thinking process more concisely. As this study examines the strategies students use to generalize a geometric pattern, it can provoke discussion on what kinds of prompts may be useful to promote a generalization ability of gifted students and what sorts of teaching strategies are possible to move from linguistic representations to algebraic representations.

• School Mathematics
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• v.10 no.3
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• pp.401-422
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• 2008

In the current school curriculum, an alternative assessment method which focuses more on the problem solving process rather than the final solution is being investigated. The goal is to evaluate students' understanding of the subject. A descriptive evaluation is being suggested as a way of examining the thought process of the students by a structured analysis of the problem solving process. But currently, there are not enough descriptive problems available for teachers to effectively carry out the alternative assessment method in the elementary school mathematics curriculum. In this research, we surveyed 197 elementary school teachers in Seoul to determine the status of descriptive evaluation in elementary school mathematics and to understand the teachers perception about the new assessment method. The goal of the survey was to find an effective implication of the new assessment method in elementary mathematics classes. The research showed that the elementary teachers use this assessment method about 4 to 7 times per month in their classes. They give descriptive problem test anytime they think it is appropriate during the Instruction of the topic. More than 90% of the teachers were using this assessment method to improve students' creativity and mathematical thinking. The teachers in the survey also commented that the teachers' administrative responsibility should be reduced and that the school environment in general should be improved for the new assessment method to be successful. Finally the study also showed that development of more descriptive problems in each grade level is needed to progress the new assessment method.

• School Mathematics
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• v.5 no.4
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• pp.421-440
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• 2003

It is difficult for the learner to understand completely the ratio concept which forms a basis of proportional reasoning. And proportional reasoning is, on the one hand, the capstone of children's elementary school arithmetic and, the other hand, it is the cornerstone of all that is to follow. But school mathematics has centered on the teachings of algorithm without dealing with its essence and meaning. The purpose of this study is to analyze the essence of ratio concept from multidimensional viewpoint. In addition, this study will show the direction for improvement of ratio concept. For this purpose, I tried to analyze the historical development of ratio concept. Most mathematicians today consider ratio as fraction and, in effect, identify ratios with what mathematicians called the denominations of ratios. But Euclid did not. In line with Euclid's theory, ratio should not have been represented in the same way as fraction, and proportion should not have been represented as equation, but in line with the other's theory they might be. The two theories of ratios were running alongside each other, but the differences between them were not always clearly stated. Ratio can be interpreted as a function of an ordered pair of numbers or magnitude values. A ratio is a numerical expression of how much there is of one quantity in relation to another quantity. So ratio can be interpreted as a binary vector which differentiates between the absolute aspect of a vector -its size- and the comparative aspect-its slope. Analysis on ratio concept shows that its basic structure implies 'proportionality' and it is formalized through transmission from the understanding of the invariance of internal ratio to the understanding of constancy of external ratio. In the study, a fittingness(or comparison) and a covariation were examined as the intuitive origins of proportion and proportional reasoning. These form the basis of the protoquantitative knowledge. The development of sequences of proportional reasoning was examined. The first attempts at quantifying the relationships are usually additive reasoning. Additive reasoning appears as a precursor to proportional reasoning. Preproportions are followed by logical proportions which refer to the understanding of the logical relationships between the four terms of a proportion. Even though developmental psychologists often speak of proportional reasoning as though it were a global ability, other psychologists insist that the evolution of proportional reasoning is characterized by a gradual increase in local competence.

• Journal of Educational Research in Mathematics
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• v.14 no.4
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• pp.367-385
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• 2004

This study intends to compare the way of introducing fractions in elementary mathematics textbooks of south and those of north Korea. After thorough investigations of the seven differences were identified. First, the mathematics textbooks of south Korea use concrete materials like apples when they introduce equal partition context, while those of north Korea do not use that kind of concrete materials. Second, in the textbooks of south Korea, equal partition of discrete quantities are considered after continuous ones are introduced. This is different from the approach of the north Korean text-books in which both quantities are regarded at the same time. Third, the quantitative fraction which refers to the rational number with unit of measure at the end of it, is hardly used in the textbooks of south. However, the textbooks of north Korea use it as the main representations of fractions. Fourth, in the textbooks of south Korea, vanous activities related to fractions are more emphasized, while in the textbooks of north Korea, various meanings of fractions textbooks from south and north Korea focused on the ways of introducing partition approach and equivalence relation as operational schemes of fractions, the following play an important role before defining fraction. Fifth, the textbooks of south Korea introduce equivalent fractions with number one using number bar, and do not consider the reason why that sort of fractions are regarded. On the contrary, the textbooks of north Korea introduce structural equivalence relation by using various contexts including length measure and volume measure situations. Sixth, whereas real-life contexts are provided for introducing equivalent fractions in the textbooks of south Korea, visual explanations and mathematical representations play an important role in the textbooks of north Korea. Seventh, the means of finding equivalent fractions are provided directly in the textbooks of south Korea, whereas the nature of equivalent fractions and the methods of making equivalent fractions are considered in the textbooks of north Korea.

• The KIPS Transactions:PartB
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• v.14B no.1 s.111
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• pp.43-50
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• 2007

This study proposes design of courseware based on scaffolding for teaching math word problem solving of students with intellectual disabilities. This courseware not only offer various technological supports to solving difficult problems of students with intellectual disabilities but also systematically withdraw that supports. Compared with previous related softwares, this courseware has potential that can adapt math strategies to meet different needs of individuals with intellectual disabilities, increase independent learning ability of learners and maintain high level of motive through successful problem solving experience.

• 전기의세계
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• v.39 no.4
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• pp.10-18
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• 1990

우리나라 전기전자공학과는 완전히 분리되어 있고 그 외에도 제어계측공학과, 전산기공학과, 전자통신공학과 등으로 분리되어 있으나 선진국에서는 하나의 학과로 되어 있다. 그리고 우리나라의 교과과정은 졸업에 필요한 과목수가 지나치게 많아서 한과목을 깊게 공부하는대산 여러과목을 훑어보는 식으로 운용되어 왔다. 전공과목수가 9개(실제로는 미분방정식과 졸업논문을 제외하면 7개) 밖에 안된다고 해서 M.I.T.의 전기전자공학 교육이 우리나라보다 못하다고 말 할 수는 없다. MIT의 교과과정이 오늘과 같이 된데에는 오랜 연구와 경험이 필요하였다. 즉 기술 과목만을 많이 가르쳐서 졸업시키면 졸업생의 대부분이 인문사회 출신 사장 아래에서 기술자 역할밖에 못한다는 것을 알았던 것이다. 2차 대전 당시 레이다를 포함한 각종 신형전자장비를 개발한 것은 공대출신보다는 물리학과 수학과 출신의 역할이 컸던 것이다. 특히, SPUTNIK이 1957년에 발사된 이후 미국의 공대들은 과학과목에 큰 비중을 두게 되었던 것이다. 최근에는 그 반작용으로 설계과목에 비중을 두기 시작하였다. 졸업후 2-3년 지나면 별로 쓸모없는 과목들을 많이 가르치는 것보다는 기초적인 과목만을 충실하게 가르치는 것이 훨씬 좋다고 본다.

• School Mathematics
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• v.19 no.2
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• pp.319-343
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• 2017

In this study, we hope to reveal specialized content knowledge(SCK) and its features necessary to analyze student's errors and difficulties about the concept of irrational numbers. The instruments and interview were administered to 3 in-service mathematics teachers with various education background and teaching experiments. The results of this study are as follows. First, specialized content knowledge(SCK) were characterized by the fixation to symbolic representation like roots when they analyzed the concentration and overlooking of the representations of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations as the standard of judgment about irrational numbers. Thirdly, In-service teachers were influenced by content of students' error when they analyzed the error and difficulties of students. Lately, we confirmed that the content knowledge about the viewpoint of procept and actual infinity of irrational numbers are most important during the analyzing process.

• Journal for History of Mathematics
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• v.25 no.1
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• pp.71-88
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• 2012

The purpose of this study is to find the way to build the concept image about natural logarithm and the method is using definite integral in calculus under GeoGebra environment. When the students approach to natural logarithm, need to use dynamic program about the definite integral in calculus. Visible reasoning process through using dynamic program(GeoGebra) is the most important part that make the concept image to students. Also, for understand mathematical concept to students, using GeoGebra environment in dynamic program is not only useful but helpful method of teaching and studying. In this article, about graph of natural logarithm using the definite integral, to explore process of understand and to find special feature under GeoGebra environment. And it was obtained from a survey of undergraduate students of mathmatics. Also, relate to this process, examine an aspect of students, how understand about connection between natural logarithm and the definite integral, definition of natural logarithm and mathematical link of e. As a result, we found that undergraduate students of mathmatics can understand clearly more about the graph of natural logarithm using the definite integral when using GeoGebra environment. Futhermore, in process of handling the dynamic program that provide opportunity that to observe and analysis about process for problem solving and real concept of mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.351-370
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• 2013

The purpose of this study is to analyze the modes of visualization which appears in the process of thinking that mathematically gifted 6th grade students get to understand components of the three-dimensional shapes on the duality of regular polyhedrons, find the duality relation between the relations of such components, and further explore on whether such duality relation comes into existence in other regular polyhedrons. The results identified in this study are as follows: First, as components required for the process of exploring the duality relation of polyhedrons, there exist primary elements such as the number of faces, the number of vertexes, and the number of edges, and secondary elements such as the number of vertexes gathered at the same face and the number of faces gathered at the same vertex. Second, when exploring the duality relation of regular polyhedrons, mathematically gifted students solved the problems by using various modes of spatial visualization. They tried mainly to use visual distinction, dimension conversion, figure-background perception, position perception, ability to create a new thing, pattern transformation, and rearrangement. In this study, by investigating students' reactions which can appear in the process of exploring geometry problems and analyzing such reactions in conjunction with modes of visualization, modes of spatial visualization which are frequently used by a majority of students have been investigated and reactions relating to spatial visualization that a few students creatively used have been examined. Through such various reactions, the students' thinking in exploring three dimensional shapes could be understood.

• Journal of The Korean Association For Science Education
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• v.34 no.3
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• pp.295-301
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• 2014

The purpose of this study is to investigate the difficulties of teachers and students on the unit about 'measuring weight.' In this research, we have acquired data about teachers through survey, interview, and self-reflection journals, at the same time we have collected information on the students through survey, assessment test, and interview. We have extracted the difficulties from analysis with constant comparison method. In addition, we have analysed the curriculum of science and mathematics to know the leaning sequence. The analysis had been checked up by experts in science education. The result of the study is as follows: The difficulties of teachers are from the lack of teachers' descriptive knowledge, disorder of conceptual hierarchy in the curriculum, poor experimental instruments, and low psychomotor skill of students. The difficulties of students are from common misconceptions, opaque concepts, lack of manipulation skill, insufficiency of mathematical ability, difficulty of application of principles to the real situation, and lack of problem-solving ability. In addition, teachers have recognized that students face more difficulties in experiment class, while students think that they face more difficulties in conceptual understanding class.