• Journal of Gifted/Talented Education
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• v.11 no.3
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• pp.99-129
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• 2001

The purpose of the present study is to determine antecedents in the area of subject matters and to compare these factors between average student group and gifted student group, based on the implicit theory proposed by Sternberg(1993). The average group consisted of 350 primary school students (boy 172; girl 178) from a primary school and 380 middle school students (boy 221; girl 159) from a middle school in Taejeon Metropolitan City. The gifted group consisted of 181 primary school students (boy 130; girl 51) and 154 middle school students (boy 92; girl 62) from the Center for the Gifted Education of the Kong Ju National University. A questionnaire was developed by the authors. It consisted of 30 research questions related to reasons why they studied those subject matters hard. It took about 40 minutes to complete the questionnaire. Several exploratory factor analyses and confirmative analyses were conducted. The main results obtained were as follows: The subject matters all the students of the present study were English and Math. The main reasons why they studied those subject matters hard were interest, utility, competition, self-esteem, entrance examination, recognition, punishment avoidance, etc. A factor analysis revealed that, for the elementary school students, recognition and interest were factors for the average students, whereas knowledge acquisition was an unique factor for the gifted. Utility was common factor for both groups. A factor analysis revealed that, for the middle school students, knowledge acquisition was the main factor for the average students, whereas competition was the unique factor for the gifted. Recognition, interest, and utility were common factors for the both groups.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.215-241
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• 2017

This study analyzed teachers' Pedagogical Content Knowledge (PCK) regarding the pedagogical aspect of the instruction of ratio and rate in order to look into teachers' problems during the process of teaching ratio and rate. This study aims to clarify problems in teachers' PCK and promote the consideration of the materialization of an effective and practical class in teaching ratio and rate by identifying the improvements based on problems indicated in PCK. We subdivided teachers' PCK into four areas: mathematical content knowledge, teaching method and evaluation knowledge, understanding knowledge about students' learning, and class situation knowledge. The conclusion of this study based on analysis of the results is as follows. First, in the 'mathematical content knowledge' aspect of PCK, teachers need to understand the concept of ratio from the perspective of multiplicative comparison of two quantities, and the concept of rate based on understanding of two quantities that are related proportionally. Also, teachers need to introduce ratio and rate by providing students with real-life context, differentiate ratios from fractions, and teach the usefulness of percentage in real life. Second, in the 'teaching method and evaluation knowledge' aspect of PCK, teachers need to establish teaching goals about the students' comprehension of the concept of ratio and rate and need to operate performance evaluation of the students' understanding of ratio and rate. Also, teachers need to improve their teaching methods such as discovery learning, research study and activity oriented methods. Third, in the 'understanding knowledge about students' learning' aspect of PCK, teachers need to diversify their teaching methods for correcting errors by suggesting activities to explore students' own errors rather than using explanation oriented correction. Also, teachers need to reflect students' affective aspects in mathematics class. Fourth, in the 'class situation knowledge' aspect of PCK, teachers need to supplement textbook activities with independent consciousness and need to diversify the form of class groups according to the character of the activities.

• Journal of Educational Research in Mathematics
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• v.26 no.2
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• pp.189-204
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• 2016

As compared with the gender differences in the achievement of mathematics of the PISA 2009, the results of this study on the PISA 2012 show that the achievement of male students sharply increased, while that of female students maintained the status quo. Based on the premise that this result is derived from the ratio differences between male and female students of high level, this study analyzed the educational context variable effects on the achievements of gender differences observed between male and female students of high level. In particular, this study inquired into the factors which influence the gender difference, by analyzing the identical variables regarding Singapore and Finland of which the achievement of female students registers high among other top high-ranking countries of the PISA 2012. Hence, the binominal logistic multi-level analysis was conducted in order to consider the characteristics of hierarchical structure of PISA, and to compare the features of the educational context variable effects between the high level (above level 5) by country and the highest level (above level 6) by group. The analysis results are as follows: in terms of after-school learning time realized either in private lessons and private institutes, no significant effects were shown in any of the students of these three countries. In terms of after-school homework time, the students of Korea and Singapore gave significant influences on the probability which would be included in the group of high level or the highest level. In particular, regarding the variables which influence the probability of inclusion of Korean female students in the group of high level or the highest level, they correspond to "Homework set by teacher", "Attitude toward school: learning activities", "ESCS of School" and "Teacher-student relations". And "Cultural possessions at home" gave main influences on the probability of inclusion of the female students of Korea, Singapore and Finland in the group of the highest level.

• Communications of Mathematical Education
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• v.30 no.3
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• pp.393-418
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• 2016

Theory and fundamentals of mathematics consist mostly of proposition form. Activities by research of the proposition which leads to determine the true or false, justify the true propositions and refute with counterexample improve logical reasoning skills of students in emphases on mathematics education. Also, utilizing of counterexamples in school mathematics combines mathematical knowledge through the process of finding a counterexample, help the concept study and increase the critical thinking. These effects have been found through previous research. But many studies say that the learners have difficulty in generating counterexamples for false propositions and materials have not been developed a lot for the counterexample utilizing that can be applied in schools. So, this study analyzed the current textbook and examined the use of counterexamples and developed educational materials for counterexamples that can be applied at schools. That materials consisted of making true & false propositions and students was divided into three groups of academic achievement level. And then this study looked at the change of the students' thinking after counterexample classes. As a study result, in all three groups was showed a positive change in the cognitive domain and affective domain. Especially, in top-level group was mainly showed a positive change in the cognitive domain, in upper-middle group was mainly showed in the cognitive and the affective domain, in the sub-group was mainly found a positive change in the affective domain. Also in this study shows that the class that makes true or false propositions in education of utilizing counterexample, made students understand a given proposition, pay attention to easily overlooked condition, carefully observe symbol sign and change thinking of cognitive domain helping concept learning regardless of academic achievement levels of learners. Also, that class gave positive affect to affective domain that increase interest in the proposition and gain confidence about proposition.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.2
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• pp.117-136
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• 2007

The purpose of this study was to analyze the effects of mathematics learning through tessellation activities on the improvement of spatial sense and to find out a better mathematics teaching method that could further develop spatial sense. For this purpose, the following questions were attempted; Can mathematics learning using tessellation activities develop spatial sense? In odor to test this hypothesis, twenty-four fifth graders of a class were selected at random. And the experimental group was divided into four groups according to gender and academic performance. The groups were protested and post-tested to determine results based on the quasi-experimental design(i.e. one-group pretest-post test design). The process of this study was checking spatial sense for a common evaluation of experimental group. In this study, tangram, pattern block, and GSP was used for mathematics learning through tessellation activities during each independent-study, discretion-activity, and math class. The instrument used in this study was a spatial sense test and pretest and post-test were implemented with the same instrument(i.e. K-WISC-III Activity Test). In conclusion, mathematics learning through tessellation activities with tangram, pattern block, and GSP is an effective teaching and learning method for the improvement of the spatial sense.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.1
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• pp.75-95
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• 2009

The purpose of the study was to investigate the scaffolding processes of children in mathematical problem solving. 3 groups of 4th grade students participated in the study and the researchers proceeded the study for 4 months. The procedures of this research were as followings. First, when the learners solved the problems, the categories of scaffolding processes(by way of unit line coding belong in open codings, the categories were made 25 concepts and integrated 20 subcategories) were produced the 7 results: invite to the learning, set the problems, affective aids, attempt self learning, re-ordering between learners and affirmation self learning. Second, the processes of scaffolding in mathematic problem solving resulted in condition, the present condition, action/interaction and the outcomes. Third, the cognitive and affective aids that discovered in the scaffolding processes were considered the main categories of learner's scaffolding processes in solving the mathematic problems. In conclusion, first, the learners' scaffolding processes, based on Vygotsky's "the zone of proximal development" in selection and presentation of mathematic problems, are very diverse. Peers' affective aids are very important in solving the problems. Second, learners in the scaffolding processes exchange the cognitive and affective aids with each other with joy and earnestness, and the aids can give assistance to all the participants. Third, in the results of observation and analysis in learners' scaffolding processes, it is meaningful to know how they think. Finally, the learners' scaffolding processes are a little unsystematic and illogical compared to those of adults, but those of scaffolders are so similar to those of learners' cognitive and affective systems that they can provide teachers with many merits in understanding and teaching learners.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.459-476
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• 2010

The purpose of this study is to suggest a new direction in using LOGO as a gifted education program and to seek an effective approach for LOGO teaching and learning, by analyzing the strategic thinking of mathematically gifted elementary students. This research is exploratory and inquisitive qualitative inquiry, involving observations and analyses of the LOGO Project learning process. Four elementary students were selected and over 12 periods utilizing LOGO programming, data were collected, including screen captures from real learning situations, audio recordings, observation data from lessons involving experiments, and interviews with students. The findings from this research are as follows: First, in LOGO Project Learning, the mathematically gifted elementary students were found to utilize such strategic ways of thinking as inferential thinking in use of prior knowledge and thinking procedures, generalization in use of variables, integrated thinking in use of the integration of various commands, critical thinking involving evaluation of prior commands for problem-solving, progressive thinking involving understanding, and applying the current situation with new viewpoints, and flexible thinking involving the devising of various problem solving skills. Second, the students' debugging in LOGO programming included comparing and constrasting grammatical information of commands, graphic and procedures according to programming types and students' abilities, analytical thinking by breaking down procedures, geometry-analysis reasoning involving analyzing diagrams with errors, visualizing diagrams drawn following procedures, and the empirical reasoning on the relationships between the whole and specifics. In conclusion, the LOGO Project Learning was found to be a program for gifted students set apart from other programs, and an effective way to promote gifted students' higher-level thinking abilities.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.1-17
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• 2014

Instructions for the commutative property of multiplication at elementary schools tend to be based on checking the equality between the quantities of 'a times b 'and b' times a, ' for example, $3{\times}4=12$ and $4{\times}3=12$. This article critically examined the approaches to teach the commutative property of multiplication from Kant's perspective of mathematical knowledge. According to Kant, mathematical knowledge is a priori. Yet, the numeric exploration by checking the equality between the amounts of 'a groups of b' and 'b groups of a' does not reflect the nature of apriority of mathematical knowledge. I suggest we teach the commutative property of multiplication in a way that it helps reveal the operational schema that is necessarily and generally involved in the transformation from the structure of 'a times b' to the structure of 'b times a.' Distributive reasoning is the mental operation that enables children to perform the structural transformation for the commutative property of multiplication by distributing a unit of one quantity across the other quantity. For example, 3 times 4 is transformed into 4 times 3 by distributing each unit of the quantity 3, which results in $3{\times}4=(1+1+1){\times}4=(1{\times}4)+(1{\times}4)+(1{\times}4)+(1{\times}4)=4+4+4=4{\times}3$. It is argued that the distributive reasoning is also critical in learning the subsequent mathematics concepts, such as (a whole number)${\times}10$ or 100 and fraction concept and fraction multiplication.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.1
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• pp.43-64
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• 2010

This study aimed to foster the learning abilities of mathematics, that is, along with the formation of a sure mathematical concept, extending the powers of doing mathematics, and bringing the creativities for 3rd grade elementary school children. In order to achieve these objects, we have executed mathematical classes for two consecutive hours of 16 times using the teaching model of [Learning contents in textbook]$\rightarrow$[The first problem Posing]$\rightarrow$[Problem solving to childrens' posing some problems]$\rightarrow$[Advanced problem posing] to 3rd grade school children during the first semester of 2009. In this paper, we analyzed problems that are made by children focusing on the four fundamental rules +, -, ${\times}$, $\div$ of arithmetic, with the view points of problem's completion, fluencies, flexibilities, buildings of concept, originalities and using materials. As a result of the comparative analysis of the first problems and advanced problems made by the children, the first problems were revealed to be rather better in of problem's completion and fluencies. And the flexibilities were improved in the division and multiplication classes carried on. Setting up the experimental and comparative class, we compared to the scholastic achievement of two classes for the beginning and end in the first semester. In the result, the former was improved in the scholastic achievement more than the latter.

• School Mathematics
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• v.5 no.4
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• pp.507-520
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• 2003

본 연구는 실질적인 의미에서 학생들로 하여금 수학을 더 잘 이해할 수 있도록 돕기 위해 테크놀로지를 학교 교실에서 직접 활용하는 방안에 대한 연구이다. 특히 여기서는 수학을 가르치고 배우는 과정에서 가상학습체계가 주요한 도구로서 적용되었다. 내용은 무게중심을 택했고 12명의 중학생을 대상으로 현직교사가 직접 지도하였다. 학생들은 수업초기에 교사에 의해 소개되는 학생중심 학습활동에 강한 관심과 호기심을 보였고 집중력이 아주 강했다. 전통적인 수업방식과는 달리 학생들이 참여하였고 테크놀로지를 이용하여 전통적인 방식의 교실에서 할 수 없었던 수업의 시작은 학생들의 호기심을 자극하는데 충분하였다. 전반적으로 테크놀로지 환경에서의 수업을 선호하였지만 아직 전통적인 방식인 칠판과 분필을 이용한 수업을 선호한 학생들도 있었다. 새로운 변화도 좋지만 새로운 환경에 친화적이지 않거나 테크놀로지를 이용한 수업의 빠른 진행이 학생을 오히려 혼란하게 만들기도 하였다. 마지막으로 교사는 가상학습체계를 교실에서 활용함에 있어서 현 교육과정과 교과서를 크게 개혁하지 않아도 잘 준비되고 계획된 테크놀로지의 활용에 대한 잠재력을 확인할 수 있었다. 우리는 현재 테크놀로지의 보급에 비해 그 활용도가 낮다는 것을 잘 알고 있고 기타 입학시험이라는 현실이 교육과정과 학습방법의 개혁을 현실적으로 추진하는 것이 어려운 일임을 잘 알고 있다. 그래서 현 상황에서 테크놀로지의 사용을 가능하게 할 수 있는 방법을 모색하였다. 이미 보급된 테크놀로지와 교사와 학생의 테크놀로지에 대한 이해가 앞으로 그 잠재력을 갖고 있다고 확인하였다.보다 낮은 일반세균수 값을 보여주었다. 봄철 시료에 있어서 소규모 도계장은 본 냉각 후 도계과정을 제외하곤 모든 도계공정 단계에서 대규모 도계장보다 높은 일반 세균수의 측정값을 보여주었다. 봄철 시료의 냉각말기의 냉각수 일반세균수는 소규모 도계장이 대규모 도계장보다 높은 측정값을 보여주었다.주었다.다.㏖/s/$m^2$에서는 이앙후 각각 18일로 두 품종 모두 늦어, 약광은 유묘기에 분화되었던 분얼아를 휴면으로 유도할 수 있음을 시사하였다. 4. 유효경비율은 1220~220 $\mu$㏖/s/$m^2$에서 다산벼는 47~55%, 화성벼는 100~72%로 다산벼가 화성벼보다 낮았다. 이것은 다산벼는 무효분얼이 많다는 것을 시사하는 것으로 품종 육성시 유효경비율을 높여야 할 것이다.타났고, \circled2 회복상태에서, 10 lu$\chi$인 경우 서간에 1.26 $\mu\textrm{V}$, 야간에 1.59 $\mu\textrm{V}$였고, 100 lu$\chi$인 경우 서간에 2.63 $\mu\textrm{V}$ 야간에 3.65 $\mu\textrm{V}$였으며, 400 lu$\chi$인 경우 서간에 2.52 $\mu\textrm{V}$, 야간에 3.67 $\mu\textrm{V}$로 나타났다.히, 흉선, F냥, 비장 등의 림프구에 초기 세포용해성 감염을 일으키는데, B