• School Mathematics
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• v.11 no.1
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• pp.71-91
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• 2009

The purpose of this study was to analyze operation sense in detail with regard to division of fraction. For this purpose, two sixth grade students who were good at calculation were clinically interviewed three times. The analysis was focused on (a) how the students would understand the multiple meanings and models of division of fraction, (b) how they would recognize the meaning of algorithm related to division of fraction, and (c) how they would employ the meanings and properties of operation in order to translate them into different modes of representation as well as to develop their own strategies. This paper includes several episodes which reveal students' qualitative difference in terms of various dimensions of operation sense. The need to develop operation sense is suggested specifically for upper grades of elementary school.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.151-170
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• 2009

The purpose of the study is to analyze the sixth graders' understanding of concepts and operation about fraction. The test was administered and analyzed to 707 sixth graders' performance on fractions after the fraction instructions in elementary schools in Seoul, Korea. The participants are asked to answer two sets of questions for 40 minutes. First, they are asked to answer to 16 problems about the concepts of fraction with respect to part-whole, ratio, operator, measure, quotient, equivalent, and operations. Second, specially, to investigate sixth graders' ability of drawing and describing the situation of division including fraction, the descriptive problem asked students (1) to describe $3\;{\div}\;\frac{1}{2}$ into pictorial representation and (2) to write the solving process. The participants of this study didn't show deep understandings about the concepts and operation of fraction. The degree of understanding of subconstructs of fraction shows that their knowledge of ratio concept with respect to fraction was highest while their understanding of measure with respect to fraction was lowest. Considering their wrong answers, about 59% of participants showed misconception to the question of naming one fraction that appears between $\frac{1}{5}$ and $\frac{1}{6}$. Further, they didn't explain their understanding with drawing about the division of fraction ($3\;{\div}\;\frac{1}{2}$).

• The Mathematical Education
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• v.61 no.3
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• pp.477-497
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• 2022

The rapidly changing world calls for reform in mathematics education from lifelong learning perspectives. This study examines adults' perception of mathematics by reflecting on their experiences of mathematics in and out of school in order to understand what the current needs of adults are. With the two questions: "what experiences do participants have during their learning of mathematics in schools?" and "how do they perceive mathematics in their current life?", we analyzed the semi-structured interviews with 10 adults who have different sociocultural backgrounds using narrative inquiry methodology. As a result, participants tended to accept school mathematics as simply a technique for solving computational problems, and when they had not known the usefulness of mathematical knowledge, they experienced frustration with mathematics in the process of learning mathematics. After formal education, participants recognized mathematics as the basic computation skill inherent in everyday life, the furniture of their mind, and the ability to efficiently express, think, and judge various situations and solve problems. Results show that adults internalized school education to clearly understand the role of mathematics in their lives, and they were using mathematics efficiently in their lives. Accordingly, there was a need to see school education and adult education on a continuum, and the need to conceptualize the mathematical abilities required for adults as mathematical literacy.

• Korean Journal of Child Education & Care
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• v.19 no.2
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• pp.19-33
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• 2019

Objective: The purpose of this study is to understand how the experience of studying mathematics education for young children based on picture books is affecting pre-service early childhood teachers with their attitude toward mathematics and mathematics teaching efficiency. Methods: For this, a total of 39 pre-service early childhood teachers majoring in early childhood education at S university located in G metropolitan city participated in the study. 20 of them are randomly assigned to the experimental group while the rest 19 were assigned to the control group. The experimental group participated in the classes of mathematics education for young children based on picture books for 15 weeks, while the control group attended the normal classes of mathematics education for young children for the same period of time. By using SPSS 18.0 Program for the collected data, t-test was conducted for differences in the results of attitude toward mathematics and mathematics teaching efficiency. Results: The results of this study are as follows. Firstly, the experience of studying mathematics education for young children based on picture books had a positive effects on pre-service early childhood teachers' attitude toward mathematics, improved values and interest in mathematics, and reduced anxiety about mathematics. Secondly, the experience of studying mathematics education for young children based on picture books had a positive effects on improving pre-service early childhood teachers' mathematics teaching efficiency. Also, both faith in ability and faith in results have improved significantly. Conclusion/Implications: These results imply that the experience of studying mathematics education for young children based on picture books is an effective teaching-learning method in improving pre-service early childhood teachers' attitude toward mathematics and mathematics teaching efficiency.

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.69-100
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• 2005

이 연구는 내신성적이 우수함에도 불구하고 수능성적이 저조한 학생들이 문제 해결과정에서 나타내는 특성과 수학불안 요인을 분석하는데 있다. 연구의 대상은 인천시 5고등학교 자연계열 2학년 학생 중 내신성적이 상위 10%안에 드나 수능성적(모의수능성적)은 그렇지 못한 학생 5명이고, 이들의 수학적 성향, 수학 성취도, 개인별 특성 등에 대한 사전 면담자료, 문제풀이과정에 대한 사후 심층면담자료, 현장노트, 수학불안검사를 바탕으로 그들의 특성과 수학불안 요인을 분석한 결과는 다음과 같다. (1) 내신성적은 좋으나 수능성적이 저조한 학생들의 수학 문제 해결 과정에서 나타나는 특성은 수학전 영역에서의 개념부족, 공식암기 부족 등으로 인하여 문제풀이계획을 세우지 못하거나 설사 문제를 푼다고 해도 계산 실수, 착각, 부주의 등으로 인해 정확한 답을 구하지 못하는 것으로 나타났다. (2) 내신성적은 좋으나 수능성적이 저조한 학생들은 어느 정도의 수학 불안은 가지고 있었다. 불안의 요인은 개념부족, 응용력 부족 등 개인적 인지능력에 의한 저조한 수학 성취수준과 수학 공부시간 부족, 풀이시간 부족 등의 환경적 요인에 때문인 것으로 밝혀졌다. 특히 수학개념이 부족한 학생일수록 수학불안 현상이 심하게 나타났다. 따라서 이들 학생들의 수학 문제풀이 과정 중에 나타나는 계산 실수, 부주의, 착각은 그들의 수학 자신감에 많은 악영향을 미치게 되므로, 교사가 이를 그냥 방관할 것이 아니라 적극적으로 확인하고 지도해줄 필요가 있다. 또 교실 수업에서도 수능시험에서 다루고 있는 수학 내적, 외적 문제해결문제, 추론문제, 응용문제, 통합문제에 대한 문제풀이 경험을 하게하여 수학불안을 해소해줄 필요가 있다.)값을 보였으나, 10,000Hz의 높은 측정주파수에서는 더 큰 $E_a$값을 나타냄으로서 반응온도변화에 민감함을 보여주었다.원으로부터 부유물을 증가로 사료되었으며, 이에 대한 대책마련이 시급한 것으로 사료되었다. 수질이 휴양용수로서 사용하는 데에 적합하도록 충분한 차집시설과 환경 기초시설의 설치 운영이 필요할 것으로 판단된다.TEX>$K_s$값이 높고 $V_m/K_s$비율은 낮아 수게에서 질소가 저농도 일 때에는 다른 미세조류와 비교하면 경쟁력이 떨어지고 질소에 대한 기질 친화력은 약한 것으로 나타났다. 낙동강 하류지역에서 M. aeruginosa가 대발생하는 시기에 수중 영양염의 농도 변동은 M. aeruginosa의 영양생리 kinetics 특성과 잘 부합하는 것으로 나타났다.부분을 보완하기 위한 연구가 이루어져야 할 것으로 보인다. 연마방법 간에 상호 연관성이 없었다. FE-SEM관찰에서 레진전색제를 적용한 후의 표면은 모든 군에서 대체적으로 평활한 표면을 나타내었다. 4. 동일한 복합레진과 연마방법으로 처리된 군에서 레진전색제 적용 전과 후의 표면조도 값은 M1B군이 M1군보다, S1B군이 S1군보다 통계학적으로 높게 나타났으며, M4B군과 M5B군은 각각 M4군과 M5군 보다. 그리고 S5B군은 S5군 보다 통계학적으로 낮게 나타났다 (p<0.05). 본 연구를 종합하여 보면, 복합레진의 종류에 따라 표면조도의 순서는 다르게 나타났고, polyester strip 하에서 복합레진이 중합된 경우 가장 낮은 표면조도 값과 평활한 표면을 제공하였으며 전반적으로 anishing bur는 가장 높은 Ra값과 거친 표면을 제공하였다.

• School Mathematics
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• v.14 no.1
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• pp.165-190
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• 2012

Recently, the Korean government develops a variety of policies for the improvement of school education. Among the policies, convergence education is considered as essential. Moreover, as the policies declare that mathematics is expected to play a central role in the convergence education, mathematics educators are required to seek for ways of how to approach convergence education in mathematics. In this context, this paper reviewed diverse viewpoints on what kind of contribution convergence education make to the improvement of school mathematics. While the argument constructed around the issue of national competitiveness is the most prevalent in the political discourse, this paper recommends to introduce the epistemological norms raised by the knowledge integration through history. In addition, this paper presents both domestic and international programs to discuss how to develop educational program for convergence education in mathematics.

• The Mathematical Education
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• v.63 no.2
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• pp.123-138
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• 2024

This study described the utilization of ChatGPT in teaching and students' learning processes for the course "Introductory Mathematics for Artificial Intelligence (Math4AI)" at 'S' University. We developed a customized ChatGPT and presented a learning model in which students supplement their knowledge of the topic at hand by utilizing this model. More specifically, first, students learn the concepts and questions of the course textbook by themselves. Then, for any question they are unsure of, students may submit any questions (keywords or open problem numbers from the textbook) to our own ChatGPT at https://math4ai.solgitmath.com/ to get help. Notably, we optimized ChatGPT and minimized inaccurate information by fully utilizing various types of data related to the subject, such as textbooks, labs, discussion records, and codes at http://matrix.skku.ac.kr/Math4AI-ChatGPT/. In this model, when students have questions while studying the textbook by themselves, they can ask mathematical concepts, keywords, theorems, examples, and problems in natural language through the ChatGPT interface. Our customized ChatGPT then provides the relevant terms, concepts, and sample answers based on previous students' discussions and/or samples of Python or R code that have been used in the discussion. Furthermore, by providing students with real-time, optimized advice based on their level, we can provide personalized education not only for the Math4AI course, but also for any other courses in college math education. The present study, which incorporates our ChatGPT model into the teaching and learning process in the course, shows promising applicability of AI technology to other college math courses (for instance, calculus, linear algebra, discrete mathematics, engineering mathematics, and basic statistics) and in K-12 math education as well as the Lifespan Learning and Continuing Education.

• Communications of Mathematical Education
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• v.32 no.3
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• pp.341-362
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• 2018

The purpose of this study is to develop a STEAM education model on the basis of mathematics curriculum using real life context, and to analyze the effect of the class based on developed model to make applicable pedagogical discussion. For this purpose, STEAM class materials that can be used in terms of recognition, connection, extension, and application of mathematical concepts, principles and laws are considered, taking into consideration the ways in which real life contexts and mathematical learning could be harmonized. As a results of using these materials, it was empirically confirmed that students' cognitive thinking and affective aspects abilities were improved. The STEAM instruction centered on the mathematics curriculum and the mathematics class based on the data developed in this study have a unique identity compared to the conventional general mathematics teaching methods using the textbooks. And it is pursuing the future class model which could present desirable creativity and personality education. The result of this study would provide preliminary data and meaningful implications to the researchers for next curriculum and concomitant instructional materials as well as the mathematics teachers.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.423-439
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• 2015

This study examines the relationship between prior learning experience, the high school records, mathematics grade in the KSAT(Korean Scholastic Aptitude Test) and mathematics achievement, GPA(grade point average) of college freshmen. It analyses how much mathematics capacities in the time of high school affect mathematics achievement of college freshmen. This study surveyed 193 freshmen, attending in a college of science and engineering, taking the 'basic differential and integral calculus' lecture, which was opened for the first semester of 2014 in the A university. The data processing was fulfilled by means of technical statistics, correlation analysis, difference test, ANOVA, ex post facto test, and regression analysis. The outcomes of this survey are followings: Firstly, over 90 percent of college freshmen underwent prior learning of mathematics when they attended high school. Secondly, their perception of effectiveness for prior learning is founded to be meaningfully lower than their perception of its needfulness. Thirdly, while there is higher positive correlation between mathematics achievement and GPA in the college, there is little correlation between high school records and GPA in the college. Also, there is little correlation between mathematics grade in the KSAT and mathematics achievement in the college. Fourthly, the accomplishments in the high school(The high school records, mathematics grade in the KSAT) and the efforts, satisfaction, necessity, etc. for prior learning had little effect on academic achievement in college mathematics. Based on these results, this study makes some suggestions for developing academical achievement in college mathematics.

• Communications of Mathematical Education
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• v.12
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• pp.463-477
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• 2001

국가의 국가경쟁력은 학창시절 학생의 학력만큼 중요하다. 성인의 경우, 학력을 위한 노하우는 체험을 통해 터득할 수 있었다. 그러나 국가경쟁력에 관해서는 우물 안 내부관점을 벗어나기 힘들어 추진 방향과 제도 운영에 자칫 시행착오를 범하기 쉽다. 이는 사안에 대해 본질적인 접근보다 껍데기만을 쫓기 때문이었다. 이 현상을 분석하려면 관점과 보이지 않는 영역의 것들을 다룰 수 있는 수학적 사고법이 필요하며, 이 능력은 현 지식정보화 사회에서 매우 긴요하다. 그러나 현실은 여러 가지 이유로 수학적 사고법을 비롯한 기초학문을 위기로 몰아가고 있고, 안타깝지만 그 중심에 수학교육이 자리잡고 있다. 수학교육의 위기를 유발하는 요인으로 제도 운영에 관한 건이 있다. 제도 운영에서 한 변수의 변화, 예로 대입의 계열교차지원 허용 건, 교원임용고시에서 교과교육학 영역의 출제 건과 복수전공, 부전공 자격소지자에 대한 가산점 부여 건은 수학교육과 교육과정에 직, 간접적으로 영향을 미친다. 이 관계를 사범대학 수학교육과 현장의 사례를 통하여 조명하고, 그 문제점을 지적하고자 한다. 현 사범교육은 졸업이수학점 140학점 체제하에서 제 7차 교육과정에 따른 복수전공, 부전공 우대 정책을 펴고 있다. 수학교육과의 경우, 부전공 열풍이 불어 전공선택 과목이 3학년 1학기부터 폐강될 위기에 처해 있다. 교양교육의 고사 또는 전광교육이 예전보다 반으로 줄어들게 된 사범대학 실상에 비애감을 느끼게 된다. 이는 전문화된 교사 양성, 나아가 미래 국가경쟁력 향상에 심각한 저해 요소로 작용할 것이다. 복잡다단한 세상에서 최적화를 향한 개선 노력이 멈춰서는 안 된다. 현행 교원임용고시 운영상의 문제점을 공론화하고, 수학교육인의 중지를 모아야 할 긴박한 시점이다. 이를 계기로 교원임용고시의 운영개선과 수학교육과 교육과정을 한층 더 견실하게 하는 데에 이바지하고자 한다. 것이라면 후속연구로 이러한 가능성을 실험연구로 검증하고자 한다.toceros resting spores/Chaetoceroe vegetative cells도 80 cm 보다 상층에서는 높게 나타나 규조온도지수 분포와도 일치하는 경향을 보인다. 이상의 규조군집 분석 결과에 의하면, 홀로세의 후빙기동안 본 연구 지역인 동해 북동부에는 대마 난류의 유입이후 현재와 유사한 환경이 우세하게 발달했으나, 난류종 P. doliolus의 변화는 동해내에서 대마난류의 세기가 반복되었음을 지시하고 있다./3 수준으로 높다. 결론적으로 풍부한 화학물질들을 함유한 제주해류는 남해 및 동해의 생지화학적 과정들에 있어 상당히 중요함을 시사한다.다. 수조 상층수 중 Cu, Cd, As 농도는 모든 FW, SW수조에서 시간이 지남에 따라 일관성 있게 감소하였고, 제거속도는 Cu가 다른 원소에 비해 빨랐다. 제거속도는 FW 3개 수조 중 FW5&6에서 세 원소 모두 가장 느렸고, SW 3개 수조 중에서는 SW1&2에서 가장 빨랐다. SW와 FW간 제거속도 차이는 세 원소 모두 명확치 않았다 Cr은 FW에서 전반적으로 감소하는 경향을 보였지만 SW에서는 실험 초기에 감소하다 24시간 이후에는 증가 후 일정한 양상을 보였다. Pb은 FW에서 전반적으로 감소했지만 SW에서는 초기에 급격히 증가 후 다시 급격히 감소하는 양상을 보였다 Pb 또한 Cu, Cd, As와 마찬가지로 SW1&2에서 제거속도가 가장 빠르게 나타났다. FW 상층수 중 Hg는 시간에 따라 급격히 감소했고, 제거속도는 Fw5&6에서 가장 느렸다. 이러한 결과에 근거할 때 벼가 자라고 있고 이분해성 유기물이 풍부한 FW1&2, FW3&4 토양과 상층수에서는 유기물의 분해 활동이 활발하였지만, 벼가 경작되지 않는 FW5&6과 SW 에서는 유기물이 상대적으로 결핍되어 유기물의 분해활동이 적었을 것으로 판단된다