• 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.

• Journal of the Korean School Mathematics Society
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• v.14 no.2
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• pp.179-198
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• 2011

Developing Mathematical Thinking has been continually emphasized in the Korean curriculum and this emphasis has demonstrated its impact on math textbooks and classes in South Korean schools. This study intends to discover how the Developmental Mechanism of Mathematical Thinking should be reflected through School Mathematics regardless of subfields of Mathematics or its levels. Finally, this study concluded that the Developmental Mechanism of Mathematical Thinking is being reflected on School Mathematics. However, more research in certain areas needs to be done. Through analyzing textbooks, it is certain that the Developmental Mechanism of Mathematical Thinking is being reflected on School Mathematics. Moreover, it appears that students are able to develop new concepts using Developmental Mechanism of Mathematical Thinking. Mathematical Thinking is a subject that many scholars and mathematicians have taken an interest in. Especially with the math curriculum in Korea, designing and implementing classes that would help students develop their mathematical thinking are increasingly being emphasized. This study defines what mathematical development mechanism is, and based on this definition, it further analyzes the math textbook of the revised 2007 curriculum. As a result, textbook developers and math teachers should examine and analyze the concepts that learners need to acquire and how they develop. Further, this study not only presents the concepts students are expected to acquire, but also looks at the flow in which concepts have been introduced to students. It concludes that activities that can help students have an idea of what they are going to learn in the future should be provided during class time.

• Journal of Educational Research in Mathematics
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• v.9 no.2
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• pp.473-491
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• 1999

The learning of mathematics happens in some situations. It is natural that students should learn mathematics in more appropriate situations. But, so far It has been hardly studied about concrete situation and milieu where math can be successfully taught. In today's math education, the situation of education as a external circumstance become realized more and more importantly with influence of open education. But they don't embody situation as an internal circumstance where the intrinsic concept of mathematics can be obtained. We started this thesis from this tried to answer it on the basis of Brousseau's question, have theory about the didactical situations. One of the purpose of this study is to understand the theory of didactical situations, which focuses on how we can elaborate situations which really make a mathematical notion function. In this study, It is attempted clarify some concepts of the theory of didactical situations. The other is to discuss about what the theory of didactical situations suggests us in math zeducation. The method of math teaching and learning and the teacher's role were discussed in the viewpoint of Brousseau's theory. Finally, We elaborated and presented some didactical situations which make the notion of the area of rectangle.

• Korean Journal of Childcare and Education
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• v.20 no.2
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• pp.17-37
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• 2024

Objective: This study aimed to examine childcare teachers' perceptions and practice of music-math integrated activities, and their understanding of these activities. Methods: This study involved 201 childcare teachers from Seoul and surrounding areas. Surveys were employed to collect data on their background, implementation of music-math integrated activities, and the challenges they encountered. Additionally, a tool was also developed and utilized to measure the actual understanding of these activities. Data were analyzed using t-tests and ANOVA. Results: The results indicated that while teachers recognize the importance of integrated activities, they seldom implement them due to challenges related to resources and comprehension of concepts. Significant differences in the understanding of these activities were found based on teachers' experience, workplace type, age group of children under their care, and education level. Conclusion/Implications: In conclusion, the findings emphasize the necessity for the development and provision of pre-service and in-service training programs, along with support in educational materials for childcare teachers. These efforts are crucial to facilitate the effective implementation of music-math integrated activities.

• Communications of Mathematical Education
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• v.36 no.4
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• pp.611-626
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• 2022

In this study, we introduced the case of college calculus course for vocational high school graduates with coding. We suggest this case as an alternative to overcome mathematics anxiety. Contents, python/SageMath codes, and textbook for this course, which help students to easily and quickly review middle and high school mathematics, were newly developed by authors. Due to the use of codes and chat with classmates in learning management system, most of the students who took this course reported that they no longer felt anxious in complex mathematics problems, had a full understanding of calculus concepts, could solve almost problems in any calculus textbooks with or without codes, and could explain calculus concepts to other students in their own words. In this way if mathematics and coding is properly used in mathematics education, it helps students with weak mathematical backgrounds or mathematics anxiety to restore confidence in mathematics in college. This could be applicable in secondary mathematics education.

• Journal of the Korean School Mathematics Society
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• v.17 no.1
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• pp.73-92
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• 2014

This study was performed in part with the task to find measures to improve the defining characteristics of feelings, value, interest, self-efficacy, and others aspects in regards to learning math among elementary and middle school students. For this study, it was essential to understand the appropriate questions that are needed to be asked during a consultation at a math clinic, for students that are having a hard time learning math. As a method for performing this study, the content of scheduled counseling over 2 years from a math clinic were collected and the questions that were given and taken were analyzed in order to figure out the types of questions needed in order to effectively examine students that are facing difficulty with learning math. The analysis was performed using Grounded theory analysis by Strauss & Corbin(1998) and went through the process of open coding, axial coding, and selective coding. For the paradigm in the categorical analysis stage, 'attitude towards learning math' was set as the casual condition, 'feelings towards learning math' was set as the contextual condition, 'confidence in one's ability to learn math' was set as the phenomenon, 'individual tendencies when learning math' was set as the intervening condition, 'self-management of learning math' was set as the action/interaction strategy, and 'method of learning' was set as the consequence. Through this, the questions that appeared during counseling were linked into categories and subcategories. Through this process, 81 concepts were deducted, which were grouped into 31 categories. I believe that this data can be used as grounded theory for standardization of consultation in clinics.

• The Korean Journal of Community Living Science
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• v.22 no.4
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• pp.519-533
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• 2011

The objective of this study was to follow up changes in knowledge related to the mathematics education field work of preliminary early childhood teachers. The subjects of this research were 28 students who were taking mathematics education courses in early childhood education departments at various universities. This research ran for 15 weeks and was conducted through field work relating to mathematics education. The study collected data from pre-service teachers' knowledge, the diagram of concept, writing journals, interviews, and materials from the internet. Through this procedure, pre-service teachers' knowledge for mathematics education could later be expanded, ordered, and integrated. In addition, pre-service teachers not only understood the importance of contents and levels of lesson plans, but also learned how to utilize educational media to make effective lessons. Furthermore, pre-service teachers realized that the mathematical concepts of students could be expanded depending on the contents and methods of pre-service teachers' lesson plans and students could then apply these concepts into daily situations.

• The Mathematical Education
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• v.44 no.4 s.111
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• pp.547-563
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• 2005

There have been many papers reporting that the axiomatic approach in Abstract Algebra is a big obstacle to overcome for the students who are not trained to think in an abstract way. Therefore an instructor must seek for ways to help students grasp mathematical concepts in Abstract Algebra and select the ones suitable for students. Mathematics faculty and students generally consider Abstract Algebra in general and quotient groups in particular to be one of the most troublesome undergraduate subjects. For, an individual's knowledge of the concept of group should include an understanding of various mathematical properties and constructions including groups consisting of undefined elements and a binary operation satisfying the axioms. Even if one begins with a very concrete group, the transition from the group to one of its quotient changes the nature of the elements and forces a student to deal with elements that are undefined. In fact, we also have found through running abstract algebra courses for several years that students have considerable difficulty in understanding the concept of quotient groups. Based on the above observation, we explore and analyze the nature of students' knowledge about $Z_n$ that is the set of congruence classes modulo n. Applying the genetic decomposition method, we propose a model to lead students to achieve the correct concept of $Z_n$.

• Journal of the Korean School Mathematics Society
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• v.19 no.4
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• pp.395-415
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• 2016

In this paper, we study the recognition of in-service teachers and pre-service teachers about the concepts of liner equations and liner functions. We chose 49 in-service teachers at secondary schools in G city and 29 pre-service teachers in M university and investigate their recognition about the concepts of liner equations and liner functions. We found following facts. First, in-service teachers and pre-service teachers tend to recognize a linear equation as an equation in one known rather than an equation in two unknowns. Second, in-service teachers and pre-service teachers tend to recognize a linear function as an explicit function rather than an implicit function. Finally, the difference between in-service teachers' recognition and pre-service teachers' recognition is not statistically significant.

• Journal of the Korean School Mathematics Society
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• v.21 no.3
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• pp.247-266
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• 2018

In this paper, three main concepts are chosen for this statistical estimation study, based on previous studies: confidence interval and reliability, sampling distribution of mean and population mean estimation, and relationships between elements of confidence interval. The main objectives of this study are as follows: 1. How are the attitudes that future math teachers and high school students have to ward the statistical estimation? 2. Is there some difference in the awareness of misconceptions about the statistical estimation that future math teachers and high school students have? A study result shows that both groups have difficulties in understanding statistical concepts and their meaning used in Unit Statistical Estimation. They tend to wrongly think that the meaning of reliability is the same as that of probability. They also have difficulties in understanding sample variance in the sampling distribution of mean, which makes it impossible to connect with population mean estimation. It is shown that relationships between elements consisting of confidence interval are not consistent.