• The Mathematical Education
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• v.63 no.3
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• pp.549-571
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• 2024

As digital·AI-based teaching and learning is emphasized, discussions on the educational use of generative AI are becoming more active. This study analyzed the mathematical performance of ChatGPT 4, Claude 3 Opus, and Gemini Advanced on solving examples and problems from five first-year high school math textbooks. As a result of examining the overall correct answer rate and characteristics of each skill for a total of 1,317 questions, ChatGPT 4 had the highest overall correct answer rate of 0.85, followed by Claude 3 Opus at 0.67, and Gemini Advanced at 0.42. By skills, all three models showed high correct answer rates in 'Find functions' and 'Prove', while relatively low correct answer rates in 'Explain' and 'Draw graphs'. In particular, in 'Count', ChatGPT 4 and Claude 3 Opus had a correct answer rate of 1.00, while Gemini Advanced was low at 0.56. Additionally, all models had difficulty in explaining using Venn diagrams and creating images. Based on the research results, teachers should identify the strengths and limitations of each AI model and use them appropriately in class. This study is significant in that it suggested the possibility of use in actual classes by analyzing the mathematical performance of generative AI. It also provided important implications for redefining the role of teachers in mathematics education in the era of artificial intelligence. Further research is needed to develop a cooperative educational model between generative AI and teachers and to study individualized learning plans using AI.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.163-192
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• 2009

Currently, our country operates gifted education only as a special curriculum, which results in many problems, e.g., there are few beneficiaries of gifted education, considerable time and effort are required to gifted students, and gifted students' educational needs are ignored during the operation of regular curriculum. In order to solve these problems, the present study formulates the following research questions, finding it advisable to conduct gifted education in elementary regular classrooms within the scope of the regular curriculum. A. To devise a teaching plan for the gifted students on mathematics in the elementary school regular classroom. B. To develop a learning program for the gifted students in the elementary school regular classroom. C. To apply an in-depth learning program to gifted students in mathematics and analyze the effectiveness of the program. In order to answer these questions, a teaching plan was provided for the gifted students in mathematics using a differentiating instruction type. This type was developed by researching literature reviews. Primarily, those on characteristics of gifted students in mathematics and teaching-learning models for gifted education. In order to instruct the gifted students on mathematics in the regular classrooms, an in-depth learning program was developed. The gifted students were selected through teachers' recommendation and an advanced placement test. Furthermore, the effectiveness of the gifted education in mathematics and the possibility of the differentiating teaching type in the regular classrooms were determined. The analysis was applied through an in-depth learning program of selected gifted students in mathematics. To this end, an in-depth learning program developed in the present study was applied to 6 gifted students in mathematics in one first grade class of D Elementary School located in Nowon-gu, Seoul through a 10-period instruction. Thereafter, learning outputs, math diaries, teacher's checklist, interviews, video tape recordings the instruction were collected and analyzed. Based on instruction research and data analysis stated above, the following results were obtained. First, it was possible to implement the gifted education in mathematics using a differentiating instruction type in the regular classrooms, without incurring any significant difficulty to the teachers, the gifted students, and the non-gifted students. Specifically, this instruction was effective for the gifted students in mathematics. Since the gifted students have self-directed learning capability, the teacher can teach lessons to the gifted students individually or in a group, while teaching lessons to the non-gifted students. The teacher can take time to check the learning state of the gifted students and advise them, while the non-gifted students are solving their problems. Second, an in-depth learning program connected with the regular curriculum, was developed for the gifted students, and greatly effective to their development of mathematical thinking skills and creativity. The in-depth learning program held the interest of the gifted students and stimulated their mathematical thinking. It led to the creative learning results, and positively changed their attitude toward mathematics. Third, the gifted students with the most favorable results who took both teacher's recommendation and advanced placement test were more self-directed capable and task committed. They also showed favorable results of the in-depth learning program. Based on the foregoing study results, the conclusions are as follows: First, gifted education using a differentiating instruction type can be conducted for gifted students on mathematics in the elementary regular classrooms. This type of instruction conforms to the characteristics of the gifted students in mathematics and is greatly effective. Since the gifted students in mathematics have self-directed learning capabilities and task-commitment, their mathematical thinking skills and creativity were enhanced during individual exploration and learning through an in-depth learning program in a differentiating instruction. Second, when a differentiating instruction type is implemented, beneficiaries of gifted education will be enhanced. Gifted students and their parents' satisfaction with what their children are learning at school will increase. Teachers will have a better understanding of gifted education. Third, an in-depth learning program for gifted students on mathematics in the regular classrooms, should conform with an instructing and learning model for gifted education. This program should include various and creative contents by deepening the regular curriculum. Fourth, if an in-depth learning program is applied to the gifted students on mathematics in the regular classrooms, it can enhance their gifted abilities, change their attitude toward mathematics positively, and increase their creativity.

• The Korean Journal of Elementary Counseling
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• v.11 no.1
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• pp.21-33
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• 2012

This study examined the differences of academic achievement by social status types through sociometry. This study analyzed 201 students in grade 6 in S elementary school. The social status is classified by 7 (popular, average, rejected, aggressive-rejected, submissive-rejected, neglected, controversial) with academic achievement of each type as dependent variables to figure out the relation between social status types and academic achievement. To classify 5 social status types, a sociometry program developed by Ahn, Ie-Hwan (2007) was used, 2 social status types was classified with experimental condition, and its dependent variable was the score by subjects in the mid-term exam of the 1st semester in 2011. The average values of humanities courses (Korean and social studies) and natural science courses (math and science) were compared by both sexes and 7 social status types. The reference group was average group. As a result, as to male students, N type had the highest score both in humanities courses and natural science courses while C type had the lowest score in both groups. As to female students, P, N, C types had the highest score in both groups with similar range while R type had the lowest score in both groups. This result demonstrates that the academic achievement of students had relatively high relevance with social status. and also, suggestion that how teachers can do to enhance the academic achievement of elementary school students.

• The Journal of Sustainable Design and Educational Environment Research
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• v.16 no.3
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• pp.37-50
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• 2017

The Ministry of Education selected and implemented 'science core school' since 2009 as a policy to strengthen science education to produce talented science students. This study judged that it is necessary to examine the current management practice and diagnose problems to propose improvement measures for more successful management of science core school in the future. To this end, we interviewed and observed teachers and students at a high school specialized in science based in Gyeonggi province which was selected as a science core school, as qualitative study methods such as interview and observation to survey and analyze the current management practice of the school. The management outcome was that the school contributed to fostering talented students in natural sciences and engineering because more varied activities were implemented at the school to develop scientific knowledge of students including experiment, excursion, and circle activity. Identified problems were increased amount of private education due to intense competition over school achievement, negligence of extracurricular activities, burdensome workload for teachers of specific subjects, and lack of expertise of math and science teachers. In conclusion, the following improvement measures are suggested for sustainable management of science core schools: greater liberty should be granted to science core schools; more training opportunities should be given to teachers; college admission program should be improved for science core school students; and it is necessary to introduce courses taught by external teachers, and provide systematic support such as increasing administration staff.

• Education of Primary School Mathematics
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• v.19 no.2
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• pp.161-175
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• 2016

The purpose of this study is to measure the differences in affective characteristics and mathematical reasoning ability between gifted students and non-gifted students. This study compares and analyzes on the relations between the affective characteristics and mathematical reasoning ability. The study subjects are comprised of 97 gifted fifth grade students and 144 non-gifted fifth grade students. The criterion is based on the questionnaire of the affective characteristics and mathematical reasoning ability. To analyze the data, t-test and multiple regression analysis were adopted. The conclusions of the study are synthetically summarized as follows. First, the mathematically gifted students show a positive response to subelement of the affective characteristics, self-conception, attitude, interest, study habits. As a result of analysis of correlation between the affective characteristic and mathematical reasoning ability, the study found a positive correlation between self-conception, attitude, interest, study habits but a negative correlation with mathematical anxieties. Therefore the more an affective characteristics are positive, the higher the mathematical reasoning ability are built. These results show the mathematically gifted students should be educated to be positive and self-confident. Second, the mathematically gifted students was influenced with mathematical anxieties to mathematical reasoning ability. Therefore we seek for solution to reduce mathematical anxieties to improve to the mathematical reasoning ability. Third, the non-gifted students that are influenced of interest of the affective characteristics will improve mathematical reasoning ability, if we make the methods to be interested math curriculum.

• Korean Journal of Applied Biomechanics
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• v.27 no.2
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• pp.117-124
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• 2017

Objective: The purpose of this study was to examine the effect of changes in degrees of freedom of the fingers (i.e., the number of the fingers involved in tasks) on the task performance during force production and releasing task. Method: Eight right-handed young men (age: $29.63{\pm}3.02yr$, height: $1.73{\pm}0.04m$, weight: $70.25{\pm}9.05kg$) participated in this study. The subjects were required to press the transducers with three combinations of fingers, including the index-middle (IM), index-middle-ring (IMR), and index-middle-ring-little (IMRL). During the trials, they were instructed to maintain a steady-state level of both normal and tangential forces within the first 5 sec. After the first 5 sec, the subjects were instructed to release the fingers on the transducers as quickly as possible at a self-selected manner within the next 5 sec, resulting in zero force at the end. Customized MATLAB codes (MathWorks Inc., Natick, MA, USA) were written for data analysis. The following variables were quantified: 1) finger force sharing pattern, 2) root mean square error (RMSE) of force to the target force in three axes at the aiming phase, 3) the time duration of the release phase (release time), and 4) the accuracy and precision indexes of the virtual firing position. Results: The RMSE was decreased with the number of fingers increased in both normal and tangential forces at the steady-state phase. The precision index was smaller (more precise) in the IMR condition than in the IM condition, while no significant difference in the accuracy index was observed between the conditions. In addition, no significant difference in release time was found between the conditions. Conclusion: The study provides evidence that the increased number of fingers resulted in better error compensation at the aiming phase and performed a more constant shooting (i.e., smaller precision index). However, the increased number of fingers did not affect the release time, which may influence the consistency of terminal performance. Thus, the number of fingers led to positive results for the current task.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.325-354
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• 2020

This study utilized longitudinal data from the 2013 year (Secondary Middle School) to 2017 year (Secondary High School) of the Seoul Education Termination Study. Using the latent growth model and the piecewise growth model, we investigated the changes in mathematics academic achievement, internal factors(self-concept, self-control, self-assessment of life satisfaction), and external factors(school climate, guardians) as students' grades increased, and examined whether internal factors and external factors influence the changes in mathematics academic achievement. We examined whether internal and external factors influence the change in academic achievement. As a result of analysis, it was found that mathematics academic achievement remained unchanged from the first grade of middle school to the second grade of middle school, and steadily increased from the second grade of middle school to the first grade of high school, and then decreased slightly in the second grade of high school. The internal and external factors had little change. It has been found that self-concept, self-control as internal factors, and school climate as external factors influence changes in mathematics academic achievement.

• Journal of Educational Research in Mathematics
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• v.23 no.3
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• pp.373-388
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• 2013

This paper is to investigate how two elementary school teacher's belief mathematics as educational content, and teaching and learning mathematics as a part of educational methodology, and what the two teachers believe towards gifted children and their education, and what the classes demonstrate and its effects on the sociomathematical norms. To investigate this matter, the study has been conducted with two teachers who have long years of experience in teaching gifted children, but fall into different belief categories. The results of the study show that teacher A falls into the following category: the essentiality of mathematics as 'traditional', teaching mathematics as 'blended', and learning mathematics as 'traditional'. In addition, teacher A views mathematically gifted children as autonomous researchers with low achievement and believes that the teacher is a learning assistant. On the other hand, teacher B falls into the following category: the essentiality of mathematics as 'non-traditional', teaching mathematics as 'non-traditional, and learning mathematics as 'non-traditional.' Also, teacher B views mathematically gifted children as autonomous researchers with high achievement and believes that the teacher is a learning guide. In the teacher A's class for gifted elementary school students, problem solving rule and the answers were considered as important factors and sociomathematical norms that valued difficult arithmetic operation were demonstrated However, in the teacher B's class for gifted elementary school students, sociomathematical norms that valued the process of problem solving, mathematical explanations and justification more than the answers were demonstrated. Based on the results, the implications regarding the education of mathematically gifted students were investigated.

• The Mathematical Education
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• v.48 no.3
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• pp.303-328
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• 2009

In this study, we developed the teaching methods using manipulative materials to teach regular polytopes, and applied these to first-year student of middle school who is attending the extra math class. In that class, we focused on the change of the mathematical representations -especially verval, visual and symbolic representations- and mathematical behavioral. By analyzing characterstics the students' work sheets, we obtained affirmative results as follows. First, manipulative materials played an important role on drawing a development figure of regular polyhtopes describing the verval representation definition of regular polytopes. Second, classes utilizing manipulative materials changed students verbalism level of representations the definition of regular polytopes. For example, in the first class about 60% of students are in the $0{\sim}2$ vervalism level, but in the third class, about 65% of students are in the $6{\sim}7$ level. Third, classes utilizing manipulative materials improved visual representation about development figure. After experiences making several development figures about regular octahedron directly, and discussion, students found out key points to be considered for draws development figure and this helped to draw development figures about other regular polytopes. Fourth, students were unaccustomed to make symbolic representations of regular polytopes. But, they obtained same improvement in symbolic representations, so in fifth the class some students try to make symbol about something in common of whole regular polytopes. Fifth, after the classes, we have significant differences in the students, especially behavioral characteristics in II items such as mind that want to study own fitness, interest, attachment, spirit of inquiry, continuously mathematics posthumously. This means that classes using manipulative materials. Specially, 'mind that want to study mathematics continuously' showed the biggest difference, and it may give positive influence to inculcates mathematics studying volition while suitable practical use of manipulative materials. To conclude, classes using manipulative materials may help students enhance the verbal, visual representation, and gestates symbol representation. Also, the class using manipulative materials may give positive influence in some part of mathematical behavioral characteristic. Therefore, if we use manipulative materials properly in the class, we have more positive effects on the students cognitive perspect and behavioral cteristics.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.707-734
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• 2009

The purpose of the study was to investigate how children understand addition and subtraction of fractions and how their understanding influences the solutions of fractional word problems. Twenty students from 4th to 6th grades were involved in the study. Children's understanding of operations with fractions was categorized into "joining", "combine" and "computational procedures (of fraction addition)" for additions, "taking away", "comparison" and "computational procedures (of fraction subtraction)" for subtractions. Most children understood additions as combining two distinct sets and subtractions as removing a subset from a given set. In addition, whether fractions had common denominators or not did not affect how they interpret operations with fractions. Some children understood the meanings for addition and subtraction of fractions as computational procedures of each operation without associating these operations with the particular situations (e.g. joining, taking away). More children understood addition and subtraction of fractions as a computational procedure when two fractions had different denominators. In case of addition, children's semantic structure of fractional addition did not influence how they solve the word problems. Furthermore, we could not find any common features among children with the same understanding of fractional addition while solving the fractional word problems. In case of subtraction, on the other hand, most children revealed a tendency to solve the word problems based on their semantic structure of the fractional subtraction. Children with the same understanding of fractional subtraction showed some commonalities while solving word problems in comparison to solving word problems involving addition of fractions. Particularly, some children who understood the meaning for addition and subtraction of fractions as computational procedures of each operation could not successfully solve the word problems with fractions compared to other children.