• Journal of Elementary Mathematics Education in Korea
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• v.22 no.3
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• pp.309-330
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• 2018

The purpose of this study is to identify possibility of a mathematical problem posing ability by presenting problem posing tasks with different degrees of structure according to the study of Stoyanova and Ellerton(1996). Also, the results of this study suggest the direction of gifted elementary mathematics education to increase mathematical creativity. The research results showed that mathematical problem posing ability is likely to be a factor in identification of gifted students, and suggested directions for problem posing activities in education for mathematically gifted by investigating the characteristics of original problems. Although there are many criteria that distinguish between gifted and ordinary students, it is most desirable to utilize the measurement of fluency through the well-structured problem posing tasks in terms of efficiency, which is consistent with the findings of Jo Seokhee et al. (2007). It is possible to obtain fairly good reliability and validity in the measurement of fluency. On the other hand, the fact that the problem with depth of solving steps of 3 or more is likely to be a unique problem suggests that students should be encouraged to create multi-steps problems when teaching creative problem posing activities for the gifted. This implies that using multi-steps problems is an alternative method to identify gifted elementary students.

• Journal of the Korean School Mathematics Society
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• v.24 no.4
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• pp.369-390
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• 2021

It would be reasonable as a teacher to make efforts not only to reflect on the class on their own but also to improve the teacher' teaching e pertise by reflecting on the class with fellow teachers through lesson reflection sharing. This paper attempted to develop a lesson reflective framework that can provide standards and focus for lesson reflection and lesson sharing. First, based on the class evaluation criteria of previous studies, class reflection elements and a draft of lesson reflection were prepared. In a class conducted on 27 third graders at C High School where the co-researcher worked as a teacher, four peer teachers at the same high school were required to write personal opinions on the class based on the draft of lesson reflection. Based on this, lesson sharing was conducted, and modifications of the lesson reflection framework were developed by analyzing the case of class sharing. The implications of this paper indicate the need to clarify the perspective of viewing the lesson by sharing the intention of each question in advance. In addition to writing lesson reflections, it is necessary to share classes simultaneously.

• The Mathematical Education
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• v.62 no.3
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• pp.327-340
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• 2023

The value that students consider important in math learning may vary depending on the student's socio-cultural background and personal experience. Although socio-cultural backgrounds are very diverse, I considered overseas vs domestic Koreans, and secondary school levels as variables in terms of students' educational experiences. Overseas students had a lower perception of the value in mathematics than domestic students, especially about understanding mathematics knowledge and the value of the latest teaching and learning methods. Middle school students perceived the value of mathematics as an activity higher than that of high school students, and high school students perceived student agency as a higher value than middle school students. In addition, I considered meta-affect as one of the individual students' experiences, finally meta-affect was a variable that could explain value perception in math learning, and in particular, affective awareness of achievement, affective evaluation of value, and affective using were significant. From the results, I suggested that research on ways to improve the value and the meta-affect in math learning, test to measure the value of students in math learning, the expansion of research subjects to investigate the value in math learning, and a teacher who teaches overseas Koreans are needed.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.333-348
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• 2023

Clear analysis and diagnosis of various characteristic factors of individual students is the most important in order to realize individual customized teaching and learning, which is considered the most essential function of math artificial intelligence-based digital textbooks. In this study, analysis factors and tools for individual customized learning diagnosis and construction models for data collection and analysis were derived from mathematical AI digital textbooks. To this end, according to the Ministry of Education's recent plan to apply AI digital textbooks, the demand for AI digital textbooks in mathematics, personalized learning and prior research on data for it, and factors for learner analysis in mathematics digital platforms were reviewed. As a result of the study, the researcher summarized the factors for learning analysis as factors for learning readiness, process and performance, achievement, weakness, and propensity analysis as factors for learning duration, problem solving time, concentration, math learning habits, and emotional analysis as factors for confidence, interest, anxiety, learning motivation, value perception, and attitude analysis as factors for learning analysis. In addition, the researcher proposed noon data on the problem, learning progress rate, screen recording data on student activities, event data, eye tracking device, and self-response questionnaires as data collection tools for these factors. Finally, a data collection model was proposed that time-series these factors before, during, and after learning.

• 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 the Korean School Mathematics Society
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• v.18 no.1
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• pp.1-14
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• 2015

In this paper, in order to improve the teaching contents on even and odd number, composition and decomposition of numbers, and (1 digit)+(1 digit) with carrying, (10 and 1 digit)-(1 digit) with borrowing, the corresponding teaching contents in ${\ll}$Math 1-1${\gg}$, ${\ll}$Math 1-2${\gg}$ are critically reviewed. Implications obtained through this review can be summarized as follows. First, the current incomplete definition of even and odd numbers would need to be reconsidered, and the appropriateness of dealing with even and odd numbers in first grade would need to be reconsidered. Second, it is necessary to deal with composition and decomposition of numbers less than 20. That is, it need to be considered to compose (10 and 1 digit) with 10 and (1 digit) and to decompose (10 and 1 digit) into 10 and (1 digit) on the basis of the 10. And the sequence dealing with composition and decomposition of 10 before dealing with composition and decomposition of (10 and 1 digit) need to be considered. And it need to be considered that composing (10 and 1 digit) with (1 digit) and (1 digit) and decomposing (10 and 1 digit) into (1 digit) and (1 digit) are substantially useless. Third, it is necessary to eliminate the logical leap in the calculation process. That is, it need to be considered to use the composing (10 and 1 digit) with 10 and (1 digit) and decomposing (10 and 1 digit) into 10 and (1 digit) on the basis of the 10 to eliminate the leap which can be seen in the explanation of calculating (1 digit)+(1 digit) with carrying, (10 and 1 digit)-(1 digit) with borrowing. And it need to be considered to deal with the vertical format for calculation of (1 digit)+(1 digit) with carrying and (10 and 1 digit)-(1 digit) with borrowing in ${\ll}$Math 1-2${\gg}$, or it need to be considered not to deal with the vertical format for calculation of (1 digit)+(1 digit) with carrying and (10 and 1 digit)-(1 digit) with borrowing in ${\ll}$Math 1-2 workbook${\gg}$ for the consistency.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.333-357
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• 2014

This study resulted from a study regarding creative STEAM System based upon an experiment with the center of gravity. The results of the study are constructed by a fusion of mathematics and physics, showing that they are the same as mathematical calculations. Also, students can find that center of gravity of an object is in equilibrium on a metal rod when the center of gravity exactly is placed on the rod. The fact that an experimental results are correspond to calculations can maximize the effectiveness of teaching. And also this study has the following effectiveness. First, the exact construction and calculations arouses good competition among students. Second, this experiment can give students a motivation for study and increase their thinking in classes because the theoretical background of center of gravity experiment is basically attributed to math and science classes in school. This study includes three different types of center-of-gravity experiments. One is a simple type of experiment in which center of gravity exists inside of an object. Another is a complicated one in which the center of gravity is also inside of an object. However, the third type is an experiment in where the center of gravity is outside of an object. Therefore, it gives students an opportunity to discuss how to confirm equilibrium on a metal rod when the object has its center of gravity outside. Having discussions in class will allow students to have a critical way of thinking. In addition, searching for a way to solve a problem will increase creativity of students as well. And the last type is finding the center of gravity of a big acrylic panel where multiple objects are on the panel. According to the survey and interview conducted by students who participated in this program, teaching based on creative STEAM system helps students to get a better understanding and more fast acquisition of knowledge. We can expect that a well-planned creative STEAM system through a continuous study will be both effective and efficient in educating critical and creative students.

• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.1-22
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• 2012

The purpose of this study is to understand Korea students' characteristics as well as to give important information of improving our education using comparative analysis of framework, test booklets, test results between PISA 2009 and NAEA 2009. PISA 2009 was administered on May of 2009 and NAEA was administered on October of same year. The summary of the results of comparing two assessment is as follows First, cut score of NAEA Advance level is bigger than the cut score of level 5, which is considered as high achievement level. The cut score of Basic level of NAEA is also higher than the level 2 of PISA, which is considered as basic achievement level. This phenomenon can show that NAEA achievement level is set little bit higher than the achievement level of PISA in mathematics domain. Second, the percentage of female students on higher level was higher than that of male students. In suburban area, the percentage of high level was small and the percentage of low level was big. Third, students of Advanced level are distributed concentrating in PISA levels 4~6, Proficient achievement level concentrating in PISA levels 3~5, Basic achievement level concentrating in PISA levels 2~4, and below basic achievement levels concentrating in below level 1 and level 3 of PISA. Fourth, the correlation between NAEA 2009 and PISA 2009 achievement scores are significantly positive. However, the correlation of subscales were low. Fifth, analysis of non-equivalent group, 11 items located in 'change and relationship', 'uncertainty', 'connection cluster' domains found to be significantly different. The percent correct showed very big difference. The analysis results presents the implication of mathematics curriculum, teaching and learning methods as well as National Assessment of Educational Achievement.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.501-525
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• 2015

This study analyzes arithmetic word problem of multiplication and division in the mathematics textbooks and workbooks of 3rd grade in elementary school according to 2009 revised curriculum. And we analyzes type of the problem solving ability which 4th graders prefer in the course of arithmetic word problem solving and the problem solving ability as per the type in order to seek efficient teaching methods on arithmetic word problem solving of students. First, in the mathematics textbook and workbook of 3rd grade, arithmetic word problem of multiplication and division suggested various things such as thought opening, activities, finish, and let's check. As per the semantic element, multiplication was classified into 5 types of cumulated addition of same number, rate, comparison, arrayal and combination while division was classified into 2 types of division into equal parts and division by equal part. According to result of analysis, the type of cumulated addition of same number was the most one for multiplication while 2 types of division into equal parts and division by equal part were evenly spread in division. Second, according to 1st test result of arithmetic word problem solving ability in the element of arithmetic operation meaning, 4th grade showed type of cumulated addition of same number as the highest correct answer ratio for multiplication. As for division, 4th grade showed 90% correct answer ratio in 4 questionnaires out of 5 questionnaires. And 2nd test showed arithmetic word problem solving ability in the element of arithmetic operation construction, as for multiplication and division, correct answer ratio was higher in the case that 4th grade students did not know the result than the case they did not know changed amount or initial amount. This was because the case of asking the result was suggested in the mathematics textbook and workbook and therefore, it was difficult for students to understand such questions as changed amount or initial amount which they did not see frequently. Therefore, it is required for students to experience more varied types of problems so that they can more easily recognize problems seen from a textbook and then, improve their understanding of problems and problem solving ability.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.321-350
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• 2013

The purpose of this study to analysis of problem posing in 5th and 6th grade mathematics textbooks and to comprehend errors in the problem posing activity of 6th graders in elementary school. For solving the research problems, problem posing contents were extracted from mathematics textbooks and practice books for the 5th and 6th grade of elementary school in the 2007 revised national curriculum, and they were analyzed, according to each grade, domain and type. Based on the analysis results, 10 problem posing questions which were extracted and developed, were modified and supplemented through a pre-examination, and a questionnaire that problem posing questions are evenly distributed, according to each grade, domain and type, was produced. This examination was conducted with 129 6th graders, and types of error in problem posing were analyzed using collected data. The implications from the research results are as follows. First, it was found that there was a big numerical difference of problem posing questions in the 5th and 6th grade, and problem posing questions weren't properly suggested in even some domains and types, because the serious concentration in each grade, type and domain. Therefore, textbooks to be developed in the future would need to suggest more various and systematic of problem posing teaching learning activity for each domain and type. Second, the 'error resulting from the lack of information' occurred the most in the problems that 6th graders posed, followed by the 'error in the understanding of problems', 'technical errors', 'logical errors' and 'others'. This implies that a majority of students missed conditions necessary for problem solving, because they have been used to finding answers to given questions only. For such reason, there should be an environment in which students can pose problems by themselves, breaking from the way of learning to only solve given problems.