• Bulletin of the Korean Mathematical Society
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• 제56권3호
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• pp.621-629
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• 2019

In this paper, we present a local convergence analysis of a three point method with convergence order $1.839{\ldots}$ for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies, we obtain: larger radius of convergence and more precise error estimates on the distances involved. Finally, numerical examples are used to show the advantages of the main results over earlier results.

• The Pure and Applied Mathematics
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• 제31권1호
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• pp.57-81
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• 2024

We introduce a new degree reduction method for homogeneous symmetric polynomials on binary variables that generalizes the conventional degree reduction methods on monomials introduced by Freedman and Ishikawa. We also design an degree reduction algorithm for general polynomials on binary variables, simulated on the graph coloring problem for random graphs, and compared the results with the conventional methods. The simulated results show that our new method produces reduced quadratic polynomials that contains less variables than the reduced quadratic polynomials produced by the conventional methods.

• Communications of Mathematical Education
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• 제28권1호
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• pp.19-44
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• 2014

This study aims to develop strategies for improving the affective characteristics of Korean students based on results from international achievement tests. In pursuing the goal, different research methods are employed including a) analysis of the theories and literature regarding the affective domains included in PISA and TIMSS studies; b) analysis of the current situation and needs of Korean students with respect to the affective factors based on PISA and TIMSS results; c) case studies of best practices in relation to students' affective domains in Korea and abroad; and d) development of strategies for improving and supporting Korean students' affective characteristics. In this paper, first of all, relevant theories on affective characteristics in literature are introduced. In other words, the concepts of three affective domains in question - interest, self-efficacy, and value - are reviewed, and their definitions for the present study are made. Also, teaching strategies and support plans for improving students' affective factors are extracted from previous studies. Furthermore, this paper reviews recent trends in research on how the affective domains are related to mathematics education and how one can teach them effectively. The teaching guidelines for each affective domain are developed according to the instruction principles extracted through literature review in general for all subjects. Based on the results of the findings mentioned above, this paper establishes and suggests the guidelines on how to teach mathematics reflecting the affective characteristic.

• School Mathematics
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• 제15권4호
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• pp.819-832
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• 2013

This study was performed to investigate the pedagogical knowledge of pre-service teachers and to explore the possibility of using Lesson Play in pre-service teacher education. Lesson Play refers to a lesson written in script form, featuring imagined interactions between a teacher and his/her students. The participants of this study were 20 pre-service teachers enrolled in mathematics education at a University in Seoul and they conducted a dialogue between a teacher and students who said that 91 is a prime number and 462 is a multiple number of 4. Conclusions were drawn based on the virtual scripts of pre-service teachers. First, it was found that the teaching strategies of pre-service teachers were not diverse. Second, pre-service teachers mainly explained the mathematical principles and concepts. Third, pre-service teachers could not understand the current state of students. Therefore, Lesson Play is helpful to analyse the pedagogical knowledge of pre-service teachers and is a applicable teaching method that can improve the practical knowledge of pre-service teachers.

• Journal of Elementary Mathematics Education in Korea
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• 제22권3호
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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 Elementary Mathematics Education in Korea
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• 제20권4호
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• pp.695-715
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• 2016

This study is on the teaching method for the students who belong to the same school (one, the gifted class, passed gifted education of Science High school ), 1-1, face-to-face learning (two, good students in regular classroom) with a teacher, paired learning teams (4 people, gifted classes), and group lessons (20 people, gifted classes) and using the justification analysis framework tool(PIRSO) of Kim(2010) analyzes the justification element of the students in the group classes regular polygons paper was to explore ways to improve the justification of the folding maps activities. As a result, the width of the largest polygon difficulty level appropriate to the class for gifted elementary school classes but the individual learning style of the 1-1 face-to-face with a teacher or discussion with colleagues and cooperative approach is justified, rather than the material of the study of origami activities it turned out to be more effective in improving the level of justification. Unlike the individual learning activities, the exploration for class is the need to strain in parallel to the student is selected as needed, rather than serial manner was confirmed that it is necessary to clearly present problems even from the beginning. Development of teaching through the implications obtained from this method of reconstruction activities and proposed improvement measures for questioning.

• Education of Primary School Mathematics
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• 제25권1호
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• pp.81-100
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• 2022

The purpose of this study is to develop a framework for analyzing the solution spaces of open-ended task and to explore their usefulness and applicability based on the analysis of solution spaces constructed by students. Based on literature reviews and previous studies, researchers developed a framework for analyzing solution spaces (OMR-framework) organized into subspaces of outcome spaces, method spaces, representation spaces which could be used in structurally analyzing students' solutions of open-ended tasks. In our research, we developed open-ended tasks which had various outcomes and methods that could be solved by using the concepts of factors and multiples and assigned the tasks to 181 elementary school fifth and sixth graders. As a result of analyzing the student's solution spaces by applying the OMR-framework, it was possible to systematically analyze the characteristics of students' understanding of the concept of factors and multiples and their approach to reversible and constructive thinking. In addition to formal mathematical representations, various informal representations constructed by students were also analyzed. It was revealed that each space(outcome, method, and representation) had a unique set of characteristics, but were closely interconnected to each other in the process. In conclusion, it can be said that method of analyzing solution spaces of open-ended tasks of this study are useful for systemizing and analyzing the solution spaces and are applicable to the analysis of the solutions of open-ended tasks.

• Communications of Mathematical Education
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• 제34권2호
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• pp.179-200
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• 2020

The study investigates how two different methods of peer tutoring impact academic achievement and student affect in a high school mathematics class. The two methods include the one-on-one non-reciprocal peer tutoring and the one-on-four interactive peer-tutoring method. We looked into students' cognitive gains and their affect toward mathematics after students had experienced peer tutoring for six weeks. Further, we analyzed student responses in a survey about peer tutoring activities. A finding is that the two methods produced no statistically significant difference in both cognitive gains and student affect toward mathematics. As students expressed views about their peer tutoring experiences, their comments, however, revealed the multifaceted aspects of peer tutoring in the classroom setting. In turn, this supports the use of diverse peer tutoring methods especially when the teacher makes incremental changes in teaching practices to improve student learning. Findings also indicate that appropriate peer tutoring experiences have the potential to create intellectually safe learning environments with high student engagement. This underscores the benefit of designing and implementing diverse peer tutoring methods that are effective in engaging students in learning and increasing the opportunity to learn and create knowledge with peers.

• Journal of Elementary Mathematics Education in Korea
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• 제19권4호
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• pp.485-499
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• 2015

In this paper, focusing on definitions of terms related to ratio (a:b, external ratio, internal ratio, percentage, proportion, bi-ui-gap(value of a:b)), elementary school mathematics textbooks of Korea and Japan are compared. We can find significant differences between Korean and Japanese textbooks. In Korean textbook, 'bi-yul' includes both of the internal ratio and the external ratio. In Japanese textbooks, the external ratio(amount of unit size) and the internal ratio(wariai) are defined independently. And a:b is set to a subconcept of the internal ratio. In addition, a:b and percentage are presented as methods to express the internal ratio. From these results, the following four implications for developing our mathematics textbooks can be presented as conclusions. First, it is necessary to limit the ratio to mean the internal ratio. Second, it is necessary to define connotatively the ratio as the internal ratio and to set it as a prior concept of a:b. Third, it is necessary to define 1% as the internal ratio 0.01. Fourth, it is necessary to define bi-ui-gap as a number for expressing a:b, when viewing a:b as the expression method of the internal ratio.

• Communications of Mathematical Education
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• 제26권1호
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• pp.109-135
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• 2012

On the standards or elements of teaching evaluation, the Korea Institute of Curriculum and Evaluation(KICE) has carried out the following research such as : 1) development of the standards on teaching evaluation between 2004 and 2006, and 2) investigation on the elements of Teacher Knowledge. The purposes of development of evaluation standards for mathematics teaching through those studies were to improve not only mathematics teachers' professionalism but also their own teaching methods or strategies. In this study, the standards were revised and modified by analyzing the results of those studies focused on the knowledge of subject matter knowledge, knowledge of learners' understanding, teaching and learning methods and assessments, and teaching contexts. For this purpose, the part of subject matter knowledge was consisted of four evaluation domains such as the knowledge of curriculum reconstruction, knowledge of mathematical contents, methodological knowledge, mathematical value. The part of Learners' unders tanding included the evaluation domains such as students' intellectual and achievement level, students' misconception in math, students' motivation on learning, students' attitude on mathematics learning, and students' learning strategies. The part of teaching methods and evaluation was consisted of seventh evaluation domains such as instruction involving instructional goal and content, instruction involving problem-solving activity, instruction involving learners' achievement level and attitude, instruction on communication skills, planning of assessment method and procedure, development on assessment tool, application on assessment result in class were new established. Also, the part of teaching context was consisted of four evaluation domains such as application of instructional tools and materials, commercial manipulatives, environment of classroom including distribution and control of class group, atmosphere of classroom, management of teaching contexts including management of student. According to those evaluation domains of each teacher knowledge, elements on teaching evaluation focused on the teacher's knowledge were established using the instructional evaluation framework, which is developed in this study, including the four areas of obtaining, planning, acting, and reflecting.