• 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.

• School Mathematics
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• v.15 no.4
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• pp.759-783
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• 2013

Both curriculum and textbooks play an important role in the process of didactical transposition from mathematics as a science to school mathematics. The 2009 revised national curriculum for mathematics introduced the system of grade-band, so its achievement criteria for mathematical contents tend to be addressed more and less generally in the curriculum. We need to investigate whether the achievement criteria were applied meaningfully in elementary textbooks for mathematics. This study aims to recognize the connection between the curriculum and the textbooks and make a suggestion for composing the following curriculum and its textbooks. To do this, we analyzed the mathematics textbooks for 1~2 grades in relation to the mathematical contents as per reconstructed one of curriculum achievement criteria, the mathematical terms and symbols, and the mathematical processes -mathematical problem solving, mathematical reasoning, mathematical communication. Based this analysis, futhermore, this study includes some didactical discussions and implications for development of mathematics textbooks in 3~4 and 5~6 grade-bands.

• Communications of Mathematical Education
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• v.24 no.4
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• pp.843-864
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• 2010

To get an undergraduate degree from mathematics education department, a student not only take a general educational technology course from education department, but also take an educational technology in mathematics education course from mathematics education department. We believe that these two courses can be integrated for preparing better mathematics teachers. For this purpose, we design an educational technology tool called JavaMAL microworld, and study strategy to integrate two courses harmoniously. This kind of approach is good for internationalization of researches on mathematics education by Korean researchers since most SSCI journal prefer an integrated approach in the educational technology related papers. In short, integrating general educational technology course and educational technology in mathematics education course is not only good to student but to professors. But just integrating two courses is not enough. Students must understand the needs and the usefulness of educational technology tool in the learning and teaching of mathematics, and must have such experience from their mathematics courses.

• Communications of Mathematical Education
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• v.27 no.3
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• pp.221-248
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• 2013

Among five types of the model textbook based on storytelling, the type of 'Inquiry into history of Mathematics' focuses on adapting the logic of mathematical discovery to the organization of mathematical contents. It enables students to recognize that mathematics has been developed by human needs and creativity while they are engaged in the story about knowledge formation. Moreover the textbook offers the context in which students are able to understand mathematical insights and logics hidden in the subject matter, so that they can reinvent and develop mathematical knowledge. In this study, we found the principles for development of the textbook based on storytelling for 'Inquiry into History of Mathematics' by analyzing the chapter about 'Complex number and Quadratic Equations' of the model textbook. The chapter was implemented in classroom environment and students' understanding of the subject matter and their perception on the textbook based on storytelling were surveyed before and after the implementation. The results showed the possibilities of adapting the textbook based on storytelling and we suggested some implications for further development.

• Communications of Mathematical Education
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• v.36 no.3
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• pp.439-467
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• 2022

The future society requires not only knowledge but also various competencies, including creativity, cooperative spirit and integrated thinking. This research develops a program for integrating mathematics and information science to enhance important mathematical competencies such as problem-solving and communication. This program does not require much prior knowledge, can be motivated using everyday language and easy-to-access tools, and is based on creative problem-solving activities with multilateral cooperation. The usefulness and rigor of mathematics are emphasized as the number of participants increases in the activities, and theoretical principles stem from the matrix theory over finite fields. Moreover, the activity highlights a connection with error-correcting codes, an important topic in information science. We expect that the real-world contexts of this program contribute to enhancing mathematical communication competence and providing an opportunity to experience the values of mathematics and that this program to be accessible to teachers since coding is not included.

• Communications of Mathematical Education
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• v.28 no.2
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• pp.179-193
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• 2014

After National Mathematics Education Advanced Plan represented in 2012, mathematics education fields began to attention to 'Storytelling'. Because the plan contains important topics, reinforcing mathematics education, improving understanding about mathematics, and enhancing self-guided learning. As one of the methods for improving understanding about mathematics, Storytelling in mathematics is emphasizing recently. The purpose of this study is to analyse the articles about 'Storytelling Mathematics' to find how the media report it. Also, we discuss the direction of Storytelling in mathematics education. The conclusion of this study is that most of the privately-owned company is using the Storytelling as a tool for advertising commercially. Readers have to make a decision which articles are true or useful. A policy makers must ponder how the 'Storytelling Mathematics' policy affect the demands and suppliers in education.

• The Mathematical Education
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• v.57 no.2
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• pp.179-196
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• 2018

The purpose of this study was to investigate the measurement equivalence and to suggest application ways in teaching aptitude and personality test results for pre-service mathematics teachers between a graduate school of education and a college of education. This study analyzed the scores of the teaching aptitude and personality test of 36 pre-service mathematics teachers enrolled in a graduate school of education and 111 pre-service mathematics teachers in a college of education by performing a multivariate generalizability analysis. The main results were as follows. First, graduate's pre-service mathematics teachers had a higher level of teaching aptitude and personality than that of college's pre-service mathematics teachers based on the total scores. In addition, graduate's pre-service mathematics teachers had higher levels of teaching aptitude and personality than those of college's pre-service mathematics teachers except for a creativity application domain based on the sub-domain scores. Second, cognitive domains were measured more precisely but affective domains were measured less precisely for graduate's pre-service mathematics teachers than for college's pre-service mathematics teachers. Third, regardless of school levels, Cronbach's ${\alpha}$ values, which might be overestimated by applying the classical test theory, were higher than dependability coefficients. Fourth, this study showed a somewhat negative result in ensuring the measurement equivalence for a problem solving exploration domain. However, regardless of school levels, this study indicated that the overall measurement was generally reliable on composite scores. Based on these results, it was confirmed that multivariate generalizability methodologies' approach can be useful for exploring the measurement equivalence issues. Finally, this study suggests how to utilize the results of the test, how to apply a multivariate generalizability analysis for detecting the measurement equivalence, and how to develop future research based on limitations.

• East Asian mathematical journal
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• v.32 no.4
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• pp.565-587
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• 2016

The purpose of this study was to analyze the understanding of the meaning of fraction division and fraction division algorithm of elementary mathematical gifted students through the process of problem posing and solving activities. For this goal, students were asked to pose more than two real-world problems with respect to the fraction division of ${\frac{3}{4}}{\div}{\frac{2}{3}}$, and to explain the validity of the operation ${\frac{3}{4}}{\div}{\frac{2}{3}}={\frac{3}{4}}{\times}{\frac{3}{2}}$ in the process of solving the posed problems. As the results, although the gifted students posed more word problems in the 'inverse of multiplication' and 'inverse of a cartesian product' situations compared to the general students and pre-service elementary teachers in the previous researches, most of them also preferred to understanding the meaning of fractional division in the 'measurement division' situation. Handling the fractional division by converting it into the division of natural numbers through reduction to a common denominator in the 'measurement division', they showed the poor understanding of the meaning of multiplication by the reciprocal of divisor in the fraction division algorithm. So we suggest following: First, instruction on fraction division based on various problem situations is necessary. Second, eliciting fractional division algorithm in partitive division situation is strongly recommended for helping students understand the meaning of the reciprocal of divisor. Third, it is necessary to incorporate real-world problem posing tasks into elementary mathematics classroom for fostering mathematical creativity as well as problem solving ability.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.745-776
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• 2010

In this research, cases of classes for enhancing mathematical creativity are examined in order to explore how to improve methods of math instructions. The objective of the research is to design a creative, efficient math class of superior quality, supplementing the current educational curricula. To this end, features and elements of creative math class are classified into three categories: assignment characteristics, teacher's role, and teaching environment. Based on these, two high school teachers were selected for case study of creative instructions. By observing and analyzing their classes, the research identified main elements of creative classes and their characteristics according to the three categories. The research also explored how to revitalize creative math class by eliciting opinions of researchers and educational experts.

• Journal of Wellness
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• v.14 no.2
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• pp.207-223
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• 2019

The purpose This study aimed at proposing class module elements for creativity and convergence and class models for creativity and convergence by integrating content elements by physical activity field(health, challenge, competition, ) for physical education and STEAM. For this, literature review, focus group interview(FGI) and discussions with experts were conducted, and the following study results have been drawn up: First, concerning the class module elements for creativity and convergence, total 11 class module elements in the health field were suggested including detecting risks by posture analysis and analyzing and designing amount of physical activity. Second, total 7 module elements in the challenge field were deduced such as anticipation of obstacles to target achievement and modeling of effective exercise. There were 17 convergence elements in the competition field including game record analysis and creation of game data storage application. Third, total 9 creativity and convergence module elements in the field include modeling of technology improvement for motion and symbolization for motion records. In addition, class modules related to convergence with engineering in the health field, convergence with technology in the challenge field, convergence with art in the competition field and convergence with art and mathematical symbols were proposed.