• Communications of Mathematical Education
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• v.37 no.1
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• pp.65-84
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• 2023

The method of Lagrange multipliers, one of the most fundamental algorithms for solving equality constrained optimization problems, has been widely used in basic mathematics for artificial intelligence (AI), linear algebra, optimization theory, and control theory. This method is an important tool that connects calculus and linear algebra. It is actively used in artificial intelligence algorithms including principal component analysis (PCA). Therefore, it is desired that instructors motivate students who first encounter this method in college calculus. In this paper, we provide an integrated perspective for instructors to teach the method of Lagrange multipliers effectively. First, we provide visualization materials and Python-based code, helping to understand the principle of this method. Second, we give a full explanation on the relation between Lagrange multiplier and eigenvalues of a matrix. Third, we give the proof of the first-order optimality condition, which is a fundamental of the method of Lagrange multipliers, and briefly introduce the generalized version of it in optimization. Finally, we give an example of PCA analysis on a real data. These materials can be utilized in class for teaching of the method of Lagrange multipliers.

• The Journal of the Korea Contents Association
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• v.17 no.10
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• pp.472-482
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• 2017

In this study, discrete mathematical items were classified into analytical items and mathematical items were analyzed on the basis of analytic framework items of mathematics and the past items of mathematics subject contents of the period 2011-2017 school year. First, the discrete mathematics evaluation areas and evaluation contents proposed by the Korea Institute for Curriculum and Evaluation should be evenly distributed. Second, the items of measuring metacognitive knowledge as a strategic knowledge on the use of cognitive methods should be given. Third, the ratio of the number of items in discrete mathematics to the number of that was 3.8%~6.8%, and the ratio according to the item weighting was 2.2%~6.3%. Fourth, it is analyzed that all the items are suitable for the evaluation goal and the pre-service math teachers who have faithfully implemented the curriculum have maintained the appropriate level of difficulty to solve. Finally, the content items such as the method of counting the discrete mathematics curriculum, the Recurrence Relation, the generation function, and the graph are matched with the teacher certification examination and the mathematics education curriculum of each teachers college. By these reasons, we conclude that the contribution of pre-service teachers to the motivation of learning is obtained and implications.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.12
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• pp.872-877
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• 2018

STEAM is an acronym for Science, Technology, Engineering, Arts, and Mathematics. It is considered important to equip students with a creative thinking ability and the core competences required in future society, helping them devise new ideas emerging from branches of study. This study is about the convergence of instructional design in private finance for the life sciences, which aims to foster talent through problem-based learning (PBL). Skills like collaboration, creativity, critical thinking, and problem solving are part of any STEAM PBL, and are needed for students to be effective. STEAM projects give students a chance to problem-solve in unique ways, because they are forced to use a variety of methods to solve problems that pop up during these types of activities. The results of this study are as follows. First is the structured process of convergence lessons. Second is the convergence lesson process. Third is the development of problems in the introduction of private finance and the life sciences for a convergence lesson at Dornod University. Learning motivation shows the following results: understanding of learning content (66.6%), effectiveness (63.3%), self-directed learning (59.9%), motivation (63.2%), and confidence (63.3%). To make an effective model, studies applying this instructional design are to be implemented.

• Journal of the Korean School Mathematics Society
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• v.17 no.2
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• pp.251-274
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• 2014

The purpose of this study is to analyze characteristics of PCK before class, investigate how these characteristics are enacted in classrooms when beginning and experienced teachers teach mathematical functions, and provide pedagogical implications. Two beginning teachers and two experienced teachers participated in the study. In order to analyze characteristics of PCK before class, interviews and survey research were conducted. An investigation of classroom discourse was used to examine how the PCK characteristics appear in classrooms. Results show that experiences teachers enacted their PCK about learner, curriculum, teaching methods, and teaching environment in classrooms, whereas beginning teachers could not show their PCK. These results suggest practical implications for the developments of teacher education curriculum and teacher training program.

• Journal of Korean Home Economics Education Association
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• v.23 no.1
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• pp.87-111
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• 2011

The purpose of this study was to develop and evaluate practical problem-based Home Economics lesson plans applying to the multiple intelligence teaching learning strategy, focused on the unit 'Nutrition & Meals' of middle school Home Economics subject matter. To achieve this purpose, the lesson plans were developed and evaluated from the 72 middle school students in Chongju after implementing the instruction. The data from the questionnaire were analyzed by SPSS/WIN 12.0 and content analysis. The results were as follows: First, the objectives of practical problem-based 'Nutrition & Meals' Instruction using multiple intelligence teaching strategy were to understand the importance of nutrition and health in an adolescent period and to develop good eating habits. The Practical Problem was 'What should I do for good eating habits?' and the learning contents were healthy life, the kinds and functions of nutriments, food pyramid and a food guide. The learning activities were progressed by various types of teaching and learning methods including 8 types of multiple intelligence teaching strategy. The lesson plans were developed according to the process of practical problem solving model. 6 periods of lesson plans and worksheets were developed. Second, the practical problem-based instruction using multiple intelligence teaching-learning strategy were evaluated to increase students' positive learning attitudes, motivation, and good eating habits.

• Korean Journal of Childcare and Education
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• v.9 no.5
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• pp.181-200
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• 2013

This study aimed at exploring how an instructor constructs meanings through content-based instruction (CBI) offered to pre-service teachers majoring in early childhood education. The course, early childhood mathematics education, was conducted during the spring semester in 2011. This study adopted a narrative inquiry, and data were collected through observations, interviews, and work samples. This study found that during the whole process from the preparation phase to the end-of-program evaluation, the instructor captured diverse challenging moments. During the preparation phase, she needed to have careful orchestration in designing lessons in order to overcome her feeling of pressure as a non-native speaker of English and design the integration of contents and English language learning to be truly powerful. In the phase of implementation, the lack of student motivation and building a good rapport between the instructor and the students were certainly challenges. The result of the student evaluations weakened her desire to implement CBI. The instructor incorporated diverse instructional strategies to overcome the obstacles. The instructor's experiences in this study will positively shape future educators' thinking and learning about meaningful and appropriate academic English instruction for content-area teaching of college students who were majoring in early childhood education.

• Journal of Science Education
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• v.41 no.3
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• pp.334-350
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• 2017

The purposes of this study are to develop scientific-inquiry based on STEAM education program and to investigate the effects of the program on middle-school students' interests, self-efficacy, and career choice about science, technology/engineering, and mathematics. In order to develop this program, the literature investigation and previous studies were conducted, so that finally the developmental direction was based on scientific inquiry and the developmental theme and model were selected. A total 92 first-graders in G middle-school of Daegu city were participated in this study. A single group pre-post test paired t-test was conducted to figure out changes of students' interest, self-efficacy, and career choices before or after applying this program. In addition, in-depth interviews were conducted with 14 students to find their specific responses. The results of this study were as follows. First, STEAM education program on the theme of 'RC Airplane' was developed on the basis of the 'ADBA' model. Second, the developed STEAM educational program not only results a decisive difference statistically but also has significant effects on middle-school students' interests, self-efficacy, and career choice in science, technology/engineering, and mathematics, who are involved in the free-semester program, across the overall affective domain. In conclusion, the STEAM educational program in this study could affect significant meanings to middle-school students during the free-semester. It could contribute to facilitate middle-school students' education for happiness and to grow the creative STEAM talents.

• Journal of Gifted/Talented Education
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• v.24 no.4
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• pp.561-576
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• 2014

The purpose of this study is to investigate the perception of the mothers of science gifted in respect to giftedness compared to the "Scale for Rating the Behavioral Characteristics of Superior Students-R(SRBCSS-R)". For that, a survey of 18 mothers of elementary school science gifted and 32 mothers of middle school science gifted was conducted in relation to giftedness. The words and frame of this survey were analyzed using the Semantic Network Analysis. The results are as follows : The mothers of Elementary school science gifted perception were found to have a connected giftedness with reading, science, making something, etc.. On the other hand, the mothers of middle school science gifted perception were found to have a connected giftedness with problem, solving problem, mathematics, etc. in words analysis. The mothers of Elementary school science gifted have a strong connection with category on creativity, motivation, etc.. On the other hand, the mothers of middle school science gifted were more inclined towards the category on learning, motivation, etc. in frame analysis. That is to say, the mothers of science gifted are perceptive about giftedness respect to some elements as the "Scale for Rating the Behavioral Characteristics of Superior Students-R" on the giftedness. Therefore, a correct understanding about giftedness in respect to the mothers of science gifted is required and parent education is needed for appropriate science gifted education.

• Journal of Gifted/Talented Education
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• v.25 no.5
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• pp.673-696
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• 2015

Students' perception of science-related career strongly influences the formation of career motivation in science. Especially, the high level of science gifted students' positive perceptions plays an important role in allowing them to continue to study science. This study compared perceptions of science-related career between general and gifted middle school students using semantic network analysis. To ensure this end, we first structuralize semantic networks of science-related careers that students perceived. Then, we identified the characters of networks that two different student groups showed based on the structure matrix indices of semantic network analysis. The findings illustrated that the number of science-related careers shown in science gifted students' answer is more than in general students' answer. In addition, the science gifted students perceived more diverse science-related careers than general students. Second, scientific career such as natural scientists and professors were shown in the core of science gifted students' perception network whereas non-research oriented careers such as science teachers and doctors were shown in the core of general students' perception network. In this study, we identified the science gifted students' perceptions of science-related career was significantly different from the general students'. The findings of current study can be used for the science teachers to advise science gifted students on science-related careers.

• Journal of Korean Home Economics Education Association
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• v.25 no.1
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• pp.55-66
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• 2013

The purposes of this study were to examine major satisfaction and career decision level of Home Economics Education major college students, to investigate factors influencing on major satisfaction and career decision level, and to provide basic informations for career counseling. A survey was conducted to students majoring Home Economics Education at four universities, and students majoring Korean Language Education and Mathematics Education at one same university in Seoul from October to November, 2011. General satisfaction in major of Home Economics Edu. students was above average, but social perception satisfaction was low. The social perception satisfaction was lower for Home Economics edu. students than Korean Language edu. and Mathematics edu. students. There were significant differences in major satisfaction by university and class standing, but no significant difference by gender. Students showed the lowest value in Home Economics teacher as considering job, and most of students considered teacher and major unconcerned job. Students considering major concerned job showed higher major satisfaction compared to students considering major unconcerned job. Career decision level was medium and there were not significant differences in career decision level by major, university, class standing, gender, considering job. Career decision level was affected positively by only general satisfaction in major.