• 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.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.199-226
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• 2024

In response to the era of transformation necessitating the introduction of Artificial Intelligence (AI) and digital technologies, educational innovation is undertaken with the implementation of AI digital textbooks in Mathematics, English, and Information subjects by 2025 in Korea. Within this context, this study analyzed the perceptions and needs of elementary school teachers regarding mathematics AI digital textbook. Based on a survey conducted in November 2023, involving 132 elementary school teachers across the country, the analysis revealed that the majority of elementary school teachers had a low perception of the introduction and need for mathematics AI digital textbooks. However, some recognized the potential for personalized learning and effective teaching support. Furthermore, among the core technologies of the AI digital textbook, teachers highly valued the necessity of learning diagnostics and teacher reconfiguration functions and had the most positive perception of their usefulness in math lessons, while their perception of interactivity was relatively low. These findings suggest the need for changing teachers' perceptions through professional development and information provision to ensure the successful adoption and use of mathematics AI digital textbooks. Specifically, providing concrete and practical ways to use the AI digital textbook, exploring alternatives to digital overload, and continuing development and research on core technologies.

• Journal of Gifted/Talented Education
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• v.13 no.4
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• pp.65-94
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• 2003

The purpose of this study is to acquire the information on the current situation of students' selection process in order to renovate the system of picking up the students. As a first step of the study, we examined the validity of the factors of the single-out system such as qualification and the process for the application and the standards and proceeding of the selection. Then we analysed the result of the entrance examination of Hansung Science Highschool in 2002. The analysis was on the correlation between the result of entrance examination and the achievement in the school and the decision of the course after graduation. To know on the achievement of the students, we investigated the records of regular tests and asked the teachers' opinion in math and science classes. As a result, we gained the following points: First, the present single-out system has a danger of excluding students who are much talented in science and math field because it is based on students' achievements in middle schools; Second, the new selection system should consider the character and attitude of the applicants in addition to their knowledge; Third, the continuous observation of the teacher in middle school should be an important factor of the picking up system; Fourth, more questions requiring divergent thinking ability and inquiry skill should be developed as selective examination question. Also examination questions should cover the various contents from mathematics to science, and do not affect pre-learning; Finally, the system of present letting all students stand in one line should be changed into that of letting students in various lines. We can consider using multi-step selection system.

• 대한공업교육학회지
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• v.41 no.1
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• pp.68-87
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• 2016

This research conducted a survey for total 166 teachers of schools so as to analyze validity and satisfaction for performance objectives of SMB administration subsidy the HRDP and the CEP in Specialized High School. The results of research are as follows. First, teachers recognize that purpose of HRDP is to expand employment of specialized high school and provide human resource of SMB. And, they recognize that HRDP is important to improve school outcomes and makes a positive effect on the improvement of school outcomes. Second, teachers recognize that objectives of HRDP are improvement of student's understanding for SMB, improvement of teacher's understanding for SMB, improvement of SMB's understanding of school, cultivation of student's occupational view, systematization of career guiding program based on employment process, strengthening of industry-academia cooperation education, improvement of the level of student's skill, fulfillment of workplace experience and practice focusing workplace learning, training of customized human resource for SMB, improvement of student's adaptation to the workplace, improvement of employment rate for SMB, expansion of job opportunities for students with SMB, preparation of the base of connection between school and SMB, publicity of school, expansion of opportunities to cooperate between SMB and school, establishment of cooperative system among industrial association and school, introduction and operation of the employment connective model for joint education and employment, strengthening of field professionalism of teachers. However, satisfaction for the achievement of objectives of HRDP except for strengthening of industry-academia cooperation education and improvement of employment rate for SMB is relatively lower than the validity. Third, teachers in charge of human resource training business of middle and small sized company's specialized high school recognize that objectives of CEP are expansion of job opportunities for students with SMB, excavation of good-quality SMB, expansion of opportunities to cooperate between SMB and school, fulfillment of workplace learning, improvement of student's major foundation and in-depth skill, improvement of literacy, math, teamwork and communication abilities for students' job performance, improvement of student's working attitude and student's proper career exploration decision. However, satisfaction for achievement of objectives of CEP is relatively lower than the validity.

• Journal of The Korean Association For Science Education
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• v.42 no.4
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• pp.417-428
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• 2022

This study analyzed the frequency and level of scientific practices presented in secondary science textbooks. A total of 1,378 student activities presented in 14 middle school science textbooks and 5 high school integrated science textbooks were analyzed, using the definition and level of scientific practice suggested in the NGSS. Findings show that most student activities focus on three practices. Compared to the textbooks for the previous science curriculum, the practice of 'obtaining, evaluating, and communicating information' was more emphasized, reflecting societal changes due to ICT development. However, the practice of 'asking a question', which can be an important element of student-led science learning, was still rarely found in textbooks, and 'developing and using models', 'using math and computational thinking' and 'arguing based on evidence' were not addressed much. The practices were mostly elementary school level except for the practice of 'constructing explanations'. Such repeated exposures to a few and low level of practices mean that many future citizens would be led to a naïve understanding of science. The findings imply that it is necessary to emphasize various practices tailored to the level of students. In the upcoming revision of the science curriculum, it is necessary to provide the definition of practices that are not currently specified and the expected level of each practice so that the curriculum can provide sufficient guidance for textbook writing. These efforts should be supported by benchmarking of overseas science curriculum and research that explore students' ability and teachers' understanding of scientific practices.

• Communications of Mathematical Education
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• v.37 no.2
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• pp.233-256
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• 2023

This study conducted foundational research to derive ways to use ChatGPT in mathematics education by analyzing ChatGPT's responses to questions from the National Assessment of Educational Achievement (NAEA) and the College Scholastic Ability Test (CSAT). ChatGPT, a generative artificial intelligence model, has gained attention in various fields, and there is a growing demand for its use in education as the number of users rapidly increases. To the best of our knowledge, there are very few reported cases of educational studies utilizing ChatGPT. In this study, we analyzed ChatGPT 3.5 responses to questions from the three-year National Assessment of Educational Achievement and the College Scholastic Ability Test, categorizing them based on the percentage of correct answers, the accuracy of the solution process, and types of errors. The correct answer rates for ChatGPT in the National Assessment of Educational Achievement and the College Scholastic Ability Test questions were 37.1% and 15.97%, respectively. The accuracy of ChatGPT's solution process was calculated as 3.44 for the National Assessment of Educational Achievement and 2.49 for the College Scholastic Ability Test. Errors in solving math problems with ChatGPT were classified into procedural and functional errors. Procedural errors referred to mistakes in connecting expressions to the next step or in calculations, while functional errors were related to how ChatGPT recognized, judged, and outputted text. This analysis suggests that relying solely on the percentage of correct answers should not be the criterion for assessing ChatGPT's mathematical performance, but rather a combination of the accuracy of the solution process and types of errors should be considered.

• International Journal of Computer Science & Network Security
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• v.24 no.4
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• pp.163-169
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• 2024

India is a developing nation and has come with comprehensive way in modernizing its reducing poverty, economy and rising living standards for an outsized fragment of its residents. The STEM (Science, Technology, Engineering, and Mathematics) education plays an important role in it. STEM is an educational curriculum that emphasis on the subjects of "science, technology, engineering, and mathematics". In traditional education scenario, these subjects are taught independently, but according to the educational philosophy of STEM that teaches these subjects together in project-based lessons. STEM helps the students in his holistic development. Youth unemployment is the biggest concern due to lack of adequate skills. There is a huge skill gap behind jobless engineers and the question arises how we can prepare engineers for a better tomorrow? Now a day's Industry 4.0 is a new fourth industrial revolution which is an intelligent networking of machines and processes for industry through ICT. It is based upon the usage of cyber-physical systems and Internet of Things (IoT). Industrial revolution does not influence only production but also educational system as well. IoT in academics is a new revolution to the Internet technology, which introduced "Smartness" in the entire IT infrastructure. To improve socio-economic status of the India students must equipped with 21st century digital skills and Universities, colleges must provide individual learning kits to their students which can help them in enhancing their productivity and learning outcomes. The major goal of this paper is to present a low cost, effective learning mechanism for STEM implementation using Raspberry Pi 3+ model (Single board computer) and Node Red open source visual programming tool which is developed by IBM for wiring hardware devices together. These tools are broadly used to provide hands on experience on IoT fundamentals during teaching and learning. This paper elaborates the appropriateness and the practicality of these concepts via an example by implementing a user interface (UI) and Dashboard in Node-RED where dashboard palette is used for demonstration with switch, slider, gauge and Raspberry pi palette is used to connect with GPIO pins present on Raspberry pi board. An LED light is connected with a GPIO pin as an output pin. In this experiment, it is shown that the Node-Red dashboard is accessing on Raspberry pi and via Smartphone as well. In the final step results are shown in an elaborate manner. Conversely, inadequate Programming skills in students are the biggest challenge because without good programming skills there would be no pioneers in engineering, robotics and other areas. Coding plays an important role to increase the level of knowledge on a wide scale and to encourage the interest of students in coding. Today Python language which is Open source and most demanding languages in the industry in order to know data science and algorithms, understanding computer science would not be possible without science, technology, engineering and math. In this paper a small experiment is also done with an LED light via writing source code in python. These tiny experiments are really helpful to encourage the students and give play way to learn these advance technologies. The cost estimation is presented in tabular form for per learning kit provided to the students for Hands on experiments. Some Popular In addition, some Open source tools for experimenting with IoT Technology are described. Students can enrich their knowledge by doing lots of experiments with these freely available software's and this low cost hardware in labs or learning kits provided to them.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.717-754
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• 2015

As a design research, this study aims to identify students' collaborative problems solving patterns using the Wiki and design factors triggering MKB(mathematical knowledge building) in virtual environment. For 70 days, 14 Korean secondary gifted students, who enrolled in calculus II courses in one of gifted institutions in Korea, solved 10 math problems together using the Wiki. In this study, I considered five design factors; motivation, practice of LaTeX, norms of participation, epistemic agency, and two types of educational settings. The primary pattern emergent in students' collaborative problem solving process is identified as 'solutions and refutations' along the double helix consisting of the constructive line and the critical line, which is very similar to the pattern of 'Conjectures and Refutations'(Lakatos, 1976). Despite that most participants had difficulty in using LaTeX for mathematical expressions, this study shows that Wikis are valuable tools for providing Korean secondary students opportunities to learn social virtue such as humility and courage (Lampert, 1990), which is considered to be have been neglected in Korean educational environment but is emphasized as precious for doing mathematics in the field of mathematics education.

• Journal of Gifted/Talented Education
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• v.13 no.2
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• pp.73-94
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• 2003

In this study, it was compared how different the adjustment, self-perception, social support and stress between science-gifted children and general children, and the difference between gifted boys and girls. And it was identified what are the effects on stress of science-gifted children. The subjects were 89 science-gifted children of the first grade in Middle School at JeonJu. Science-gifted students in this study were identified through the teacher nomination and CNU(ChonbukNational University) Science & Math Tests. We used the standard object as the comparative group (general children). The results of this study were as follow; First, all personal-adjustment and social-adjustment domains, self-perception and teacher support of science-gifted children were significantly higher than those of general children. All disadjustment domains, parent support and friend support of science-gifted children were significantly lower than those of general children. Second, the self-planning, prejudice, social competence, behavioral conduct, global self worth, parent support, teacher support and classmate support of the science-gifted children had the significant difference according to the gender. Third, the motive of accomplishment, self-planning, attachment and social-affirmation of the science-gifted children correlated negatively with their stress. Fourth, the social competence, athletic competence, physical appearance, behavioral conduct, global self worth and social support of the science-gifted children correlated negatively with their stress. The global self worth of the science-gifted children had the significant difference according to the variables such as teacher support, close friend support, parent support and classmate support in the other of name. The most influential factor was teacher support. The stress of the science-gifted children had the significant difference according to the variables such as parent support, close friend support and global self worth in the other of name. The most influential factor was parent support.

• Journal of the Korea Convergence Society
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• v.8 no.8
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• pp.215-224
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• 2017

The purpose of this study was to analyze the cases of verbal interactions occurring during the mathematics lessons taught in middle school special classes in order to examine the elements and types of verbal interactions that occur between the teachers and students. Data were collected and analyzed for the sessions on geometric units that formed part of the mathematics lessons routinely implemented in the special classes. The analysis showed that the teachers initiated 237 (84.1%) of the 291 instances of verbal linguistic interactions. A total of 240 teachers' questions were analyzed, and questions in the area of knowledge occurred the most frequently, at 160 times (66.7%). A total of 617 student responses were analyzed, and short answers occurred the most frequently, at 367 times (59.5%). Teacher feedback occurred 581 times in total, and correct/incorrect (simple) feedback occurred the most frequently, at 234 times (40.3%). A total of 237 verbal interactions were observed between the teachers and children, and the I (RF) type (one teacher question, one student response, and one instance of teacher feedback) occurred most frequently, at 83 times (35.0%).