• 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 Mathematical Education
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• v.63 no.2
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• pp.165-186
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• 2024

Despite the growing attention on artificial intelligence-based automated scoring technology as a support method for the introduction of descriptive items in school environments and large-scale assessments, there is a noticeable lack of foundational research in mathematics compared to other subjects. This study developed an automated scoring model for two descriptive items in first-year middle school mathematics using the Random Forest algorithm, evaluated its performance, and explored ways to enhance this performance. The accuracy of the final models for the two items was found to be between 0.95 to 1.00 and 0.73 to 0.89, respectively, which is relatively high compared to automated scoring models in other subjects. We discovered that the strategic selection of the number of evaluation categories, taking into account the amount of data, is crucial for the effective development and performance of automated scoring models. Additionally, text preprocessing by mathematics education experts proved effective in improving both the performance and interpretability of the automated scoring model. Selecting a vectorization method that matches the characteristics of the items and data was identified as one way to enhance model performance. Furthermore, we confirmed that oversampling is a useful method to supplement performance in situations where practical limitations hinder balanced data collection. To enhance educational utility, further research is needed on how to utilize feature importance derived from the Random Forest-based automated scoring model to generate useful information for teaching and learning, such as feedback. This study is significant as foundational research in the field of mathematics descriptive automatic scoring, and there is a need for various subsequent studies through close collaboration between AI experts and math education experts.

• Communications of Mathematical Education
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• v.38 no.1
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• pp.27-48
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• 2024

In order to prepare for changes in future society, cross-curricular learning is emphasized, and the need to link cross-curricular learning topics and subjects is increasing. However, there are few studies on how to deal with cross-curricular learning in mathematics education. This study analyzed the contents and methods of cross-curricular learning topics in subject-specific curriculum and mathematics textbooks. As a result of the study, the curriculum can be categorized into four types according to the variety of cross-curricular learning topics applied and the presence or absence of a main cross-curricular learning topic, and the mathematics curriculum belongs to the type where some cross-curricular learning topics are dealt with passively and there is no main topic. On the other hand, the analysis of 10 math textbooks for grades 5 and 6 according to the 2015 revised curriculum showed that, unlike the curriculum, various cross-curricular learning topics were applied in the textbooks, mainly environment and sustainable development education, safety and health education, career education, character education, and economic and financial education. In addition, in mathematics textbooks, cross-curricular learning topics appeared in various types such as materials, questions, explanations, illustrations, and in many cases, they appeared mainly as materials or illustrations. Based on these findings, implications were explored and suggested on how to integrate and apply cross-curricular learning topics in mathematics.

• 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.

• 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 Animal Environmental Science
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• v.18 no.3
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• pp.257-266
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• 2012

Near infrared reflectance spectroscopy (NIRS) has become increasingly used as a rapid, accurate method of evaluating some chemical constituents in cereal and dired animal forages. Analysis of forage quality by NIRS usually involves dry grinding samples. Costs might be reduced if samples could be analyzed without drying or grinding. The objective of this study was to investigate effect of sample preparations on prediction ability of chemical composition and fermentation parameter for Italian ryegrass silages by NIRS. A population of 147 Italian ryegrass silages representing a wide range in chemical parameters were used in this investigation. Samples were scanned at 1nm intervals over the wavelength range 680-2500 nm and the optical data recorded as log 1/Reflectance (log 1/R) and scanned in oven-dried grinding and fresh ungrinding condition. The spectral data were regressed against a range of chemical parameters using partial least squares (PLS) multivariate analysis in conjunction with four spectral math treatments to reduced the effect of extraneous noise. The optimum calibrations were selected on the basis of minimizing the standard error of cross validation (SECV) and maximizing the correlation coefficient of cross validation (${R^2}_{CV}$). The results of this study show that NIRS predicted the chemical parameters with high degree of accuracy in oven-dried grinding treatment except for moisture contents. Prediction accuracy of the moisture contents was better for fresh ungrinding treatment (SECV 1.37%, $R^2$ 0.96) than for oven-dried grinding treatments (SECV 4.31%, $R^2$ 0.68). Although the statistical indexes for accuracy of the prediction were the lower in fresh ungrinding treatment, fresh treatment may be acceptable when processing is costly or when some changes in component due to the processing are expected. Results of this experiment showed the possibility of NIRS method to predict the chemical composition and fermentation parameter of Italian ryegrass silages as routine analysis method in feeding value evaluation and for farmer advice.

• Journal of The Korean Society of Grassland and Forage Science
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• v.39 no.4
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• pp.258-263
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• 2019

Near infrared reflectance spectroscopy (NIRS) has become increasingly used as a rapid and accurate method of evaluating some chemical compositions in forages. The objective of this study was to evaluate the potential of NIRS, applied to imported forage, to estimate the moisture and chemical parameters for imported hays. A population of 392 imported hay representing a wide range in chemical parameters was used in this study. Samples of forage were scanned at 1 nm intervals over the wavelength range 680-2500nm and the optical data was recorded as log 1/Reflectance(log 1/R), which scanned in intact fresh condition. The spectral data were regressed against a range of chemical parameters using partial least squares(PLS) multivariate analysis in conjunction with spectral math treatments to reduced the effect of extraneous noise. The optimum calibrations were selected based on the highest coefficients of determination in cross validation(R²) and the lowest standard error of cross-validation(SECV). The results of this study showed that NIRS predicted the chemical parameters with very high degree of accuracy. The R² and SECV for imported hay calibration were 0.92(SECV 0.61%) for moisture, 0.98(SECV 0.65%) for acid detergent fiber, 0.97(SECV 0.40%) for neutral detergent fiber, 0.99(SECV 0.06%) for crude protein and 0.97(SECV 3.04%) for relative feed value on a dry matter(%), respectively. Results of this experiment showed the possibility of NIRS method to predict the moisture and chemical composition of imported hay in Korea for routine analysis method to evaluate the feed value.

• Journal of Gifted/Talented Education
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• v.24 no.6
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• pp.1001-1024
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• 2014

The purpose of the study is to explore the experiences and meaning of the AP (Advanced Placement) at the specialized school for the highly gifted through the in-depth interview with 39 college students who had graduated from the specialized schools with the AP experiences. It is expected that the AP will be expanded to the students at the Science High Schools from the year of 2015, however, there has been no study to examine the realities of the AP in-depth especially through the voices of the AP participants. Students have taken 8 required and/or selective courses as AP in average. Students usually start to take AP from the second year of the specialized school for the highly gifted, but some start from the first year through the placement test. Numbers of available AP courses vary by subjects, but relatively more courses open in the areas of math and physics. Students' opinions regarding the AP were quite positive. Specifically, the high quality of the AP class and energetic interaction between student and teacher compared to the college classes were preferred by the students. However, it was controversial whether C+ is enough for the pass condition of the AP. Students were using the shortened time by AP in diverse ways, such as early graduation, double majors, exchange students, individual researches, and so on. Most of all, they tried to search for their career interests through the AP experiences. In closing, the present study provides some advices and future directions for the better AP management, including the improvement of administrative system between schools for the gifted and the universities, and the expansion of the number of university which approves the AP system.

• Journal of Intelligence and Information Systems
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• v.20 no.2
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• pp.149-162
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• 2014

Course guidance is a mentoring process which is performed before students register for coming classes. The course guidance plays a very important role to students in checking degree audits of students and mentoring classes which will be taken in coming semester. Also, it is intimately involved with a graduation assessment or a completion of ABEEK certification. Currently, course guidance is manually performed by some advisers at most of universities in Korea because they have no electronic systems for the course guidance. By the lack of the systems, the advisers should analyze each degree audit of students and curriculum information of their own departments. This process often causes the human error during the course guidance process due to the complexity of the process. The electronic system thus is essential to avoid the human error for the course guidance. If the relation data model-based system is applied to the mentoring process, then the problems in manual way can be solved. However, the relational data model-based systems have some limitations. Curriculums of a department and certification systems can be changed depending on a new policy of a university or surrounding environments. If the curriculums and the systems are changed, a scheme of the existing system should be changed in accordance with the variations. It is also not sufficient to provide semantic search due to the difficulty of extracting semantic relationships between subjects. In this paper, we model a course mentoring ontology based on the analysis of a curriculum of computer science department, a structure of degree audit, and ABEEK certification. Ontology-based course guidance system is also proposed to overcome the limitation of the existing methods and to provide the effectiveness of course mentoring process for both of advisors and students. In the proposed system, all data of the system consists of ontology instances. To create ontology instances, ontology population module is developed by using JENA framework which is for building semantic web and linked data applications. In the ontology population module, the mapping rules to connect parts of degree audit to certain parts of course mentoring ontology are designed. All ontology instances are generated based on degree audits of students who participate in course mentoring test. The generated instances are saved to JENA TDB as a triple repository after an inference process using JENA inference engine. A user interface for course guidance is implemented by using Java and JENA framework. Once a advisor or a student input student's information such as student name and student number at an information request form in user interface, the proposed system provides mentoring results based on a degree audit of current student and rules to check scores for each part of a curriculum such as special cultural subject, major subject, and MSC subject containing math and basic science. Recall and precision are used to evaluate the performance of the proposed system. The recall is used to check that the proposed system retrieves all relevant subjects. The precision is used to check whether the retrieved subjects are relevant to the mentoring results. An officer of computer science department attends the verification on the results derived from the proposed system. Experimental results using real data of the participating students show that the proposed course guidance system based on course mentoring ontology provides correct course mentoring results to students at all times. Advisors can also reduce their time cost to analyze a degree audit of corresponding student and to calculate each score for the each part. As a result, the proposed system based on ontology techniques solves the difficulty of mentoring methods in manual way and the proposed system derive correct mentoring results as human conduct.

• Journal of Dental Rehabilitation and Applied Science
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• v.28 no.4
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• pp.371-383
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• 2012

Shaping the root canal system to maintain original canal curvature is essential to clinical success in endodontic treatment. Opposed to most root canals that are curved, endodontic instruments are made from straight metal blanks. They have a tendency of straightening the root canal during preparation and frequently result in procedural errors. A new treatment method to maintain original canal curvature during shaping has been introduced for preventing procedural errors. The aim of this study was to compare the ability of instruments to maintain original canal curvature of continuous rotary system and single file system. Thirty ISO 15, 0.02 taper, Endo Training Blocks(Dentsplay Maillefer) were used. Specimens were assigned to 1 of 3 groups for shaping: specimens in group 1 were shaped with ProFile #20/.06 at the WL. Specimens in group 2 were shaped with Mtwo #35/.04 at the WL. Specimens in group 3 were shaped with WaveOne Primary reciprocating files at the WL after the glide path was achieved with PathFile. Pre- and postinstrumentation digital images were superimposed and processed with Matlab r2010b(The MathWorks Inc, Natick, MA) software to analyze the curvature-radius ratio(CRr), representing canal curvature modification. Data for comparison on the ability of instruments to maintain original canal curvature depending on each Ni-Ti file were analyzed with 1-way ANOVA(P<.05). Data for comparison on the ability of instruments to maintain original canal curvature depending on each Ni-Ti file system were analyzed with independent t-test(P<.05). A statistically significant difference(P<0.05) was noted on each Ni-Ti file. ProFile and WaveOne instrumentations maintained the original canal curvature significantly better(P<0.05) than Mtwo file. There were no significant difference(P>0.05) between continuous rotary system and single file system. Under the conditions of this study, ProFile and WaveOne instruments maintained the original curvature significantly better than Mtwo file and were less modification of the canal curvature compared. There was no significant difference between continuous rotary system and single file system in shaping of simulated canals. As clinical practitioners, it may be advantages to use hybrid approach when root canal shapes depending on the design and usage of Ni-Ti files.