• Communications of Mathematical Education
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• v.28 no.3
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• pp.339-352
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• 2014

In this paper we introduce mathematical modellings in teaching and learning differential equations which were adopted by 2009 revised curriculum. The textbook of 'Advanced Mathematics II' published in 2014 with one publisher includes the content of the second order differential equation y"+y=0 by the power series method. This paper discusses the issue of the power series and gives an alternative method to explain problems of differential equation. Also, we found that the textbook of 'Advanced Mathematics II' used the mechanical system not electrical system in solving differential equation problems. Thus this paper suggests a method using an electric circuit in teaching and learning the first order differential equation. Finally we suggest some terminologies in the teaching and learning of differential equations.

• Korean Journal of Child Studies
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• v.36 no.5
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• pp.95-113
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• 2015

This study aimed to develop and validate a scale which could be used to evaluate mathematical interactions of parents with their young children. The subjects comprised 408 mothers of 4-6-year-old children. Means, standard deviation, $x^2$, Cramer's V, exploratory factor analysis, confirmatory factor analysis, Pearson correlations, and Cronbach's ${\alpha}$ were calculated. First, 49 items were developed through a review of relevant research, parent interviews, confirmation of item adequacy and content validity. These items were then edited down to a final list of 24 items representing 4 factors identified by exploratory factor analysis. Second, this 24-item. 4-factor scale was shown to have adequate construct validity, norm validity, and reliability by confirmatory factor analysis, Pearson correlation analysis, Cronbach's ${\alpha}$. In conclusion, the final mathematical interaction scale for young children's parents was composed of 24 items with 4 factors: "interaction regarding numbers and operations, measurements, and patterns", "interaction regarding data collection and result presentation", "interaction with picture books", and "interaction regarding shapes and figures"

• Communications of Mathematical Education
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• v.23 no.3
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• pp.507-522
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• 2009

In general, we do fold paper and unfold, it remain paper traces. We can be obtained by using rectangular paper, a mathematical fact and the program had a combination. Depending on the direction of the rectangle, folding paper in the form of variety shows valley and ridge signs of the appearance of this paper. By using (0,1)-code and (0,1)-matrix, we study four kinds of research. Therefore, traces of this view upside down rectangle folding paper how to fold inductive reasoning ability of the code and explore the relationship of traces. Finally, the mathematical content and program development can practice in the field.

• Geomechanics and Engineering
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• v.29 no.5
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• pp.549-565
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• 2022

Severe acid rains can be a major source for geotechnical and environmental problems in any soil depending on the acid type and concentration. Hence, this study investigates the individual severe effects of sulfuric, hydrochloric and nitric acids on the geotechnical properties of real field soil through a series of experimental laboratory tests. The laboratory program consists of experimental tests such as consistency, compaction, unconfined compression, pH determination, electrical conductivity, total dissolved salts, total suspended solids, gypsum and carbonates contents. The experimental tests have been performed on the untreated soil and individual acid treated soil for acid concentrations range of 0% to 20% by weight. In addition, a unique hyperbolic mathematical model has been used to predict significant geotechnical characteristics for acid treated soil. The plastic and liquid limits and optimum moisture content have been increased under the effect of all the used acids whereas the maximum dry density and unconfined stress-strain behavior have been decreased with increasing the acid concentrations. Moreover, the used hyperbolic mathematical model has predicted all the geotechnical characteristics very well with a very high coefficient of determination (R²) value and lowest root mean square error (RMSE) estimate.

• East Asian mathematical journal
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• v.40 no.2
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• pp.149-166
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• 2024

This study is to establish the domains and the standards of instructional evaluation on the teacher knowledge dealing with the knowledge of 'teaching and learning methods and assessment'. Especially, in this study, the instruction assessment standards are developed focused on the five types of mathematics competencies such as problem solving, communication, reasoning, connection, information and handling, which were emphasized in the mathematical curriculum revised in 2022. By the result, ten domains such as an instruction involving instruction goal and content, problem-solving competency, data treatment competency, learners' achievement level and attitude, communication competency, reasoning competency, connection competency, the assessment method and procedure based on the competency, the assessment tool development based on the competency, assessment result based on the competency were new established. According to those domains, the total 20 instructional evaluation standards were developed. This study is limited to consider the domain of 'teaching and learning methods and assessment' among the domains of teacher knowledge, while dealing with the elements of mathematics competencies in the standards. However, instructional evaluation standards reflecting these competencies should be developed in the other diverse domains of teacher knowledge.

• Education of Primary School Mathematics
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• v.27 no.2
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• pp.139-153
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• 2024

This analysis was intended to present pedagogical implications related to the guidance of solid figures in elementary mathematics textbooks. The definitions of mathematical concepts and visually represented examples presented in the prism and pyramid units were analyzed. As a result of the analysis, differences were observed in both the method and content of defining mathematical concepts, even though the same curriculum was reflected. Additionally, various forms of visual examples were provided during the learning process of prisms and pyramids. Based on the results of this analysis, it is necessary to understand the definition of mathematical concepts and to teach students in an appropriate manner, considering the goals of each session and the objectives of the activities involved in presenting visual examples.

• Journal of the Korean School Mathematics Society
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• v.3 no.1
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• pp.131-148
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• 2000

Above all, the ability to solve problems must be emphasized as a basic skill of mathematics, but it is neglected when we teach. In this study, learning task means ［same meaning］ ［same form］ ［same technique］, so I tried to extend mathematical scholastic ability of the students as an extensional problem solving that is a basic element of mathematics. The purpose of this study is the investigation of level type learning, using the basic learning elements to extend thinking ability. From the constructed hypothesis as follows and then implement it. I selected basic learning elements from an analyzed textbook and then task learning material was created for each level type learning. The problem solving ability will be extended through the level type learning of the small group, using the level type learning task material. The conclusions this study are as follows. The level type learning in small group learning, using and making level type learning material, having basic learning elements in analysed text are. Basic learning content is understood clearly and deeply, so, fundamentally, it is effective in achieving the problem solving in mathematics. It is an effective method to achieve the meta-cognitive faculty because achieved the expected method of solving problems and resulted in the true learning of content.

• The Mathematical Education
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• v.55 no.4
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• pp.485-501
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• 2016

This study was to explore the factors that mathematics teachers actually need to improve their students' creativity and character to pursue education in the direction of the revised curriculum. We first temporarily extracted the elements to reinforce mathematics teachers' professionalism for creativity and character education through literature review, and then conducted the modified delphi technique and interview by targeting secondary school mathematics teachers. Based on the discussion of previous studies, we divided into five areas for mathematics teachers' professional development of creativity and character education: 1. understanding of creativity and character education, 2. creating an environment, 3. understanding curriculum for creativity and character education, 4. instructional design and apply for creativity and character education, 5. evaluating for creativity and character education. Actually content elements highly required by mathematics teachers were reset 17 items. The results of this study are expected to be used as the basis for teachers' professional development of creativity and character education in mathematics education.

• Journal of Biosystems Engineering
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• v.43 no.4
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• pp.369-378
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• 2018

Purpose: The aim of this study was to construct a saponin content-predicting model using shortwave infrared imaging spectroscopy. Methods: The experiment used a shortwave imaging spectrometer and ENVI spectral acquisition software sampling a spectrum of 910 nm-2500 nm. The corresponding preprocessing and mathematical modeling analysis was performed by Unscrambler 9.7 software to establish a ginsenoside nondestructive spectral testing prediction model. Results: The optimal preprocessing method was determined to be a standard normal variable transformation combined with the second-order differential method. The coefficient of determination, $R^2$, of the mathematical model established by the partial least squares method was found to be 0.9999, while the root mean squared error of prediction, RMSEP, was found to be 0.0043, and root mean squared error of calibration, RMSEC, was 0.0041. The residuals of the majority of the samples used for the prediction were between ${\pm}1$. Conclusion: The experiment showed that the predicted model featured a high correlation with real values and a good prediction result, such that this technique can be appropriately applied for the nondestructive testing of ginseng quality.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.427-438
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• 2015

The Schensted algorithm first described by Robinson [5] is a remarkable combinatorial correspondence associated with the theory of symmetric functions. $Sch{\ddot{u}}tzenberger's$ jeu de taquin[10] can be used to give alternative descriptions of both P- and Q-tableaux of the Schensted algorithm as well as the ordinary and dual Knuth relations. In this paper we describe the jeu de taquin on shifted rim hook tableaux using the switching rule, which shows that the sum of the weights of the shifted rim hook tableaux of a given shape and content does not depend on the order of the content if content parts are all odd.