• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.337-347
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• 1995

In the problem of some sequential estimation, the stopping times may be written in the form $N(c) = inf{n \geq n_0; n \geq c^2 S^2_n/\delta^2 (\bar{X}_n)}$ where ${s^2_n}$ and ${\bar{X}_n}$ are the sequences of sample variance and sample mean of the independently and identically distributed (i.i.d.) random variables with distribution $F_{\theta}(x), \theta \in \Theta$, respectively, and $\delta$ is either constant or any given positive real valued function. We obtain some asymptotic normality and asymptotic expectation of the N(c) in various limiting situations. Specially, uniform asymptotic normality and uniform asymptotic expectation of the N(c) are given.

• Communications for Statistical Applications and Methods
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• v.26 no.4
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• pp.347-357
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• 2019

We propose new classes of estimators of population mean under non-response using bivariate auxiliary information. Some improved regression (or difference) type estimators have been proposed in four different situations of non response along with their properties and the expressions for the bias and mean square errors of the proposed estimators are derived under double (two-stage) sampling scheme. The properties of the suggested class of estimators are studied and it is observed that the proposed estimators performed better when compared to conventional estimators proposed by Singh and Kumar (Journal of Statistical Planning and Inference, 140, 2536-2550, 2010b), Shabbir and Khan (Communications in Statistics - Theory and Methods, 42, 4127-4145, 2013) and Bhushan and Naqvi (Journal of Statistics and Management Systems, 18, 573-602, 2015). A comparative study is also conducted both theoretically as well as empirically in order to support the results.

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.287-313
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• 2005

The decimal fraction concept plays an important role in understanding the real number which is one of the major concepts in school mathematics. In the school mathematics of Korea, the decimal fraction is treated merely as a sort of name of the common fraction, while many other important aspects of the decimal fraction concept are ignored. In consequence students fail to understand the decimal fraction concept properly, and merely consider it as a kind of number for formal computation. Preceding studies also identified students' narrow understanding of the decimal fraction concept. But none of them succeeded in clarifying the essences of the decimal fraction concept, which are crucial for discussing the didactical problems of it. In this study we attempted a didactical analysis of the decimal fraction concept and disclosed the roots of didactical problems and presented measures for its improvement. First, we attempted a phenomenological analysis of the decimal fraction concept and extracted 9 elements of the decimal fraction concept. Second, we has analyzed of the essence of the decimal fraction concept more clearly by relating it to the situations where it functions and its representations. For this we tried to construct the conceptual field of the decimal fraction. Third, we categorized he developmental levels of the decimal fraction concept from the aspect of external manifestation of the internal order. On the basis of these results, we attempted hierarchical structuring of the elements of the decimal fraction concept. And using the results of such a didactical analysis on the decimal number concept we analyzed the mathematics curriculum and textbooks of our country, investigated levels of students' understanding of the decimal fraction concept, and disclosed related problems. Finally we suggested directions and measures for the improvement of teaching decimal fraction concept.

• 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.

• Journal of the Korea Society for Simulation
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• v.31 no.2
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• pp.11-20
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• 2022

There is a critical need for AI assistance in guard operations of Army base perimeters, which is exacerbated by changes in the national defense and security environment such as force reduction. In addition, the possibility for human error inherent to perimeter guard operations attests to the need for an innovative revamp of current systems. The purpose of this study is to propose a real-time object detection AI tailored to military CCTV surveillance with three unique characteristics. First, training data suitable for situations in which relatively small objects must be recognized is used due to the characteristics of military CCTV. Second, we utilize a data augmentation algorithm suited for military context applied in the data preparation step. Third, a noise reduction algorithm is applied to account for military-specific situations, such as camouflaged targets and unfavorable weather conditions. The proposed system has been field-tested in a real-world setting, and its performance has been verified.

• Journal of Educational Research in Mathematics
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• v.15 no.1
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• pp.75-105
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• 2005

This study explored a mathematical modeling flow and the effect of interactions among students and between a student and Excel on modeling in a small group modeling environment with Excel. This is a case study of three 8th graders' modeling activity using Excel during their extra lessons. The conclusions drawn from this study are as follows: First, small group modeling using Excel was formed by formulating 4∼10 modeling cycles in each task. Students mainly formed tables and graphs and refined and simplified these models. Second, students mainly formed tables, algebraic formulas and graphs and refined tables considering each variable in detail by obtaining new data with inserting rows. In tables, students mainly explored many expected cases by changing the values of the parameters. In Graphs, students mainly identified a solution or confirmed the solution founded in a table. Meanwhile, students sometimes constructed graphs without a purpose and explored the problem situations by graphs mainly as related with searching a solution, identifying solutions that are found in the tables. Thus, the teacher's intervention is needed to help students use diverse representations properly in problem situations and explore floatingly and interactively using multi-representations that are connected numerically, symbolically and graphically. Sometimes students also perform unnecessary activities in producing data by dragging, searching a solution by 'trial and error' and exploring 'what if' modeling. It is considered that these unnecessary activities were caused by over-reliance on the Excel environment. Thus, the teacher's intervention is needed to complement the Excel environment and the paper-and-pencil environment properly.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.569-590
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• 2023

The purpose of this case study is to compare and analyze the covariational reasoning levels of two middle school students revealed in the process of solving and generalizing algebra word problems. A class was conducted with two middle school students who had not learned quadratic equations in school mathematics. During the retrospective analysis after the class was over, a noticeable difference between the two students was revealed in solving algebra word problems, including situations where speed changes. Accordingly, this study compared and analyzed the level of covariational reasoning revealed in the process of solving or generalizing algebra word problems including situations where speed is constant or changing, based on the theoretical framework proposed by Thompson & Carlson(2017). As a result, this study confirmed that students' covariational reasoning levels may be different even if the problem-solving methods and results of algebra word problems are similar, and the similarity of problem-solving revealed in the process of solving and generalizing algebra word problems was analyzed from a covariation perspective. This study suggests that in the teaching and learning algebra word problems, rather than focusing on finding solutions by quickly converting problem situations into equations, activities of finding changing quantities and representing the relationships between them in various ways.

• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.189-206
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• 2015

There has been a recurring call for using visual representations in textbooks to improve the teaching and learning of proportional reasoning. However, the quantity as well as quality of visual representations used in textbooks is still very limited. In this article, we analyzed visual representations presented in a Grade 6 textbook from two perspectives of proportional reasoning, multiple-batches perspective and variable-parts perspective, and discussed the potential of the double number line and the double tape diagram to help develop the idea 'things covary while something stays the same', which is critical to reason proportionally. We also classified situations that require proportional reasoning into five categories and provided ways of using the double number line and the double tape diagram for each category.

• School Mathematics
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• v.19 no.2
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• pp.345-367
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• 2017

The purpose of this study is to investigate the proportional reasoning of middle school students during the process of expressing and interpreting the graphs. We collected data from a teaching experiment with four 7th grade students who participated in 23 teaching episodes. For this study, the differences between student A and student B-who joined theteaching experiment from the $1^{st}$ teaching episode through the $8^{th}$ -in understanding graphs are compared and the reason for their differences are discussed. The results showed different proportional solving strategies between the two students, which revealed in the course of adjusting values of two given variables to seek new values; student B, due to a limited ability for proportional reasoning, had difficulty in constructing graphs for given situations and interpreting given graphs.

• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.483-498
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• 2010

The purpose of this paper is to investigate the dispositions of university students' understanding and reasoning about rational number concept. For this, we surveyed for the subject groups of prospective math teachers(33), engineering major students(35), American engineering and science major students(28). The questionnaire consists of four problems related to understanding of rational number concept and three problems related to rational number operation reasoning. We asked multi-answers for the front four problem and the order of favorite algorithms for the back three problems. As a result, we found that university students don't understand exactly the facets of rational number and prefer the mechanic approaches rather than conceptual one. Furthermore, they reasoned illogically in many situations related to fraction, ratio, proportion, rational number and don't recognize exactly the connection between them, and confuse about rational number concept.