• Communications of Mathematical Education
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• v.37 no.3
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• pp.443-465
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• 2023

This study examines the content of vectors and matrices in Artificial Intelligence Mathematics textbooks (AIMTs) from the 2015 revised mathematics curriculum. We analyzed the implementation of foundational mathematical concepts, specifically definitions and related sub-concepts of vectors and matrices, in these textbooks, given their importance for understanding AI. The findings reveal significant variations in the presentation of vector-related concepts, definitions, sub-concepts, and levels of contextual information and descriptions such as vector size, distance between vectors, and mathematical interpretation. While there are few discrepancies in the presentation of fundamental matrix concepts, differences emerge in the subtypes of matrices used and the matrix operations applied in image data processing across textbooks. There is also variation in how textbooks emphasize the interconnectedness of mathematics for explaining vector-related concepts versus the textbooks place more emphasis on AI-related knowledge than on mathematical concepts and principles. The implications for future curriculum development and textbook design are discussed, providing insights into improving AI mathematics education.

• The Mathematical Education
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• v.62 no.4
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• pp.515-529
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• 2023

The purpose of this study is to analyze teachers' understanding of the number and operations area of grades 3 to 6 in elementary school mathematics curriculum and to derive implications for improving teachers' understanding of the mathematics curriculum. To this end, elementary school teachers were asked to develop items to evaluate curriculum achievement standards at each grade level, and then the teachers' understanding of the curriculum was examined based on the collected items. As a result of the study, there was a misinterpretation of the achievement standards in approximately 25% of the questions collected. Typically, cases where the content covered by each grade was confused when using textbooks as a standard, or cases where the difference between the content covered by the two achievement standards could not be completely distinguished were found.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.281-301
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• 2024

Many students have experienced difficulties due to the discontinuity in instruction between arithmetic and algebra, and in the field of elementary education, algebra is often treated somewhat implicitly. However, algebra must be learned as algebraic thinking in accordance with the developmental stage at the elementary level through the expansion of numerical systems, principles, and thinking. In this study, algebraic thinking-based classes were developed and conducted for 6th graders in elementary school, and the effect on the ability to solve word-problems in fraction division was analyzed. During the 11 instructional sessions, the students generalized the solution by exploring the relationship between the dividend and the divisor, and further explored generalized representations applicable to all cases. The results of the study confirmed that algebraic thinking-based classes have positive effects on their ability to solve fractional division word-problems. In the problem-solving process, algebraic thinking elements such as symbolization, generalization, reasoning, and justification appeared, with students discovering various mathematical ideas and structures, and using them to solve problems Based on the research results, we induced some implications for early algebraic guidance in elementary school mathematics.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2017.11a
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• pp.236-237
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• 2017

In this research, experimental seakeeping results of Warped hull form 2 on the regular waves were compared with numerical results of strip method and CFD. In case of ship's speed, there are 3 cases (3.4m/s, 4.6m/s, 5.75m/s) for numerical simulation, and they are belong to semi-planing and planing condition. Consequently, in case of strip method, it is shown that the resonance phenomena occurred from around ${\lambda}/L_{OA}=2$ to 4 and RAO value were significantly higher than that of other. this is different from experimental results. In case of CFD, overall trends were similar with experimental values except there are somewhat excessive RAO values around ${\lambda}/L_{OA}=0.5$ to 2.5. these phenomena is confirmed that it became larger as the ship's speed increased, and it was considered that the error occurred because the number of mesh in vertical direction of wave height at ${\lambda}/L_{OA}=0.5$ to 2.5 were relatively less than those of wave height at ${\lambda}/L_{OA}=2.5$ to 5.2.

• Communications of Mathematical Education
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• v.31 no.4
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• pp.433-456
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• 2017

The purpose of this study is to suggest the directions for the development and improvement of mathematics textbooks in Korea by examining these characteristics of German textbooks. As a result, German mathematics textbooks were free for unit order and names of units. German mathematics textbooks defined a function for various real life and natural phenomena, relation after intuitively knowing the correspondence between two variables through a graph. In addition, it exercises interpreting the characteristics and information of the graph, guides the activity of graphing various functional situations, and contents to convert various expression methods such as graphs, tables, relational expressions, mathematical terms and sentences. In the German mathematics textbooks, mathematical expressions of the functional relations of the materials in various contexts of daily life, and the activities of predicting and predicting the future, were made to feel the usefulness of mathematics. It has raised functional thinking and provided problems related to other subjects, thus enhancing connectivity with other disciplines. It also included open issues and issues that required mathematical communication.

• Journal of Navigation and Port Research
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• v.31 no.5 s.121
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• pp.435-445
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• 2007

Ship structures are thin-walled structures and lots of cutouts, for example, of inner bottom structure, girder, upper deck hatch, floor and dia-frame etc. In the case where a plate has cutout it experiences reduced buckling and ultimate strength and at the same time the in-plane stress under compressive load produced by hull girder bending will be redistributed. In the present paper, we investigated several kinds of perforated stiffened model from actual ship structure and series of elasto-plastic large deflection analyses were performed to investigate into the influence of perforation on the buckling and ultimate strength of the perforated stiffened plate varying the cutout ratio, web height, thickness and type of cross-section by commercial FEA program(ANSYS). Closed-form formulas for predicting the ultimate strength of the perforated stiffened plate are empirically derived by curve fitting based on the Finite Element Analysis results. These formulas are used to evaluate the ultimate strength, which showed good correlation with FEM results. These results will be useful for evaluating the ultimate strength of the perforated stiffened plate in the preliminary design.

• Education of Primary School Mathematics
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• v.23 no.3
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• pp.135-156
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• 2020

The purpose of this study is to analyze the effect of average unit learning on the knowledge of the representative value of 5th grade elementary school students. In the information-oriented society, the ability to organize and summarize the data has become an essential resource. In the process of correctly analyzing statistical data and making reasonable decisions, the summary of the data plays an important role, and it is necessary to learn the concept of representative values in order to describe the center of the data in a series of numbers. For research, an informal knowledge type possessed by a fifth grade elementary school student with respect to a representative value before learning an average unit is examined and compared with the representative value after learning the average unit. A suggestion point for representative value guidance in school mathematics is provided while examining the change in knowledge with respect to the representative value. Seeing the informal types of elementary school students' representative values will help them learn how to formalize the concept of representative values in middle and high schools. It will give suggestions about the concept of representative values and the method of instruction that should be dealt with in elementary schools. The informal knowledge about the representative value can help with formal representative value that will be learned later. Therefore, This study's discussions on statistical learning of elementary school students are expected to present meaningful implications for statistical education.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.137-154
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• 2012

Approximation' is one of central conceptions in calculus. A basic conception for explaining 'approximation' is 'tangent', and 'tangent' is a 'line' with special condition. In this study, we will study pedagogically these mathematical knowledge on the ground of a viewpoint on the teaching of secondary geometry, and in connection with these we will suggest the teaching program and the chief end for the probable teaching. For this, we will examine point, line, circle, straight line, tangent line, approximation, and drive meaningfully mathematical knowledge for algebraic operation through the process translating from the above into analytic geometry. And we will construct the stream line of mathematical knowledge for approximation from a view of modern mathematics. This study help mathematics teachers to promote the pedagogical content knowledge, and to provide the basis for development of teaching model guiding the mathematical knowledge. Moreover, this study help students to recognize that mathematics is a systematic discipline and school mathematics are activities constructed under a fixed purpose.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.599-624
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• 2009

The purpose of this study was to investigate the relationship between error types and Polya's problem solving process. For doing this, we selected 106 sophomore students in a middle school and gave them algebra word problem test. With this test, we analyzed the students' error types in solving algebra word problems. First, We analyzed students' errors in solving algebra word problems into the following six error types. The result showed that the rate of student's errors in each type is as follows: "misinterpreted language"(39.7%), "distorted theorem or solution"(38.2%), "technical error"(11.8%), "unverified solution"(7.4%), "misused data"(2.9%) and "logically invalid inference"(0%). Therefore, we found that the most of student's errors occur in "misinterpreted language" and "distorted theorem or solution" types. According to the analysis of the relationship between students' error types and Polya's problem-solving process, we found that students who made errors of "misinterpreted language" and "distorted theorem or solution" types had some problems in the stage of "understanding", "planning" and "looking back". Also those who made errors of "unverified solution" type showed some problems in "planing" and "looking back" steps. Finally, errors of "misused data" and "technical error" types were related in "carrying out" and "looking back" steps, respectively.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.343-360
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• 2022

In mathematics classes, the verbal explanation may contain diverse mathematical concepts and principles in short sentences. It may also include mathematics symbols and terms that might not be used in everyday life. Therefore, students may need particular listening ability in order to understand and participate in mathematics communication. Unlike general listening, the listening ability for mathematics classes may require student to integrate their mathematical and linguistic knowledge. The aim of this study is to reveal the subdomains of listening ability for mathematics classes in a elementary school. I categorized listening ability for mathematics classes in a elementary school from the literature. The categories of listening ability for mathematics are Interpretive Listening, Evaluative Listening, Hermeneutic Listening, Selective Listening, Pretend Listening, and Ignored Listening. In order to develop a framework for understanding listening ability for mathematics classes, I investigated a hierarchy of 412 South Korean elementary teachers' perception. Through a web-based survey, the teachers were asked to rank order their beliefs about and students' listening ability. Findings show that teachers' perceptions about listening ability for mathematics classes are divergent from current research trends. South Korean elementary teachers perceived Interpretive Listening as the most important listening.