• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.523-544
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• 2009

The object of this study is to analyze manipulative materials in the Pattern & Algebra field of Maths300-Maths with Attitude, Australian school mathematics program with manipulative materials to search meaningful ways for school mathematics. To accomplish these projects, 20 manipulative materials in the Pattern & Algebra field of the Maths with Attitude are introduced and each manipulative materials can be used are searched according to grades and fields of Korean educational course. And 4 mathematics classes for 3rd and 5th grades(two for each grades) with manipulative materials are performed and effect of these classes are examined by recorded data and students' opinions are inquired by questionnaire. First, We analyze Pattern & Algebra of the Maths with Attitude 20 manipulative materials such as 4ARM SHAPES, ADDITION TOTALS, ICE CREAM FLAVOURS, THE LAND OF ET, etc. In this analysis, plans for utilizing the manipulative materials are categorized in 9 types. Second, by students' handling these kinds of manipulative materials in classes, their interest in mathematics is increased and voluntary and creative classes out of the conventional ones can be made. Also, students' self-confidence in mathematics and active participation is animated. This kind of manipulative materials are introduced in the educational field of elementary schools, plans for utilizing the teaching aids in the field are analyzed, the teaching aids are practically applied to classes, and the effect and meanings for mathematics classes are examined. With this research, another researches about the introduction and utilization of other various manipulative materials for motivating students to efficiently understand what they learn in mathematics class of elementary schools are required.

• School Mathematics
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• v.14 no.4
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• pp.445-468
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• 2012

This study is tried in order to link informal arithmetic reasoning to formal algebraic reasoning. In this study, we investigated elementary school student's non-formal algebraic reasoning used in algebraic problem solving. The result of we investigated algebraic reasoning of 839 students from grade 1 to 6 in two schools, Korea, we could recognize that they used various arithmetic reasoning and pre-formal algebraic reasoning which is the other than that is proposed in the text book in word problem solving related to the linear systems of equation. Reasoning strategies were diverse depending on structure of meaning and operational of problems. And we analyzed the cause of failure of reasoning in algebraic problem solving. Especially, 'quantitative reasoning', 'proportional reasoning' are turned into 'non-formal method of substitution' and 'non-formal method of addition and subtraction'. We discussed possibilities that we are able to connect these pre-formal algebraic reasoning to formal algebraic reasoning.

• Journal of the Institute of Convergence Signal Processing
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• v.24 no.3
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• pp.147-152
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• 2023

This paper is a study of a linear algebra course taught in a high school on-demand course. Compared to the regular course, flipped learning was added to the course, and applications to signal processing related problems were covered in consideration of students' career aspirations. Overall, the class was a mixture of traditional lectures and flipped learning. Flipped learning was implemented twice. The flipped class consisted of pre-class, in-class and post-class. To verify the effectiveness of the course, a survey was conducted and most of the evaluation items were above 4. The topics of the flipped learning were Markov chains and least squares problem, which are very important in the field of signal processing.

• 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.

• The Mathematical Education
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• v.45 no.1 s.112
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• pp.61-74
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• 2006

The ability of understanding the number and number systems, grasping the properties of number systems, and manipulating number systems is the foundation to understand algebra. It is useful to deepen students' mathematical understanding of number systems and operations. The authentic understanding of numbers and operations can make it possible for the students to manipulate algebraic symbols, to represent relationship among sets of numbers, and to use variables to investigate the properties of sets of numbers. The high school students need to understand the number systems from more abstract perspective. The purpose of this study is to study on understanding and application ability of eleventh graders of basic properties of operations with real numbers.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.469-485
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• 2023

Let 𝓐 be a unital Banach *-algebra and 𝓜 be a unital *-𝓐-bimodule. If W is a left separating point of 𝓜, we show that every *-derivable mapping at W is a Jordan derivation, and every *-left derivable mapping at W is a Jordan left derivation under the condition W𝓐 = 𝓐W. Moreover we give a complete description of linear mappings 𝛿 and 𝜏 from 𝓐 into 𝓜 satisfying 𝛿(A)B^* + A𝜏(B)^* = 0 for any A, B ∈ 𝓐 with AB^* = 0 or 𝛿(A)◦B^* + A◦𝜏(B)^* = 0 for any A, B ∈ 𝓐 with A◦B^* = 0, where A◦B = AB + BA is the Jordan product.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.307-313
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• 2023

In this paper, we study the n-dimensional Möbius transformation. We obtain several conjugacy invariants and give a conjugacy classification for n-dimensional Möbius transformation.

• Communications of Mathematical Education
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• v.31 no.3
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• pp.241-255
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• 2017

The 4th industrial revolution is coming. In order to prepare for the new learning environment with it, we may need digital mathematics textbooks that fully utilize all possible technologies. So various attempts have been made in elementary and middle school mathematics education. However, despite the importance of higher mathematics, we haven't seen a best possible math digital textbooks yet in Korea. In this paper, we introduce our new model of interactive math digital textbook about Linear Algebra/ Calculus/ Differential Equations/ Statistics/ Engineering Math. Especially, this manuscript focuses on our experience of using digital contents and interactive labs for developing a new model for linear algebra digital textbook. We introduce our works on linear algebra digital textbooks which include pdf e-book, web contents, video clips of lectures, interactive lab. Using this linear algebra digital textbook, students can freely use any mobile devices to access diverse learning materials, lessons, and hands-on exercises without any limitations. Also, times saved in the computation, coding, and typing process can be used to have more discussions for deeper understanding of mathematical concepts. This type of linear algebra digital textbook, which contains all interactive free cyber-lab with codes and all lectures for each sections, can be considered as a new model for the next generation of math digital textbook.

• 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.

• The Mathematical Education
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• v.50 no.1
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• pp.41-59
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• 2011

Given the importance of algebra in the early grades, this paper analyzed the contents of whole numbers and their operations from the perspectives of generalized arithmetic. In particular, the focus of analysis was given to the properties of 0 and 1, those of operations such as commutativity, associativity, and distributivity, and the relations between operations. As such, this paper analyzed in detail how such properties and relations were introduced and expanded across different grades. It is expected that many issues in this paper will serve basic information to develop instructional materials in a way to fostering students' algebraic thinking in the elementary grades.