• School Mathematics
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• v.17 no.4
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• pp.613-632
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• 2015

In this study, we hope to reveal teacher knowledge necessary to address student errors and difficulties about ratio and rate. The instruments and interview were administered to 3 in-service primary teachers with various education background and teaching experiments. The results of this study are as follows. Specialized content knowledge(SCK) consists of profound knowledge about ratio and rate beyond multiplicative comparison of two quantities and professional knowledge about the definitions of textbook. Knowledge of content and students(KCS) is the ability to recognize students' understanding the concept and the representation about ratio and rate. Knowledge of content and teaching(KCT) is made up of knowledge about various context and visual models for understanding ratio and rate.

• 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.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.381-405
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• 2015

The nature of school mathematics has not been asked from the epistemological perspective. In this paper, I compare two dominant perspectives of school mathematics: ethnomathematics and didactical transposition theory. Then, I show that there exist some examples from Old Babylonian (OB) mathematics, which is considered as the oldest school mathematics by the recent contextualized anthropological research, cannot be explained by above two perspectives. From this, I argue that the nature of school mathematics needs to be understand from new perspective and its meaning needs to be extended to include students' and teachers' products emergent from the process of teaching and learning. From my investigation about OB school mathematics, I assume that there exist an intrinsic function of school mathematics: Linking scholarly Mathematics(M) and everyday mathematics(m). Based on my assumption, I suggest the chain of ESMPR(Educational Setting for Mathematics Practice and Readiness) and ESMCE(Educational Setting For Mathematical Creativity and Errors) as a mechanism of the function of school mathematics.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.8
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• pp.1823-1832
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• 1997

In this ppaer, fault coverage analysis of a conformance test case for communication protocols, specified as a deterministic finite state machine(DFSM) is presented. The fault coverage analysis of a test case is defined by measuring the extent of the faults detected using a generated test case. The method that evaluates fault coverage analysis for a test case, has been researched by arithmetic analysis and simulation. In this paper, we designed and implemented a simulator for fault coverage analysis of a communication protocol teat case. With this result for Inres protocol, output fault and state merge and split fault have a high fault coverage of 100%. This simulator can be widely used with new fault coverage analysis tools by applying it to various protocols.

• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.379-388
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• 2005

일차변환은 선형대수에서 가장 중요한 개념 중 하나이다. 그럼에도 많은 학생들에게서 나타나는 이 개념에 대한 오류는 무엇이며 또 어디에 근거하는가? 이 논문은 효과적인 선형대수 교수학습 연구의 일부로, 주어진 여러 함수 중에서 일차변환인 것을 찾는 과정 중에 나타난 학생들의 오류와 그 근거를 알아보았다. 본 연구 결과는 선형대수 학습에 어려움을 겪는 학생들에게 보다 효율적인 교수디자인 설계를 위한 기초 자료의 의미를 갖는다.

• Education of Primary School Mathematics
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• v.12 no.2
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• pp.117-132
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• 2009

The purpose of this study was analysis on types of strategies and errors when the sixth grade students were solving proportion problems of mathematics textbooks. For this study, proportion problems in mathematics textbooks were investigated and 17 representative problems were chosen. The 277 students of two elementary schools solved the problems. The types of strategies and errors in solving proportion problems were analyzed. The result of this study were as follows; The percentage of correct answers is high if the problems could be solved by proportional expression and the expression is in constant rate. But the percentage of correct answers is low, if the problems were expressed with non-constant rate.

• Journal of KIISE:Computing Practices and Letters
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• v.14 no.1
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• pp.101-105
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• 2008

This paper proposes an analytical model to calculate VoIP (Voice of IP) capacity over wireless LANs with frequent bit errors. Since the traditional analytical models for VoIP capacity have not included the effect of bit errors, simulations ould only evaluate VoIP capacity over erroneous channels. For analytically accurate estimation of VoIP capacity over noisy channels, we extend the conventional model to include the effect of propagation errors, end-to-end delay, voice quality, the waiting time in AP(Access Point). The experiments show that our model predicts the VoIP capacity of a given network within the range from 3% to 9% difference comparing with the simulation results.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.85-108
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• 2012

The comprehensive implication in justification activity that includes the proof in the elementary school level where the logical and formative verification is hard to come has to be instructed. Therefore, this study has set the following issues. First, what is the mathematical justification type shown in the Number and Operations, and Geometry? Second, what are the errors shown by students in the justification process? In order to solve these research issues, the test was implemented on 62 third grade elementary school students in D City and analyzed the mathematical justification type. The research result could be summarized as follows. First, in solving the justification type test for the number and operations, students evenly used the empirical justification type and the analytical justification type. Second, in the geometry, the ratio of the empirical justification was shown to be higher than the analytical justification, and it had a difference from the number and operations that evenly disclosed the ratio of the empirical justification and the analytical justification. And third, as a result of analyzing the errors of students occurring during the justification process, it was shown to show in the order of the error of omitting the problem solving process, error of concept and principle, error in understanding the questions, and technical error. Therefore, it is prudent to provide substantial justification experiences to students. And, since it is difficult to correct the erroneous concept and mistaken principle once it is accepted as familiar content that it is required to find out the principle accepted in error or mistake and re-instruct to correct it.

• The Mathematical Education
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• v.60 no.2
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• pp.229-247
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• 2021

Students' mathematical thinking is represented via various forms of outcomes, such as written response and verbal expression, and teachers could infer and respond to their mathematical thinking by using them. This study analyzed 39 elementary teachers' competency to notice students' problem-solving strategies containing mathematical errors in fraction addition and subtraction with uncommon denominators problems. Participants were provided three types of students' problem-solving strategies with regard to fraction addition and subtraction problems and asked to identify and interpret students' mathematical understanding and errors represented in their artifacts. Moreover, participants were asked to design additional questions and problems to correct students' mathematical errors. The findings revealed that first, teachers' noticing competency was the highest on identifying, followed by interpreting and responding. Second, responding could be categorized according to the teachers' intentions and the types of problem, and it tended to focus on certain types of responding. For example, in giving questions responding type, checking the hypothesized error took the largest proportion, followed by checking the student's prior knowledge. Moreover, in posing problems responding type, posing problems related to student's prior knowledge with simple computation took the largest proportion. Based on these findings, we suggested implications for the teacher noticing research on students' artifacts.

• Communications of Mathematical Education
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• v.8
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• pp.189-207
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• 1999

본 연구의 목적은 초 ${\cdot}$ 중학생들의 수학적 신념을 알아보고, 그러한 신념을 형성하는 요인들을 수학 교실의 상호작용에서 찾아보는 것이었다. 이를 위해, 초등학교 5, 6학년과 중학교 1, 2, 3학년 학생들의 수학적 신념을 질문지로 조사하였으며 각급 학교의 수학 교실에서 벌어지는 교수-학습 과정을 비디오로 촬영하여 각 교실의 사회적 규범들을 비교 분석하였다. 그 결과로서, 학생들은 수학은 이미 만들어진 규칙과 용어들로 이루어졌고 그 규칙에 따라 주어진 문제를 풀어 답을 구하는 것이 수학적 활동이라고 인식하고 있었다. 한편, 이러한 신념은 각급 교실에 형성된 사회수학적 규범과 일치했으며, 특히 개념설명과 새로운 전략 및 오류에 대한 반응과 관련된 사회수학적 규범이 학생들의 수학적 활동을 제한함으로써 그들의 신념을 결정하고 있었다.