• Journal of the Korean School Mathematics Society
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• v.9 no.2
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• pp.195-208
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• 2006

Among different geometrical representations of a mathematical concept, learners are likely to form their geometrical concept image of the given concept based on a specific one. A learner's image is not always in accord with the definition of a concept. This can induce his or her errors in mathematical problem solving. We need to analyse types of such errors and the cause of the errors. In this study, we analyse learners' geometrical concept images for geometrical concepts and errors related to such images. Furthermore we propose a theoretical framework for error analysis related to a learner's concept image for a general mathematical concept in mathematical problem solving.

• East Asian mathematical journal
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• v.27 no.2
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• pp.163-180
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• 2011

The purpose of this study is to look for the plan of reconstructing a textbook through error analysis and the process of its correction in numbers and operations of the first grade. The Research materials are collected and analyzed through the journal about every lessons, the recording sheets of students' activity, the recording videotapes during lessons, the individual interview and observation. This study investigated 4 errors which are useful for reconstructing textbook, the errors of understanding relation between numerical expression and number line, the errors of drawing-strategy, the errors of understanding relation between additive expression and subtractive expression, the errors of subtraction has to be regrouped. The errors are classified into some types and analyzed focusing on content of each error. Reinstructing are carried out based on material analyzed for correcting errors.

• 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.

• East Asian mathematical journal
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• v.31 no.4
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• pp.609-625
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• 2015

This study was subjected to 9th graders after making a conformity analysis about errors in function from a selected linear function domain learned in 8th grade, and using this we analyzed some errors learners have in the linear function domain. Learners showed the most deficiency in mastery of prerequisite facts concepts out of errors in linear functions and lack of skill in interpreting the content of the questions and technical errors occurred often as well. How the pre-service secondary school teachers prescribed these errors of linear function was analyzed from the point of problem solving strategies, accessing methods and whether or not the learner's error was used. Looking into the pre-service secondary teachers' prescription of the learners' errors in 3 fields, for the problem solving strategy a procedural strategy was used more than a conceptual strategy, and as for the accessing methods over 90% gave teacher led type explanations to the students. Also over 90% of pre-service secondary teachers did not use the learner's errors that turned up in problems.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.71-78
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• 2005

In this paper, the iterative solution is studied for equation Tx = f with a uniformly continuous ${\varphi}$-strongly accretive operators in arbitrary real Banach spaces. Our results extend, generalize and improve the corresponding results obtained by Zeng [11].

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.309-319
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• 2002

We consider the nonlinear autoregressive model with nonlinear ARCH errors, and find sufficient conditions for the existence of a strictly stationary process. New results are obtained, and known results are shown to emerge as special oases.

• East Asian mathematical journal
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• v.24 no.4
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• pp.339-345
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• 2008

Some equivalence conditions for the convergence of iterative sequences for set-valued contraction mapping in Banach spaces are obtained.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.503-522
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• 2015

In this paper, we consider the problem of testing for a parameter change in nonlinear time series models with GARCH type errors. We introduce two types of cumulative sum (CUSUM) tests: estimates-based and residual-based tests. It is shown that under regularity conditions, their limiting null distributions are the sup of independent Brownian bridges. A simulation study is conducted for illustration.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.367-374
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• 2009

The errors take place in the communication channel but they are often burst-error types. From properties of the Fi-bonacci code, it is not difficult to detect the burst-errors accompanying with this code. Fibonacci codes for correcting the double-burst-error patterns are presented. Given the channel length with the double-burst-error type, Fibonacci code correcting these errors is constructed by a simple formula.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.267-281
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• 2004

In this paper, we establish almost stability of Ishikawa iterative schemes with errors for the classes of Lipschitz $\phi$-strongly quasi-accretive operators and Lipschitz $\phi$-hemicontractive operators in arbitrary Banach spaces. The results of this paper extend a few well-known recent results.