• Korean Journal of Child Studies
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• v.28 no.3
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• pp.175-185
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• 2007

This study examined types of errors made by young children on the Mathematical Ability Picture Test for Young Children(Hwang & Choi, 2007). The subjects were 30 5-year-old children. The process of taking the Mathematical Ability Picture Test was videotaped and the videotape was transcribed for analysis of errors. Findings were that in most of the sub-areas, strategy selection errors were dominant, followed by comprehension errors. Second, there was a tendency for boys and girls to make similar types of errors in every sub-area of the Mathematical Ability Picture Test for Young Children.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.239-266
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• 2004

This article presents new perspectives for analysing and diagnosing students' mathematical errors on the basis of Pascaul-Leone's neo-Piagetian theory. Although Pascaul-Leone's theory is a cognitive developmental theory, its psychological mechanism gives us new insights on mathematical errors. We analyze mathematical errors in the domain of proof problem solving comparing Pascaul-Leone's psychological mechanism with mathematical errors and diagnose misleading factors using Schoenfeld's levels of analysis and structure and fuzzy cognitive map(FCM). FCM can present with cause and effect among preconceptions or misconceptions that students have about prerequisite proof knowledge and problem solving. Conclusions could be summarized as follows: 1) Students' mathematical errors on proof problem solving and LC learning structures have the same nature. 2) Structures in items of students' mathematical errors and misleading factor structures in cognitive tasks affect mental processes with the same activation mechanism. 3) LC learning structures were activated preferentially in knowledge structures by F operator. With the same activation mechanism, the process students' mathematical errors were activated firstly among conceptions could be explained.

• East Asian mathematical journal
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• v.30 no.4
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• pp.527-544
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• 2014

The purpose of this thesis is to analyze mathematical errors in descriptive problems of the Mathematics Level Assessment(MLA) which is conducted in P University. We classified mathematical errors, which are easily made in solving the descriptive problems of the MLA, into nine types as misused data, misinterpreted language, logically invalid inference, misunderstood theorem or definition, unmatched solution, technical errors, omission of solving process, ambiguous errors, and unattempted errors. With classifying the errors in nine types, we analyzed the errors of students, who are in intermediate and low level grades, by descriptive problems. On the basis of these analysis results, we suggest plans for improving the implementation of the MLA and the teaching-learning methods about College General Mathematics.

• Research in Mathematical Education
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• v.15 no.4
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• pp.357-371
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• 2011

In mathematical problem solving, students may make various errors. In order to draw useful lessons from the errors, and then correct them, we surveyed 24 eighth-grade students' performances in geometrical problem solving according to Casey's hierarchy of errors. It was found that: 1. Students' effect can lead to errors at the stage of "comprehension", "strategy selection", and "skills manipulation"; and 2. Students' geometric schemas also influenced their strategy selection".

• East Asian mathematical journal
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• v.31 no.3
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• pp.379-382
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• 2015

The purpose of this note is to study the estimation of errors of the implicit Mann iterative process with random errors.

• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.461-488
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• 2005

This article presents new perspectives for classification of students' mathematical errors on the basis of experiential structuralism. Experiential structuralism's mechanism gives us new insights on mathematical errors. The hard core of mechanism is consist of 6 autonomous capacity spheres that are responsible for the representation and processing of different reality domains. There are specific forces that are responsible for this organization of mind. There are expressed in terms of a set of five organizational principles. Classification of mathematical errors is ascribed by the theory to the interaction between the 6 autonomous capacity spheres. Different types of classification require different autonomous capacity spheres. We can classify mathematical errors in the domain of linear function problem solving comparing cognitive psychological mechanism of experiential structuralism.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.461-467
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• 2004

In this paper, we study the Ishikawa iterative sequences with errors for Lipschitzian strongly pseudo-contractive operator in arbitrary real Banach spaces. Our results improve the results obtained previously by C. E. Chidume [3] and Zeng [9].

• Honam Mathematical Journal
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• v.30 no.1
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• pp.33-45
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• 2008

Lee weight is more appropriate for some practical situations than Hamming weight as it takes into account magnitude of each digit of the word. In this paper, we obtain a sufficient condition over the number of parity check digits for codes correcting random errors and simultaneously detecting burst errors with Lee weight consideration.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.847-860
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• 2006

In this paper, some new convergence theorems of the modified Ishikawa and Mann iterative sequences with errors for asymptotically set-valued pseudocontractive mappings in uniformly smooth Banach spaces are given.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.309-323
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• 2000

The purposes of this paper are to revise the definitions of Ishikawa and Mann type iterative processes with errors, to study the unique solution of the m-accretive operator equation x+Tx=f and the convergence problem of Ishikawa and Mann type iterative processes with errors for m-accretive mappings without the Lipschitz condition. The results presented in this paper improve, extend, and unify the corresponding results in [4, 7, 8, 12, 16] in more general setting.