• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.53-80
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• 2012

This study was designed to find the characteristics of mathematical errors and discourse in simultaneous equations and inequalities for migrant students from North Korea. 5 sample students participated, who attended in an alternative school for the migrant students from North Korea at the study in Seoul, Korea. A total of 8 lesson units were performed as an extra curriculum activity once a week during the 1st semester, 2011. The results indicated that students showed technical errors, encoding errors, misunderstood symbols, misinterpreted language, and misunderstood Chines characters of Koreans and the discourse levels improved from the zero level to the third level, but the scenes of the third level did not constantly happen. Nevertheless, the components of discourse, explanation & justification, were activated and as a result, evaluation & elaboration increased in ERE pattern on communication.

• The Mathematical Education
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• v.51 no.1
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• pp.1-19
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• 2012

In this study, contents of 'the 2007 revised curriculum handbook' and 16 kinds of mathematics textbooks were analyzed first. The purpose of this study is to examine the understanding state of students at general high schools by making questionnaires to survey the understanding state on contents of chapter of complex number based on above analysis. Results of research can be summarized as follows. First, the content of chapter of complex number in textbook was not logically organized. In the introduction of imaginary number unit, two kinds of marks were presented without any reason and it has led to two kinds of notation of negative square root. There was no explanation of difference between delimiter symbol and operator symbol at all. The concepts were presented as definition without logical explanations. Second, students who learned with textbook in which problems were pointed out above did not have concept of complex number for granted, and recognized it as expansion of operation of set of real numbers. It meant that they were confused of operation of complex numbers and did not form the image about number system itself of complex number. Implications from this study can be obtained as follows. First, as we came over to the 7th curriculum, the contents of chapter of complex number were too abbreviated to have the logical configuration of chapter in order to remove the burden for learning. Therefore, the quantitative expansion and logical configuration fit to the level for high school students corresponding to the formal operating stage are required for correct configuration of contents of chapter. Second, teachers realize the importance of chapter of complex number and reconstruct the contents of chapter to let students think conceptually and logically.

• Journal of the Korean School Mathematics Society
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• v.14 no.4
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• pp.477-490
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• 2011

The concept of pedagogical content knowledge (PCK) has been developed and expanded to identify essential components of mathematical knowledge for teaching (MKT) by Ball and her colleagues (2008). This study proposes an alternative perspective to view MKT focusing on key developmental understandings (KDUs) that carry through an instructional sequence, that are foundational for learning other ideas. In this study we provide constructive components of KDUs in fraction multiplication by focusing on the constructs of 'three-level-of-units structure' and 'recursive partitioning operation'. Expecially, our participating preservice elementary teacher, Jane, demonstrated that recursive partitioning operations with her length model played a significant role as a KDU in fraction multiplication.

• School Mathematics
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• v.13 no.4
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• pp.581-598
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• 2011

Given the growing agreement that algebra should be taught in the early stage of the curriculum, considerable studies have been conducted with regard to early algebra in the elementary school. However, there has been lack of research on how to organize mathematic lessons to develop of algebraic reasoning ability of the elementary school students. This research attempted to gain specific and practical information on effective algebraic teaching and learning in the elementary school. An exploratory qualitative case study was conducted to the fourth graders. This paper focused on the associative law of the multiplication. This paper showed what kinds of activities a teacher may organize following three steps: (a) focus on the properties of numbers and operations in specific situations, (b) discovery of the properties of numbers and operations with many examples, and (c) generalization of the properties of numbers and operations in arbitrary situations. Given the steps, this paper included an analysis on how the students developed their algebraic reasoning. This study provides implications on the important factors that lead to the development of algebraic reasoning ability for elementary students.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.477-494
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• 2012

This study is to review the content organization and developmental ways of the unit on the mixed calculations and explore the alternatives on the basis of students' responsive examples and error patterns with relation to the mixed calculations, mnemonics of PEMDAS and historical context with relation to the order of operations. Then I analyzed the textbook and manual for teachers of the unit of mixed calculations of fourth grade and improvement about teaching the mixed calculations. First, I pointed out illogical connection between practical problem and rules of order of operations. Second, I suggested constructing a textbook by considering conventional character of order of operations. Third, I pointed out the importance of structural understanding of an expression of mixed calculations and various strategies with relation to teaching and learning. This study is suggestive for textbook development of the mixed calculations.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.1-22
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• 2017

This study investigated three $10^{th}$ grade students' concept of rate of change while they perceived changing values of given functions. We have conducted a teaching experiment consisting of 6 teaching episodes on how the students understood and expressed changing values of functions on certain intervals in accordance with the concept of rate of change. The result showed that the students did use the same word of 'rate of change' in their analysis of functions, but their understanding and expression of the word varied, which turned out to have diverse perceptions with regard to average rate of change. To consider these differences as qualitatively different levels might need further research, but we expect that this research will serve as a foundational study for further research in students' learning 'differential calculus' from the perspective of rate of change.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.23-49
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• 2017

This study examined two current learning models for covariational reasoning(Carlson et al.(2002), Thompson, & Carlson(2017)), applied the models to teaching two $9^{th}$ grade students, and analyzed the results according to the types of graphs(a quantitative graph or qualitative graph). Results showed that the model of Thompson and Carlson(2017) was more useful than that of Carlson et al.(2002) in figuring out the students' levels in their quantitative graphing activities. Applying Carlson et al.(2002)'s model made it possible to classify levels of the students in their qualitative graphs. The results of this study suggest that not only quantitative understanding but also qualitative understanding is important in investigating students' covariational reasoning levels. The model of Thompson and Carlson(2017) reveals more various aspects in exploring students' levels of quantitative understanding, and the model of Carlson et al.(2002) revealing more of qualitative understanding.

• Journal of the Korean School Mathematics Society
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• v.18 no.3
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• pp.281-309
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• 2015

The purpose of this study is provides an implication of further teaching learning process by analyze the common and difference and characteristic of mathematical self-efficiency between three peer tutoring groups discourse in the mathematical teaching leaning process that use peer tutoring. To achieve this goal, three groups formed that consist of one peer tutor who received a first grade of mathematic achievement and one peer student. Peer student of each group is divided into high grade, middle grade, low grade of mathematic achievement. Then analyze the discourse in the exponential function problem solving process. Based on the results of study, this paper provides a concrete example of merit of peer tutoring on the peer tutor. Result of study also provides a practical help to make a peer tutoring group by considering a difference of grades between peer tutor and peer student. Because there is a possibility of mutual discourse on the tutoring group that consist of similar grades.

• Journal of the Korean School Mathematics Society
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• v.8 no.3
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• pp.357-366
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• 2005

This Study suggests some ideas how we develop a network of content structure based on informal context and method how we decide a sequence of mathematical syllabus from those Structures. 10th grade students in the process conceptual development was observed and interviewed in 2 hour teaching and learning experiment. Three related characteristics of student's thought in structuring math. Content and sequencing it were investigated as follows : (a) the reasoning that they do reflective abstraction well(or do not well) in acquisition of conceptual knowledge. (b) the method that teacher can use resuits in (a) to organize the content structure. (c) the ways that teacher find the process knowledge in informal content structure. That is, this study investigated the way we, curriculum designer, can create well defined content structure and instructional sequence strongly based on the learners' understanding.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.3
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• pp.457-477
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• 2016

The purpose of this study is to analyze and diagnose the type of errors indicated by the students in the process of calculation of the fractional multiplication and division, and to propose teaching methods, to effectively correct errors. The results obtained through this study are as follows. First, based on the results of the preliminary examination, 6 types of errors of the fractional multiplication and division has been organized. In particular, the most frequent types of errors are algorithm errors. Therefore, a teacher should explain the meaning and concept of fractional multiplication and division. Second, 4 prescription methods are proposed for understanding fractional multiplication and division. Third, according to the results of this study, it was effective to diagnose underachievers' error types and give corrective lesson according to the cause of the error types. Throughout the study, it's concluded that it is necessary to analyze and diagnose the error types of fractional multiplication and division, and then a teacher can correct error types by 4 proposed prescription methods. Also, 5 students showed interest while learning, and participated actively.