• The Mathematical Education
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• v.47 no.3
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• pp.291-310
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• 2008

This article is based on an international collaborative study that aimed to investigate mathematical preparation of prospective elementary teachers in several selected education systems in East Asia. This article reports the Korean portion of the study. A survey instrument was developed to explore not only prospective teachers' knowledge of elementary mathematics curriculum and their beliefs in their preparation and mathematics instruction but also their subject matter knowledge and pedagogical content knowledge on the topic of fraction division. A total of 291 seniors in 3 universities participated in the survey. The results reveal these prospective teachers' strengths and weaknesses with regard to their knowledge of fraction division, and suggest that content-specific pedagogical knowledge needs to be emphasized in the teacher preparation program.

• Communications of Mathematical Education
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• v.32 no.3
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• pp.297-314
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• 2018

This article aims at providing implication for teacher preparation program through interpreting pre-service teachers' knowledge by using Shulman-Fischbein framework. Shulman-Fischbein framework combines two dimensions (SMK and PCK) from Shulman with three components of mathematical knowledge (algorithmic, formal, and intuitive) from Fischbein, which results in six cells about teachers' knowledge (mathematical algorithmic-, formal-, intuitive- SMK and mathematical algorithmic-, formal-, intuitive- PCK). To accomplish the purpose, five pre-service teachers participated in this research and they performed a series of tasks that were designed to investigate their SMK and PCK with regard to students' misconception in the area of geometry. The analysis revealed that pre-service teachers had fairly strong SMK in that they could solve the problems of tasks and suggest prerequisite knowledge to solve the problems. They tended to emphasize formal aspect of mathematics, especially logic, mathematical rigor, rather than algorithmic and intuitive knowledge. When they analyzed students' misconception, pre-service teachers did not deeply consider the levels of students' thinking in that they asked 4-6 grade students to show abstract and formal thinking. When they suggested instructional strategies to correct students' misconception, pre-service teachers provided superficial answers. In order to enhance their knowledge of students, these findings imply that pre-service teachers need to be provided with opportunity to investigate students' conception and misconception.

• School Mathematics
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• v.18 no.3
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• pp.571-587
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• 2016

Nam(2008a) suggested that the role of teacher for helping students to learn mathematical structures should be the manifestor of tacit knowledge. But there have been lack of researches on embodying the manifestation of tacit knowledge. This study embodies the manifestation of tacit knowledge by showing that exemplification is one way of manifestation of tacit knowledge in terms of goal, contents, and method. First, the goal of the manifestation of tacit knowledge through exemplification is helping students to learn mathematical structures. Second, the manifestation of tacit knowledge through exemplification intends to teach students mathematical structures in the tacit dimension by perceiving invariance in the midst of change. Third, the manifestation of tacit knowledge through exemplification intends to teach students mathematical structures in the tacit dimension by constructing explicit knowledge creatively, reflection on constructive activity and social interaction. In conclusion, exemplification could be seen one way of embodying the manifestation of tacit knowledge in terms of goal, contents, and method.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.67-85
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• 2005

This study investigated elementary teachers' subject matter knowledge and pedagogical content knowledge of fractions. The subject for data collection were 12 in-service elementary teachers and data were collected through written test problems. The finding imply that most elementary teachers understand fraction construct as part-whole, show low level of understanding of operator, ratio, and measurement constructions and word problem posing, using models, and developing the algorithms to divide fractions. The research results indicates that experienced teachers possess poor knowledge of fractions against novice teachers.

• East Asian mathematical journal
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• v.29 no.2
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• pp.109-135
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• 2013

The purpose of the study was to investigate the reality of middle school mathematics teachers' subject matter knowledge for teaching mathematical conjecture and justification. Data in the study were collected through interviewing nine Chinese and ten Korean middle school mathematics teachers. The teachers responded to the question that was designed in the form of a scenario that presents a teaching task related to a geometrical topic. The teachers' oral responses were audiotaped and transcribed, and their written notes were collected. The results of the study were compared to the analysis of American and Chinese elementary and secondary teachers' responses to the same task in Ball (1988) and Ma (1999). The findings of the study suggested that teachers' approaches to explaining and demonstrating a mathematical topic were significantly influenced by their knowledge of learners and knowledge of the curriculum they teach. One of the practical implications of the study is that teachers should recognize the advantages of learning the conceptual structure of a mathematical topic. It allows the teachers to have the flexibility to come up with meaningful mathematical approaches to teaching the topic, which are comprehensible to the learners whatever the grade levels they teach, rather than rule-based algorithms.

• Research in Mathematical Education
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• v.18 no.2
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• pp.129-148
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• 2014

In this study, we examined the relationships among years of teaching experience, professional rank, number of courses taken, and knowledge of algebra for teaching (KAT). 338 in-service and 376 pre-service secondary mathematics teachers in China completed a KAT questionnaire. Various statistical techniques were employed to examine these relationships. The pre-service participants teachers performed statistically significantly higher in advanced mathematics knowledge than their in-service counterparts. Among the inservice teachers, senior teachers had scored higher in school mathematics and teaching mathematics, compared with junior teachers. Yet participants' advanced mathematics knowledge decreased as their professional rank advanced or their teaching experience increased. The number of courses taken has significantly positive correlation with school mathematics knowledge and advanced mathematics knowledge. The implications of these findings for mathematics teacher education are discussed.

• Research in Mathematical Education
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• v.7 no.1
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• pp.1-10
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• 2003

This research reviewed literatures on proof in mathematics education. Several views of proof can be classified (and identified) such as psychological approach (Platonism, empiricism), structural approach (logicism, formalism, intuitionism) and social approach (ontology, axiomatic systems). All these views of proof are valuable in mathematics education society. The concept of proof can be found in the form of analytic knowledge not of constructive knowledge. Human beings developed their knowledge in the sequence of constructive knowledge to analytic knowledge. Therefore, in mathematics education, the curriculum of mathematics should involve the process of cognitive knowledge development.

• East Asian mathematical journal
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• v.38 no.1
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• pp.85-94
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• 2022

Recently, an LWE-based commitment scheme is proposed. Their construction is statistically hiding as well as computationally binding. On the other hand, the construction of related zero-knowledge protocols is left as an open problem. In this paper, we present zero-knowledge protocols with hardness based on the LWE problem. we show how to instantiate efficient zero-knowledge protocols that can be used to prove linear and sum relations among these commitments. In addition, we show how the variant of LWE, spLWE problem, can be used to instantiate efficient zero-knowledge protocols.

• Research in Mathematical Education
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• v.5 no.1
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• pp.13-24
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• 2001

Using computer technology in teaching school mathematics creates new instructional environments. The emphases on the use of computer technology in the classrooms and in particular the use of computer-based exploration as a context of mathematics instruction have been reflected in the recommendation of the NCTM (Curriculum and Evaluation Standards for School Mathematics, 1989). Although the power of using computer technology in the exploration of mathematical problems has been recognized and stressed by many educators, we do not have many research studies on mathematics in computer-based explorations. Especially research has failed to clarify how computer technology can contribute to the construction of procedural and conceptual knowledge of mathematics. Up to now most researches on procedural and conceptual knowledge in computer environments have only focused on classifying programming languages which program language has more random access and rich interrelationship characteristic in relation to conceptual knowledge in humans, and which computer language has more characteristic flavor of procedural knowledge. How computer-based explorations affect the knowledge construction of mathematics, therefore, emerges as an issue of research on teacher education program for theoretical framework. This situation leads to do research on the effectiveness of using computer explorations in pre-service teacher education in terms of procedural and conceptual knowledge construction.

• Journal of Information Technology Applications and Management
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• v.25 no.1
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• pp.33-45
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• 2018

This study was initiated to investigate the essential skill factors for system designers in order to build the right information systems. The predicted variables are mathematical modeling skill, verbal modeling skill, general IT knowledge, and general business knowledge. The test was administrated to 43 students majoring in Management Information Systems (MIS) at Hannam University, South Korea. In this study, we used Pearson Correlation Analysis to test the relationships among variables. Overall, our study suggested that there is a strong positive relationship between mathematical and verbal skills and IS modeling ability. A marginal positive relationship between the general IT knowledge and IS modeling ability was also found. Unexpectedly, there was no significant relationship between general business knowledge and IS modeling ability.