• Journal of Educational Research in Mathematics
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• v.20 no.1
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• pp.57-71
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• 2010

Similarity between concept and concept, principle and principle, theory and theory is known as a strong motivation to mathematical knowledge construction. Metaphor and analogy are reasoning skills based on similarity. These two reasoning skills have been introduced as useful not only for mathematicians but also for students to make meaningful conjectures, by which mathematical knowledge is constructed. However, there has been lack of researches connecting the two reasoning skills. In particular, no research focused on the interplay between the two in didactic transposition. This study investigated the process of knowledge construction by metaphor and analogy and their roles in didactic transposition. In conclusion, three kinds of models using metaphor and analogy in didactic transposition were elaborated.

• East Asian mathematical journal
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• v.33 no.2
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• pp.177-197
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• 2017

The purpose of this study is to investigate and analyze the understandings of elementary pre-service teachers about 'estimation' in the elementary mathematics. Together with this analysis, we identify elementary pre-service teacher's Mathematical Pedagogical Contents Knowledge(MPCK), especially focusing to Subject Matter Knowledge(SMK). In order to this goals, we investigate contents relating to 'estimation' from $1^{st}$ curriculum to 2009 revised curriculum and compare 'rounding up', 'rounding off', 'rounding' in the elementary mathematics textbooks. As results of investigations, 'estimation' has been teaching at the 'Measurement' domain from $3^{rd}$ curriculum, but contexts of measuring weaken from $7^{th}$ curriculum. 'Rounding up(off)' is defined three types in the textbooks from $1^{st}$ to 2009 revised curriculum. And we examine elementary pre-service teachers through the questions on these 'estimation' contents. On the analysis of pre-service teacher's understanding relating MPCK, four themes is summarized as followings; the understanding of '0' in the 'rounding up', the cognitive gap between 'rounding up' and 'rounding off', the difference of percentage of correct answers according to types of question in the 'rounding up', and the difference between the definition of 'rounding up' and the definition of 'rounding'.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.345-363
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• 2010

The purpose of this study is to investigate and analyze informal knowledge of students who do not learn the conception of proportion and to identify how the informal knowledge can be used for teaching the conception of proportion in order to present an effective method of teaching the conception. For doing this, proportion was classified into direct and inverse proportion, and 'What are the informal knowledge of students?' were researched. The subjects of this study were 117 sixth-graders who did not have prior learning on direct and inverse proportion. A total eleven problems including seven for direct proportion and four for inverse proportion, all of them related to daily life. The result are as follows; Even though students didn't learn about proportion, they solve the problems of proportion using informal knowledge such as multiplicative reasoning, proportion reasoning, single-unit strategy etc. This result implies mathematics education emphasizes student's informal knowledge for improving their mathematical ability.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.137-154
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• 2012

Approximation' is one of central conceptions in calculus. A basic conception for explaining 'approximation' is 'tangent', and 'tangent' is a 'line' with special condition. In this study, we will study pedagogically these mathematical knowledge on the ground of a viewpoint on the teaching of secondary geometry, and in connection with these we will suggest the teaching program and the chief end for the probable teaching. For this, we will examine point, line, circle, straight line, tangent line, approximation, and drive meaningfully mathematical knowledge for algebraic operation through the process translating from the above into analytic geometry. And we will construct the stream line of mathematical knowledge for approximation from a view of modern mathematics. This study help mathematics teachers to promote the pedagogical content knowledge, and to provide the basis for development of teaching model guiding the mathematical knowledge. Moreover, this study help students to recognize that mathematics is a systematic discipline and school mathematics are activities constructed under a fixed purpose.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2001.01a
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• pp.410-420
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• 2001

A primitive conceptualization is defined as the set of all intended situations. A non-primitive conceptualization is defined as the set of all the pairs every of which consists of an intended knowledge system and the set of all the situations admitted by the knowledge system. The reality of a domain is considered as the set of all the situation which have ever taken place in the past, are taking place now and will take place in the future. A conceptualization is defined as precise if the set of intended situations is equal to the domain reality. The representation of various elements of a domain ontology in a model of the ontology is considered. These elements are terms for situation description and situations themselves, terms for knowledge description and knowledge systems themselves, mathematical terms and constructions, auxiliary terms and ontological agreements. It has been shown that any ontology representing a conceptualization has to be non-primitive if either (1) a conceptualization contains intended situations of different structures, or (2) a conceptualization contains concepts designated by terms for knowledge description, or (3) a conceptualization contains concept classes and determines properties of the concepts belonging to these classes, but the concepts themselves are introduced by domain knowledge, or (4) some restrictions on meanings of terms for situation description in a conceptualization depend on the meaning of terms for knowledge description.

• The Mathematical Education
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• v.48 no.1
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• pp.93-105
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• 2009

Considering the fact that PCK(pedogogical content knowledge) tends to guarantee the identity of mathematics education as a discipline and the teacher professionalism, PCK is one of the core concepts in the research on subject matter education. The purpose of this study is to review domestic and international researches on the definition and the components of PCK in mathematics. Based on the review, this study identified 3 knowledges which consist PCK; knowedge of mathematic content, knowledge of learner's understanding, and knowledge of teaching. Then this study provided some examples of PKC in the topic, the limit of sequences, and introduced the LMT and TEDS-M items, which were designed to measure the teacher's PCK. Lastly, this study attempted to evaluate the items on mathematics education included in the Teacher Employment Test administered for pre-service/. teachers in Korea based on PCK.

• Research in Mathematical Education
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• v.25 no.1
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• pp.1-20
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• 2022

Collaborative learning has been highlighted as an effective method of teachers' professional development in various studies. To disclose teachers' discourse threads in the process of collaborative learning for developing their knowledge, this paper adopted two methods including "content analysis" and "time-sequential analysis" of learning analytics. Such analyses were implemented for mining teachers' updated knowledge and the discourse threads in the discussion during collaborative learning. The materials for analysis involved two aspects: one was from the video-taped lesson observation reports written by teachers before and after discussing, and the other was from their discourses during the discussion process. The results proved that teachers' knowledge for teaching the centroid of a triangle was updated in the collaborative learning period, and also revealed the discourse threads of teachers' collaboration contained "requesting information or opinions", "building on ideas", and "providing evidence or reasoning", with the emphasis on "challenging ideas or re-focusing talk"

• Research in Mathematical Education
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• v.27 no.2
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• pp.195-210
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• 2024

Researchers and curricula continue to call for proof to serve a central role in learning of mathematics throughout kindergarten to grade 12 and beyond. Despite its prominence and recognition gained during past decades, proof is still a stumbling block for both teachers and students. Research efforts have been made to address issues related to teaching and learning of proof. An area in which such research efforts have been made is analysis of curriculum material (i.e. textbook analysis) with a focus on proof. This study is another research effort in this area of research through investigating the guidance offered in curriculum materials with the following research question: What is the nature (e.g., kinds of content knowledge, pedagogical content knowledge) of guidance is offered for teachers to implement proof tasks in grade 8 geometry textbooks? Results indicate that the guidance offered for proof tasks are concerned more with content knowledge about the content-specific instructional goals than with pedagogical content knowledge which supports teachers in preparing in-class interactions with students to teach proof.

• The Mathematical Education
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• v.42 no.5
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• pp.607-622
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• 2003

The research was aimed at finding the dynamic aspects of the linguistic and social interaction with mathematical concept development using a graphing calculator in collaborative learning. This study was broadly divided into two categories: "Knowledge Construction Statement" for understanding how the verbal interaction works when a graphing calculator is used, and "Teacher's Instructional Role" for the research on the reaction of the students and on the teacher's role as a guide in helping students to construct their knowledge. This research used a case study in a collaborative learning environment. An attempt was made to show clearly how the students interacted with one another in a technology environment using a graphing calculator as a tool. A graphing calculator promoted the students' linguistic interaction and changed the characteristics of the linguistic interaction. Although it didn't show the different aspects completely, some changes of the linguistic traits were perceived.aits were perceived.

• Management Science and Financial Engineering
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• v.5 no.1
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• pp.27-49
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• 1999

WebME is an Web-based integrated modeling environment that implements a multi-facetted modeling approach to mathematical model representation and management. Key features of WebME include the following: (i) sharing of modeling knowledge on the Web, (ii) a user-friendly interface for creating, maintaining, and solving models, (iii) independent management of mathematical models from conceptual models, (iv) object-oriented conceptual blackboard concept, (v) multi-facetted mathematical modeling modeling, and (vi) declarative representation of mathematical knowledge. This paper presents details of design and implementation issues that were encountered in the development of WebME.