• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.221-237
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• 2004

This research analyzed mathematical discourse of the students in an RME-based differential equations course at a university in order to investigate the social transformation of the students' conceptual model of differential equations. The analysis focused on the change in the students' use of conceptual metaphor for differential equations and pedagogical factors promoting the change. The analysis shows that discrete and quantitative conceptual model was prevalent in the beginning of the semester However, continuous and qualitative conceptual model emerged through the negotiation of mathematical meaning based on the inquiry of context problems. The participation in the project class has a positive impact on the extension of the students' conceptual model of differential equations and increases the fluency of the students' problem solving in differential equations. Moreover, this paper provides a discussion to identify the pedagogical factors Involved with the transformation of the students' conceptual model. The discussion highlights the sociocultural aspect of teaching and learning of mathematics and provides implications to improve teaching of mathematics in school.

• The Mathematical Education
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• v.62 no.2
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• pp.237-255
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• 2023

The objective of this study is to explore the meaning generated through discourse in three different types of 1st-grade middle school textbooks in Korea and CMP textbook in the United States, specifically focusing on histograms. Through a discursive perspective, the study aims to analyze the characteristics of questioning within the stages of statistical problem-solving found in histogram tasks. The findings highlight several significant points. Firstly, variations exist in the definitions of histograms between Korean and US CMP textbooks. Secondly, diverse discursive structures contribute to the interpretation and understanding of histograms in textbooks. Thirdly, limitations are observed in the stages of statistical problem-solving reflected in histogram tasks. Lastly, distinctions are identified in the types of questioning employed in histogram tasks between Korean and US CMP textbooks. Building on these insights, the study suggests concrete ideas for enhancing the process of defining histograms and refining the questioning in histogram tasks.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.377-394
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• 2019

The purpose of this study is to scrutinize the characteristics of a teacher's discursive competence on the basis of mathematical competencies. For this purpose, we observed all semester-long classes of a middle school teacher, who changed her own teaching methods for the last 20 years, collected video clips on them, and analyzed classroom discourse. Data analysis shows that in problem solving competency, she helped students focus on mathematically important components for problem understanding, and in reasoning competency, there was a discursive competence which articulated thinking processes for understanding the needs of mathematical justification. And in creativity and confluence competency, there was a discursive competence which developed class discussions by sharing peers' problem solving methods and encouraging students to apply alternative problem solving methods, whereas in communication competency, there was a discursive competency which explored mathematical relationships through the need for multiple mathematical representations and discussions about their differences. These results can provide concrete directions to developing curricula for future teacher education by suggesting ideas about how to combine practices with PCK needed for mathematics teaching.

• School Mathematics
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• v.17 no.2
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• pp.355-376
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• 2015

This study aims to inspect the effect of the yungbokhap education on the development of students' mathematical competence by analyzing students' mathematical discourse in math-based yungbokhap instruction designed by Moon(2014). Specifically, this research focused on the analysis of students' participation structure. The reuslts shows that the students' competence for mathematical communication and inquiry has been improved through the instruction. In particular, the students were increasingly engaged with consensual talk. Also, in the beginning stage, the students tended to unconditionally criticize for others' mathematical opinion. Through the class participation, they gradually developed the competence to express their mathematical ideas to their peers with reasonable mathematical bases. These results suggests that the mathematics-based yungbokhap instruction has positively contributed to the improvement of students' mathematical competence. Based on the results, this paper presented implications for mathematics-based yungbokhap instrcution.

• The Mathematical Education
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• v.54 no.3
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• pp.283-298
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• 2015

This research is the case study of collaborative mentoring in the professional development of multi-tiered mathematics teacher community. We observed the procedures of mentoring, and contents of mentoring in PD program. For this purpose, we implemented PD program with participant unit composed of 3 or 4 teachers in the same school and total 25 teachers from 4 elementary schools and 4 high schools. Also there were 1 mentor and 1 sub-mentor to support each school. Observed mentoring processes were all recorded and the participants not only were interviewed several times but also wrote reflection notes after meetings. While mentoring PD program was implemented, mentor and mentee had joint responsibility about lessons implemented by mentee. Furthermore It showed possibility of change of teacher learning culture, learning culture of community. It means that teacher would improve their professionalism more effectively within teacher community instead of individual. 4 reflection contents was founded in collaborative mentring; 1)purpose of mathematics education, 2)motivation and connection between previous lecture and present lecture 3)lack of mathematical contents in lesson 4)discourse between teacher and students.

• School Mathematics
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• v.2 no.1
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• pp.29-51
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• 2000

In this study, we tried to suggest an example of the analysis on the use of mathematical manipulatives. Taking algebra tiles as an example of mathematical manipulatives, we analysed several effects resulted from the use of algebra tiles. The algebra tiles make it possible to do activities that are needed to introduce and explain the distributive law and factoring. The algebra tiles have a several advantages; First of all, This model is simple. Even though they cannot make algebra easy, this model can play an important role in the transition to a new algebra course. This model provides access to symbol manipulation for students who had previously been frozen out of the course because of their weak number sense. This model provides a geometric interpretation of symbol manipulation, thereby enriching students' understanding, This model supports cooperative learning, and help improve discourse in the algebra class by giving students objects to think with and talk about. On the other hand, The disadvantages of this model are as follows; the model reinforces the misconception that -x is negative, and x is positive; the area model of multiplication is not geometrically sound when minus is involved; only the simplest expressions involving minus can be represented; It is ineffective when be used the learning of already known concept. Mathematics teachers must have a correct understanding about these advantages and disadvantages of manipulatives. Therefore, they have to plan classroom work that be maximized the positive effect of manipulatives and minimized the negative effect of manipulatives.

• Education of Primary School Mathematics
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• v.21 no.2
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• pp.163-192
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• 2018

The purpose of this study was to examine the relations among mathematics teachers' beliefs, classroom norms and discourse, and equity issues in mathematics classrooms. In order to achieve this purpose, three teachers who work in the same school were analyzed. The analysis revealed that the participating teachers' beliefs about mathematics teaching and learning and about their students' abilities and motivation influenced the establishment of classroom norms and discourses that defined what students needed to do to be successful mathematics learners. Also, classroom norms and discourse affected the development of students' identity and power and the level of equity in the classroom.

• Journal of Digital Contents Society
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• v.9 no.1
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• pp.53-60
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• 2008

Based on similarities between fuzzy set theory and mathematical morphology, Grabish proposed a fuzzy morphology based on the Sugeno fuzzy integral. This paper proposes a fuzzy mathematical morphology based on the defuzzification of the fuzzy measure which corresponds to fuzzy integral. Its process makes a fuzzy set used as a measure of the inclusion of each fuzzy measure for subsets. To calculate such an integral a $\lambda$-fuzzy measure is defined which gives every subsets associated with the universe of discourse, a definite non-negative weight. Fast implementable definitions for erosion and dilation based on the fuzzy measure was given. An application for robust skeletonization of two-dimensional objects was presented. Simulation examples showed that the object reconstruction from their skeletal subsets that can be achieved by using the proposed was better than by using the binary mathematical morphology in most cases.

• Journal of architectural history
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• v.15 no.4
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• pp.23-36
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• 2006

Since he was a leading figure in nineteenth century architecture, Viollet-le-Duc's architectural theory is crucial to the foundation of modern architecture. He has been called a Gothic Revivalist, a Structural Rationalist and a Positivist. The first title was perhaps due to his vigorous restoration of Gothic works such as $N\hat{o}tre$ Dame, but he did not adore the Gothic style just for itself. Rather, he hoped to deduce some principles from the style. So how did he manage this? In his book "Entretiens sur l'Architecture (Lectures on Architecture), published between 1864 and 1872, he mentions using Descartes' four rules for reaching architectural certainty in contrast with the chaotic situation during that modernising period. Furthermore Viollet-le-Duc's theory can be seen as a serious attempt to translates Descartes' philosophical rules into systems of architectural speculation. Descartes' four rules of doubt are anchored in mathematical propositions, and without mathematical distinctions, none of these rules are valid. In other word, mathematics for Viollet is the yardstick of judgement between distinctness and indistinctness. Many architectural problems arise from this view. In this paper, the validities of applying Descartes' method of doubt to architectural discourse will be discussed in order to address the question:-Did Viollet-le-Duc clearly grasp Cartesian method by which memory was erased from the world?

• Communications of Mathematical Education
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• v.32 no.4
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• pp.555-573
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• 2018

The purpose of this study is to identify the emotional language of math teachers in math class using text mining techniques. For this purpose, we collected the discourse data of the teachers in the class by using the excellent class video. The analysis of the extracted unstructured data proceeded to three stages: data collection, data preprocessing, and text mining analysis. According to text mining analysis, there was few emotional language in teacher's response in mathematics class. This result can infer the characteristics of mathematics class in the aspect of affective domain.