• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.163-180
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• 2002

The purpose of this paper is to reconsider the meaning of mathematical literacy based on the investigation of the nature of mathematical knowledge communicated in university level mathematics classes. The analysis of classroom discourse has revealed three different kinds of mathematical knowledge circulated in mathematics class, which include 'factual mathematics', 'mathematical fantasy', and 'mathematical savior faire.' The fact that a mathematics teacher delivers diverse categories of mathematics knowledge suggests that the mathematical literacy is not confined to the development of technical competence. More specifically, the kinds of mathematical knowledge identified above tell that mathematical literacy developed through learning mathematics reflects the cultural norms and values of doing mathematics. This means that mathematical literacy is not merely involve with technical competence but rather with cultural competence. In this regard, this paper highlights the meaning of mathematical literacy as a cultural identity, which has been underestimated in the theory and practice of mathematics education dominated by technocracy of the twentieth century In particular, the notion of mathematical savior faire implies that teaching and teaming mathematics ultimately deals with a system of cultural meaning. Hence, through learning mathematics, a learner gets transformed as a whole person according to the cultural norms and values. In this regard, it is concluded that mathematical literacy can be considered as a necessary condition to become a competent member of mathematics community sharing cultural norms of doing mathematics as well as a repertoire of mathematical skills.

• The Mathematical Education
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• v.41 no.3
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• pp.329-339
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• 2002

This study analyzes the epistemological meaning of‘social construction’in mathematical instruction. The perspective that consider the cognition of mathematical concept as a social construction is explained by a cyclic scheme of an academic context and a school context. Both of the contexts require a public procedure, social conversation. However, there is a considerable difference that in the academic context it is Lakatos' ‘logic of mathematical discovery’In the school context, it is Vygotsky's‘instructional and learning interaction’. In the situation of mathematics education, the‘society’which has an influence on learner's cognition does not only mean‘collective members’, but‘form of life’which is constituted by the activity with purposes, language, discourse, etc. Teachers have to play a central role that guide and coordinate the educational process involving interactions with learners in this context. We can get useful suggestions to mathematics education through this consideration of the social contexts and levels to form didactical situations of mathematics.

• The Mathematical Education
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• v.50 no.3
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• pp.263-284
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• 2011

We took note of the fact that there were not many studies on improvement of mathematics learning in the field of statistics for the minority students from the families who belonged to the Low-SES. This study was to help them understand the concepts and principles of mathematics, motivate them for mathematics learning, and have them feel familiar with it. The subjects were 12 students from the low-SES families among the sophomores of 00 High School in Gyeonggi-do. Although it could not be achieved effectively in the short-term of learning for the slow learners, their understanding of basic concepts and confidence, interests and concerns in statistical learning were remarkably changed, compared to their work in the beginning period. Our discourse classes using various topics and examples were well perceived by the students whose performance was improved up to the 3rd thinking level of Mooney's framework. Also, a meaningful instructional model for slow learners(IMSL) was found through the discourse.

• The Mathematical Education
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• v.43 no.3
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• pp.257-273
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• 2004

In this paper, we analyze what the components of mathematics teacher` knowledge are, and find that mathematics teacher need knowledge of three areas: subject matter knowledge, pedagogical knowledge, and pedagogical content knowledge. Studies of practicing teachers suggest that When teachers lack understanding in their respective disciplines, it inhibits them from providing students the best learning opportunities, but that a teacher possessing pedagogical content knowledge provides learners with multiple approaches into learning. Some teachers having sound knowledge of mathematics and students were able to respond appropriately to students' questions, design appropriate learning activities involving a variety of mathematical representations, and orchestrate mathematical discourse in the classroom. Thus, it appears that mathematics teachers' knowledge positively affect teaching and student learning..

• East Asian mathematical journal
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• v.36 no.4
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• pp.455-474
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• 2020

In this study, we investigate the latus rectum, one of the geometric measures of the conics, as one of the ways in which learners harmonize the geometric and algebraic approaches to conics from a pedagogical point of view. We also introduce the conical curve of Biot as presented in 'The Discourse on the Latus Rectum in conics(2013)' by Takeshi Sugimoto and reinterpret it for visualization and use as teaching material. Therefore, we expect that the importance of mathematical concepts will be recognized in conics and students can experience geometry learning that is explored in the school field and have a positive effect in developing the power to apply even in the context of applied problems.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.283-304
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• 2004

This study is to make strides toward an enriched understanding of changing a prevailing teacher-centered mathematics classroom culture to a student-centered culture by analyzing six reform-oriented classrooms of three elementary school teachers throughout a year This study provided a detailed description of important classroom episodes to explore how the participants in each class established a reform-oriented mathematics microculture. Despite the exemplary form of student-centered instruction, the content and qualities of the teaching practices are somewhat different in the extent to which students' ideas become the center of mathematical discourse and activity. Given the similarities in terms of general social norms and the differences in terms of socio-mathematical norms and mathematical practice, this study addresses some crucial issues on understanding the culture of elementary mathematics classroom in transition.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.173-192
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• 2007

We define mathematical learning as a process of overcoming framing difference of teachers and students, two main subjects in a mathematics class. We have reached this definition to the effect that we can grasp a mathematical classroom per so and understand students' mathematical learning in the context. We could clearly understand the process in which the framing differences are overcome by analyzing mutual negotiation of informants in specific cultural models, both in its form as well as in its meaning. We review both of the direct and indirect forms of negotiation while keeping track of 'evolution of subject' in terms of content of negotiation. More specifically, we discuss direct negotiation briefly and review indirect negotiation from three distinct themes of (1) argument structure, (2) revoicing, and (3) development patterns and narrative structure of proof. In addition, we describe the content of negotiation under the title of 'Evolution of Subject.' We found that major modes of mutual negotiation are inter-reference and appropriation while the product of continued negotiation is inter-resemblance.

• Research in Mathematical Education
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• v.21 no.1
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• pp.35-46
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• 2018

In this perspective paper, we present seven elements of the appropriate educator mindset for teaching in the constructivist elementary mathematics classroom. The elements include supporting students as they construct their own understanding, eliminating deficit view of slow learners, setting new understanding and growth as the learning objective, providing opportunities to co-construct meaning with peers, using student contributions as the source of curricular material, encouraging all students to participate in learning, and providing instruction not bounded by time. In our struggles to provide authentic, inclusive elementary classrooms, we hope that our discussion of the educator mindset can increase discourse on constructivism from philosophy to practice in the community of mathematics education and policy makers.

• Research in Mathematical Education
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• v.22 no.3
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• pp.223-243
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• 2019

Researchers have been attending to the potential of curriculum materials as resources for professional development. In order for a curriculum material to fulfil such purpose, curriculum authors should intentionally attend to educativeness of the material. A feature of educative material is that its voice speaks to teachers. In this study, I explore educativeness of Algebra teacher guides by attending to their voice. In particular, I focused on the use of pronouns, modality, and imperatives. Findings indicate that some teacher guides have more educative voice than the others and that the amount each guide talk to teachers were less than sufficient. Implications for future research and practice are discussed.

• School Mathematics
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• v.5 no.1
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• pp.135-149
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• 2003

We present an understanding about students' conceptual model of differential equations, based on the discourse data that were collected in a differential equations course at a university in Korea. An interpretive approach is taken to analyze classroom discourse. This paper consists of three main parts. First, we completely analyze the students' use of conceptual metaphor in a university differential equations class. Secondly, we identify conceptual metaphors representing students' conceptual model of differential equations. Finally, we describe the mathematical characteristics of the conceptual metaphors identified in detail. Among other things, this paper reveals that there exists dual aspects of the students' conceptual model of differential equations. In other words, in the differential equations course observed we found that the students very often used two kinds of conceptual metaphor,“machine metaphor”and“fictive motion metaphor”, that have contrastingly different mathematical characteristics. In order to interpret the duality, we take a sociocultural perspective, and this perspective suggests and helps us to realize the significance of understanding of cognitive diversity in mathematics classroom.