• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.273-289
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• 2001

Given that the culture of the mathematics classroom has been perceived as an important topic in mathematics education research, this paper deals with the construct of sociomathematical norms which can be used as an analytical tool in understanding classroom mathematical culture. This paper first reviews the theoretical foundations of the construct such as symbolic interactionism and ethnomethodology, and describes the actual classroom contexts in which social and sociomathematical norms were originally identified. This paper then provides a critical analysis of the previous studies with regard to sociomathematical norms. Whereas such studies analyze how sociomathematical norms become constituted and stabilized in the specific classroom contexts, they tend to briefly document sociomathematical norms mainly as a precursor to the detailed analysis of classroom mathematical practice. This paper reveals that the trend stems from the following two facts. First, the construct of sociomathematical norms evolved out of a classroom teaching experiment in which Cobb and his colleagues attempted to account for students' conceptual loaming as it occurred in the social context of an inquiry mathematics classroom. Second, the researchers' main role was to design instructional devices and sequences of specific mathematical content and to support the classroom teacher to foster students' mathematical learning using those sequences Given the limitations in terms of the utility of sociomathematical norms, this paper suggests the possibility of positioning the sociomathematical norms construct as more centrally reflecting the quality of students' mathematical engagement in collective classroom processes and predicting their conceptual teaming opportunities. This notion reflects the fact that the construct of sociomathematical norms is intended to capture the essence of the mathematical microculture established in a classroom community rather than its general social structure. The notion also allows us to see a teacher as promoting sociomathematical norms to the extent that she or he attends to concordance between the social processes of the classroom, and the characteristically mathematical ways of engaging. In this way, the construct of sociomathematical norms include, but in no ways needs to be limited to, teacher's mediation of mathematics discussions.

• Journal of the Korean School Mathematics Society
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• v.17 no.2
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• pp.207-234
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• 2014

There has been an increasing concern of how mathematical idea indicates and shares in a way to promote students' mathematical development. Such ideas highlighting need of the culture of mathematics classroom in mathematical education. The culture of mathematics classroom was constructed classroom social norms, sociomathematical norms, and classroom mathematical practice. This paper investigated how sociomathematical norms were constructed in two elementary mathematics classrooms by two different teachers.

• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.11-35
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• 2001

Many teachers report familiarity with and adherence to reform ideas, but their actual teaching practices do not reflect a deep understanding of reform. Given the challenges in implementing reform, this study intended to explore the breakdown that may occur between teachers' adoption of reform objectives and their successful incorporation of reform ideals. To this end, this study compared and contrasted the classroom social norms and sociomathematical norms of two United States second-grade teachers who aspired to implement reform. This study is an exploratory, qualitative, comparative case study. This study uses the grounded theory methodology based on the constant comparative analysis for which the primary data sources were classroom video recordings and transcripts. The two classrooms established similar social norms including an open and permissive learning environment, stressing group cooperation, employing enjoyable activity formats for students, and orchestrating individual or small group session followed by whole group discussion. Despite these similar social participation structures, the two classes were remarkably different in terms of sociomathematical norms. In one class, the students were involved in mathematical processes by which being accurate or automatic was evaluated as a more important contribution to the classroom community than being insightful or creative. In the other class, the students were continually engaged in significant mathematical processes by which they could develop an appreciation of characteristically mathematical ways of thinking, communi-eating, arguing, proving, and valuing. It was apparent from this study that sociomathematical norms are an important construct reflecting the quality of students' mathematical engagement and anticipating their conceptual learning opportunities. A re-theorization of sociomathematical norms was offered so as to highlight the importance of this construct in the analysis of reform-oriented classrooms.

• Journal of the Korean School Mathematics Society
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• v.8 no.3
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• pp.343-356
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• 2005

The purpose of this study is to search whether mathematical beliefs have changed when new social norms are formed in math classroom through research using survey papers about mathematical beliefs and math class video photographing. In addition, it would search for social norms of mathematical classroom which affects to students' mathematical beliefs by analyzing culture of mathematical classroom. The result was that the class focusing only general social norms wasn't enough to change students' mathematical beliefs. And as we have examined sociomathematical norms of math classroom through analyzing culture of mathematics classroom, it has affected students' mathematical beliefs.

• Journal of Educational Research in Mathematics
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• v.23 no.3
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• pp.373-388
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• 2013

This paper is to investigate how two elementary school teacher's belief mathematics as educational content, and teaching and learning mathematics as a part of educational methodology, and what the two teachers believe towards gifted children and their education, and what the classes demonstrate and its effects on the sociomathematical norms. To investigate this matter, the study has been conducted with two teachers who have long years of experience in teaching gifted children, but fall into different belief categories. The results of the study show that teacher A falls into the following category: the essentiality of mathematics as 'traditional', teaching mathematics as 'blended', and learning mathematics as 'traditional'. In addition, teacher A views mathematically gifted children as autonomous researchers with low achievement and believes that the teacher is a learning assistant. On the other hand, teacher B falls into the following category: the essentiality of mathematics as 'non-traditional', teaching mathematics as 'non-traditional, and learning mathematics as 'non-traditional.' Also, teacher B views mathematically gifted children as autonomous researchers with high achievement and believes that the teacher is a learning guide. In the teacher A's class for gifted elementary school students, problem solving rule and the answers were considered as important factors and sociomathematical norms that valued difficult arithmetic operation were demonstrated However, in the teacher B's class for gifted elementary school students, sociomathematical norms that valued the process of problem solving, mathematical explanations and justification more than the answers were demonstrated. Based on the results, the implications regarding the education of mathematically gifted students were investigated.

• The Mathematical Education
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• v.45 no.4 s.115
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• pp.459-479
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• 2006

There has been an increasing concern of whether a real instructional change happens in a way to promote students' mathematical development. Against this background, this paper dealt with successes and difficulties an elementary school teacher went through as she moved on to student-centered instruction. The analysis drew on classroom observations for one year to illustrate how the teacher and students established social norms, sociomathematical norms, and classroom mathematical practices that could emphasize mathematical sense-making and justification of ideas. Close analysis showed many gradual but dramatic changes in terms of mathematics classroom culture. This led to consider possibly subtle but crucial issues with regard to implementing student-centered instruction.

• Education of Primary School Mathematics
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• v.4 no.2
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• pp.111-125
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• 2000

This paper presents cross-national perspectives on challenges in implementing current mathematics education reform ideals. This paper includes detailed qualitative descriptions of mathematics instruction from unevenly successful second-grade classrooms both in Koran and in the U. S with regared to reform recommendations. Despits dramatic differences in mathematics achivement between Korean and the U.S student. problems in both countries with regard to mathematics education are perceived to be very similar. The shared problems have a common origin in teacher-centered instruction. Educational leaders in both countries have persistently attempted to change the teacher-centered pedagogy to a student-centered approach. Many teachers report familiarity with and adherence to reform ideas, but their actual classroom teaching practices do not reflect the full implications of the reform ideals. Given the challenges in implementing reform, this study explored the breakdown that may occur between teachers adoption of reform objectives and their successful incorporation of reform ideals by comparing and contrasting two reform-oriented classrooms in both countries. This comparison and contrast provided a unique opportunity to reflect on possible subtle but crucial issues with regard to reform implementation. Thus, this study departed from past international comparisons in which the common objective has been to compare general social norma of typical mathematics classes across countries. This study was and exploratory, qualitative, comparative case study using grounded theory methodology based on constant comparative analysis for which the primary data sources were classroom video recordings and transcripts. The Korean portion of this study was conducted by the team of four researchers, including the author. The U.S portion of this study and a brief joint analysis were conducted by the author. This study compared and contrasted the classroom general social norms and sociomathematical norms of two Korean and two U.S second-grade teachers who aspired to implement reform. The two classrooms in each country were chosen because of their unequal success in activating the reform recommendation. Four mathematics lessons were videotaped from Korean classes, whereas fourteen lessons were videotaped from the U.S. classes. Intensive interviews were conducted with each teacher. The two classes within each country established similar participation patterns but very different sociomathematical norms. In both classes open-ended questioning, collaborative group work, and students own problem solving constituted the primary modes of classroom participation. However in one class mathematical significance was constituted as using standard algorithm with accuracy, whereas the other established a focus on providing reasonable and convincing arguments. Given these different mathematical foci, the students in the latter class had more opportunities to develop conceptual understanding than their counterparts. The similarities and differences to between the two teaching practices within each country clearly show that students learning opportunities do not arise social norms of a classroom community. Instead, they are closely related to its sociomathematical norms. Thus this study suggests that reform efforts highlight the importance of sociomathematical norms that established in the classroom microculture. This study also provides a more caution for the Korean reform movement than for its U.S. counterpart.

• 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.

• Education of Primary School Mathematics
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• v.5 no.2
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• pp.163-172
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• 2001

Recently, higher discussions are made up on the culture of mathematics classrooms. These discussions are mostly about desirable culture and reform of culture in mathematics education. This paper is to offer a view point of seeing the culture of mathematics classroom. We need to look straightly our classroom as well as to reform the culture of mathematice classroom. This paper recommend sociomathematical norms to analyze and reform classroom culture. A elementary mathematics classroom was analyzed to understand our own culture of mathematics classroom.

• School Mathematics
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• v.4 no.3
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• pp.415-433
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• 2002

The mathematics education community is seeking to change a teacher-centered class-room culture to a student-centered culture. However, the real transition is not easy, even for teachers who are eager and willing to teach differently. The challenge for teachers is to use the social structure of the classrooms to nurture students' development toward mathematical ways of thinking and communicating as well as their under-standing of mathematical concepts and processes. By introducing an elementary teacher's teaching practice and professional develop-ment along with her classroom episodes, this paper is to make strides toward an enriched understanding of the culture of the elementary mathematics classrooms in which students may have a lot of opportunities to develop conceptual under standing and math-ematical disposition. This paper first provides a detailed description of the classroom flow in terms of general social norms and sociomathematical norms in order to explore how the teacher and the students have established such a student-centered math-ematics microculture. This paper then analyzes the teacher's teaching approach and professional development.