• 대한수학교육학회지:수학교육학연구
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• 제11권2호
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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.

• 한국학교수학회논문집
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• 제17권2호
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• pp.207-234
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• 2014

본 연구의 목적은 초등학교 4학년 두 수학수업에서 나타나는 교실사회규범과 사회수학적 규범을 분석하고 두 교실의 교실사회규범, 사회수학적 규범을 비교함으로써 이 규범에 대한 형성을 알아보고자 한다. 이를 위해 1년 동안 26차시의 수학수업을 관찰하였으며 교사와 학생의 인터뷰를 진행하였다. 그 결과 초등학교 두 교사가 수업 상황에서 흐름, 수학적 개념이나 원리를 가르치는 방법에 대해 교실사회규범, 사회수학적 규범 등에서 어떤 유형과 의미를 선택하여 수업하느냐에 따라 교실의 전반적인 분위기, 교사와 학생의 상호작용 패턴, 규범에 의한 수학활동의 모습이 다르게 나타났다.

• 대한수학교육학회지:수학교육학연구
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• 제11권1호
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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.

• 한국학교수학회논문집
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• 제8권3호
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• pp.343-356
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• 2005

본 연구는 수학적 신념에 대한 검사지를 활용한 조사연구와 수학 교실 비디오 촬영을 통해 수학 교실에 새로운 사회적 규범이 형성되었을 때 수학적 신념의 변화가 일어나는지 알아보고 수학 교실의 문화 분석을 통해 학생들의 수학적 신념에 영향을 주는 수학 교실의 사회적 규범을 찾고자 하였다. 연구 결과는 일반적인 사회적 규범에만 초점을 두는 수업으로는 학생들의 수학적 신념을 변화시키기에 충분하지 않았다. 또한 수학 교실의 문화분석을 통해 살펴본 수학 교실의 사회수학적 규범은 학생들의 수학적 신념에 영향을 미쳤다.

• 대한수학교육학회지:수학교육학연구
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• 제23권3호
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• pp.373-388
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• 2013

본 논문은 2명의 수학 영재 지도 교사가 갖고 있는 (1)교육 내용으로서의 수학, (2)교육 방법으로서의 수학 교수 학습, 그리고 (3)영재 교육(대상자, 목표/방향, 교사의 역할)에 대한 신념에 따라 수학영재교실에서의 사회 수학적 규범은 어떠한 양태로 나타나는지를 분석하는 것을 목적으로 한다. 이를 위해 충분한 영재지도 경력을 갖고 있으면서 신념의 범주가 다른 두 교사(이하 A교사, B교사라 함)를 선정하여 그들의 수업을 비교 분석하였다. 수학은 '전통', 수학교수는 '혼합', 수학학습은 '전통'적 신념을 가진 A교사는 영재교육에서 수학영재아들을 성취 수준이 높은 자율적 탐구자로 보고 자신은 조력자라고 생각하고 있었다. 수학은 '비전통', 수학교수는 '비전통', 수학학습은 '비전통'적 신념을 가진 B교사는 영재교육에서 수학영재아들을 성취 수준이 높지 않은 자율적 탐구자로 보고 자신은 안내자라고 생각하고 있었다. A교사의 수업에서는 문제 해결의 다양한 규칙과 답을 중요시하며 어려운 문제의 해결을 가치롭게 여기는 사회수학적 규범이 나타났고, B교사의 수업에서는 일반적인 정답보다는 문제 해결의 과정에서 드러나는 수학적 설명과 정당화를 가치롭게 여기는 사회수학적 규범이 나타났다. 그리고 그들의 서로 다른 신념에 따른 수업의 양태와 그 수업에 참여한 학생들의 반응을 통해 수학영재교육에 주는 몇 가지 시사점을 확인할 수 있었다.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권4호
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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.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제4권2호
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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.

• 대한수학교육학회지:수학교육학연구
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• 제14권3호
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• pp.283-304
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• 2004

본 논문은 1년 동안 학생중심 수학교실문화를 구현하려고 노력하는 3명의 초등학교 교사들을 대상으로 6개의 수학교실문화를 분석함으로써 교사중심에서 학생중심의 문화로 바꿔나가는 과정을 상세하게 탐색한다. 연구대상 교실 모두에서 일반적인 사회적 규범과 관련하여 학생중심 교수법의 전형적인 양상이 구현된 반면에, 사회수학적 규범과 수학적 관행 측면에서는 학생들의 아이디어가 수학적 담화와 활동의 중심이 되는 정도에 따라서 유사성보다는 차이점이 부각되었다. 이러한 연구 결과를 바탕으로 수학교실문화 개선의 난제, 사회수학적 규범과 수학적 관행의 중요성, 교사의 역할 등에 관해 논의한다.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제5권2호
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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.

• 대한수학교육학회지:학교수학
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• 제4권3호
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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.