• 제목/요약/키워드: sources of mathematical ideas

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개정 교육과정의 실험 적용에서 나타나는 수학적 의사소통 분석 - 초등 1.2학년 탐구 활동과 이야기 마당을 중심으로 - (An Analysis of Mathematical Communication in Preliminary Application of the Revised Curriculum - Focused on 'Exploratory Activity' and 'Story Corner' in Elementary Textbooks for the First and Second Grades -)

  • 박미혜;방정숙
    • 대한수학교육학회지:수학교육학연구
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    • 제19권1호
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    • pp.163-183
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    • 2009
  • 본 연구는 2007년 개정 교육과정에 따라 초등학교 수학 실험용 교과서에 신설된 활동인 탐구 활동과 이야기 마당을 다루는 수업에서 교사와 학생의 수학적 의사소통이 어떻게 이루어지는지 알아보기 위한 것이다. 이를 위하여 초등학교 1, 2학년 각각 두 교실의 수업을 관찰하고 수학적 의사소통을 질문하기, 설명하기, 수학적 아이디어의 근원의 세 요소로 나누어 분석하였다. 분석 결과, 학생들의 사고과정에 초점을 두고 학생들의 아이디어를 탐색한 교실이 있는 반면에, 정답을 도출하는데 초점을 두거나 학생들의 아이디어를 깊이 탐구하지 않고 교사가 직접 아이디어를 평가하는 교실이 있었다. 특히, 탐구 활동보다는 이야기 마당을 다루는 수업에서 이러한 경향이 더 많이 나타났으며 이는 교사들이 이야기를 통하여 수학 수업을 진행하는데 익숙하지 않고 교사용 지도서에도 구체적인 발문이나 학생들의 예상 답안을제시하지 않은데 원인이 있다고 볼 수 있다. 실험 적용에서 드러나는 수학적 의사 소통을 면밀히 분석함으로써 추후 탐구 활동과 이야기 마당 관련 수업에서의 지도 방향에 대한 시사점을 도출하였다.

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Teaching Practices for All Learners in the Mathematics Classroom

  • Kim, Jinho;Yeo, Sheunghyun
    • 한국수학교육학회지시리즈D:수학교육연구
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    • 제22권2호
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    • pp.123-134
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    • 2019
  • In this paper, we articulate what is a lesson for all learners with different cognitive levels and what kind of teaching practices are required to implement this type of lesson. For all learners' own sense-making, open-ended tasks are the primary sources to bring their various mathematical ideas. These tasks can be meaningfully implemented by appropriate teaching practices: providing enough time (for thinking deeply and for preparing a reply), acting intentionally (alternative wrapping up activities and appointment of a struggling student), and cultivating collaborative classroom norms (respecting peer's thinking and learning from peers). This exploratory study has the potential to help practitioners and researchers understand the complexity of the work of teaching and clarify how to deal with such complexity.

Perceptions of Change and Reform Efforts by Secondary School Mathematics Teachers in the People's Republic of China and the United States

  • Carter, Jack;Lu, Shihu;Ferrucci, Beverly J.
    • 한국수학교육학회지시리즈D:수학교육연구
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    • 제3권1호
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    • pp.1-8
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    • 1999
  • The present study extends previous research in this area by investigating perceptions of change and reactions to reform efforts by pre-service and practicing secondary school mathematics teachers in the People's Republic of China (PRC) and the United States of America. Interviews were used to gather data about school experiences, teaching practices, and planned changes in mathematics programs. Analysis of the interview data supported earlier findings with respect to the well-planned nature of lessons by PRC teachers and the influence of mathematics contents and examination systems in the PRC. Findings also indicated a general agreement among teachers from both countries favoring less lecturing and more discussion and interactive activities. There were contrasts by nationality in descriptions of future teaching, ideal lessons, sources of teaching ideas, and preferences about school mathematics programs.

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우수수업 사례를 통해서 본 초등 수학 교실에서의 의사소통 (The Communication of Elementary Math Classes Through Observing the Excellent Lesson Videos)

  • 최은아;이광호
    • 대한수학교육학회지:학교수학
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    • 제12권4호
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    • pp.507-530
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    • 2010
  • 본 연구는 지역별 우수수업 동영상에서 나타나는 수학적 의사소통이 어떻게 이루어지고 있는지를 분석하여 양질의 수업을 찾아 교사의 수업 관행에 도움을 주고자한 것이다. 교사와 교실 전체 간에 이루어지는 담화를 중심으로 수업을 분석하기 위해 다음과 같은 연구문제를 설정하였다. 첫째, 지역별 우수수업 동영상의 수학적 의사소통 수업유형은 무엇인가? 둘째, 지역별 우수수업은 의사소통이 어떻게 이루어지고 있는가? 셋째, 담화중심 수업의 수학적 의사소통 수준은 어떠한가? 공개된 24개의 수업을 수업 유형에 따라 분류한 결과 초등학교 수학 수업의 특성상 조작 중심수업 유형이 가장 많은 것으로 나타나 다른 유형의 수업도 좀 더 이루어질 필요가 있음을 알 수 있었다. 그리고 교수 학습 지도안에서 수학적 의사소통 능력을 고려한 수업은 5개이며 이 중 1개 수업만이 수학적 의사소통 능력을 인지적 영역에 포함시키고 있어, 수학적 의사소통 능력에 대해 교사가 정확히 알 필요가 있었다. 또한, 학생 간 질문하기를 수업에 반영할 필요가 있었다.

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교실문화 비교를 통한 수학교육개혁에 관한 소고 (A Study on the Reform of Mathematics Education from the Comparison of Classroom Culture)

  • 방정숙
    • 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.

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변화가 변화를 일으키지 못할 때: 한국과 미국 초등수학 수업 관찰로부터의 소고 (When Changes Don\`t Make Changes: Insights from Korean and the U.S Elementary Mathematics Classrooms)

  • 방정숙
    • 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.

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기업의 SNS 노출과 주식 수익률간의 관계 분석 (The Analysis on the Relationship between Firms' Exposures to SNS and Stock Prices in Korea)

  • 김태환;정우진;이상용
    • Asia pacific journal of information systems
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    • 제24권2호
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    • pp.233-253
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    • 2014
  • Can the stock market really be predicted? Stock market prediction has attracted much attention from many fields including business, economics, statistics, and mathematics. Early research on stock market prediction was based on random walk theory (RWT) and the efficient market hypothesis (EMH). According to the EMH, stock market are largely driven by new information rather than present and past prices. Since it is unpredictable, stock market will follow a random walk. Even though these theories, Schumaker [2010] asserted that people keep trying to predict the stock market by using artificial intelligence, statistical estimates, and mathematical models. Mathematical approaches include Percolation Methods, Log-Periodic Oscillations and Wavelet Transforms to model future prices. Examples of artificial intelligence approaches that deals with optimization and machine learning are Genetic Algorithms, Support Vector Machines (SVM) and Neural Networks. Statistical approaches typically predicts the future by using past stock market data. Recently, financial engineers have started to predict the stock prices movement pattern by using the SNS data. SNS is the place where peoples opinions and ideas are freely flow and affect others' beliefs on certain things. Through word-of-mouth in SNS, people share product usage experiences, subjective feelings, and commonly accompanying sentiment or mood with others. An increasing number of empirical analyses of sentiment and mood are based on textual collections of public user generated data on the web. The Opinion mining is one domain of the data mining fields extracting public opinions exposed in SNS by utilizing data mining. There have been many studies on the issues of opinion mining from Web sources such as product reviews, forum posts and blogs. In relation to this literatures, we are trying to understand the effects of SNS exposures of firms on stock prices in Korea. Similarly to Bollen et al. [2011], we empirically analyze the impact of SNS exposures on stock return rates. We use Social Metrics by Daum Soft, an SNS big data analysis company in Korea. Social Metrics provides trends and public opinions in Twitter and blogs by using natural language process and analysis tools. It collects the sentences circulated in the Twitter in real time, and breaks down these sentences into the word units and then extracts keywords. In this study, we classify firms' exposures in SNS into two groups: positive and negative. To test the correlation and causation relationship between SNS exposures and stock price returns, we first collect 252 firms' stock prices and KRX100 index in the Korea Stock Exchange (KRX) from May 25, 2012 to September 1, 2012. We also gather the public attitudes (positive, negative) about these firms from Social Metrics over the same period of time. We conduct regression analysis between stock prices and the number of SNS exposures. Having checked the correlation between the two variables, we perform Granger causality test to see the causation direction between the two variables. The research result is that the number of total SNS exposures is positively related with stock market returns. The number of positive mentions of has also positive relationship with stock market returns. Contrarily, the number of negative mentions has negative relationship with stock market returns, but this relationship is statistically not significant. This means that the impact of positive mentions is statistically bigger than the impact of negative mentions. We also investigate whether the impacts are moderated by industry type and firm's size. We find that the SNS exposures impacts are bigger for IT firms than for non-IT firms, and bigger for small sized firms than for large sized firms. The results of Granger causality test shows change of stock price return is caused by SNS exposures, while the causation of the other way round is not significant. Therefore the correlation relationship between SNS exposures and stock prices has uni-direction causality. The more a firm is exposed in SNS, the more is the stock price likely to increase, while stock price changes may not cause more SNS mentions.