• Journal for History of Mathematics
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• v.21 no.1
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• pp.157-166
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• 2008

Mathematical communication is an important goal of recent educational reform. The NCTM's Principle and Standards for School Mathematics, consulting an emphasis on mathematical discourse from 1991 Professional Standards for Teaching Mathematics, has a Communication Standard at each grade level. This paper examines Socrates's educational philosophy and the mathematical dialogue in Plato's. Further it examines mathematical dialogues between teachers and students from antiquity through the nineteenth century.

• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.465-494
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• 2017

Teachers' conceptions about teaching are important driving and also interfering forces which might affect their actual practice and training. This research explores preservice mathematics teachers' conceptions of teacher discourse, through tasks analyzing and evaluating teachers' moment-to-moment discourse moves which occur in authoritative and dialogical classroom discourse. Some facets of the preservice teachers' conceptions were congruent with dialogical discourse: they criticized teacher's one-way communication and ignoring students' voices; they supported teacher's questions probing students' thinking and receptive attitude to ward students' wrong answers. However, some deep and subtle facets of their conceptions were more congruent with authoritative discourse rather than dialogical discourse: they positively perceived teacher's closed, information seeking questions that funnel students' thinking to the predetermined procedure; they emotionally resisted teacher's questions which might facilitate dialogical engagement by allowing students to judge mathematical correctness of ideas from their peers. Preservice teachers' conceptions of teacher discourse explored in this research provide useful foundations on which to build continuous and coherent teacher professional development programs about classroom discourse.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.511-536
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• 2017

The present study aims to investigate ways in which pre-service secondary mathematics teachers anticipate 1) students' responses to specific mathematical tasks which are chosen or devised by the participating pre-service teachers as requiring students' higher cognitive demand and, 2) their roles as math teachers to scaffold students' mathematical thinking. To achieve the goal, we had our pre-service teachers to engage in an adapted version of Spangler & Hallman-Thrasher(2014)'s Task Dialogue writing activity whose focus was to develop pre-service elementary teachers' ability to orchestrate mathematical discussion. 14 pre-service teachers who were junior at the time enrolled in the Mathematics Teaching Method Course were subjects of the current study. In-depth analysis of both Task Dialogues which pre-service secondary mathematics teachers wrote and audiotapes of the group discussions while they wrote the dialogues suggests the following results: First, the pre-service secondary teachers anticipated how students would approach a task based on their own teaching experiences. Second, they were challenged not only to anticipate more than one correct students' responses but to generate questions for the predicted correct-responses to bring forth students' divergent thinking. Finally, although they were aware that students' knowledge should be the crucial element guiding their decision-making process in teaching, they tended to lower the cognitive demands of tasks by providing students with too much guidance which brought forth the use of procedural knowledge. The study contributes to the field as it provides insights as to what to attend in designing teacher education course whose goal is to provide a foundation for developing pre-service teachers' ability to effectively orchestrate mathematical discussion.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.321-332
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• 1999

This article made overtures of the relationship between interactive mathematics texts nd the prototype design of computer application with Computer Algebra System Math. Engine, linking together in the school mathematics. School teachers and researchers would try to construct mathematical materials with computers in educating students in the middle and high school grades. As the individual users come to manage hyper-media materials, so they meet with the problem of 'Who does control?'A mass user would be concerned with interactive mathematics materials directly or off-line at realtime and manipulate the process of problem-solving symbolically with MathView/sup 11)/ and ON-Math/sup 12)/. Discussion was made in developing the factor in the domestic situation and reaching out their hands for it. In conclusion, a user may reform the information of math-curriculum limitedly.

• Communications of Mathematical Education
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• v.11
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• pp.471-481
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• 2001

우리 나라 수학교육이 ICME를 만난 날부터 지금까지의 이야기, 향후의 계획을 간단히 소개한다. 우리가 ICME11을 유치하고자 노력을 시작했는데 그 성공적인 개최를 위하여 그리고 장차 우리가 세계 수학교육에서 중심적인 역할을 감당하기 위하여 몇 가지 제안을 우리 수학교육계에 한다. 이러한 제안은 현재 논란이 되고있는 교육과정 교사교육에도 관련이 있다. 이 글에서 하는 제안은 주로 여러 신문 기사와 여러 어른들과의 대화 내용에 근거한다.

• The Journal of Korean Association of Computer Education
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• v.3 no.1
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• pp.65-74
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• 2000

Based on recent fast development of computer and telecommunication technologies, the Distance Education System(DES) was introduced and utilized widely in the area of education. For an immediate and fluent communication between the teacher and the student under DES, the chatting subsystem was effectively used. However, the current chatting systems are not able to receive and transmit the mathematical symbols despite their indispensability in the process of problem and solution setting under remote mathematical education. In this study, thus, Equation Chatting System that can receive and send the mathematical symbols under the graphical user interface was designed and implemented.

• Journal of the Korean School Mathematics Society
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• v.22 no.4
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• pp.439-460
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• 2019

In this study, we examined classroom interaction to explore the relationships among teacher questions, turn-taking patterns, and student talks in mathematics classrooms. We analyzed lessons given by three elementary teachers (two first-grade teachers and one second-grade teacher) who worked in the same school using a conversation-analytic approach. We observed individual classrooms three times in a year. The results revealed that when teachers provided open-ended questions, such as "why and how" questions and "agree and disagree" questions, and used a non-IRE pattern (teacher initiation-student response-teacher feedback; Mehan, 1979), students more actively engaged in classroom discourse by justifying their ideas and refuting others' thinking. Conversely, when teachers provided closed-ended questions, such as "what" questions, and used an IRE pattern, students tended to give short answers focusing on only one point. The findings suggested teachers should use open-ended questions and non-IRE turn-taking patterns to create an effective math-talk learning community. In addition, school administrators and mathematics educators should support teachers to acquire practical knowledge regarding this approach.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.4 no.5
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• pp.919-930
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• 2000

This paper treats a development of visual interactive modeling(VIM) system for ship scheduling problem in integer formulation. The ship scheduling problem can be described as "A problem which assigns ships and cargos to achieve maximum revenue from transportation" in brief. Since late 1970s there has been rapid growth in development and use of VIM as MS10R technology due to the development of computer technology and now VIM has become a important discipline in MS/OR and MIS society. Visual Interactive Modeling is a process that decision maker takes part in modeling life cycle -data collection, formulation, derivation of optimal solution and representation of solution - and interacts with a modeling system to achieve a user-solution appropriate for his/her ultimate goal. This paper suggests the methodology how to collect data, build and modify model, and represent solution using computer graphics as a major driving tool and demonstrates effective performance of a prototype system.pe system.

• Communications of Mathematical Education
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• v.15
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• pp.29-34
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• 2003

물리학, 공학, 경제학, 생물학, 생태학 등의 자연현상, 사회 현상 그리고 심리상황 등과 관련된 내용들의 모델링 과정을 거쳐 나온 미분방정식의 해를 구하고 해의 의미를 파악하는 작업은 바로 우리의 생활의 진면목을 직접 확인하는 것과 같다. 모델링 과정의 효율성은 교사와 학생간의 충분한 수학적 대화속에서 더욱 의미가 커질 것이다. 아울러 학생들에게 미분방정식의 해의 실제적인 의미를 상상하게 하고 그 결과를 발표하게 하는 것과 해를 구하는 과정에 관한 이론의 이해를 돕는 것이 바람직한 학습 지도 방법이 될 것이다. 전 교육과정을 통해 미분방정식의 모델링 과정을 소개하면서 해의 존재성, 해의 유일성, 해법, 해의 의미 등의 학습 및 지도를 학습자 중심으로 운영할 필요가 있다.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2006.04a
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• pp.25-37
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• 2006

영재를 위한 수학교육은 우리의 당면과제 중 하나이다. 능력 있는 학생들의 학습이 속진에 한정되는 것 보다는 심화자료 및 수학적 소프트웨어와 함께 하는 것이 더 의미 있을 것으로 기대된다. 본 연구는 스프레트쉬트를 사용한 수학적 아이디어의 탐구에 관한 것이다. 다음에 대해 논의하기로 하겠다. i) 스프레드쉬트는 비전통적이면서도 이용이 용이하며, 수학적 통찰을 위한 매개물이다. ii) 풍부하고, 흥미릅고, 가치있는 수학적 주제에 대해 스프레드쉬트를 이용할 수 있다. iii) 스프레드쉬트를 사용하여 학생들이 수학적 아이디어에 대한 흥미를 고취시킬 수 있다. iv) 스프레드쉬트는 학생들에게 그들의 창의적인 시각화 기술을 공개할 기회를 줌으로써 수학에 대한 폭넓은 도식적 이해를 제공한다. v) animation을 포함한 스프레드쉬트 도식들의 적절한 사용은 유익하면서도 흥미롭다. vi) 학생들은 일상생활에 나타나는 수학의 흥미로움을 발견할 것이다. vii) 교사는 지금의 지도방식에 스프레드쉬트를 통합할 수 있다. 특히 스프레드쉬트는 다음과 같은 면모도 가지고 있다. i) 창의적인 수학적 스프레드쉬트 모델들의 실제 과정들이 그 자체로써 수학적 개념발달에 이용될수 있다. ii) 스프레드쉬트 모델은 심화된 주제의 탐색을 위한 의미 있는 탐구과제를 제공한다. iii) 스프레드쉬트는 현장에서 사용되는 실제적 수학 도구이다. - 과학자나 공학도들의 사용도 증가되고 있다. 이것의 사용은 학생들이 현장에서 사용할 기술을 취득하게 할 수 있고, 같은 컴퓨터의 소프트웨어를 사용하는 가족의 대화 수단이 되기도 한다. 본 연구에서 우리는 스프레드쉬트의 4가지 실증적 예를 들어 보겠다. 또한 다른 영역에서 발전된 스프레드쉬트 모델의 몇 가지 도식적 산출물도 포함 할 것이다. 우리는 가장 대중적인 스프레드 쉬트인 Microsoft Excel 프로그램을 사용하였다. Excel의 수행과 Excel 연산의 설명을 담은 CD와 함께 다양한 사례들에 대한 논의는 (8)을 참고하기 바란다. 본고에서는 graphic animation 기술, 스크롤바의 사용을 간단하게 개괄하겠다. '동적형상들(movies)'를 만들 수 있는 간단한 매크로의 사용 등의 내용들은 각 자료를 사용할 수 있는 Excel 파일의 예와 함께 [1]과 [8]에 설명하였었다. 많은 인쇄물과 on-line 참고문헌, 매체자료들도 함께 제공하였다.