• 한국수학교육학회지시리즈A:수학교육
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• 제41권2호
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• pp.189-202
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• 2002

Problem-centered learning reflects learning strategy based on constructivism. In this learning, students should find the solution in a small group discussion, and share their solutions with classmates in whole class discussion. So students participate in mathematics instruction actively and interact with other students about the strategies. We expect students would change their attitudes on mathematics and mathematical learning in these processes. In this study, we analyzed students' attitudes on mathematics and mathematical learning when they participated the problem-centered learning program. We found the change of students' attitudes to mathematics via problem-centered learning.

• 한국과학교육학회지
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• 제38권1호
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• pp.11-26
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• 2018

본 연구는 소집단 논변 활동을 도입한 과학 수업에서 소집단 논의 후 이루어지는 교실 전체 논의에서의 반응적 교수 실행을 탐색하고, 이로부터 드러나는 교사의 인식론적 프레이밍을 파악했다. 이를 위해 교사 3명과 이 교사들이 담당한 학급의 학생들 총 84명이 본 연구에 참여했고, 자극과 반응 단원의 학습 개념을 바탕으로 설계된 논변 수업을 진행했다. 연구자들은 수업에서 이루어진 학생들의 논의를 녹화하고 교사와의 인터뷰를 실시했으며, 교사와 학생들의 담화와 인터뷰 내용을 전사하여 분석 자료로 활용했다. 연구 결과, 교사의 반응적 교수 실행은 교실 구성원 간의 상호작용의 특성과, 논변을 발전시키는 과정에서 활용되는 개념적 또는 인식론적 자원이 누구로 부터 활성되었는지에 따라 네 가지로 구분되었다. 교사가 전체 논의를 '학생들이 논의를 통해 정답에 도달하는 활동'으로서 프레이밍한 경우에는 각 소집단의 논변을 과학 개념과의 비교하고 과학 개념을 전달했고, '적절한 개념적 자원을 이끌어내어 논변을 비판적으로 검토하고 수정하는 활동'으로 프레이밍한 경우에는 각 소집단의 논변을 과학 개념으로 나아갈 수 있는 자원으로서 여기며 교사가 직접 논의에 참여하여 학생과 함께 정당화를 수정하는 반응적 실행을 보였다. 전체 논의를 '소집단의 논변을 명확히 표현하여 공유하는 활동'으로서 프레이밍한 경우에는 각 소집단의 논변을 하나의 나름대로 타당한 논변으로 보아 이를 구체적으로 표현하도록 지원했으며, '비판적 평가를 바탕으로 교실 전체에서 합의된 논변을 구성하는 활동'으로 프레이밍한 경우 각 소집단의 논변을 교실 전체의 합의된 논변을 구성하기 위한 자원으로 여기고 학생들 간 상호작용을 통해 논변의 비판적 검토와 발달이 이루어지도록 중재했다. 본 연구는 다양한 맥락에서 드러나는 교사의 프레이밍과 반응적 교수 실행이 지니는 의의와 제한점을 살펴보아, 현장의 상황을 고려한 논변 활동에서의 반응적 교수 전략을 마련하는 데에 기여할 것이다.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권4호
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• pp.423-443
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• 2007

Based on the framework of Huffered-Ackles, Fuson and Sherin(2004), data were analyzed in terms of 3 components: explaining(E), questioning(Q) and justifying(J) of students' mathematical concepts and problem solving in a math classroom. The students used varied presentations to explain and justify their mathematical concepts and ideas. They corrected their mathematical errors or misconceptions through discourses. In addition, they constructed and clarified their concepts and thinking while they were interacted. We were able to recognize there was a special feature in discourses that encouraged the students to construct and develop their mathematical concepts. As they participated in math class and received feedback on their learning, the whole class worked cooperatively in a positive way. Their discourse was improved from the level of the actual development to the level of the potential development and the pattern of interaction moved from ERE(Elicitaion-Response-Elaboration to PD(Proposition Discussion).

• 대한수학회지
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• 제56권2호
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• pp.289-309
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• 2019

This paper is intended as a discussion of some generalizations of the notion of a reversible ring, which may be obtained by the restriction of the zero commutative property from the whole ring to some of its subsets. By the INCZ property we will mean the commutativity of idempotent elements of a ring with its nilpotent elements at zero, and by ICZ property we will mean the commutativity of idempotent elements of a ring at zero. We will prove that the INCZ property is equivalent to the abelianity even for nonunital rings. Thus the INCZ property implies the ICZ property. Under the assumption on the existence of unit, also the ICZ property implies the INCZ property. As we will see, in the case of nonunital rings, there are a few classes of rings separating the class of INCZ rings from the class of ICZ rings. We will prove that the classes of rings, that will be discussed in this note, are closed under extending to the rings of polynomials and formal power series.

• 한국초등과학교육학회지:초등과학교육
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• 제25권3호
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• pp.307-317
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• 2006

Those students with ability and interest in science should be supported to develop their potential and to reach high levels of achievement in science and technology. In order to ensure that gifted pupils are able to enhance their creativity as well as research abilities, appropriate learning programs and environments are essential. One of the various teaching and learning models for the gifted in science is the discovery learning model based on inductive science activities. There is a clear line of continuity between knowledge discovery at the forefront of research and student's learning activities. If students receive excellent training in organizing scientific concepts for themselves, they will be able to skillfully apply appropriate scientific concepts and solve problems when facing unfamiliar situations. It is very important to offer an appropriate learning environment to maximize the learning effect whilst, at the same time, understanding individual student's characteristics. In this study, the authors took great pains to research effective learning environments for gifted science students. Firstly, appropriate classroom learning environments thought by the teacher to offer the most potential were investigated. 3 different classes in which a revised teaching and learning environment was applied in sequence were examined. Inquiries were conducted into students' activities and achievement through observation, interviews, and examination of students' worksheets. A Science Education expert and 5 elementary school teachers specializing in gifted education also observed the class to examine the specific character of gifted science students. A number of suggestions in discovery learning classes for elementary students gifted in science are possible; 1) Readiness is essential in attitudes related to the inquiry. 2) The interaction between students should be developed. A permissive atmosphere is needed in small group activities. 3) Students require training in listening to others. In a whole class discussion, a permissive atmosphere needs to be restricted somewhat in order to promote full and inclusive discussion. 4) Students should have a chance to practice induction and abduction methods in solving problems.

• 대한물리치료과학회지
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• 제9권4호
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• pp.83-94
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• 2002

Within physical therapy education, there has been increased attention to curricula and course that emphasize problem solving, clinical reasoning, and synthesis of information across traditional discipline-specific boundaries. This article describes the development implementation, and outcomes of a problem-based learning course in Physical therapy. The course was designed to help students to integrate the various elements of a physical therapy curriculum and to enhance their abilities to respond to an ever-changing health care environment. An evaluation of the course by the first 50 students who completed it revealed both strengths and weaknesses. Students responded that the course enhanced their professional behavior, including interpersonal communication skills, team work, and follow-through with professional responsibilities. The learning package was developed by the authors and implemented to a college students during three weeks of the first semester of 2001. Most studies which conducted PBL module development were short period or temporary PBL package application and evaluation rather than a whole semester's. While, this study carried on partial integrated PBL curriculum development and application with recomposing content of the two subjects to one subject Physical therapy which includes four PBL packages. This package was developed from a simple concept to complex and partial integrated PBL curriculum application systematically variable learning methods such as discussion, practice, lecture, video. There are 2 classes, each class has 25 students, in the college. Each class has 5 small groups consisting 5 students. Two tutors proceeded discussion charging each class also, they used multiple methods and materials like tutorials, self-directed learning, lecture, and video. The package is 5 grades and 5 hours per week and the rate of discussion, lecture is 4, 1 respectively. One of the most change is the increase of interaction between students and tutors. Whenever students need information and suggestion, they can visit tutors who provide reading materials and guide for the direction of self learning. Therefore, this study describes the PBL package development process and application during one semester recomposing contents of two subjects to Physical therapy concepts. Besides, it will contribute to active application of existing each subject to tutors who intend to convert as PBL methods. The study has significant meaning to show potentiality of partially integrated PBL application, using systematic PBL package development from two subjects contents. However, when students' need of yearning is over the extent of Introduction of Physical therapy and Rehabilitation medicine, tutors should set learning extent. So, there is limitation to attain completely integrated PBL education within one subject, therefore, it is high lighted to proceed development of integrated curriculum to maximize learning effects of PBL. It is exected that partial integrated PBL package development and application will distribute to prosper excellent physiotherapist in practice.

• 대한수학교육학회지:수학교육학연구
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• 제8권1호
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• pp.137-144
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• 1998

A common geoboard puzzel serves as the point of departure for an investigation that lends itself to whole-group discussion with a class of prospective secondary school teachers. Students are provided with opportunities to devise and carry out problem-solving strategies (called 'heuristics' by Polya); exploit inerrelationships among geometry, arithmetic and algebra; formulate generalizations and conjectures; plan and execute an computational project; construct mathematical arguments to establish theorems; and find counter-examples to dispose of a false conjecture. In recent tears, Eugene F. Krause wrote two papers having the same title except for the numeral In that papers he arrives at an theorem about the sizes of squares with lattice point vertices in the coordinate plane, In this paper we follow a different path genearlization to coordinate 3-space

• 한국수학교육학회지시리즈A:수학교육
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• 제48권3호
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• pp.303-328
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• 2009

In this study, we developed the teaching methods using manipulative materials to teach regular polytopes, and applied these to first-year student of middle school who is attending the extra math class. In that class, we focused on the change of the mathematical representations -especially verval, visual and symbolic representations- and mathematical behavioral. By analyzing characterstics the students' work sheets, we obtained affirmative results as follows. First, manipulative materials played an important role on drawing a development figure of regular polyhtopes describing the verval representation definition of regular polytopes. Second, classes utilizing manipulative materials changed students verbalism level of representations the definition of regular polytopes. For example, in the first class about 60% of students are in the $0{\sim}2$ vervalism level, but in the third class, about 65% of students are in the $6{\sim}7$ level. Third, classes utilizing manipulative materials improved visual representation about development figure. After experiences making several development figures about regular octahedron directly, and discussion, students found out key points to be considered for draws development figure and this helped to draw development figures about other regular polytopes. Fourth, students were unaccustomed to make symbolic representations of regular polytopes. But, they obtained same improvement in symbolic representations, so in fifth the class some students try to make symbol about something in common of whole regular polytopes. Fifth, after the classes, we have significant differences in the students, especially behavioral characteristics in II items such as mind that want to study own fitness, interest, attachment, spirit of inquiry, continuously mathematics posthumously. This means that classes using manipulative materials. Specially, 'mind that want to study mathematics continuously' showed the biggest difference, and it may give positive influence to inculcates mathematics studying volition while suitable practical use of manipulative materials. To conclude, classes using manipulative materials may help students enhance the verbal, visual representation, and gestates symbol representation. Also, the class using manipulative materials may give positive influence in some part of mathematical behavioral characteristic. Therefore, if we use manipulative materials properly in the class, we have more positive effects on the students cognitive perspect and behavioral cteristics.

• 한국과학교육학회지
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• 제35권2호
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• pp.217-229
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• 2015

본 연구의 목적은 연소 모델의 사회적 구성 과정에서 나타나는 소집단 활동의 특징을 살펴보는 것이었다. 본 연구를 위해, 중학교 2학년 1개 반을 대상으로, 8개의 소집단으로 나누고, 각 소집단이 3차례의 논의를 통해 연소에 관한 모델 구성을 하도록 MIS과정에 따라 2차시로 수업을 구성하였다. 수업 내용 및 학생과 학생, 학생과 교사의 담화 내용은 비디오 촬영 및 녹음을 한 후 전사하여 분석하였다. 분석 결과, 소집단별 모델 생성에서 협력 유형은 비협동형인 나열형과 의존형, 협동형이 있었으며, 모델 생성과정을 경험함에 따라 2개의 소집단을 제외한 6개의 소집단이 협동형으로 발달하였다. 또한 연소에 관한 모델의 발달을 살펴본 결과, 플로지스톤설에서 산소설로 발전하는 과정에서 나타난 과학자들의 사고와 비슷한 사고 발달이 보였으며, 이를 통해 연소현상에 대한 이해가 발전되고 현상을 설명할 수 있는 모델로 발전하는 것이 나타났다. 협동형 소집단 중 구성원간의 존중, 리더의 민주적인 태도가 높을수록 목표 모델 도달 횟수가 높았다. 또한 성공적인 모델 생성을 위해서는 구성한 모델에 대한 소집단 내, 소집단 간 비판적 검토가 필요하며, 교사의 도움을 모델 수정과 평가에 활용할 줄 아는 능력 또한 요구됨을 알 수 있었다. 이 연구는 과학 모델의 사회적 구성 과정이 학생들의 현상에 대한 이해를 높이는 과학 탐구의 한 방법으로서 교육적으로 의미가 있으며, 모델링 수업 중 교사의 역할에 대한 시사점을 얻는데 그 의의가 있다.

• 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.