• 제목/요약/키워드: Open-ended Task and Problem

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개방형 과제를 활용한 수학 영재아 수업 사례 분석 (A Case Study on Instruction for Mathematically Gifted Children through The Application of Open-ended Problem Solving Tasks)

  • 박화영;김수환
    • 한국수학교육학회지시리즈E:수학교육논문집
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    • 제20권1호
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    • pp.117-145
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    • 2006
  • 수학 영재들은 타고난 수학적 소질과 적성, 지적인 능력과 창의성을 바탕으로 참신한 과제에 대한 도전적이고 창조적인 호기심을 가지고 있다. 영재아들의 창의적인 사고력을 길러주기 위해서는 다양한 방법으로 문제 해결에 접근하게 하고 전략적 시도를 할 수 있도록 만들어주어야 한다. 이런 관점에서 볼 때 개방적이고 비정형적인 문제를 영재 교육프로그램의 과제로 선정하는 것은 바람직하다 할 수 있다. 본 논문에서는 다양한 유형의 개방형 문제를 구안하고, 이를 토대로 영재 학급에서 학습 활동을 전개한 후, 문제해결 과정에서 영재아들의 수학적 사고 능력의 특성과 문제 해결 전략 사례를 분석하여, 개방형 과제를 활용한 초등학교 영재 수업에 관한 시사점을 얻고자 하였다.

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개방형 문제 중심의 프로그램이 수학적 창의력에 미치는 효과 (Cultivating Mathematical Creativity through Open-ended Approaches: Development of a Program and Effectiveness Analysis)

  • 권오남;박정숙;박지현;조영미
    • 한국수학교육학회지시리즈A:수학교육
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    • 제44권2호
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    • pp.307-323
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    • 2005
  • The purpose of this study was to develop a program to cultivate mathematical creativity based on open-ended problem and to investigate its effect. The major features of this innovative program are (a) breaking up fixations, (b) multiple answers, (c) various strategies, (d) problem posing, (e) exploring strategies, (f) selecting and estimating, (g) active exploration through open-ended problems. 20 units for 7th grade mathematics were developed. This study hypothesizes that experimental students may develop more divergent thinking abilities than their traditional counterparts. The participants were 7th grade students attending middle schools in Seoul. Instruments were pre and post tests to measure mainly divergent thinking skills through open-ended problems. The results indicated that the experimental students achieved better than the comparison students on overall and each component of fluency, flexibility, and originality of divergent thinking skills, when deleting the effect of covariance of the pretest. The developed program can be a useful resource for teachers to use in enhancing their students' creative thinking skills. Further this open-ended approach can be served as a model to implement in classes. This study suggests that further investigations are needed in order to examine effects on affective domains such as motivation and task perseverance which are also considered as important factors of creativity.

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A Case Study on Gifted Education in Mathematics

  • Kim, Soo-Hwan
    • 한국수학교육학회지시리즈D:수학교육연구
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    • 제5권2호
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    • pp.87-98
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    • 2001
  • The Center for Science Gifted Education (CSGE) of Chongju National University of Education was established in 1998 with the financial support of the Korea. Science & Engineering Foundation (KOSEF). In fact, we had prepared mathematics and science gifted education program beginning in 1997. It was possible due to the commitment of faculty members with an interest in gifted education. Now we have 5 classes in Mathematics, two of which are fundamental, one of which is a strengthened second-grade class gifted elementary school students, and one a fundamental class, and one a strengthened class for gifted middle school students in Chungbuk province. Each class consists of 16 students selected by a rigorous examination and filtering process. Also we have a mentoring system for particularly gifted students in mathematics. We have a number of programs for Super-Saturday, Summer School, Winter School, and Mathematics and Science Gifted Camp. Each program is suitable for 90 or 180 minutes of class time. The types of tasks developed can be divided into experimental, group discussion, open-ended problem solving, and exposition and problem solving tasks. Levels of the tasks developed for talented elementary students in mathematics can be further divided into grade 5 and under, grade 6, and grade 7 and over. Types of the tasks developed can be divided into experimental, group discussion, open-ended problem solving, and exposition and problem solving task. Also levels of the tasks developed for talented elementary students in mathematics can be divided into the level of lower than grade 5, level of grade 6, and level of more than grade 7. Three tasks developed and practiced are reported in this article.

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초등학교 5학년 수학과 수행평가 과제 개발에 관한 연구 (A Study on Development of Mathematics Performance Assessment Tasks for the Fifth Graders in the Primary School)

  • 유현주;정영옥;류순선
    • 대한수학교육학회지:학교수학
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    • 제2권1호
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    • pp.203-241
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    • 2000
  • This study aims to suggest a model of task development for mathematics performance assessment and to develop performance tasks for the fifth graders in the primary school on the basis of this model. In order to achieve these aims, the following inquiry questions were set up: (1) to develop open-ended tasks and projects for the fifth graders, (2) to develop checklists for measuring the abilities of mathematical reasoning, problem solving, connection, communication of the fifth graders more deeply when performance assessment tasks are implemented and (3) to examine the appropriateness of performance tasks and checklists and to modify them when is needed through applying these tasks to pupils. The consequences of applying some tasks and analysing some work samples of pupils are as follows. Firstly, pupils need more diverse thinking ability. Secondly, pupils want in the ability of analysing the meaning of mathematical concepts in relation to real world. Thirdly, pupils can calculate precisely but they want in the ability of explaining their ideas and strategies. Fourthly, pupils can find patterns in sequences of numbers or figures but they have difficulty in generalizing these patterns, predicting and demonstrating. Fifthly, pupils are familiar with procedural knowledge more than conceptual knowledge. From these analyses, it is concluded that performance tasks and checklists developed in this study are improved assessment tools for measuring mathematical abilities of pupils, and that we should improve mathematics instruction for pupils to understand mathematical concepts deeply, solve problems, reason mathematically, connect mathematics to real world and other disciplines, and communicate about mathematics.

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학습자 중심 수학 수업을 위한 수업자료의 몇 가지 특징 (On Some Characteristics of Instructional Materials for Learner-Centered Mathematics Instruction)

  • 김진호
    • 한국수학교육학회지시리즈C:초등수학교육
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    • 제15권3호
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    • pp.189-199
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    • 2012
  • 제7차 교육과정 이후로 학습자 중심 수업이 지속적으로 강조되고 있음에도 불구하고, 초등수학교과서에 제공되어 있는 수업자료로 수업을 할 때 학습자 중심 수업의 진면목이 들어나고 있지 않은 것이 현실이다. 이에 학습자 중심 수학 수업을 실천에 옮기기에 적합한 수업자료가 지녀야 하는 몇 가지 특징에 대하여 살펴보았다. 지속적으로 교육과정을 개정하고 그에 따른 수학교과서 개발시에 본 고에서 논의한 특징들이 반영된 수업자료가 개발되기를 기대해 본다.

입원아동과 간호사가 지각한 돌봄에 대한 연구 (Hospitalized Children and Their Nurses각 Perception of Caring)

  • 김정선;김신정
    • 대한간호학회지
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    • 제22권3호
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    • pp.297-315
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    • 1992
  • Caring has been identified as the essence and unifying domin of nursing(Leininger). Many nurses believe that the art of nursing is comprised of actions that are predominantly caring in nature. Although caring has been the traditional ideology of nurses, it is only now beginning to emerge as the central construct for the development of nut sing research, theory and practice. The problem addressed by this study was to identify how hospitalized children and their nurses express the meaning of caring, how they think nurses should care for children and to describe their experiences of being cared for. The purpose was to provide theoretical understanding of caring as perceived in Korea to contribute to the development of Korean nursing knowledge. The subjects were 76 hospitalized children admitted to pediatric units in five teaching hospitals and 66 nurses who were caring for these children. In this descriptive study, data were collected from Nov 11, 1991 to Jan 30, 1992 by interviews and an open-ended questionnaire and analysed by van Kaam's method. Caring themes perceived by the children and their nurses were classified into eight categories, -helping, comfort, love, warmth(only by children), recovery from illness, health maintenance (only by nurses), presence, nurturance and responsibility. Ideal caring behaviors perceived by the children and their nurses were six categories, -to give help, provide comfort, give love, stay with, treat warmly and aid recovery. Subcategories of giving help were promptness and competence, detailed explanations and support and encouragement. Other subcategories of giving help reported only by nurses were individualizing care, recognizing needs and providing a familiar enviornment. Subcategories of maintaining comfort were making comfortable, alleviating pain ; one subcategory reported only by children was consolating. A subcategory of giving love was concern, two subcategories reported only by nurses were compassion and respect. Subcategories of staying with were playing with and touching : only nurses reported empathy, Subcategories of treating warmly were tenderness and kindness. In the experience of caring, there were 4 categories, -to give help, stay with, show concern and provide comfort. Both the hospitalized children and their nurses had experienced caring primarily from their mothers. Mothers' caring behaviors were direct, personal, basic, supportive nursing acts. On the other hand, nurses caring behaviors were task oriented skilled procedures and medically delegated acts. This study contributes understanding of the complexity of caring, more specifically the meaning and experience of caring and ideal caring behaviors. Research may be able to move into verification when instruments are developed to measure the complexity of caring beliefs, values and behaviors in Korea and other cultural settings.

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제 1, 2회 학생 과학 공동탐구 토론대회의 종합적 평가 (Summative Evaluation of 1993, 1994 Discussion Contest of Scientific Investigation)

  • 김은숙;윤혜경
    • 한국과학교육학회지
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    • 제16권4호
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    • pp.376-388
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    • 1996
  • The first and the second "Discussion Contest of Scientific Investigation" was evaluated in this study. This contest was a part of 'Korean Youth Science Festival' held in 1993 and 1994. The evaluation was based on the data collected from the middle school students of final teams, their teachers, a large number of middle school students and college students who were audience of the final competition. Questionnaires, interviews, reports of final teams, and video tape of final competition were used to collect data. The study focussed on three research questions. The first was about the preparation and the research process of students of final teams. The second was about the format and the proceeding of the Contest. The third was whether participating the Contest was useful experience for the students and the teachers of the final teams. The first area, the preparation and the research process of students, were investigated in three aspects. One was the level of cooperation, participation, support and the role of teachers. The second was the information search and experiment, and the third was the report writing. The students of the final teams from both years, had positive opinion about the cooperation, students' active involvement, and support from family and school. Students considered their teachers to be a guide or a counsellor, showing their level of active participation. On the other hand, the interview of 1993 participants showed that there were times that teachers took strong leading role. Therefore one can conclude that students took active roles most of the time while the room for improvement still exists. To search the information they need during the period of the preparation, student visited various places such as libraries, bookstores, universities, and research institutes. Their search was not limited to reading the books, although the books were primary source of information. Students also learned how to organize the information they found and considered leaning of organizing skill useful and fun. Variety of experiments was an important part of preparation and students had positive opinion about it. Understanding related theory was considered most difficult and important, while designing and building proper equipments was considered difficult but not important. This reflects the students' school experience where the equipments were all set in advance and students were asked to confirm the theories presented in the previous class hours. About the reports recording the research process, students recognize the importance and the necessity of the report but had difficulty in writing it. Their reports showed tendency to list everything they did without clear connection to the problem to be solved. Most of the reports did not record the references and some of them confused report writing with story telling. Therefore most of them need training in writing the reports. It is also desirable to describe the process of student learning when theory or mathematics that are beyond the level of middle school curriculum were used because it is part of their investigation. The second area of evaluation was about the format and the proceeding of the Contest, the problems given to students, and the process of student discussion. The format of the Contests, which consisted of four parts, presentation, refutation, debate and review, received good evaluation from students because it made students think more and gave more difficult time but was meaningful and helped to remember longer time according to students. On the other hand, students said the time given to each part of the contest was too short. The problems given to students were short and open ended to stimulate students' imagination and to offer various possible routes to the solution. This type of problem was very unfamiliar and gave a lot of difficulty to students. Student had positive opinion about the research process they experienced but did not recognize the fact that such a process was possible because of the oneness of the task. The level of the problems was rated as too difficult by teachers and college students but as appropriate by the middle school students in audience and participating students. This suggests that it is possible for student to convert the problems to be challengeable and intellectually satisfactory appropriate for their level of understanding even when the problems were difficult for middle school students. During the process of student discussion, a few problems were observed. Some problems were related to the technics of the discussion, such as inappropriate behavior for the role he/she was taking, mismatching answers to the questions. Some problems were related to thinking. For example, students thinking was off balanced toward deductive reasoning, and reasoning based on experimental data was weak. The last area of evaluation was the effect of the Contest. It was measured through the change of the attitude toward science and science classes, and willingness to attend the next Contest. According to the result of the questionnaire, no meaningful change in attitude was observed. However, through the interview several students were observed to have significant positive change in attitude while no student with negative change was observed. Most of the students participated in Contest said they would participate again or recommend their friend to participate. Most of the teachers agreed that the Contest should continue and they would recommend their colleagues or students to participate. As described above, the "Discussion Contest of Scientific Investigation", which was developed and tried as a new science contest, had positive response from participating students and teachers, and the audience. Two among the list of results especially demonstrated that the goal of the Contest, "active and cooperative science learning experience", was reached. One is the fact that students recognized the experience of cooperation, discussion, information search, variety of experiments to be fun and valuable. The other is the fact that the students recognized the format of the contest consisting of presentation, refutation, discussion and review, required more thinking and was challenging, but was more meaningful. Despite a few problems such as, unfamiliarity with the technics of discussion, weakness in inductive and/or experiment based reasoning, and difficulty in report writing, The Contest demonstrated the possibility of new science learning environment and science contest by offering the chance to challenge open tasks by utilizing student science knowledge and ability to inquire and to discuss rationally and critically with other students.

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