• 제목/요약/키워드: Mathematics Reasoning

검색결과 376건 처리시간 0.024초

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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통계적 개념 발달에 관한 인식론적 고찰 (An Epistemological Inquiry on the Development of Statistical Concepts)

  • 이영하;남주현
    • 한국수학교육학회지시리즈A:수학교육
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    • 제44권3호
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    • pp.457-475
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    • 2005
  • We have inquired on what the statistical classes of the secondary schools had been aiming to, say the epistermlogical objects. And we now appreciate that the main obstacle to the systematic articulation is the lack of anticipation on what the statistical concepts are. This study focuses on the ingredients of the statistical concepts. Those are to be the ground of the systematic articulation of statistic courses, especially of the one for the school kids. Thus we required that those ingredients must satisfy the followings. i) directly related to the contents of statistics ii) psychologically developing iii) mutually exclusive each other as much as possible iv) exhaustive enough to cover all statistical concepts We examined what and how statisticians had been doing and the various previous views on these. After all we suggest the following three concepts are the core of conceptual developments of statistic, say the concept of distributions, the summarizing ability and the concept of samples. By the concepts of distributions we mean the frequency views on each random categories and that is developing from the count through the probability along ages. Summarizing ability is another important resources to embed his probe with the data set. It is not only viewed as a number but also to be anticipated as one reflecting a random phenomena. Inductive generalization is one of the most hazardous thing. Statistical induction is a scientific way of challenging this and this starts from distinguishing the chance with the inevitable consequences. One's inductive logic grows up along with one's deductive arguments, nevertheless they are different. The concept of samples reflects' one's view on the sample data and the way of compounding one's logic with the data within one's hypothesis. With these three in mind we observed Korean Statistic Curriculum from K to 12. Distributional concepts are dealt with throughout but not sequenced well. The way of summarization has been introduced in the 1 st, 5th, 7th and the 10th grade as a numerical value only. One activity on the concept of sample is given at the 6th grade. And it jumps into the statistical reasoning at the selective courses of ' Mathematics I ' or of ' Probability and Statistics ' in the grades of 11-12. We want to suggest further studies on the developing stages of these three conceptual features so as to obtain a firm basis of successive statistical articulation.

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K-12 학생 및 교사를 위한 인공지능 교육에 대한 고찰 (Review on Artificial Intelligence Education for K-12 Students and Teachers)

  • 김수환;김성훈;이민정;김현철
    • 컴퓨터교육학회논문지
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    • 제23권4호
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    • pp.1-11
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    • 2020
  • 본 연구의 목적은 최근 초중등 교육에 도입되고 있는 인공지능 교육의 목적, 내용, 방법 등을 교육과정의 측면과 교사교육에 필요한 요인 측면을 조사하고 분석하여 우리나라 초중등 인공지능 교육의 방향을 제안하는 것이다. 1차 문헌으로는 국내외 논문 9편, 2차 문헌으로는 11편의 국내외 정책 보고서를 수집하고 분석하였다. 수집된 문헌을 서술적 고찰방법을 적용하여 분석하였으며, 문헌의 다각도 분석을 위해 교육과정 구성요소 측면과 TPACK 요소 측면에서 분석하여 시사점을 도출하였다. 본 연구의 결과로 인공지능 교육 대상을 인공지능 사용자, 활용자, 개발자의 3단계로 구분하였다. 초중등 인공지능 교육에서는 사용자와 활용자 단계가 적합하고, 사용자 교육을 위해 인공지능 리터러시를 포함해야 한다. 활용자 교육을 위해 현재의 컴퓨팅 사고력 및 코딩 역량을 기반으로 하여 인공지능의 기능을 적용하여 창의적인 산출물을 만들어 낼 수 있는 역량을 목표로 삼는 것이 필요하다는 시사점을 도출하였다. 또한, 교사는 교수 지식 및 플랫폼 사용 능력 외에도 문제해결, 추론, 학습, 인식 영역 및 일부 응용수학, 인지/심리학/윤리에 대한 내용 지식이 필요하므로 이에 대한 연수가 필요하다.

수학 영재 교육 대상 학생의 기하 인지 수준과 증명 정당화 특성 분석 (An Analysis of Justification Process in the Proofs by Mathematically Gifted Elementary Students)

  • 김지영;박만구
    • 한국수학교육학회지시리즈C:초등수학교육
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    • 제14권1호
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    • pp.13-26
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    • 2011
  • 본 연구의 목적은 초등수학 영재 교육 대상 학생들의 기하 인지 수준과 그들이 증명을 전개하는 과정에서 논리적인 정당화의 특성을 분석하고 이를 기반으로 수학 영재 교육을 위한 시사점을 제시하는 것이다. 이를 위하여 서울특별시 A영재교육원에 재학 중인 5, 6학년 학생 18명을 대상으로 그들의 기하 수준을 확인하고 그들이 기하문제를 증명을 하고 설명하는 과정에서 어떤 논리적인 정당화를 해 가는지 분석하였다. 연구 결과 이들은 van Hieles의 기하 사고의 0수준부터 4수준 중에서 대부분 2∼3수준에 있었다. 그리고 증명의 정당화 과정에서 이 영재 교육 대상 학생들은 잘라 붙이기와 수치적 접근을 사용하려는 시도와 이미 선행으로 학습한 내용의 기억을 되살려 사용하는 예가 많았고, 독창적이고 일반적인 증명으로 이끌어가는 데는 어려움을 가지고 있었다. 따라서 초등수학 영재 교육 대상자들을 위한 교육은 이들의 수준에 맞는 보다 정교화된 과제로 이들이 자신들의 증명의 정당화 과정을 인지하면서 보다 창의적이고 연역적 사고의 수준으로 이끌어 줄 필요가 있다.

단위 조정 3단계 학생의 비례 문제 해결에서 나타나는 분수 지식 (Exploring fraction knowledge of the stage 3 students in proportion problem solving)

  • 이진아;이수진
    • 한국수학교육학회지시리즈A:수학교육
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    • 제61권1호
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    • pp.1-28
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    • 2022
  • 본 연구의 목적은 비례 문제 해결 과정에서 학생의 분수 지식이 어떻게 관련되어 나타나는지를 탐구하는 것이다. 이를 위해 단위 조정 3단계로 판단되는 중학교 1학년 학생 2명에 주목하여 분수 지식과 비례 문제 해결 과정에 대한 임상 면담 자료를 분석하였다. 분석 결과 자연수 맥락에서 단위 조정 3단계 학생으로 판단되었던 두 학생은 분수 맥락에서는 '활동을 통해' 3수준 단위를 조정하며 서로 다른 양적 조작 방식을 보여주었다. 특히 두 학생이 가분수가 포함된 곱셈 연산 과제에서 보여주었던 분할 조작과 단위 조정 활동에서 식별되었던 차이는 두 학생의 비례 문제에 대한 접근 방식에 있어서 중요한 차이로 나타났다. 이 과정에서 하나의 3수준 단위로부터 또 다른 3수준 단위 사이의 구조적 전환이 '재귀 분할의 내재화'와 관련이 되며, 합성 단위에 대한 스플리팅 조작에 중요한 근거가 됨을 시사하였다.

수학적 사고력에 관한 인지신경학적 연구 개관 (A Review of the Neurocognitive Mechanisms for Mathematical Thinking Ability)

  • 김연미
    • 인지과학
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    • 제27권2호
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    • pp.159-219
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    • 2016
  • 수학적 사고력은 STEM(science, technology, engineering, mathematics) 분야에서의 학업적인 성취와 과학기술의 혁신에서 중요한 역할을 하고 있다. 본 연구에서는 학제 간 연구 분야인 수 인지(numerical cognition) 및 수학적 인지와 관련된 최근의 인지신경학적 연구 결과들을 종합하여 개관하였다. 첫째로 수학적 사고의 기초가 되는 뇌 기제의 위치와 정보처리 메커니즘을 확인하였다. 수학적 사고는 영역 특정적(domain specific)인 기능인 수 감각과 시공간적 능력뿐만 아니라 영역 일반적(domain general)인 기능인 언어, 장기기억, 작업 기억(working memory) 등을 기초로 하며 이를 토대로 추상화, 추론 등의 고차원적인 사고를 한다. 이 중에서 수 감각과 시공간적 능력은 두정엽(parietal lobe)을 기반으로 한다. 두 번째로는 수학적 사고 능력에서 관찰되는 개인 차이에 대하여 고찰하였다. 특히 수학 영재들의 신경학적인 특성을 신경망 효율성(neural efficiency)의 관점에서 고찰해 보았다. 그 결과 높은 지능이란 두뇌가 얼마나 많이 일하느냐가 아니라 얼마나 효율적으로 일하는가에 달렸다는 사실을 확인하였다. 수학 영재들의 또 다른 특성은 좌반구와 우반구 간의 연결과 반구 내에서 전두엽과 두정엽의 연결이 뛰어나다는 사실이다. 세 번째로는 학습과 훈련, 그리고 성장에 따른 변화 및 발전에 대한 분석이다. 개인이 성장하며, 수학 학습과 훈련을 하게 될 때 이에 따라 두뇌 피질에서도 변화가 반영되어 나타난다. 그 변화를 피질에서의 활성화 수준의 변화, 재분배, 구조적 변화라는 관점에서 해석하였다. 이 중에서 구조적 변화는 결국 신경 가소성(neural plasticity)을 의미한다. 마지막으로 수학적 창의성은 수학적 지식(개념)을 기초로 하여 수학적 개념들을 결합하는 단계가 요구되며, 그 후 결합된 개념들 중에서 심미적인 선택을 통해 수학적 발명(발견)으로 연결된다. 전문성이 높아질수록 결합과 선택이라는 두 단계가 더욱 중요해진다.