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연구자-교사 연구공동체의 교수학적 변환
고등학교 통계적 추정에 대한 교수학적 변환 사례 분석

DC Field Value Language
dc.contributor.advisor이경화-
dc.contributor.author송창근-
dc.date.accessioned2019-05-07T03:55:26Z-
dc.date.available2019-05-07T03:55:26Z-
dc.date.issued2019-02-
dc.identifier.other000000155681-
dc.identifier.urihttps://hdl.handle.net/10371/151201-
dc.description학위논문 (석사)-- 서울대학교 대학원 : 사범대학 수학교육과, 2019. 2. 이경화.-
dc.description.abstractMathematics Teachers didactic transposition for teaching starts from the planning of lessons. They implement the lesson based on the planning, and they can learn by reflecting on their own didactic transposition. In many cases, this kind of process is conducted by individual teachers, but it is not the necessary condition. Recently, many researchers insist that teachers can solve didactic problems and develop their professional capacity by conducting didactic transpositions by researchers and teachers inquiry community.
The main goal of this study is to analyze the didactic transposition by a researcher-teacher inquiry community and to explore how teachers can learn as they participate in the activity with researchers and other teachers. This paper analyzed the case of an inquiry community which conducted the didactic transposition on statistical inference and describe teachers reflection and learning. I organized a researcher-teacher inquiry community with other two researchers and four teachers. Teachers, with researchers, carried out didactic transposition on statistical inference for 7 months and reflected on the whole process. I collected qualitative data and described the activity of the researcher-teacher community.
Results of analysis on the didactic transposition of inquiry community are as follows. First, when teachers interpret textbooks for the declaration of knowledge, they explained that knowledge about sampling is insufficient in textbooks, and the motivation for studying sampling distributions is lacking. In particular, teachers considered which mathematical knowledge was treated in textbooks as well as which questions are answered by those knowledge. Secondly, teachers declared knowledge about sampling, knowledge about sampling distribution, and knowledge about confidence intervals as knowledge to be taught. And as teachers declare the knowledge to be taught, they considered textbooks and curriculum all together. In particular, as teachers pondered which questions could be answered by given mathematical knowledge, they also considered the hierarchy of
knowledge and decided the sequence of teaching. Finally, teachers designed and modified the tasks incessantly through the inquiry community activity. Researchers provided the references including the tasks about sample representativeness and variability which are treated insufficiently in textbooks. The references were useful for teachers to design and modify tasks. Also, I observed teachers discussing the aspect of mathematical knowledge and aspect of learning opportunity of tasks while they designing the tasks. It contributes to design tasks with more explicit objectives.
Results of analysis on teachers reflection and learning are as follows. Firstly, teachers could overcome some difficulties with planning instructions with others in inquiry community. Also, reflection on the process could contribute to the professional developments of teachers. In particular, the focused questions(What are the most important things and complexities in designing tasks?) could facilitate the teachers reflection. Secondly, while teachers and researcher design, implement and reflection collaboratively, the activity of describing aspects of mathematical knowledge and aspects of learning opportunities of tasks could contribute to the development of teachers professionals. Teachers could notice the aspects which were not noticed before by collective reflection. Lastly, teachers noticed the relations of results of teaching and students learning as they considering how to improve designed tasks. In particular, the teacher who implemented lessons thought that the settings for checking the understandings of students should be prepared while designing tasks.
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dc.description.abstract수업을 위한 교사의 교수학적 변환은 수업 계획에서부터 이루어지기 시작한다. 수업 계획에 기초하여 수업을 실행하고, 그 과정에서 이루어진 자신의 교수학적 변환에 대해 반성하며 교사는 학습할 수 있다. 이러한 과정은 많은 경우 개별 교사에 의해 이루어지지만, 교사의 교수학적 변환과 그에 대한 반성이 반드시 교사 개인이 맡아야 할 과업은 아니다. 최근에는 연구자와 교사의 공동체 활동을 통해서 교수학적 변환을 함으로써, 교사 개인이 해결하기 어려운 교수학적 문제에 대처하고 이로부터
교사의 전문성을 개발할 수 있다는 주장이 제기되고 있다.
본 연구의 목표는 연구자와 교사로 이루어진 연구자-교사의 연구공동체 활동에 의한 교수학적 변환이 어떻게 이루어지며, 이로부터의 교사의 학습의 양상이 어떠한지 분석하는 것이다. 본고는 이를 위해 연구자-교사의 연구공동체에서 통계적 추정에 대한 교수학적 변환을 행한 사례를 분석하여, 교수학적 변환이 어떻게 이루어지는지 파악하고 교사의 반성과 학습의 양상을 설명하였다. 본 연구자는 세 명의 연구자와 네 명의 교사로 이루어진 연구자-교사 공동체를 구성하여 약 7개월 간 통계적 추
정에 대한 정규수업을 위한 교수학적 변환을 행하고 그에 대해 반성하는 활동을 진행하였다. 본고는 질적 자료를 수집하고 분석하며, 연구자-교사 공동체의 활동 내용을 상세히 기술하고 분석 결과를 제시하였다.
연구공동체의 교수학적 변환에 대한 분석 결과는 다음과 같다. 첫째, 교사들은 지식의 선언을 위해 교과서를 해석할 때, 표본추출과 관련된 수학적 지식이 충분히 다루어지지 않으며, 표집분포에 대한 학습을 이끄는 질문이 미비하다고 해석하였다. 특히, 교사들은 어떤 수학적 지식이 교과서에서 다루어지느냐뿐만 아니라, 그러한 수학적 지식이 어떤 질문에 대한 답이 될 수 있는지를 중요하게 고려하였다. 둘째, 교사들은 교과서에서 제한적으로 다루어지고 있다고 해석한 지식을 포함하여 표본
추출에 관한 지식, 표집분포에 관한 지식, 구간 추정에 관한 지식을 가르칠 지식으로 선언하였다. 그리고 교사가 교수학적 변환을 위해 가르칠 지식을 선언하는 과정에서, 수학적 개념에 대한 고려와 교과서와 교육과정에 대한 고려가 모두 이루어졌다. 특히, 수학적 지식이 어떤 질문에 대한 답이 될 수 있는지를 고려하며 교사들은 특정 수학적 지식을 가르치기 위해 필요한 또 다른 수학적 지식이 무엇인지를 추론하며 지식의 위계를 고려하고, 지도의 순서를 정하였다. 셋째, 연구공동체에서의 활동을 통해 교사는 과제를 설계하고 이를 지속적으로 수정하였다. 그 과정에서 연구자는 통계 교과서에서 제약적으로 다루어지는 수학적 지식인 표본대표성과 표집변이성에 관한 과제가 담긴 수학 교육 문헌을 참고자료로 교사들에게 제시했고, 이는 교사가 과제 수정을 통해 과제를 설계할 수 있도록 도왔다. 또한, 공동체 활동을 통해 과제를 설계하는 과정에서 과제의 수학적 지식의 측면과 학습 기회의 측면이 어떤 것인지를 논의하는 모습이 관찰되었으며, 이는 보다 뚜렷한 목표를 가진 과제를
설계하는 데 기여하였다.
연구공동체 활동을 통한 교사의 반성과 학습에 대한 분석 결과는 다음과 같다. 첫째, 교사가 수업 계획에서 겪은 어려움을 공동체 활동을 통해서 극복할 수 있었으며, 그 과정을 반성하는 것은 교사의 전문성 개발에 기여할 수 있었다. 특히, 연구진이 제시한 초점화된 질문(교수실험을 하기 위해 과제를 설계할 때 가장 중점적으로 고려한 사항과 설계 과정에서 겪은 어려움은 각각 무엇인가?)을 통해 교사의 반성을 촉진할 수 있었다. 둘째, 연구자와 교사의 협력적인 과제 설계, 실행 및 반성 활동의 과정 중, 수학 과제의 수학적 측면과 학습 기회의 측면에 대해서 서술하는 활동은 교사의 과제 선택, 수정과 관련된 전문성을 개발하는 데 기여하였다. 공동의 반성을 통해서 교사는 이전에는 주목하지 못했던 과제의 수학적 측면과 학습 기회의 측면에 주목할 수 있었다. 셋째, 과제를 어떻게 개선할 수 있을지 고려하며 교사는 교수 실행의 결과와 학생의 학습 사이의 관계에 주목하고 반성할 수 있었다. 특히, 수업을 실행한 교사는 반성을 거치며, 과제 실행에서 학생의 이해를 확인할 수 있는 장치를 과제 설계 시 마련해야 한다고 인식하게 되었다.
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dc.description.tableofcontents제 1 장 서론 ·········································································· 1
1. 연구의 필요성 ················································································ 1
2. 연구 목적과 연구 문제 ································································ 2
제 2 장 이론적 배경 ··························································· 4
제 1 절 연구자-교사의 연구공동체 ············································ 4
1. 연구공동체와 교사의 학습 ·························································· 4
2. 연구자와 교사의 협력·································································· 6
3. 연구공동체와 교사의 반성 ·························································· 8
제 2 절 인류학적 교수이론(ATD) ··············································· 11
1. ATD와 교수학적 변환론 ···························································· 11
2. 프락시올로지 ················································································ 13
제 3 절 통계적 추정에 관한 선행연구 ···································· 16
제 3 장 연구 방법 ······························································ 20
제 1 절 사례연구 ············································································ 20
제 2 절 연구 참여자 ······································································ 21
제 3 절 연구공동체 활동 ····························································· 22
1. 반성적 저널 작성을 통한 평소 교수 실행의 반성·············· 22
2. 수업 계획······················································································ 23
3. 수업 실행······················································································ 24
4. 수업 반성······················································································ 26
제 4 절 자료의 수집과 분석······················································· 28
제 4 장 분석 및 논의 ······················································· 31
제 1 절 수업 계획 과정의 분석 및 논의 ······························ 31
1. 1 단계: 교육과정의 해석과 가르칠 지식의 선언 ················· 31
2. 2 단계: 과제 설계 ······································································· 40
제 2 절 수업 반성 과정의 분석 및 논의 ······························ 54
1. 3 단계: 반성과 교사의 학습 ····················································· 54
제 5 장 요약 및 결론 ······················································· 64
1. 요약································································································ 64
2. 결론································································································ 65
참고문헌··········································································································· 67
Abstract ·············································································································· 79
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dc.language.isokor-
dc.publisher서울대학교 대학원-
dc.subject.ddc510.7-
dc.title연구자-교사 연구공동체의 교수학적 변환-
dc.typeThesis-
dc.typeDissertation-
dc.description.degreeMaster-
dc.contributor.affiliation사범대학 수학교육과-
dc.date.awarded2019-02-
dc.title.subtitle고등학교 통계적 추정에 대한 교수학적 변환 사례 분석-
dc.identifier.uciI804:11032-000000155681-
dc.identifier.holdings000000000026▲000000000039▲000000155681▲-
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