효과적인 수학적 논의를 위해 교사가 알아야 할 5가지 관행

헌정 ················································································································ iii
옮긴이의 글 ····································································································· iv
감사의 말 ······································································································ viii
머리말 ············································································································· ix

도입··············································································································· 3

성공적인가 아니면 피상적인가? 마니만 교실에서의 논의············ 7
잎사귀와 애벌레: 마니만 교사의 사례 ···························································· 8
마니만 교사의 사례 분석······································································ 10
결론·············································································································· 13

Ch 1 5가지 관행 소개··················································································· 17

5가지 관행································································································· 18
예상하기 ···································································································· 18
점검하기 ···································································································· 20
선정하기 ···································································································· 23
계열짓기 ···································································································· 24
연결하기 ···································································································· 25
결론·············································································································· 26

Ch 2 발판 마련: 목표 설정과 과제 선정하기···································· 31

수업 목표 설정하기················································································· 31
학습을 확인하기 위한 자원·································································· 35
적절한 과제 선정하기············································································· 35
높은 수준의 과제 찾기·········································································· 39
학습 목표에 맞는 과제 선정하기························································ 42
결론·············································································································· 48

Ch 3 실행 중의 5가지 관행 탐색하기··················································· 51

5가지 관행의 실행: 최유연 교사의 사례········································· 51
최유연 교사의 사례 분석······································································ 58
5가지 관행의 증거 ···················································································· 58
예상하기 ···································································································· 59
점검하기 ···································································································· 59
선정하기 ···································································································· 60
계열짓기 ···································································································· 60
연결하기 ···································································································· 61
5가지 관행과 학습 기회의 관련성 ································································ 62
최 교사의 사례에서 주목할 만한 다른 측면 ················································· 63
효과적인 교수 관행의 활용 ······································································· 63
형평성과 정체성 주목 ··············································································· 64
모든 학생의 참여 ······················································································ 65
결론·············································································································· 65

Ch 4 시작: 학생들의 반응 예상하기와 학생 활동 점검하기······ 69

예상하기······································································································ 69
전략을 예상하기 ························································································ 70
학생들에게 반응하기 ················································································· 72
수학적 목표에 부합하는 반응 확인하기 ···················································· 78
신중남 교사의 사례에서 예상하기 분석··········································· 85
학생들이 무엇을 할지 예상하기 ································································ 85
학생들의 접근 방법에 어떻게 반응할지 계획하기 ···································· 86
수학적 목표에 부합하는 반응 확인하기 ···················································· 87
점검하기······································································································ 88
신중남 교사의 사례에서 점검하기 분석··········································· 94
결론·············································································································· 96

Ch 5 논의 방향 정하기······································································································ 101

선정하기와 계열짓기 및 학생들의 반응 연결하기············· 101
선정하기와 계열짓기············································································· 102
피자 비교하기 과제··············································································· 105
신중남 교사의 사례에서 선정하기와 계열짓기 분석··················· 111
연결하기···································································································· 112
신중남 교사의 사례에서 연결하기 분석········································· 124
수학적 아이디어: 교점의 의미 ································································ 124
수학적 아이디어: 교점에서 함수의 위치가 바뀐다 ································· 125
수학적 아이디어: 표현 연결하기 ····························································· 126
결론············································································································ 127

Ch 6 능동적 사고와 참여를 확실하게 하기······································································································ 133

좋은 질문하기와 학생들에게 책임 부여하기························· 133
좋은 질문하기························································································· 134
윤이나 교사의 교실 ················································································· 136
윤이나 교사의 교실에서 질문 분석하기 ·················································· 141
책임 부여를 위한 행동········································································ 144
다시 말하기 ····························································································· 145
다른 사람의 추론을 다시 말해 보게 하기 ·············································· 146
자신의 추론을 다른 사람의 추론에 적용하게 하기 ································· 147
학생들에게 후속 참여를 독려하기 ··························································· 149
기다리는 시간 활용하기 ·········································································· 149
결론············································································································ 151

Ch 7 5가지 관행을 더 넓은 수업 계획 맥락에 포함하기·········· 155

수업 계획하기························································································· 156
사려 깊고 철저한 수업 계획하기 ···························································· 160
수업 계획 프로토콜과 5가지 관행 사이의 관계 ····································· 162
5가지 관행 뛰어넘기 ··············································································· 163
과제 준비 및 시작하기 ··········································································· 165
수업 계획의 역할 ···················································································· 170
결론············································································································ 174

Ch 8 교실 논의를 향상하기 위해 학교 환경에서 일하기··········· 177

나도해 교사의 사례 분석···································································· 182
5가지 관행을 학습하는 교사를 돕기 위한 또 다른 노력················ 185
교사가 취할 수 있는 조치·································································· 187
결론············································································································ 189

Ch 9 5가지 관행: 실행을 통해 배운 교훈과 잠재적 이점········ 193

실행을 통해 배운 교훈········································································ 193
첫 번째 교훈 ························································································· 193
두 번째 교훈 ························································································· 195
세 번째 교훈 ························································································· 197
네 번째 교훈 ························································································· 198
다섯 번째 교훈 ······················································································ 200
여섯 번째 교훈 ······················································································ 202
잠재적 이점····························································································· 203
결론············································································································ 206

부록··········································································································· 207
부록 A 과제 및 수업 계획을 위한 웹 기반 자원······················· 207
부록 B 놀이터 만들기 과제를 위한 수업 계획··························· 209
부록 C 구슬 주머니 과제에 대한 점검표····································· 217

참고문헌···································································································· 219

5가지 관행 전문성 개발 지침··························································· 227