이 책은 수학적 의사소통의 중요성을 인식함에도 불구하고, 수학 시간에 학생 활동 및 사고를 바탕으로 의미 있는 논의를 하기 어려워하는 교사들을 위해서 구체적으로 무엇을 어떻게 해야 할지에 대한 지침을 체계적으로 안내한다. 저자들은 수학적으로 의미 있는 논의를 위해 교사가 5가지 관행(five practices)을 충실히 실행해야 한다고 강조한다.

차례

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

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