학생들이 즐거운 수학교실 1학년 2학기 연산 수업 > 교과교육(각교과교육론)

꿀잼이 흐르는 수학교실의 비법!

우리는 가르치는 것이 좋은 사람들입니다. 가르치는 기쁨을 사랑합니다. 그래서 언제나 꿈꿉니다.

호기심으로 반짝이는 아이들의 눈망울, 작은 아르키메데스들이 저마다의 유레카를 외치는 교실의 풍경을. 그리고 그 한가운데서 열정적으로 무언가를 가르치고 있는 자신의 모습을 상상합니다.

하지만 무대 아래 관객으로 남아버린 학생들에게 수학하기는 여전히 즐거운 것일까요? 이 책은 오롯이 학생들의 아이디어가 주인공이 되는 수학교실 속으로 우리를 초대합니다.

이곳에서 학생들은 저마다의 기상천외한 생각으로 덧셈과 뺄셈의 방식을 창조합니다. 서툴렀던 아이디어들은 서로 간의 소통에 의해 더 큰 앎으로 번져갑니다. 친구의 생각을 지렛대 삼아 수학적 개념들은 점차 연결되고 학생들은 모두 자신만의 수학을 구성해 갑니다.

이 책을 읽는 내내 여러분은 도전적인 과제도 이해해보려 안간힘을 쓰는 학생들의 끈기에 놀라고 그들의 새로운 발상에 감탄할 것입니다. 여느 학자들만큼이나 진지한 토론으로 수학적 오류들을 수정해가는 학생들의 열렬한 팬이 되어갈 것입니다. 그리고 마침내 여러분의 마음속엔 ‘모든 아이들은 스스로 생각해내는 기쁨 속에서 성장할 수 있다’는 굳건한 믿음이 자리 잡게 될 것입니다.

전국의 모든 예비교사와 좋은 수업을 고민하는 모든 분들이 이 책을 읽기를 소망합니다. 책의 마지막을 덮을 땐 제가 그랬듯 여러분의 가슴도 뛰고 있을 것입니다. 우리가 늘 꿈꾸던, ‘모든 아이들이 즐거운 수학교실’의 구체적인 모습이 바로 여기 있기 때문입니다.

(대구교육대학교 영어교육과 예비교사 채민지)

목차

추천사1 / iii

추천사2 / vi

서문 / ix

Chapter 1. 100 수배열표 만들기 1

교수 학습활동안 ·································································· 2

수업의 실제：1차시 ······································································ 5

<활동 소개> ··························································································· 5

<시범 보이기> ······················································································ 13

수업의 실제：2차시 ··································································· 21

<전체 학급 활동：활동 1> ··································································· 21

수업의 실제：3차시 ··································································· 34

<전체 학급 활동：활동 2> ·································································· 34

참고문헌 / 48

Chapter 2. 도깨비 나라의 동전 49

교수 학습활동안 ································································ 50

수업의 실제：1차시 ··································································· 54

<활동 소개> ························································································· 54

<개별 활동하기> ·················································································· 63

<전체 학급 토론> ················································································· 65

수업의 실제：2차시 ··································································· 72

<지난 시간 발생한 상황들 상기> ·························································· 72

<개별 활동> ························································································· 79

<전체 학급 토론> ················································································· 80

참고문헌 / 87

Chapter 3. 추석에 만난 가족의 수 89

교수 학습활동안 ································································ 90

수업의 실제：1차시 ··································································· 93

<활동 소개 1: 가족 그림 그리기> ························································· 93

<활동 소개 2: 모둠별 친척의 수 구하기> ············································· 97

<전체 학급 토론> ················································································· 99

수업의 실제：2차시 ································································· 103

<전체 학급 토론> ··············································································· 103

<심화 활동 2: 우리 반 친구들이 만난 친척의 수> ······························ 108

참고문헌 / 114

Chapter 4. 등호 115

교수 학습활동안 ······························································ 116

수업의 실제 ·············································································· 119

<활동 소개> ······················································································ 119

<개별 활동 시작> ··············································································· 120

<전체 학급 토론> ··············································································· 121

<과제 2> 관계로서의 등호 이해하기 ·················································· 128

<과제 3> 0의 성질을 이용한 등호 이해하기 ······································ 132

참고문헌 / 135

Chapter 5. 주사위 굴리기 137

교수 학습활동안 ······························································ 138

수업의 실제：1차시 ································································· 142

<덧셈 게임：기본 과제> ···································································· 142

<덧셈 게임：기본 과제>：짝 활동 시작 ············································· 149

<덧셈 게임：심화 과제> 소개 및 짝 활동 시작 ·································· 149

수업의 실제：2차시 ································································· 152

<덧셈 게임：심화 과제>：짝 활동 시작 ············································· 152

<전체 학급 토론> ··············································································· 153

수업의 실제：3차시 ································································· 164

<뺄셈 게임：기본 과제> 소개하기 ····················································· 164

<뺄셈 게임：기본 과제>：짝 활동으로 시작 ······································ 171

<전체 학급 토론> ··············································································· 172

수업의 실제：4차시 ································································· 184

<뺄셈 게임：기본 과제 및 심화 과제> 수행하기 ································ 184

<전체 학급 토론> ··············································································· 185

수업의 실제：5차시 ································································· 195

<덧셈 게임：심화 과제> 및 <뺄셈 게임：심화 과제> 소개 ················· 195

<2인 1모둠 활동> ·············································································· 201

<전체 학급 토론> ··············································································· 201

수업의 실제：6차시 ································································· 209

<전시학습 확인 및 <뺄셈 게임：심화 과제> 활동 재개> ····················· 209

<전체 학급 토론> ··············································································· 210

수업의 실제：7차시 ································································· 223

<전체 학급 토론> ··············································································· 223

수업의 실제：8차시 ································································· 239

<전체 학급 토론> ··············································································· 239

참고문헌 / 256

Chapter 6. 무당벌레 257

교수 학습활동안 ······························································ 258

수업의 실제 1 ··········································································· 262

<활동 소개하기> ················································································ 262

<학생 활동 1: 이야기 꾸미기> ·························································· 269

<학생 활동 2：한 벌 활동> ······························································ 270

수업의 실제 2 ··········································································· 273

<내가 만든 이야기 공유하기> ···························································· 273

참고문헌 / 293

▪ 찾아보기 ····················································································· 294

저자소개

서울교육대학교, 한국교원대학교, 미국 Columbia University에서 수학교육학으로 각각 학사, 석사, 박사 학위를 취득하고 현재는 대구교육대학교 수학교육과에서 교수로 재직 중이다. 박사학위를 취득 후 줄곧 학습자 중심 수학 수업이란 분야를 급진적 구성주의를 바탕으로 연구하고 있다. 이 철학을 수학교육에서 적용하기 어렵다고 판단하는 많은 연구자는 사회적 구성주의를 토대로 학습자 중심 수업을 연구하고 있다. 하지만 저자는 구성주의의 절정은 급진적 구성주의에 있다고 보고 그 관점을 교육에서 실천할 수 있는 방안을 탐구하고 있다. 현재 그 가능성을 탐구하고 있으며, 점차 초등학교 전 영역에서 이 접근을 실현할 수 있는지를 탐구할 것이다. 물론, 현재 발달시키고 있는 이론들을 좀 더 세련시키는 작업도 동반할 것이다. 많은 연구자들이 자신의 연구 결과물의 끝이 어딘지 모르겠다고 하였듯이, 저자 또한 자신의 연구의 결과물이 어디에서 멈출지 모른다. 다만, 저자는 많은 초등학생들이 수학을 즐기면서 학습할 수 있는 방안을 탐구하기를 멈추지 않을 것이다.

∙ 미국 컬럼비아대학교 사범대학 수학교육과 교육학박사

∙ 2007 개정 교육과정 초등수학과 집필

∙ 2009 개정 교육과정 초등수학과 집필

∙ 2015 개정 교육과정 초등수학과 집필

∙ 한국수학교육학회 영문학술지 “수학교육학연구” 편집위원장

∙ 대구교육대학교 수학교육과 교수

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