Ⅰ.
데스모스

1.
데스모스 ··························································································································· 9
가.
데스모스의 역사와 뜻 ···························································································· 11
나.
데스모스 회원가입 ·································································································· 12
다.
데스모스 교사 홈페이지 구성 ·············································································· 13
1) 언어설정 바꾸기 ··································································································· 13
2) Desmos 실험기능 체크 ······················································································ 14
3) 액티비티 탐색 ······································································································· 14
4) 사용자 지정 액티비티 ························································································· 16
라.
액티비티 수업에 사용하기 ···················································································· 16
1) 학생들 접속시키기 ······························································································· 16
2) 대시보드 사용방법 ······························································································· 18
마.
액티비티 번역하기 ·································································································· 19
바.
액티비티 새로 만들기 ···························································································· 20
1) 액티비티 제작페이지 둘러보기 ·········································································· 21
2) 구슬 굴리기 ··········································································································· 22
3) 카드 정렬 ··············································································································· 22
4) 그래핑 계산기 ······································································································· 22


Ⅱ.
그래핑 계산기 사용방법

가.
그래프 저장 및 붙여넣기 ······················································································ 25
1) 그래프 저장하기 ··································································································· 25
2) 그래프 복사하여 붙여넣기 ················································································· 26
나.
점 표현하기 ············································································································· 27
1) 변수를 사용하여 슬라이더로 조절할 수 있는 점 만들기 ····························· 27
2) 점의 스타일 바꾸기 ····························································································· 28
3) 리스트로 여러 개의 점 표현하기 ······································································ 30
〈실습문제 1〉 ····················································································································· 31
다.
색깔 추가하기 ········································································································· 32
〈실습문제 2〉 ····················································································································· 33
라.
다각형 표현하기 ····································································································· 33
1) polygon 함수 사용하기 ······················································································ 33
2) 변수에 따라 변하는 사각형의 넓이 표현하기 ················································ 34
〈실습문제 3〉 ····················································································································· 35
마.
선분 표현하기 ········································································································· 36
1) polygon함수로 선분 표현하기 ··········································································· 36
〈실습문제 4〉 ····················································································································· 37
2) 매개변수 를 사용하여 선분 표현하기 ······························································ 37
〈실습문제 5〉 ····················································································································· 38
바.
원 표현하기 ············································································································· 38
1) xy 좌표평면에서 원 표현하기 ············································································ 38
2) 극좌표 방정식으로 원 표현하기 ········································································ 38
3) 매개변수 t 를 사용하여 원 표현하기 ······························································ 39
〈실습문제 6〉 ····················································································································· 39
사.
조건이 걸린 함수 ··································································································· 40
1) 제한된 영역의 그래프 표현하기 ········································································ 40
2) 조건이 있는 세 함수를 하나의 함수로 표현하기 ·········································· 41
아.
여러 가지 함수 사용하기 ······················································································ 42
1) mod 함수 ·············································································································· 42
2) floor 함수 ·············································································································· 43
3) min 함수 ··············································································································· 43
〈실습문제 7〉 ····················································································································· 43
〈실습문제 8〉 ····················································································································· 44
〈실습문제 9〉 ····················································································································· 44


Ⅲ.
버튼과 그래프

가.
“클릭 전쟁” 따라잡기 ···························································································· 47
1) 행동버튼 탐색하기 ······························································································· 47
2) pressCount 사용방법 ························································································· 49
3) 버튼을 클릭할 때마다 높이가 0.2씩 커지는 직사각형만들기 ··················· 51
4) 클릭한 횟수 표현하기 ························································································· 52
5) 클릭한 지 5초 후에 버튼이 비활성화되게 하기 ············································ 54
6) 버튼의 레이블 바뀌게 하기 ··············································································· 57
7) 두 버튼을 클릭한 횟수 직사각형 높이에 반영하기 ······································ 57
나.
“직사각형의 넓이와 반비례” 따라잡기 ······························································· 59
1) 넓이가 36으로 일정한 직사각형 만들기 ························································· 59
2) 변수에 의해 채워지는 직사각형의 내부 ·························································· 61
3) 변수와 timeSincePress 연결하기 ·································································· 63
4) when, otherwise 로 조건에 따라 변하는 문장 입력하기 ·························· 63
5) resetOnChange 로 버튼 기능 초기화 하기 ·················································· 67
6) 레이블에 조건 걸기 ····························································································· 67


Ⅳ.
수식입력란과 그래프

가.
“과녁맞추기” 따라잡기 ·························································································· 71
1) 수식입력란 탐색하기 ··························································································· 71
2) parseOrderedPair 사용방법 ············································································· 73
3) 과녁만들기 ············································································································· 75
4) 수식입력란에 입력한 순서쌍을 그래프 화면에 점으로 나타내기 ··············· 76
5) correct, readOnly 사용방법 ·············································································· 78
나.
“풍선으로 띄워요” 따라잡기 ················································································ 80
1) 풍선이미지 그래프에 업로드하기 ······································································ 81
2) 대응값이 수열리스트인 함수 ············································································ 82
3) 풍선 이미지 중심의 위치 이해하기 ·································································· 83
4) 이미지 회전시키기 ······························································································· 86
5) 풍선실의 끝이 원점을 향하게 하기 ································································ 87
6) 수식입력창의 숫자를 받아 풍선의 개수 결정하기 ········································ 90
7) 수식입력란의 제출을 누르면 풍선이 위로 올라가게 하기 ··························· 92


Ⅴ.
그림판과 그래프

가.
“거북이 달리기 대회” 따라잡기 ·········································································· 96
1) 그래프에 달리기 대회 배경 만들기 ·································································· 96
2) 레인 위를 움직이는 캐릭터 나타내기 ······························································ 97
3) 그래프화면 동영상으로 만들기 ·········································································· 98
4) 그림판의 그림과 캐릭터의 움직임 연결하기 ·················································· 99
5) 캐릭터의 움직임 색깔별로 연결하기 ······························································ 102
6) 움직이는 거북이 표현하기 ··············································································· 103
나.
“닮은 도형 그리기” 따라잡기 ············································································ 108
1) currentX, currentY 사용하기 ········································································· 108
2) currentStroke 사용방법 ·················································································· 109
3) currentStroke과 sketch 비교 ········································································ 111
4) 그림색깔 다르게 보이게 하기 ········································································· 112
5) 닮음 도형 그려주는 기계장치 표현하기 ························································ 114


부록
〈부록1 : 실습문제 정답〉 ······························································································ 118
〈부록2 : 그래핑 계산기 자료 안내 〉 ········································································· 125
〈부록3 : 액티비티 제작에 관한 자료 안내 〉 ··························································· 126

잘 구성된 데스모스 액티비티는 너무나 바쁜 선생님들이 손쉽게 좋은 수업을 할 수 있도록 도와주는 선물 같습니다.
저는 2018년 국제수학교육컨퍼런스의 한 강의에서 Water Line 이라는 액티비티를 처음 접하였는데 너무 충격적이었습니다.
흥미로운 수업 소재, 개별탐색활동, 적절한 발문, 체험을 하면서 스스로 깨달은 것을 답으로 적고 있는 나 자신을 발견하고 이상적인 수업 예시라고 생각했습니다.
또한 작년 9월 초 수업 활용에 최적화된 교사대시보드, 코딩으로 연결되는 액티비티 제작기능에 대해 알게 되면서 데스모스의 매력에 풍덩 빠져 버렸습니다.
액티비티를 수업에 적용할 때 교사대시보드를 사용하는 것은 엄청난 장점들이 있습니다.
수업 속도를 조절하면서 접속한 학생들이 무슨 생각을 적는지 모두 살펴볼 수 있고 개별 피드백도 줄 수 있으며 칠판에 판서하듯 주의 집중시켜 전체 수업도 진행할 수 있습니다.
코로나 19 로 인한 온라인 수업에서 대부분의 수업방법이 “동영상 + 과제제시수업, 실시간 쌍방향 수업” 등 이었을 것입니다.
그러나 아무리 실시간 쌍방향으로 수업을 해도 학생들이 수업을 듣고 있는지 얼마나 이해하고 있는지 알 수가 없고 실제로 학생들의 학습격차가 큰 문제점으로 대두되었습니다.
데스모스 액티비티로 수업을 진행하면 그러한 문제점들을 많이 해결할 수있습니다.
데스모스 액티비티는 온라인 뿐만아니라 대면 수업에 적용해도 장점이 많습니다.
다음은 경남에서 운영중인 ‘데스모스 수업에의 활용’ 전문적학습공동체 구성원 선생님들께서 실제 대면 수업에 데스모스 액티비티를 적용하신 후의 소감을 모은 것입니다.
『컴퓨터실에서 “고양이 리본 디자인”으로 일차함수 수업을 진행했는데 학생들이 딴 짓을 할 수
없었습니다.
자신들이 작성한 대답이 앞쪽 대형 화면에 모두 나타났기 때문입니다.
학생들이 적은 답을 보면 성취수준이 어디까지인지 알 수 있어 지도할 때 도움이 되었습니다』
『스마트폰으로 이차함수와 구슬굴리기, 과녁의 정중앙을 찾으며 좌표공부, 클리노미터 각 측정과 삼각비 등의 체험에 참여한 학생들이 매우 즐거워하였습니다.
많은 학생들이 흥미로운 과제를 해결하는 재미에 푹 빠져 계속 데스모스로 수업하면 좋겠다고 말했습니다』
『고등학생을 대상으로 전혀 화려하지 않은 액티비티 “함수의 그래프와 대칭 이동”로 수업을 하였습니다.
학교에 구비된 태블릿을 사용했습니다.
액티비티가 화려하지 않더라도 좋은 질문만으로도 학생들이 옹기 종기 모여 토론하는 모습이 나타났습니다.
먼저 고민한 교사들의 노력의 결실인 액티비티를 사용하면서 수업 설계를 그 교사와 함께 고민하고 교류한 것 같은 느낌이 들었습니다』
그런데 액티비티 활용 수업을 하다 보면 이런 자료는 누가 어떻게 만들었을까? 나도 만들 수 있을까?라는 생각이 들 수 있습니다.
다행히 외국에서 만들어 놓은 좋은 자료들이 많이 있고 데스모스 현지화 번역팀 선생님들께서 한글로 번역해 놓은 자료도 많이 있습니다.
처음엔 일단 만들어진 데스모스 액티비티를 사용하시면 될 것 같습니다.
사용하시다 보면 자연스럽게 선생님만의 수업 의도를 기존 액티비티에 반영해 보고 싶다는 생각과 수업 아이디어를 액티비티로 구현해보고 싶은 생각이 들게 되는데 그 때부터 액티비티 편집창을 열어보시면 될 것 같습니다.
이 책을 쓰는 가장 큰 이유는 선생님들께서 데스모스를 더욱 자유롭게 사용하실 수 있도록 도움드리기 위함입니다.
여섯 가지 액티비티의 일부분을 만들 수 있는 실습 위주의 내용으로 구성하였고 따라하면서 자연스럽게 그래프와 CL(연산레이어) 사용방법을 익힐 수 있으리라 생각합니다.
이를 통해 우리나라 수업 문화에 꼭 맞는 액티비티가 더 많이 개발되고 공유되어 손쉽게 좋은 수업할 수 있는 기회가 더 많아지면 좋겠습니다.
또한 저는 액티비티 편집 및 제작을 위해 그래프에 대해 공부하면서 작도 가능한 것은 수식으로도 표현이 가능한 것을 알게 되었고 행렬식이 예상치 못한 곳에서 사용되는 장면을 목격하였으며 각종 애니메이션이 수식으로 제어되는 원리를 발견하였습니다.
이런 과정은 수학이 어떻게 응용되는지 좀 더 알게 되는 멋진 경험이었습니다.
수학을 좋아하는 학생들은 그래핑 계산기를 통한 심도 깊은 수학공부도 이 책을 통해 할 수 있을 것으로 기대합니다.