t mat 0907693 table of content
DAFTAR ISI
Halaman
LEMBAR PENGESAHAN
PERNYATAAN
KATA PENGANTAR ....................................................................................
i
UCAPAN TERIMA KASIH ............................................................................
ii
ABSTRAK .......................................................................................................
iv
DAFTAR ISI ....................................................................................................
v
DAFTAR TABEL ............................................................................................
ix
DAFTAR GAMBAR .......................................................................................
xi
DAFTAR LAMPIRAN ....................................................................................
xii
BAB I PENDAHULUAN
A. Latar Belakang Masalah ............................................................
1
B. Rumusan Masalah .....................................................................
12
C. Tujuan Penelitian .......................................................................
13
D. Manfaat Penelitian......................................................................
14
E. Definisi Operasional ..................................................................
14
BAB II KAJIAN PUSTAKA
A. Pembelajaran Matematika ..........................................................
17
B. Pemahaman Matematik ..............................................................
19
C. Komunikasi Matematik ..............................................................
26
D. Model Pembelajaran Generatif...................................................
30
v
E. Pembelajaran Konvensional .......................................................
35
F. Kaitan antara Pembelajaran Generatif dengan Peningkatan
Kemampuan Pemahaman dan Komunikasi Matematik ............
36
G. Sikap ...........................................................................................
38
H. Karakter ......................................................................................
39
I. Hipotesis Penelitian ...................................................................
40
BAB III METODE PENELITIAN
A. Desain Penelitian .......................................................................
42
B. Populasi dan Sampel ..................................................................
43
C. Instrumen Penelitian ...................................................................
44
1. Tes Kemampuan Pemahaman dan Komunikasi Matematika
44
a. Analisis Validitas Butir Soal ..............................................
48
b. Analisis Realibilitas ..........................................................
49
c. Analisis Daya Pembeda .....................................................
50
d. Analisis Tingkat Kesukaran ...............................................
52
e. Rekapitulasi Analisis Hasil Uji Coba .................................
54
2. Angket Skala Sikap ................................................................
55
3. Angket Perkembangan Karakter Siswa .................................
56
4. Lembar Observasi .................................................................
57
D. Bahan Ajar ..................................................................................
58
E. Teknik Analisis Data ..................................................................
59
1. ....................................................................................... Data
Hasil Tes Kemampuan Pemahaman dan Komunikasi
vi
Matematik ..........................................................................
59
2. ....................................................................................... Data
Hasil Angket Sikap dan Angket Karakter.............................
62
F. Prosedur Penelitian ...................................................................
65
BAB IV HASIL PENELITIAN DAN PEMBAHASAN
A. Hasil Penelitian Kemampuan Pemahaman Matematik .............
67
1. ....................................................................................... Desk
ripsi Statistik Data Hasil Tes Kemampuan Pemahaman Matematik ....................................................................
67
2. ....................................................................................... Data
Hasil Tes Kemampuan Pemahaman Matematik ..................
68
a. ................................................................................. Tes
Awal (Pretes) .................................................................
70
b. ................................................................................. Tes
Akhir (Postes) .................................................................
73
B. Hasil Penelitian Kemampuan Komunikasi Matematik ..............
77
1. ....................................................................................... Desk
ripsi Statistik Data Hasil Tes Kemampuan Komunikasi Matematik ....................................................................
77
2. ....................................................................................... Data
Hasil Tes Kemampuan Komunikasi Matematik .................
78
a. ................................................................................. Tes
Awal (Pretes) .................................................................
vii
79
b. ................................................................................. Tes
Akhir (Postes) ................................................................
82
3. ....................................................................................... Anali
sis Angket ............................................................................
85
a. ................................................................................. Angk
et Skala Sikap ................................................................
85
b. ................................................................................. Angk
et Perkembangan Karakter Siswa ..................................
89
C. Pembahasan ...............................................................................
91
1. ....................................................................................... Kem
ampuan Pemahaman dan Komunikasi Matematik
Siswa ....................................................................................
91
2. Sikap Siswa terhadap Pembelajaran Generatif.....................
98
3. Perkembangan Karakter Siswa..............................................
100
4. Hasil Observasi ...................................................................
101
BAB V KESIMPULAN DAN SARAN
A. Kesimpulan.................................................................................
103
B. Saran ..........................................................................................
104
DAFTAR PUSTAKA ......................................................................................
106
LAMPIRAN-LAMPIRAN:
A. Instrumen Penelitian ...................................................................
B. Analisis
Hasil
Uji
Coba
Tes
Kemampuan
Pemahaman dan Komunikasi Matematik ...................................
viii
110
179
C. Analisis Data Hasil Penelitian ....................................................
191
D. Skala Sikap dan Perkembangan Karakter...................................
207
E. Dokumentasi Penelitian .............................................................
213
RIWAYAT HIDUP ..........................................................................................
234
DAFTAR TABEL
Tabel 3.1 Penskoran untuk Perangkat Tes Kemampuan Pemahaman
Matematik .....................................................................................
46
Tabel 3.2 Penskoran untuk Perangkat Tes Kemampuan Komunikasi
Matematik .....................................................................................
47
Tabel 3.3 Interpretasi Koefisien Validitas ....................................................
48
Tabel 3.4 Rekapitulasi Uji Validitas Tes Pemahaman Matematik ...............
48
Tabel 3.5 Rekapitulasi Uji Validitas Tes Komunikasi Matematik ...............
49
Tabel 3.6 Klasifikasi Tingkat Reliabilitas ....................................................
50
Tabel 3.7 Klasifikasi Daya Pembeda ...........................................................
51
ix
Tabel 3.8 Daya Pembeda Tes Pemahaman Matematik ................................
51
Tabel 3.9 Daya Pembeda Tes Komunikasi Matematik ................................
51
Tabel 3.10 Kriteria Tingkat Kesukaran ..........................................................
52
Tabel 3.11 Tingkat Kesukaran Butir Soal Pemahaman Matematik ...............
53
Tabel 3.12 Tingkat Kesukaran Butir Soal Komunikasi Matematik ...............
53
Tabel 3.13 Rekapitulasi Analisis Hasil Uji Coba Soal Tes Pemahaman
Matematik .....................................................................................
54
Tabel 3.14 Rekapitulasi Analisis Hasil Uji Coba Soal Tes Komunikasi
Matematik .....................................................................................
54
Tabel 3.15 Kriteria Skor Gain Ternormalisasi ................................................
60
Tabel 3.16 Aturan Pemberian Skor Item Skala Sikap.....................................
63
Tabel 4.1 Rekapitulasi Hasil Pretes dan Postes Kemampuan Pemahaman
Matematik Siswa ..........................................................................
68
Tabel 4.2 Rata-rata Pretes dan Postes Kemampuan Pemahaman
Matematik Siswa ..........................................................................
68
Tabel 4.3 Hasil Uji Normalitas Skor Pretes Kemampuan Pemahaman
Matematik Siswa ..........................................................................
70
Tabel 4.4 Hasil Uji Homogenitas Varians Skor Pretes Kemampuan
Pemahaman Matematik Siswa .....................................................
71
Tabel 4.5 Hasil Uji Kesamaan Rata-rata Pretes Kemampuan Pemahaman
Matematik Siswa ..........................................................................
73
Tabel 4.6 Hasil Uji Normalitas Skor Postes Kemampuan Pemahaman
Matematik Siswa ..........................................................................
74
Tabel 4.7 Hasil Uji Homogenitas Varians Skor Postes Kemampuan
Pemahaman Matematik Siswa .....................................................
75
Tabel 4.8 Hasil Uji Perbedaan Rata-rata Postes Kemampuan
Pemahaman Matematik Siswa .....................................................
76
Tabel 4.9 Rekapitulasi Hasil Pretes dan Postes Kemampuan Komunikasi
Matematik Siswa ..........................................................................
77
Tabel 4.10 Rata-rata Pretes dan Postes Kemampuan Komunikasi
Matematik Siswa ..........................................................................
Tabel 4.11 Hasil Uji Normalitas Skor Pretes Kemampuan
x
78
Komunikasi Matematik Siswa .....................................................
80
Tabel 4.12 Hasil Uji Homogenitas Varians Skor Pretes Kemampuan
Komunikasi Matematik Siswa .....................................................
80
Tabel 4.13 Hasil Uji Kesamaan Rata-rata Pretes Kemampuan Komunikasi
Matematik Siswa ..........................................................................
82
Tabel 4.14 Hasil Uji Normalitas Skor Postes Kemampuan Komunikasi
Matematik Siswa ..........................................................................
83
Tabel 4.15 Hasil Uji Homogenitas Varians Skor Postes Kemampuan
Komunikasi Matematik Siswa ......................................................
83
Tabel 4.16 Hasil Uji Perbedaan Rata-rata Postes Kemampuan
Komunikasi Matematik Siswa .....................................................
85
Tabel 4.17 Distribusi Skor Sikap Siswa terhadap Pelajaran Matematika .......
86
Tabel 4.18 Distribusi Skor Sikap Siswa terhadap Model Pembelajaran
Generatif .......................................................................................
87
Tabel 4.19 Distribusi Skor Sikap Siswa terhadap Soal-soal Pemahaman
dan Komunikasi Matematik .........................................................
88
Tabel 4.20 Distribusi Perkembangan Karakter Rasa Ingin Tahu Siswa ........
89
Tabel 4.21 Distribusi Perkembangan Karakter Kejujuran Siswa ...................
90
Tabel 4.22 Distribusi Perkembangan Karakter Kedisiplinan Siswa ..............
91
xi
DAFTAR GAMBAR
Gambar 3.1
Diagram Alur Penelitian...........................................................
Gambar 4.1
Diagram Batang Perbandingan Rataan Pretes dan Postes
Kemampuan Pemahaman Matematis Siswa.............................
Gambar 4.2
69
Diagram Batang Perbandingan Rataan Pretes dan Postes
Kemampuan Komunikasi Matematis Siswa.............................
Gambar 4.3
66
78
Sebagian Pekerjaan Siswa dalam Menyelesaikan Tes Kemampuan Komunikasi Matematik ...................................................
96
Gambar 4.4 Sebagian Pekerjaan Siswa dalam Menentukan Solusi .............
98
xii
DAFTAR LAMPIRAN
LAMPIRAN A: INSTRUMEN PENELITIAN ......................................
110
A.1 Bahan Ajar ...............................................................................
111
A.2 Silabus dan RPP .......................................................................
148
A.3 Kisi-kisi Soal dan Tes Kemampuan Pemahaman dan
Komunikasi Matemati ...............................................................
158
A.4 Jawaban Tes Matematika .........................................................
161
A.5 Kisi-kisi Angket Skala Sikap Siswa.........................................
170
A.6 Kisi-kisi Angket Perkembangan Karakter ...............................
174
A.7 PedomanObservasi ...................................................................
177
LAMPIRAN B: ANALISIS HASIL UJI COBA TES MATEMATIKA
179
B.1 Skor Uji Coba Tes Pemahaman Matematik .............................
180
B.2 Skor Uji Coba Tes Komunikasi Matematik .............................
181
B.3 Perhitungan Hasil Uji Coba Tes Matematika dengan
Anates 4.0 .................................................................................
182
LAMPIRAN C: ANALISIS DATA HASIL PENELITIAN...................
191
C.1 Data Hasil Pretes ......................................................................
192
C.2 Data Hasil Postes ......................................................................
196
C.3 Analisis Data Hasil Tes Kemampuan Pemahaman Matematik
200
C.4 Analisis Data Hasil Tes Kemampuan Komunikasi Matematik
203
LAMPIRAN D: ANALISIS DATA SKALA SIKAP DAN
OBSERVASI ................................................................
207
D.1 Data Skala Sikap Kelas Eksperimen ........................................
208
D.2 Penyekoran Skala Sikap ...........................................................
209
D.3 Data Angket Karakter ..............................................................
210
D.4 Hasil Observasi Pelaksanaan Pembelajaran .............................
211
LAMPIRAN E: DOKUMENTASI PENELITIAN ................................
213
E.1 Foto-foto pada Saat Pembelajaran ............................................
214
E.2 Sebagian Hasil Kerja dan Respon Siswa ..................................
216
E.3 Surat Keterangan dan Ijin Penelitian ........................................
233
xiii
Halaman
LEMBAR PENGESAHAN
PERNYATAAN
KATA PENGANTAR ....................................................................................
i
UCAPAN TERIMA KASIH ............................................................................
ii
ABSTRAK .......................................................................................................
iv
DAFTAR ISI ....................................................................................................
v
DAFTAR TABEL ............................................................................................
ix
DAFTAR GAMBAR .......................................................................................
xi
DAFTAR LAMPIRAN ....................................................................................
xii
BAB I PENDAHULUAN
A. Latar Belakang Masalah ............................................................
1
B. Rumusan Masalah .....................................................................
12
C. Tujuan Penelitian .......................................................................
13
D. Manfaat Penelitian......................................................................
14
E. Definisi Operasional ..................................................................
14
BAB II KAJIAN PUSTAKA
A. Pembelajaran Matematika ..........................................................
17
B. Pemahaman Matematik ..............................................................
19
C. Komunikasi Matematik ..............................................................
26
D. Model Pembelajaran Generatif...................................................
30
v
E. Pembelajaran Konvensional .......................................................
35
F. Kaitan antara Pembelajaran Generatif dengan Peningkatan
Kemampuan Pemahaman dan Komunikasi Matematik ............
36
G. Sikap ...........................................................................................
38
H. Karakter ......................................................................................
39
I. Hipotesis Penelitian ...................................................................
40
BAB III METODE PENELITIAN
A. Desain Penelitian .......................................................................
42
B. Populasi dan Sampel ..................................................................
43
C. Instrumen Penelitian ...................................................................
44
1. Tes Kemampuan Pemahaman dan Komunikasi Matematika
44
a. Analisis Validitas Butir Soal ..............................................
48
b. Analisis Realibilitas ..........................................................
49
c. Analisis Daya Pembeda .....................................................
50
d. Analisis Tingkat Kesukaran ...............................................
52
e. Rekapitulasi Analisis Hasil Uji Coba .................................
54
2. Angket Skala Sikap ................................................................
55
3. Angket Perkembangan Karakter Siswa .................................
56
4. Lembar Observasi .................................................................
57
D. Bahan Ajar ..................................................................................
58
E. Teknik Analisis Data ..................................................................
59
1. ....................................................................................... Data
Hasil Tes Kemampuan Pemahaman dan Komunikasi
vi
Matematik ..........................................................................
59
2. ....................................................................................... Data
Hasil Angket Sikap dan Angket Karakter.............................
62
F. Prosedur Penelitian ...................................................................
65
BAB IV HASIL PENELITIAN DAN PEMBAHASAN
A. Hasil Penelitian Kemampuan Pemahaman Matematik .............
67
1. ....................................................................................... Desk
ripsi Statistik Data Hasil Tes Kemampuan Pemahaman Matematik ....................................................................
67
2. ....................................................................................... Data
Hasil Tes Kemampuan Pemahaman Matematik ..................
68
a. ................................................................................. Tes
Awal (Pretes) .................................................................
70
b. ................................................................................. Tes
Akhir (Postes) .................................................................
73
B. Hasil Penelitian Kemampuan Komunikasi Matematik ..............
77
1. ....................................................................................... Desk
ripsi Statistik Data Hasil Tes Kemampuan Komunikasi Matematik ....................................................................
77
2. ....................................................................................... Data
Hasil Tes Kemampuan Komunikasi Matematik .................
78
a. ................................................................................. Tes
Awal (Pretes) .................................................................
vii
79
b. ................................................................................. Tes
Akhir (Postes) ................................................................
82
3. ....................................................................................... Anali
sis Angket ............................................................................
85
a. ................................................................................. Angk
et Skala Sikap ................................................................
85
b. ................................................................................. Angk
et Perkembangan Karakter Siswa ..................................
89
C. Pembahasan ...............................................................................
91
1. ....................................................................................... Kem
ampuan Pemahaman dan Komunikasi Matematik
Siswa ....................................................................................
91
2. Sikap Siswa terhadap Pembelajaran Generatif.....................
98
3. Perkembangan Karakter Siswa..............................................
100
4. Hasil Observasi ...................................................................
101
BAB V KESIMPULAN DAN SARAN
A. Kesimpulan.................................................................................
103
B. Saran ..........................................................................................
104
DAFTAR PUSTAKA ......................................................................................
106
LAMPIRAN-LAMPIRAN:
A. Instrumen Penelitian ...................................................................
B. Analisis
Hasil
Uji
Coba
Tes
Kemampuan
Pemahaman dan Komunikasi Matematik ...................................
viii
110
179
C. Analisis Data Hasil Penelitian ....................................................
191
D. Skala Sikap dan Perkembangan Karakter...................................
207
E. Dokumentasi Penelitian .............................................................
213
RIWAYAT HIDUP ..........................................................................................
234
DAFTAR TABEL
Tabel 3.1 Penskoran untuk Perangkat Tes Kemampuan Pemahaman
Matematik .....................................................................................
46
Tabel 3.2 Penskoran untuk Perangkat Tes Kemampuan Komunikasi
Matematik .....................................................................................
47
Tabel 3.3 Interpretasi Koefisien Validitas ....................................................
48
Tabel 3.4 Rekapitulasi Uji Validitas Tes Pemahaman Matematik ...............
48
Tabel 3.5 Rekapitulasi Uji Validitas Tes Komunikasi Matematik ...............
49
Tabel 3.6 Klasifikasi Tingkat Reliabilitas ....................................................
50
Tabel 3.7 Klasifikasi Daya Pembeda ...........................................................
51
ix
Tabel 3.8 Daya Pembeda Tes Pemahaman Matematik ................................
51
Tabel 3.9 Daya Pembeda Tes Komunikasi Matematik ................................
51
Tabel 3.10 Kriteria Tingkat Kesukaran ..........................................................
52
Tabel 3.11 Tingkat Kesukaran Butir Soal Pemahaman Matematik ...............
53
Tabel 3.12 Tingkat Kesukaran Butir Soal Komunikasi Matematik ...............
53
Tabel 3.13 Rekapitulasi Analisis Hasil Uji Coba Soal Tes Pemahaman
Matematik .....................................................................................
54
Tabel 3.14 Rekapitulasi Analisis Hasil Uji Coba Soal Tes Komunikasi
Matematik .....................................................................................
54
Tabel 3.15 Kriteria Skor Gain Ternormalisasi ................................................
60
Tabel 3.16 Aturan Pemberian Skor Item Skala Sikap.....................................
63
Tabel 4.1 Rekapitulasi Hasil Pretes dan Postes Kemampuan Pemahaman
Matematik Siswa ..........................................................................
68
Tabel 4.2 Rata-rata Pretes dan Postes Kemampuan Pemahaman
Matematik Siswa ..........................................................................
68
Tabel 4.3 Hasil Uji Normalitas Skor Pretes Kemampuan Pemahaman
Matematik Siswa ..........................................................................
70
Tabel 4.4 Hasil Uji Homogenitas Varians Skor Pretes Kemampuan
Pemahaman Matematik Siswa .....................................................
71
Tabel 4.5 Hasil Uji Kesamaan Rata-rata Pretes Kemampuan Pemahaman
Matematik Siswa ..........................................................................
73
Tabel 4.6 Hasil Uji Normalitas Skor Postes Kemampuan Pemahaman
Matematik Siswa ..........................................................................
74
Tabel 4.7 Hasil Uji Homogenitas Varians Skor Postes Kemampuan
Pemahaman Matematik Siswa .....................................................
75
Tabel 4.8 Hasil Uji Perbedaan Rata-rata Postes Kemampuan
Pemahaman Matematik Siswa .....................................................
76
Tabel 4.9 Rekapitulasi Hasil Pretes dan Postes Kemampuan Komunikasi
Matematik Siswa ..........................................................................
77
Tabel 4.10 Rata-rata Pretes dan Postes Kemampuan Komunikasi
Matematik Siswa ..........................................................................
Tabel 4.11 Hasil Uji Normalitas Skor Pretes Kemampuan
x
78
Komunikasi Matematik Siswa .....................................................
80
Tabel 4.12 Hasil Uji Homogenitas Varians Skor Pretes Kemampuan
Komunikasi Matematik Siswa .....................................................
80
Tabel 4.13 Hasil Uji Kesamaan Rata-rata Pretes Kemampuan Komunikasi
Matematik Siswa ..........................................................................
82
Tabel 4.14 Hasil Uji Normalitas Skor Postes Kemampuan Komunikasi
Matematik Siswa ..........................................................................
83
Tabel 4.15 Hasil Uji Homogenitas Varians Skor Postes Kemampuan
Komunikasi Matematik Siswa ......................................................
83
Tabel 4.16 Hasil Uji Perbedaan Rata-rata Postes Kemampuan
Komunikasi Matematik Siswa .....................................................
85
Tabel 4.17 Distribusi Skor Sikap Siswa terhadap Pelajaran Matematika .......
86
Tabel 4.18 Distribusi Skor Sikap Siswa terhadap Model Pembelajaran
Generatif .......................................................................................
87
Tabel 4.19 Distribusi Skor Sikap Siswa terhadap Soal-soal Pemahaman
dan Komunikasi Matematik .........................................................
88
Tabel 4.20 Distribusi Perkembangan Karakter Rasa Ingin Tahu Siswa ........
89
Tabel 4.21 Distribusi Perkembangan Karakter Kejujuran Siswa ...................
90
Tabel 4.22 Distribusi Perkembangan Karakter Kedisiplinan Siswa ..............
91
xi
DAFTAR GAMBAR
Gambar 3.1
Diagram Alur Penelitian...........................................................
Gambar 4.1
Diagram Batang Perbandingan Rataan Pretes dan Postes
Kemampuan Pemahaman Matematis Siswa.............................
Gambar 4.2
69
Diagram Batang Perbandingan Rataan Pretes dan Postes
Kemampuan Komunikasi Matematis Siswa.............................
Gambar 4.3
66
78
Sebagian Pekerjaan Siswa dalam Menyelesaikan Tes Kemampuan Komunikasi Matematik ...................................................
96
Gambar 4.4 Sebagian Pekerjaan Siswa dalam Menentukan Solusi .............
98
xii
DAFTAR LAMPIRAN
LAMPIRAN A: INSTRUMEN PENELITIAN ......................................
110
A.1 Bahan Ajar ...............................................................................
111
A.2 Silabus dan RPP .......................................................................
148
A.3 Kisi-kisi Soal dan Tes Kemampuan Pemahaman dan
Komunikasi Matemati ...............................................................
158
A.4 Jawaban Tes Matematika .........................................................
161
A.5 Kisi-kisi Angket Skala Sikap Siswa.........................................
170
A.6 Kisi-kisi Angket Perkembangan Karakter ...............................
174
A.7 PedomanObservasi ...................................................................
177
LAMPIRAN B: ANALISIS HASIL UJI COBA TES MATEMATIKA
179
B.1 Skor Uji Coba Tes Pemahaman Matematik .............................
180
B.2 Skor Uji Coba Tes Komunikasi Matematik .............................
181
B.3 Perhitungan Hasil Uji Coba Tes Matematika dengan
Anates 4.0 .................................................................................
182
LAMPIRAN C: ANALISIS DATA HASIL PENELITIAN...................
191
C.1 Data Hasil Pretes ......................................................................
192
C.2 Data Hasil Postes ......................................................................
196
C.3 Analisis Data Hasil Tes Kemampuan Pemahaman Matematik
200
C.4 Analisis Data Hasil Tes Kemampuan Komunikasi Matematik
203
LAMPIRAN D: ANALISIS DATA SKALA SIKAP DAN
OBSERVASI ................................................................
207
D.1 Data Skala Sikap Kelas Eksperimen ........................................
208
D.2 Penyekoran Skala Sikap ...........................................................
209
D.3 Data Angket Karakter ..............................................................
210
D.4 Hasil Observasi Pelaksanaan Pembelajaran .............................
211
LAMPIRAN E: DOKUMENTASI PENELITIAN ................................
213
E.1 Foto-foto pada Saat Pembelajaran ............................................
214
E.2 Sebagian Hasil Kerja dan Respon Siswa ..................................
216
E.3 Surat Keterangan dan Ijin Penelitian ........................................
233
xiii