DAFTAR ISI
LEMBAR PERNYATAAN .............................................................................. i ABSTRAK ........................................................................................................ ii KATA PENGANTAR ....................................................................................... iii UCAPAN TERIMA KASIH ............................................................................ iv DAFTAR ISI ..................................................................................................... vi DAFTAR TABEL ............................................................................................. viii DAFTARGAMBAR .......................................................................................... x DAFTAR LAMPIRAN ..................................................................................... xi BAB I PENDAHULUAN .................................................................................. 1 A. Latar Belakang ........................................................................................ 1 B. Rumusan dan Batasan Masalah ............................................................... 6 C. Tujuan Penelitian .................................................................................... 7 D. Manfaat Penelitian .................................................................................. 8 E. Struktur Organisasi Skripsi ..................................................................... 9 BAB II STUDI LITERATUR ......................................................................... 11 A. Hakikat Pembelajaran Matematika di SD .............................................. 11 1. Pengertian Matematika...................................................................... 11 2. Tujuan Pembelajaran Matematika di SD .......................................... 12 3. Karakteristik Pembelajaran Matematika di SD ................................. 13 4. Ruang Lingkup Pembelajaran Matematika di Sekolah Dasar ........... 14 5. Perbandingan dan Skala .................................................................... 16 6. Skala .................................................................................................. 17 B. Teori Belajar-Mengajar Matematika ...................................................... 18 1. Teori Bruner ..................................................................................... 18 2. Teori Dienes ...................................................................................... 19 3. Teori David Ausubel ......................................................................... 20 4. Teory Vygotsky................................................................................. 20 5. Teori Thorndike ................................................................................ 21 C. Pendekatan Realistic Mathematics Education (RME) ............................ 22 1. Sejarah Pendekatan RME .................................................................. 22 2. Pengertian Pendekatan RME ............................................................. 23 3. Prinsip-prinsip Pendekatan RME ...................................................... 24 4. Karakteristik Pendekatan RME ......................................................... 25 5. Langkah-langkah Pembelajaran dengan Menggunakan Pendekatan RME .................................................................................................. 27 6. Kelebihan dan Kekurangan RME ..................................................... 28
vi
D. E. F. G. H.
Representasi Matematis ......................................................................... Koneksi Matematis ................................................................................. Hasil Penelitian yang Relevan................................................................. Kerangka Berpikir ................................................................................... Hipotesis ..................................................................................................
29 31 32 33 35
BAB III METODE PENELITIAN .................................................................. 36 A. Metode dan Desain Penelitian................................................................. 1. MetodePenelitian............................................................................... 2. Desain Penelitian ............................................................................... B. Populasi dan Sampel Penelitian .............................................................. 1. Populasi ............................................................................................. 2. Sampel Penelitian .............................................................................. C. Lokasi dan Waktu Penelitian .................................................................. D. Variabel dalam Penelitian ....................................................................... E. Definisi Operasional................................................................................ F. Instrumen Penelitian................................................................................ 1. Tes Kemampuan Koneksi dan Representasi ..................................... a. Validitas Butir Soal ..................................................................... b. Reliabilitas Butir Soal ................................................................. c. Indeks Kesukaran ........................................................................ d. Daya embeda ............................................................................... 2. Observasi ........................................................................................... 3. Wawancara ........................................................................................ 4. Catatan Langan.................................................................................. G. Prosedur Penelitian.................................................................................. 1. Tahappersiapan ................................................................................. 2. Tahappelaksanaan ............................................................................. 3. Tahappengelolaan Data ..................................................................... H. Teknik Pengolahan dan Analisis Data .................................................... 1. Data Kuantitatif ................................................................................. 2. Data Kualitatif ...................................................................................
36 36 36 37 37 38 38 38 39 40 40 41 44 45 46 48 49 50 50 50 50 51 51 51 55
BAB IV HASIL PENELITIAN DAN PEMBAHASAN ................................. 57 A. Hasil Penelitian ....................................................................................... 57 1. Data Kuantitatif ................................................................................. 57 2. Data Kualitatif ................................................................................... 101 B. Pembahasan ............................................................................................ 111 BAB V SIMPULAN DAN SARAN .................................................................. 121 DAFTAR PUSTAKA ........................................................................................ 126 LAMPIRAN ....................................................................................................... 128
vii
DAFTAR TABEL Tabel Halaman 2.1 Standar Kompetensi dan Kompetensi Dasar Mata Pelajaran Matematika Kelas V Semester 2 ................................................................ 15 2.2 Indikator Kemampuan Representasi Matematis ........................................ 30 3.1 Klasifikasi Koefisien Validitas .................................................................. 39 3.2 Validitas Instrumen tes............................................................................... 40 3.3 Validitas Butir Soal .................................................................................... 41 3.4 Klasifikasi Koefisien Reliabilitas............................................................... 42 3.5 Reliabilitas ................................................................................................. 42 3.6 Klasifikasi Indeks Kesukaran ..................................................................... 43 3.7 Indeks Kesukaran ....................................................................................... 43 3.8 Kriteria Daya Pembeda .............................................................................. 44 3.9 Daya Pembeda Instrumen tes ..................................................................... 44 3.10 Kriteria Gain Normal ................................................................................. 51 4.1 Data Nilai Awal dan Nilai Akhir Kemampuan Koneksi Matematis Kelas Kontrol ............................................................................................. 58 4.2 Uji Normalitas Data Pretes dan Postes Kelas Kemampuan Koneksi Matematis Kelas Kontrol ........................................................................... 59 4.3 Hasil Uji Beda Rata-rata Data Pretes dan Postes Kelas Kemampuan Koneksi Matematis Kelas Kontrol ............................................................. 61 4.4 Hasil Perhitungan Koefisien Korelasi ........................................................ 62 4.5 Data Nilai Awal dan Nilai Akhir Kemampuan Koneksi Matematis Kelas Eksperimen....................................................................................... 64 4.6 Uji Normalitas Data Pretes dan Postes Kelas Kemampuan Koneksi Matematis Kelas Eksperimen ..................................................................... 65 4.7 Hasil Uji Wilcoxon Nilai Awal dan Nilai Akhir Kemampuan Koneksi Matematis Kelas Eksperimen ..................................................................... 67 4.8 Hasil Perhitungan Koefisien Korelasi ........................................................ 68 4.9 Data Nilai Awal dan Nilai Akhir Kemampuan Representasi Matematis Kelas Kontrol ............................................................................................. 69 4.10 Uji Normalitas Data Pretes dan Postes Kelas Kemampuan Representasi Matematis Kelas Kontrol ...................................................... 71 4.11 Hasil Uji Wilcoxon Nilai Awal dan Nilai Akhir Kemampuan Representasi Matematis Kelas Kontrol ..................................................... 73 4.12 Hasil Perhitungan Koefisien Korelasi ........................................................ 74 4.13 Data Nilai Awal dan Nilai Akhir Kemampuan Representasi Matematis Kelas Eksperimen....................................................................................... 75 4.14 Uji Normalitas Data Pretes dan Postes Kelas Kemampuan Representasi Matematis Kelas Eksperimen ............................................... 76
viii
ix
4.15 Hasil Uji Beda Rata-rata Data Pretes dan Postes Kelas Kemampuan Koneksi Matematis Kelas Eksperimen ..................................................... 78 4.16 Hasil Perhitungan Koefisien Korelasi ........................................................ 79 4.17 Data Nilai Awal.......................................................................................... 81 4.18 Rekapitulasi Statistik Deskriptif Data Hasil Nilai Awal ............................ 82 4.19 Uji Normalitas Nilai Awal Kemampuan Koneksi Matematis.................... 83 4.20 Uji Homogenitas Nilai Awal Kelas Eksperimen dan Kelas Kontrol ......... 84 4.21 Uji Beda rata-rata Nilai Awal Kemampuan Koneksi Matematis ............... 85 4.22 Data Nilai Akhir Kelas Eksperimen dan Kelas Kontrol ............................ 85 4.23 Rekapitulasi Statistik Deskriptif Data Hasil Nilai Akhir ........................... 87 4.24 Uji Normalitas Data Nilai Akhir ................................................................ 88 4.25 Uji Beda rata-rata Nilai Akhir Kemampuan Koneksi Matematis .............. 89 4.26 Data Nilai Awal.......................................................................................... 90 4.27 Rekapitulasi Statistik Deskriptif Data Hasil Nilai Awal ............................ 91 4.28 Uji Normalitas Data Nilai Awal ................................................................. 92 4.29 Uji Beda rata-rata Nilai Awal Kemampuan Representasi Matematis ........ 93 4.30 Data Nilai Akhir ......................................................................................... 94 4.31 Rekapitulasi Statistik Deskriptif Data Hasil Nilai Akhir ........................... 95 4.32 Uji Normalitas Data Nilai Akhir ................................................................ 96 4.33 Uji Homogenitas Nilai Akhir Kelas Eksperimen dan Kelas Kontrol ........ 97 4.34 Uji Beda rata-rata Nilai Awal Kemampuan Representasi Matematis ........ 98 4.35 Data Nilai Gain .......................................................................................... 98 4.36 Uji Normalitas Data Gain........................................................................... 100 4.37 Data UjiHomogenitasGain ......................................................................... 100 4.38 Uji Beda Rata-rata Data Gain .................................................................... 101 4.39 Rekapitulasi Hasil Observasi Kinerja Guru ............................................... 106 4.40 Rekapitulasi Hasil Observasi Aktivitas Siswa ........................................... 107 4.41 Hasil Wawancara ....................................................................................... 110
x
DAFTAR GAMBAR Gambar 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8
Halaman
Histogram Pretes Kemampuan Koneksi Matematis Kelas Kontrol ........... Histogram Postes Kemampuan Koneksi Matematis Kelas Kontrol .......... Histogram Pretes Kemampuan Koneksi Matematis KelasEksperimen ..... Histogram Postes Kemampuan Koneksi Matematis Kelas Eksperimen .... Histogram Pretes Kemampuan Representasi Matematis Kelas Kontrol .... Histogram Postes Kemampuan Representasi Matematis Kelas Kontrol ... Histogram Pretes Kemampuan Representasi Matematis Kelas Eksperimen................................................................................................. Histogram Pretes Kemampuan Representasi Matematis Kelas Kontrol ....
60 60 66 66 71 72 77 77
xi
DAFTAR LAMPIRAN Lampiran A Persiapan Pembelajaran ......................................................... A.1 RPP Kelas Kontrol ........................................................................... 128 A.2 RPP Kelas Eksperimen..................................................................... 142 A.3LKS ................................................................................................... 155 Lampiran B TES ............................................................................................ B.1Kisi-Kisi Soal Pretest Dan Postest .................................................... B.2 Format Instrumen ............................................................................ B.3Kunci Jawaban Dan Pedoman Penskoran .........................................
168 168 169 171
Lampiran C NONTES ................................................................................... 173 C.1 Lembar Observasi Kinerja Guru ...................................................... 173 C.2 Pedoman Observasi Kinerja Guru Di Kelas Eksperimen ................. 176 C.3 Lembar Observasi Kinerja Guru ...................................................... 181 C.4 Pedoman Observasi Kinerja Guru Di Kelas Kontrol ....................... 183 C.5 Lembar Observasi Aktivitas Siswa ................................................. 186 C.6 Kisi-Kisi Pedoman Observasi Aktivitas Siswa ................................ 187 C.7 Lembar Observasi Aktivitas Siswa .................................................. 189 C.8 Kisi-Kisi Pedoman Observasi Aktivitas Siswa ................................ 190 C.9 Format Catatan Lapangan................................................................. 192 C.10 Pedoman Wawancara ..................................................................... 193 C.11 Pertanyaan Wawancara ........................................................................ 194 Lampiran D Hasil Uji Coba Instrumen ....................................................... D.1 Hasil Ujicoba Instrumen Tes ............................................................ D.2Validitasdan Reliabilitas Soal ........................................................... D.3Indeks Kesukaran .............................................................................. D.4Daya Pembeda ...................................................................................
195 195 197 203 204
Lampiran E ..................................................................................................... 205 E.1 Lampiran Data PretesKemampuanKoneksiMatematisKelompokSampel ................. 205 E.2 NilaiPostesKemampuanKoneksiMatematis ...................................... 207 E.3 AnalisisPerbandinganNilaiKemampuanKoneksiMatematis ............. 209 E.4 Data PretesKemampuanRepresentasiMatematis ............................... 210 E.5 Data PostesKemampuanRepresentasiMatematis .............................. 212 E.6 Analisis Data PerbandinganKemampuanRepresentasiMatematis .... 214 E.7 Analisis Data Gain ............................................................................ 215 E.8 Lampiran Data HasilObservasi ......................................................... 246 E.9 DokumentasiKegiatanPenelitian ............................................................ 285 Lampiran F ..................................................................................................... 288 F.1 Surat Keputusan (SK) Bimbingan Skripsi ........................................ 288
xii
F.2 Surat Izin Penelitian ......................................................................... 289 F.3 Surat Keterangan Telah Melaksanakan Penelitian dari SD .............. 292 F.4 Daftar Monitoring ............................................................................. 294
