perjalanan itu memang penuh tanttangan.
dari dunia luar ataupun dari dunia dalam.
kekuasaan yang memegang puncaknya.
kroco seperti kita bukanlah apa apa dmatanya
seperti panasnya kicuan burung diantara riuhnya buih laut.
menggema tak didengar.
menepi tak ditarik.
jika kita punya tulang yang besar barulah ada mata memandang.
jika tulang kita kecil hanya bisa di injak injak.
peradaban takkan pernah berubah jika manusianya seperti peubah yang variabelnya acak dan tak terdefinisi.
lebih baik tak hingga dari pada tak terhinggakan.

Skripsi Berpikir Kreatif

“MENINGKATKAN KEMAMPUAN BERPIKIR KREATIF SISWA
DALAM BELAJAR MATEMATIKA DENGAN MENGGUNAKAN
PENDEKATAN PEMECAHAN MASALAH (PROBLEM SOLVING)
PADA SISWA KELAS VIID SMP N 2 DEPOK”
Oleh:
Agung Wahyudi

ABSTRAK
Penelitian ini dilaksanakan dengan tujuan untuk mendeskripsikan
pelaksanaan pembelajaran matematika dengan menggunakan pendekatan
pemecahan masalah (problem solving) untuk meningkatkan kemampuan berpikir
kreatif siswa dalam belajar matematika pada siswa kelas VIID SMP N 2 Depok.
Penelitian ini merupakan Penelitian Tindakan Kelas (PTK) yang dilakukan
secara kolaboratif antara guru mata pelajaran matematika kelas VIID SMP N 2
Depok dengan peneliti. Tindakan dilaksanakan dalam 2 siklus dengan setiap
siklus terdiri dari 3 kali pertemuan. Instrumen penelitian terdiri dari lembar
observasi, angket, wawancara, catatan lapangan dan tes akhir siklus. Aspek
kemampuan berpikir kreatif yang diamati yaitu aspek kognitif dan afektif. Aspek
kognitif digunakan untuk pedoman tes akhir siklus sedangkan aspek afektif
digunakan untuk pedoman lembar observasi siswa. Untuk angket menggunakan
pedoman dari aspek kognitif dan afektif dari berpikir kreatif.
Hasil penelitian menunjukkan bahwa pembelajaran matematika dengan
pendekatan pemecahan masalah dapat meningkatkan kemampuan berpikir kreatif
siswa. Pelaksanaan pembelajaran dengan pendekatan pemecahan masalah melalui
beberapa tahap yaitu (1) Guru menyampaikan tujuan, motivasi dan apersepsi, (2)
guru membentuk siswa menjadi 8 kelompok, (3) Guru memberikan masalah
dalam bentuk LKS yang dapat diselesaikan dengan beberapa cara tetapi satu
jawaban, (4) Siswa berdiskusi dalam menyelesaikan masalah di LKS, (5)
beberapa siswa mengerjakan hasil diskusinya di depan kelas, (6) guru bersamasama
dengan siswa menyimpulkan hasil diskusi. Setelah dilaksanakan
pembelajaran dengan pendekatan pemecahan masalah kemampuan berpikir kreatif
siswa meningkat. Hal ini ditunjukan dengan (1) Peningkatan hasil lembar
observasi berpikir kreatif siswa dari 39,62% pada siklus I meningkat menjadi
63,66% pada siklus II, (2) Peningkatan hasil tes berpikir kreatif siswa dari 60,83%
pada siklus I meningkat menjadi 76,39% pada siklus II, (3) Hasil angket berpikir
kreatif siswa termasuk dalam kategori tinggi yaitu sebesar 71.68%.

RPP MATRIKS

Rencana Pelaksanaan Pembelajaran
(RPP)

Mata Pelajaran : Matematika
Kelas / Semester : X Broadcasting / 2
Pertemuan ke : 1
Alokasi Waktu : 45 x 2 Menit
Standar Kompetensi : 4 Memecahkan masalah berkaitan dengan konsep matriks
Kompetensi Dasar : 4. 1 Mendiskripsikan macam-macam matriks
Indikator
Matrik ditentukan unsur dan notasinya.
Matrik dibedakan menurut jenis dan relasinya.
Membedakan baris, kolom, elemen, dan ordo matrik.

Tujuan Pembelajaran
Siswa dapat menentukan unsur dan notasinya
Siswa dapat menyebutkan beberapa contoh dari masing-masing jenis matriks.
Siswa dapat membedakan baris, kolom elemen dan ordo matrik.
Materi Pembelajaran
Matriks adalah susunan beberapa bilangan atau huruf dalam bentuk persegi panjang, yang diatur menurut baris dan kolom serta dituliskan diantara tanda kurung dan setiap bilangan atau huruf tersebut dinamakan elemen matriks.

Contoh matriks:
A_(m×n)=[■(a_11&a_12&a_13@a_21&…..&…..@a_31&…..&…..)]

Jenis jenis matriks:
Matriks Baris
Adalah matriks yang hanya terdiri dari satu baris. Secara umum matriks baris berordo 1 x n.
Contoh : P_(1×2)=(3 2)
Matriks Kolom
Adalah matriks yang hanya terdiri dari satu kolom. Secara umum matriks kolom berordo m x 1.
Contoh :
X_(3×1)=[■(2@4@1)]

Matriks Nol
Adalah suatu matriks yang semua elemennya adalah nol. Matrik nol dilambangkan dengan O.
O = [■(0&0@0&0)]
Matriks Persegi
Adalah matriks yang banyaknya baris dan kolomnya sama. Secara umum matriks persegi berordo n×n.
R = [■(2&3@3&4)]
Matriks Diagonal
Adalah matriks persegi dimana elemen-elemen pada diagonal utamanya minimal terdapat sebuah elemen yang bukan 0. Sedangkan elemen diluar diagonal utamanya adalah 0.
A = [■(0&0&0@0&4&0@0&0&1)]
Matriks Identitas
Adalah matriks diagonal dimana semua elemen pada diagonal utamanya adalah 1.
Matriks P = [■(1&0&0@0&1&0@0&0&1)], Q = [■(1&0@0&1)]
Matriks segitiga atas
Adalah matriks diagonal dimana elemen-elemen yang berada diatas diagoanal utama minimal ada satu yang bukan 0, sedangkan semua elemen di bawah diagonal utama adalah 0.
Matriks K = [■(2&7@0&1)], L = [■(1&0&0@0&0&-6@0&0&1)]
Matriks segitiga bawah
Matriks diagonal dimana elemen-elemen yang berada di bawah diagonal utama minimal ada sebuah elemen yang bukan nol.
Matriks Transpose
Transpose dari suatu matriks A ditulis A^Tadalah suatu matriks yang diperoleh dengan cara mengubah setiap baris dari matriks A menjadi kolom pada matriks A^T.
Langkah-Langlah Pembelajaran
Kegiatan Awal
Guru membuka pelajaran dengan salam dan dilanjutkan dengan berdoa. Guru mengabsen siswa dengan menanyakan kepada siswa siapa pada hari ini yang tidak masuk. Setelah itu guru menjelaskan tujuan dari pembelajaran dan memberikan motivasi bahwa pembelajaran matematika sangat bermamfaat bagi kehidupan nyata. Kemudian guru memberikan apersepsi mengenai materi yang akan diberikan yaitu invers dan determinan matriks.

Kegiatan Inti
Eksplorasi
Guru mengulas kembali mengenai operasi pada matriks
Guru membentuk siswa menjadi 4 kelompok dengan 2 kelompok beranggotakan 4 orang siswa dan 2 kelompok yang lain beranggotakan 3 orang siswa.
Guru membagikan permasalahan kepada siswa dalam bentuk LKS dengan masing-masing kelompok berbeda.
Guru mengawasi jalannya diskusi dengan berjalan mengelilingi siswa dan apabila ada yang bertanya mengenai permasalahan dalam LKS guru bersedia membantu.
Elaborasi
Guru menghentikan jalannya diskusi
Guru memberi kesempatan kepada siswa untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Setelah satu orang selesai mengerjakan ke depan kelas guru mennyuruh anak yang maju untuk menunjuk salah satu teman yang lain untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Guru bersama-sama dengan siswa membahas permasalahan yang telah dikerjakan siswa di papan tulis.
Guru memberikan umpan balik untuk mengambil kata sepakat bahwa jawaban itu benar atau tidak.
Konfirmasi
Guru memberikan kesempatan kepada siswa untuk mencatat jawaban yang ada di papan tulis.
Guru bersama-sama dengan siswa menarik kesimpulan tentang pembelajaran pada pertemuaan kali ini.
Penuntup
Guru menuliskan 5 soal mengenai permasalah yang berupa invers matriks dan determinan matriks untuk dikerjakan siswa di rumah atau di kost.
Guru menutup pelajaran dengan berdoa dan salam.
Metode Pembelajaran
Metode pembelajaran yang digunakan adalah pendekatan pemecahan masalah (problem solving)
Alat dan Bahan
Buku paket dan LKS
Penilaian
Observasi dan diskusi

Banyumas, 29 April 2011
Guru Mata Pelajaran Mahasiswa


Nursamsiyah, S.Pd Agung Wahyudi
NIP.19740621 200604 2 004 NIM. 06301244005
Rencana Pelaksanaan Pembelajaran
(RPP)

Mata Pelajaran : Matematika
Kelas / Semester : X Broadcasting / 2
Pertemuan ke : 2
Alokasi Waktu : 45 x 2 Menit
Standar Kompetensi : 4 Memecahkan masalah berkaitan dengan konsep matriks
Kompetensi Dasar : 4. 1 Mendiskripsikan macam-macam matriks
Indikator
Matrik ditentukan unsur dan notasinya
Matrik dibedakan menurut jenis dan relasinya.
Tujuan Pembelajaran
Siswa dapat menjelaskan kesamaan matrik.
Siswa dapat menjelaskan transpose matrik.
Materi Pembelajaran
Kesamaan Matriks dan Tranpose Matriks
Kesamaan Matriks
Dua matriks A dan B dikatakan sama (A=B), jika dan hanya jika ordo kedua matriks sama dan elemen-elemennya yang bersesuaian (seletak) juga sama.
Tranpose Matriks
Transpose dari suatu matriks A ditulis A^Tadalah suatu matriks yang diperoleh dengan cara mengubah setiap baris dari matriks A menjadi kolom pada matriks A^T.
A =[■(a&b@c&d)], maka A^t=[■(a&c@b&d)]
Langkah-Langlah Pembelajaran
Kegiatan Awal
Salam pembuka
Guru mengabsen kehadiran siswa.
Guru memberikan motivasi belajar siswa.
Guru memberikan apersepsi yaitu mengingat kembali materi mengenai pengertian, notasi, ordo dan macam-macam matrik
Kegiatan Inti
Eksplorasi
Guru mengulas kembali mengenai operasi pada matriks
Guru membentuk siswa menjadi berkelompok
Guru membagikan permasalahan kepada siswa dalam bentuk LKS dengan masing-masing kelompok berbeda.
Guru mengawasi jalannya diskusi dengan berjalan mengelilingi siswa dan apabila ada yang bertanya mengenai permasalahan dalam LKS guru bersedia membantu.
Elaborasi
Guru menghentikan jalannya diskusi
Guru memberi kesempatan kepada siswa untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Setelah satu orang selesai mengerjakan ke depan kelas guru mennyuruh anak yang maju untuk menunjuk salah satu teman yang lain untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Guru bersama-sama dengan siswa membahas permasalahan yang telah dikerjakan siswa di papan tulis.
Guru memberikan umpan balik untuk mengambil kata sepakat bahwa jawaban itu benar atau tidak.
Konfirmasi
Guru memberikan kesempatan kepada siswa untuk mencatat jawaban yang ada di papan tulis.
Guru bersama-sama dengan siswa menarik kesimpulan tentang pembelajaran pada pertemuaan kali ini.

Penuntup
Guru menuliskan 5 soal mengenai permasalah yang berupa invers matriks dan determinan matriks untuk dikerjakan siswa di rumah atau di kost.
Guru menutup pelajaran dengan berdoa dan salam.

Metode Pembelajaran
Metode pembelajaran yang digunakan adalah pendekatan pemecahan masalah (problem solving)

Alat dan Bahan
Buku paket dan LKS

Penilaian
Observasi dan diskusi
Banyumas, 3 Mei 2011
Guru Mata Pelajaran Mahasiswa



Nursamsiyah, S.Pd Agung Wahyudi
NIP.19740621 200604 2 004 NIM. 06301244005








































Rencana Pelaksanaan Pembelajaran
(RPP)

Mata Pelajaran : Matematika
Kelas / Semester : X Broadcasting / 2
Pertemuan ke : 3
Alokasi Waktu : 45 x 2 Menit
Standar Kompetensi : 3. Memecahkan masalah berkaitan dengan konsep matriks
Kompetensi Dasar : 3. 2 Menyelesaikan operasi matriks.
Indikator
Melakukan operasi penjumlahan pada matriks.
Melakukan operasi pengurangan pada matriks.

Tujuan Pembelajaran
Siswa dapat melakukan operasi penjumlahan pada matriks.
Siswa dapat melakukan operasi pengurangan pada matriks.

Materi Pembelajaran
Operasi penjumlahan dan pengurangan pada matriks
Penjumlahan matriks
Dua matriks dapat dijumlahkan jika kedua matriks tersebut memiliki ordo yang sama. Penjumlahan matriks dilakukan dengan menjumlahkan elemen-elemen yang seletak dari masing-masing matriks tersebut.
Contoh :
Jika matriks A = [■(a&b@c&d)] dan B = [■(a&b@c&d)],
maka penjumlahan matriks A + B = [■(a+a&b+b@c+c&d+d)]
Pengurangan matriks
Dua matriks dapat dikurangkan jika kedua matriks tersebut memiliki ordo yang sama. Pengurangan matriks dilakukan dengan mengurangkan elemen-elemen yang seletak dari masing-masing matriks tersebut.
Jika matriks A = [■(a&b@c&d)] dan B = [■(e&f@g&g)],
maka penjumlahan matriks A - B = [■(a-e&b-f@c-g&d-g)]
Langkah-Langlah Pembelajaran
Kegiatan Awal
Guru membuka pelajaran dengan salam dan dilanjutkan dengan berdoa. Guru mengabsen siswa dengan menanyakan kepada siswa siapa pada hari ini yang tidak masuk. Setelah itu guru menjelaskan tujuan dari pembelajaran dan memberikan motivasi bahwa pembelajaran matematika sangat bermamfaat bagi kehidupan nyata. Kemudian guru memberikan apersepsi mengenai materi yang akan deiberikan yaitu invers dan determinan matriks.
Kegiatan Inti
Eksplorasi
Guru mengulas kembali mengenai jenis-jenis matriks
Guru membentuk siswa menjadi 4 kelompok dengan 2 kelompok beranggotakan 4 orang siswa dan 2 kelompok yang lain beranggotakan 3 orang siswa.
Guru membagikan permasalahan kepada siswa dalam bentuk LKS dengan masing-masing kelompok berbeda.
Guru mengawasi jalannya diskusi dengan berjalan mengelilingi siswa dan apabila ada yang bertanya mengenai permasalahan dalam LKS guru bersedia membantu.
Elaborasi
Guru menghentikan jalannya diskusi
Guru memberi kesempatan kepada siswa untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Setelah satu orang selesai mengerjakan ke depan kelas guru mennyuruh anak yang maju untuk menunjuk salah satu teman yang lain untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Guru bersama-sama dengan siswa membahas permasalahan yang telah dikerjakan siswa di papan tulis.
Guru memberikan umpan balik untuk mengambil kata sepakat bahwa jawaban itu benar atau tidak.

Konfirmasi
Guru memberikan kesempatan kepada siswa untuk mencatat jawban yang ada di papan tulis.
Guru bersama-sama dengan siswa menarik kesimpulan tentang pembelajaran pada pertemuaan kali ini.
Penuntup
Guru menuliskan 5 soal mengenai permasalah yang berupa invers matriks dan determinan matriks untuk dikerjakan siswa di rumah atau di kost.
Guru menutup pelajaran dengan berdoa dan salam.
Metode Pembelajaran
Metode pembelajaran yang digunakan adalah pendekatan pemecahan masalah (problem solving)

Alat dan Bahan
Buku paket dan lembar latihan
Penilaian
Observasi dan diskusi
Banyumas, 7 Mei 2011
Guru Mata Pelajaran Mahasiswa


Nursamsiyah, S.Pd Agung Wahyudi
NIP.19740621 200604 2 004 NIM. 06301244005













Rencana Pelaksanaan Pembelajaran
(RPP)

Mata Pelajaran : Matematika
Kelas / Semester : X Broadcasting / 2
Pertemuan ke : 4
Alokasi Waktu : 45 x 2 Menit
Standar Kompetensi : 3. Memecahkan masalah berkaitan dengan konsep matriks
Kompetensi Dasar : 3. 2 Menyelesaikan operasi matriks.
Indikator
Melakukan operasi perkalian matriks dengan bilangan real
Melakukan operasi perkalian matriks dengan matriks.

Tujuan Pembelajaran
Siswa dapat melakukan operasi perkalian matriks dengan bilangan real
Siswa dapat melakukan operasi perkalian matriks dengan matriks.

Materi Pembelajaran
Operasi perkalian pada matriks
Perkalian matriks dengan bilangan real
Jika k adalah suatu bilangan real, dan A adalah suatu matriks maka k.A adalah matriks yang diperoleh dengan mengalikan setiap elemen matriks A dengan k, sehingga:
Jika matriks A = [■(a&b@c&d)], maka k.A = k.[■(a&b@c&d)]=[■(k.a&k.b@k.c&k.d)],
Perkalian matriks dengan matriks
Operasi yang dilakukan dengan mengalikan tiap elemen pada baris matriks sebelah kiri dengan kolom matriks sebelah kanan, lalu hasilnya dijumlahkan.
Jika matriks A = [■(a&b@c&d)] dan B = [■(p&q@r&s)], maka perkalian A dengan B dapat ditentukan persamaannya:
A.B = [■(a&b@c&d)][■(p&q@r&s)]=[■(ap+br&aq+bs@cp+dr&cq+ds)]
Langkah-Langlah Pembelajaran
Kegiatan Awal
Guru membuka pelajaran dengan salam dan dilanjutkan dengan berdoa. Guru mengabsen siswa dengan menanyakan kepada siswa siapa pada hari ini yang tidak masuk. Setelah itu guru menjelaskan tujuan dari pembelajaran dan memberikan motivasi bahwa pembelajaran matematika sangat bermamfaat bagi kehidupan nyata. Kemudian guru memberikan apersepsi mengenai materi yang akan deiberikan yaitu invers dan determinan matriks.
Kegiatan Inti
Eksplorasi
Guru mengulas kembali mengenai operasi penjumlahan dan pengurangan matriks.
Guru membentuk siswa menjadi 4 kelompok dengan 2 kelompok beranggotakan 4 orang siswa dan 2 kelompok yang lain beranggotakan 3 orang siswa.
Guru membagikan permasalahan kepada siswa dalam bentuk LKS dengan masing-masing kelompok berbeda.
Guru mengawasi jalannya diskusi dengan berjalan mengelilingi siswa dan apabila ada yang bertanya mengenai permasalahan dalam LKS guru bersedia membantu.
Elaborasi
Guru menghentikan jalannya diskusi
Guru memberi kesempatan kepada siswa untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Setelah satu orang selesai mengerjakan ke depan kelas guru mennyuruh anak yang maju untuk menunjuk salah satu teman yang lain untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Guru bersama-sama dengan siswa membahas permasalahan yang telah dikerjakan siswa di papan tulis.
Guru memberikan umpan balik untuk mengambil kata sepakat bahwa jawaban itu benar atau tidak.
Konfirmasi
Guru memberikan kesempatan kepada siswa untuk mencatat jawban yang ada di papan tulis.
Guru bersama-sama dengan siswa menarik kesimpulan tentang pembelajaran pada pertemuaan kali ini.
Penuntup
Guru menuliskan 5 soal mengenai permasalah yang berupa invers matriks dan determinan matriks untuk dikerjakan siswa di rumah atau di kost.
Guru menutup pelajaran dengan berdoa dan salam.
Metode Pembelajaran
Metode pembelajaran yang digunakan adalah pendekatan pemecahan masalah (problem solving)

Alat dan Bahan
Buku paket dan lembar latihan
Penilaian
Observasi dan diskusi
Banyumas, 10 Mei 2011
Guru Mata Pelajaran Mahasiswa


Nursamsiyah, S.Pd Agung Wahyudi
NIP.19740621 200604 2 004 NIM. 06301244005















Rencana Pelaksanaan Pembelajaran
(RPP)

Mata Pelajaran : Matematika
Kelas / Semester : X Broadcasting / 2
Pertemuan ke : 5
Alokasi Waktu : 45 x 2 Menit
Standar Kompetensi : 3. Memecahkan masalah berkaitan dengan konsep matriks
Kompetensi Dasar : 3. 2 Menyelesaikan operasi matriks.
Indikator :
Menyelesaikan kesamaan matrik melalui operasi penjumlahan, pengurangan matrik
Tujuan Pembelajaran
Siswa dapat menyelesaikan kesamaan matrik melalui operasi penjumlahan dan pengurangan matrik

Materi Pembelajaran
Kesamaan matrik yang diselesaikan dengan operasi penjumlahan dan pengurangan matrik

Model Pembelajaran
Kooperatif learning model STAD

Metode Pembelajaran
Ceramah, tanya jawab, dan pemberian tugas

Langkah-Langkah Pembelajaran
Kegiatan Awal
Salam pembuka
Guru mengabsen kehadiran siswa.
Guru memberikan motivasi belajar siswa.
Guru memberikan apersepsi yaitu mengingat kembali materi sebelumnya tentang kesamaan matrik, penjumlahan dan pengurangan matrik
Kegiatan Inti
Eksplorasi
Guru menanyakan kepada siswa cara menyelesaikan kesamaan matrik melalui operasi penjumlahan dan pengurangan matrik
Elaborasi
Siswa menyampaikan pendapatnya tentang cara menyelesaikan kesamaan matrik melalui operasi penjumlahan dan pengurangan matrik
Guru menanggapi pendapat siswa dengan memberikan contoh cara menyelesaikan kesamaan matrik melalui operasi penjumlahan dan pengurangan matrik
Konfirmasi
Guru menjelaskan cara menyelesaikan kesamaan matrik melalui operasi penjumlahan dan pengurangan matrik
Kegiatan Akhir
Membuat kesimpulan tentang cara menyelesaikan kesamaan matrik melalui operasi penjumlahan dan pengurangan matrik
Memberikan tugas kepada siswa tentang cara menyelesaikan kesamaan matrik melalui operasi penjumlahan dan pengurangan matrik

Alat / Bahan / Sumber Belajar :
Alat / Bahan
Penggaris
Bolpoin, buku tulis.
Sumber belajar
Modul Bahan Ajar Matematika untuk SMK.
Buku Matematika untuk SMK Kelas X.

Penilaian
Tes tertulis
Pengamatan
Penugasan

Banyumas, 13 Mei 2011
Guru Mata Pelajaran Mahasiswa


Nursamsiyah, S.Pd Agung Wahyudi
NIP.19740621 200604 2 004 NIM. 06301244005

































Rencana Pelaksanaan Pembelajaran
(RPP)

Mata Pelajaran : Matematika
Kelas / Semester : X Broadcasting / 2
Pertemuan ke : 6 & 7
Alokasi Waktu : 45 x 2 Menit
Standar Kompetensi : 3. Memecahkan masalah berkaitan dengan konsep matriks
Kompetensi Dasar : 3. 2 Menyelesaikan operasi matriks.
Indikator
Menentukan determinan matriks berordo 2 x 2
Menentukan invers matriks berordo 2 x 2

Tujuan Pembelajaran
Siswa dapat menentukan determinan matriks berordo 2 x 2.
Siswa dapat dapat menentukan invers matriks berordo 2 x 2 .

Materi Pembelajaran
Determinan dan invers matriks berordo 2 x 2
Determinan Matriks Berordo 2 x 2
Misalkan A suatu matriks persegi berordo 2 x 2, yang secara umum dapt ditulis sebagai berikut:
A = [■(a&b@c&d)], hasil kali dari diagonal (a.d) dan diagonal (b.c) yaitu (a.d – b.c) disebut determinan matriks A dan biasanya dinotasikan dengan det A.



Invers matriks berordo 2 x 2
Jika A dan B adalah matriks persegi yang berordo sama dan AB = BA = I, maka A disebut invers B, ditulis A = B^(-1), dan B disebut invers A, ditulis B = A^(-1).
Rumus matriks ordo 2 x 2 dinotasikan sebagai berikut:
Missal matriks A = [■(a&b@c&d)], Invers matriks A dinyatakan sebgai berikut:



Langkah-Langlah Pembelajaran
Kegiatan Awal
Guru membuka pelajaran dengan salam dan dilanjutkan dengan berdoa. Guru mengabsen siswa dengan menanyakan kepada siswa siapa pada hari ini yang tidak masuk. Setelah itu guru menjelaskan tujuan dari pembelajaran dan memberikan motivasi bahwa pembelajaran matematika sangat bermamfaat bagi kehidupan nyata. Kemudian guru memberikan apersepsi mengenai materi yang akan deiberikan yaitu invers dan determinan matriks.
Kegiatan Inti
Eksplorasi
Guru mengulas kembali mengenai operasi penjumlahan dan pengurangan matriks.
Guru membentuk siswa menjadi 4 kelompok dengan 2 kelompok beranggotakan 4 orang siswa dan 2 kelompok yang lain beranggotakan 3 orang siswa.
Guru membagikan permasalahan kepada siswa dalam bentuk LKS dengan masing-masing kelompok berbeda.
Guru mengawasi jalannya diskusi dengan berjalan mengelilingi siswa dan apabila ada yang bertanya mengenai permasalahan dalam LKS guru bersedia membantu.
Elaborasi
Guru menghentikan jalannya diskusi
Guru memberi kesempatan kepada siswa untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Setelah satu orang selesai mengerjakan ke depan kelas guru mennyuruh anak yang maju untuk menunjuk salah satu teman yang lain untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Guru bersama-sama dengan siswa membahas permasalahan yang telah dikerjakan siswa di papan tulis.
Guru memberikan umpan balik untuk mengambil kata sepakat bahwa jawaban itu benar atau tidak.
Konfirmasi
Guru memberikan kesempatan kepada siswa untuk mencatat jawban yang ada di papan tulis.
Guru bersama-sama dengan siswa menarik kesimpulan tentang pembelajaran pada pertemuaan kali ini.
Penuntup
Guru menuliskan 5 soal mengenai permasalah yang berupa invers matriks dan determinan matriks untuk dikerjakan siswa di rumah atau di kost.
Guru menutup pelajaran dengan berdoa dan salam.
Metode Pembelajaran
Metode pembelajaran yang digunakan adalah pendekatan pemecahan masalah (problem solving)

Alat dan Bahan
Buku paket dan lembar latihan
Penilaian
Observasi dan diskusi
Banyumas, 20 Mei 2011
Guru Mata Pelajaran Mahasiswa


Nursamsiyah, S.Pd Agung Wahyudi
NIP.19740621 200604 2 004 NIM. 06301244005







Rencana Pelaksanaan Pembelajaran
(RPP)

Mata Pelajaran : Matematika
Kelas / Semester : X Broadcasting / 2
Pertemuan ke : 8
Alokasi Waktu : 45 x 2 Menit
Standar Kompetensi : 3. Memecahkan masalah berkaitan dengan konsep matriks
Kompetensi Dasar : 3. 2 Menyelesaikan operasi matriks.
Indikator
Menyelesaikan bentuk persamaan matrik dengan menggunakan invers matrik.
Tujuan Pembelajaran
Siswa dapat menyelesaikan bentuk persamaan matrik dengan menggunakan invers matrik.

Materi Pembelajaran
Penyelesaian persamaan matriks dengan invers matriks
Misal A dan B adalah matriks persegi berordo sama. Dan missal terdapat matriks X sedemikian sehingga AX = B, maka X dapat ditentukan dengan mengalikan kedua ruas persamaan dari kiri dengan A^(-1) .




Contoh :
Tentukan matriks X berordo 2 x 1 pada persamaan [■(2&5@1&3)]X=[■(4@7)]
Jawab:
A.X = B, maka X = A^(-1).B
X = 1/det⁡A [■(3&-5@-1&2)][■(4@7)]
X = [■(-23@10)]

Langkah-Langlah Pembelajaran
Kegiatan Awal
Guru membuka pelajaran dengan salam dan dilanjutkan dengan berdoa. Guru mengabsen siswa dengan menanyakan kepada siswa siapa pada hari ini yang tidak masuk. Setelah itu guru menjelaskan tujuan dari pembelajaran dan memberikan motivasi bahwa pembelajaran matematika sangat bermamfaat bagi kehidupan nyata. Kemudian guru memberikan apersepsi mengenai materi yang akan deiberikan yaitu invers dan determinan matriks.
Kegiatan Inti
Eksplorasi
Guru mengulas kembali mengenai invers dan determinan matriks berordo 2 x 2.
Guru membentuk siswa menjadi 4 kelompok dengan 2 kelompok beranggotakan 4 orang siswa dan 2 kelompok yang lain beranggotakan 3 orang siswa.
Guru membagikan permasalahan kepada siswa dalam bentuk LKS dengan masing-masing kelompok berbeda.
Guru mengawasi jalannya diskusi dengan berjalan mengelilingi siswa dan apabila ada yang bertanya mengenai permasalahan dalam LKS guru bersedia membantu.
Elaborasi
Guru menghentikan jalannya diskusi
Guru memberi kesempatan kepada siswa untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Setelah satu orang selesai mengerjakan ke depan kelas guru mennyuruh anak yang maju untuk menunjuk salah satu teman yang lain untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Guru bersama-sama dengan siswa membahas permasalahan yang telah dikerjakan siswa di papan tulis.
Guru memberikan umpan balik untuk mengambil kata sepakat bahwa jawaban itu benar atau tidak.
Konfirmasi
Guru memberikan kesempatan kepada siswa untuk mencatat jawban yang ada di papan tulis.
Guru bersama-sama dengan siswa menarik kesimpulan tentang pembelajaran pada pertemuaan kali ini.
Penuntup
Guru menuliskan 5 soal mengenai permasalah yang berupa invers matriks dan determinan matriks untuk dikerjakan siswa di rumah atau di kost.
Guru menutup pelajaran dengan berdoa dan salam.
Metode Pembelajaran
Metode pembelajaran yang digunakan adalah Team Games Tournament (TGT)

Alat dan Bahan
Buku paket dan lembar latihan
Penilaian
Observasi dan diskusi


Banyumas, 27 Mei 2011
Guru Mata Pelajaran Mahasiswa


Nursamsiyah, S.Pd Agung Wahyudi
NIP.19740621 200604 2 004 NIM. 06301244005










Rencana Pelaksanaan Pembelajaran
(RPP)

Mata Pelajaran : Matematika
Kelas / Semester : X Broadcasting / 2
Pertemuan ke : 9
Alokasi Waktu : 45 x 2 Menit
Standar Kompetensi : 3. Memecahkan masalah berkaitan dengan konsep matriks
Kompetensi Dasar : 3. 2 Menyelesaikan operasi matriks.
Indikator
Menyelesaikan system persamaan linier dua variable dengan menggunakan matriks.
Tujuan Pembelajaran
Siswa dapat menyelesaikan system persamaan linier dua variable dengan menggunakan matriks.

Materi Pembelajaran
Menyelesaikan system persamaan linier dua variable dengan menggunakan matriks
Bentuk umum persamaan linier dua variable:
a_1 x+b_1 y=c_1
a_2 x+b_2 y=c_2
Bentuk umum tersebut dapat dinyatakan dalam bentuk matriks, yaitu:
[■(a_1 x+b_1 y@a_2 x+b_2 y)]=[■(c_1@c_2 )]↔[■(a_1&b_1@a_2&b_2 )][■(x@y)]=[■(c_1@c_2 )]
Missal A = [■(a_1&b_1@a_2&b_2 )], X = [■(x@y)] dan B = [■(c_1@c_2 )], maka persamaan matriks diatas dapat kita tulis sebagai A.X = B, dan dapat diselesaikan X = A^(-1).B

Langkah-Langlah Pembelajaran
Kegiatan Awal
Guru membuka pelajaran dengan salam dan dilanjutkan dengan berdoa. Guru mengabsen siswa dengan menanyakan kepada siswa siapa pada hari ini yang tidak masuk. Setelah itu guru menjelaskan tujuan dari pembelajaran dan memberikan motivasi bahwa pembelajaran matematika sangat bermamfaat bagi kehidupan nyata. Kemudian guru memberikan apersepsi mengenai materi yang akan deiberikan yaitu invers dan determinan matriks.
Kegiatan Inti
Eksplorasi
Guru mengulas kembali mengenai invers dan determinan matriks berordo 2 x 2.
Guru membentuk siswa menjadi 4 kelompok dengan 2 kelompok beranggotakan 4 orang siswa dan 2 kelompok yang lain beranggotakan 3 orang siswa.
Guru membagikan permasalahan kepada siswa dalam bentuk LKS dengan masing-masing kelompok berbeda.
Guru mengawasi jalannya diskusi dengan berjalan mengelilingi siswa dan apabila ada yang bertanya mengenai permasalahan dalam LKS guru bersedia membantu.
Elaborasi
Guru menghentikan jalannya diskusi
Guru memberi kesempatan kepada siswa untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Setelah satu orang selesai mengerjakan ke depan kelas guru mennyuruh anak yang maju untuk menunjuk salah satu teman yang lain untuk mengerjakan permasalahan yang ada di LKS ke depan kelas.
Guru bersama-sama dengan siswa membahas permasalahan yang telah dikerjakan siswa di papan tulis.
Guru memberikan umpan balik untuk mengambil kata sepakat bahwa jawaban itu benar atau tidak.
Konfirmasi
Guru memberikan kesempatan kepada siswa untuk mencatat jawban yang ada di papan tulis.
Guru bersama-sama dengan siswa menarik kesimpulan tentang pembelajaran pada pertemuaan kali ini.
Penuntup
Guru menuliskan 5 soal mengenai permasalah yang berupa invers matriks dan determinan matriks untuk dikerjakan siswa di rumah atau di kost.
Guru menutup pelajaran dengan berdoa dan salam.
Metode Pembelajaran
Metode pembelajaran yang digunakan adalah Team Games Tournament (TGT)

Alat dan Bahan
Buku paket dan lembar latihan
Penilaian
Observasi dan diskusi

Banyumas, 31 Mei 2011
Guru Mata Pelajaran Mahasiswa


Nursamsiyah, S.Pd Agung Wahyudi
NIP.19740621 200604 2 004 NIM. 06301244005

threetoon.com

Latihan Untuk siswa SMP Kls VII

Dari pernyataan di bawah ini manakah pernyataan yang bernilai benar?

2>-2
3<-2
-5>-2
2=(-2)

Manakah yang termasuk lawan dari bilangan bulat -90 dan 122?

+90 & 122
90 & (-122)
+90 &-(-122)
-90 &-(-122)

Manakah yang paling benar dari urutan bilanagan bulat berikut ini dari yang terkecil ke yang terbesar?
-9,-6,3,5,-8,11,-11
-13,-6,-5,5,9,12
-9,-6,6 ,-5,4,3,2
8,7 ,6 ,5 ,-5 ,-8 ,-15
Bilangan bulat yang letaknya di antara bilangan bulat -3 dan 2 adalah

(-3,-2,-1,0 ,1 ,2)
(-2,-1,0,1,2)
(-2,-1, 0, 1,)
(-1,0)

Hitunglah penjumlahan berikut ini : 30+(-19)+5-(-8)=⋯

33
-33
-24
24

Berapakah hasil dari [(-4+9)-(-34+23)-21]=⋯

-4
-5
-8
9

Berapakah hasil dari -6×5×(-7)=⋯

120
-120
210
-210

Berapakah hasil dari {(-9×8)÷[18÷(-3) ] }=⋯

34
- 23
- 43
12

Hitunglah nilai dari ((-120 ÷ -40)÷5=⋯

-2/5
2/5
-3/5
3/5

Isilah titik – titik yang ada pada soal berikut :
36 : ( -12 : …..) = -12

4
-4
3
-3


Hasil dari (42)3 adalah….

4^4
4^5
4^6
2^12


Hitunglah nilai dari 18 : [{-27: (-1 x (-3))}] = ….

1
2
-1
-2


Dengan memperhatikan tanda kurung hitunglah operasi berikut
[{(8 x (-2)) : (-4)}2]6 x (47) =…..

419
412
224
2-12


Hitunglah √169+ √144-(-√36)=⋯

34
32
17
31

Nilai dari 2,25 % dari 20000adalah……

450
350
250
120

Hitunglah (2 )/3+ 3/6-(-4/3)=⋯

2/12
15/6
-2/12
-15/6

Hitunglah ((1 )/4 x 4/5)÷(-2/3)=⋯

6/12
6/24
6/20
6/30

Ubahlah pecahan berikut ini kedalam bentuk pecahan biasa 30 3/4

120/6
123/5
123/4
220/2

Selesaikanlah soal berikut ini (3 3/5 × 1 3/4)+1=⋯

7 3/10
6 3/10
8 6/10
9 4/10

Pecahan berikut senilai dengan 4/5, kecuali….

8/10
12/15
16/25
20/25

Sederhanakanlah 〖3/4〗^(-2)×〖 3/4〗^6=⋯

〖(3/4)〗^4
〖(3/4)〗^8
〖(3/4)〗^(-4)
〖(3/4)〗^(-8)





Hitunglah penjumlahan bilangan berikut, 23,45 + 123,456 = …..
146,906
145.650
143,345
146,606
Hitunglah perkalian bilangan decimal berikut ini (3,12 ×1,5=⋯) dengan pembulatan dua angka di belakang koma.

4,68
4,65
6,56
6,65


Hitunglah 5,41 : 0,6 =….. ( dengan pembulatan 2 tempat decimal di belakang koma)

9,01666
9,0166
9,016
9,02

Taksiran hasil 839,87 : 9,73 adalah

83
84
85
90

Tulislah bilangan 3.546 x 106 berikut dalam bentuk bilangan decimal !

3546
34560
345600
3456000


Selesaikanlah 4,5666 x 3,345 x 345,09 x 0 =….

123,456
1224,67
12,08
0

Suatu kelas terdiri atas 25 perempuan dan 30 laki – laki. Perbandingan seluruh siswa laki – laki terhadap seluruh siswa adalah

5 : 6
6 : 5
5 : 11
6 : 11

Perbandingan yang paling sederhana antara 20 menit dan 2 jam adalah….

1 : 2
1 : 3
1 : 6
1 : 15

Suatu akuarium mengandung 23/27 liter air dan sisanya adalah campuran minyak. Berapakah nilai dari campuran minyak tersebut ?

23/27 liter
2/27 liter
4/27 liter
20/27 liter

THE SCIENTIFIC PHILOSOPHY

Social philosophy, political philosophy, legal philosophy, the philosophy of education, aesthetics, the philosophy of religion and other branches of philosophy have been excluded from the above quadrivium either because they have been absorbed by the sciences of man or because they may be regarded as applications of both fundamental philosophy and logic. Nor has logic been included in the Treatise although it is as much a part of philosophy as it is of mathematics. The reason for this exclusion is that logic has become a subject so technical that only mathematicians can hope to make original contributions to it. We have just borrowed whatever logic we use.
The philosophy expounded in the Treatise is systematic and, to some extent, also exact and scientific. That is, the philosophical theories formulated in these volumes are (a) formulated in certain exact (mathematical) languages and (b) hoped to be consistent with contemporary science.
Now a word of apology for attempting to build a system of basic philosophy. As we are supposed to live in the age of analysis, it may well be wondered whether there is any room left, except in the cemeteries of ideas, for philosophical syntheses. The author's opinion is that analysis, though necessary, is insufficient - except of course for destruction. The ultimate goal of theoretical research, be it in philosophy, science, or mathematics, is the construction of systems, i.e. theories. Moreover these theories should be articulated into systems rather than being disjoint, let alone mutually at odds.
Once we have got a system we may proceed to taking it apart. First the tree, then the sawdust. And having attained the sawdust stage we should move on to the next, namely the building of further systems. And this for three reasons : because the world itself is systemic, because no idea can become fully clear unless it is embedded in some system or other, and because sawdust philosophy is rather boring.

A. TREATISE ON BASIC PHILOSOPHY
This is a study of the concepts of reference, representation, sense, truth, and their kin. These semantic concepts are prominent in the following sample statements: 'The field tensor refers to the field', 'A field theory represents the field it refers to', 'The sense of the field tensor is sketched by the field equations', and 'Experiment indicates that the field theory is approximately true'. Ours is, then, a work in philosophical semantics and moreover one centered on the semantics of factual (natural or social) science rather than on the semantics of either pure mathematics or of the natural languages. The semantics of science is, in a nutshell, the study of the symbol-construct-fact triangle whenever the construct of interest belongs to science. Thus conceived our discipline is closer to epistemology than to mathematics, linguistics, or the philosophy of language. The central aim of this work is to constitute a semantics of science -- not any theory but one capable of bringing some clarity to certain burning issues in contemporary science, that can be settled neither by computation nor by measurement. To illustrate: What are the genuine referents of quantum mechanics or of the theory of evolution?, and Which is the best way to endow a mathematical formalism with a precise factual sense and a definite factual reference -- quite apart from questions of truth? A consequence of the restriction of our field of inquiry is that entire topics, such as the theory of quotation marks, the semantics of proper names, the paradoxes of self-reference, the norms of linguistic felicity, and even modal logic have been discarded as irrelevant to our concern. Likewise most model theoretic concepts, notably those of satisfaction, formal truth, and consequence, have been treated cursorily for not being directly relevant to factual science and for being in good hands anyway. We have focused our attention upon the semantic notions that are usually neglected or ill treated, mainly those of factual meaning and factual truth, and have tried to keep close to live science. The treatment of the various subjects is systematic or nearly so: every basic concept has been the object of a theory, and the various theories have been articulated into a single framework


B. THE RELATIONS OF LOGIC AND SEMANTICS TO ONTOLOGY
Philosophers have argued untiringly, over many centuries, about the ties of logic with ontology. While some have followed Parmenides in identifying the two, others - particularly since Abelard - have asserted the ontological neutrality of logic and, finally, a third party has oscillated between those two extremes.
Unfortunately it has seldom been clear exactly what is meant by the 'ontological commitment' of logic: mere reference to extralogical objects, the presupposition of definite ontological theses, or the ontological interpretation of logical formulas? Nor has an adequate tool for investigating this problem - namely a full-fledged semantical theory - been available. (Recall that the only existing semantical theory proper, i.e. model theory, is not competent to handle this problem because it is solely concerned with the relations between an abstract theory and its models, as well as with the relations among the latter.) Much the same holds for semantics, though with a remarkable difference. If semantics presupposes logic, and the latter is ontologically committed, so must be semantics. But of course semantics could be tied to ontology even if logic were ontologically neutral. Therefore we need an independent investigation of the ontological commitment, if any, of semantics.
The purpose of this paper is to investigate the relations of logic and mathematics to ontology and to do it with the help of a theory of meaning. This theory has been sketched elsewhere (Bunge 1972, 1973) and will be fully expanded in a forthcoming book. We assign meanings to constructs, in particular predicates and propositions, and distinguish two meaning components : sense and reference.

C. SCIENTIFIC REALISM AND INSTRUMENTALISM
Scientific realists claim that science aims at truth and that one ought to regard scientific theories as true, approximately true, or likely true. Conversely, a scientific antirealist or instrumentalist argues that science does not aim (or at least does not succeed) at truth and that we should not regard scientific theories as true.[7] Some antirealists claim that scientific theories aim at being instrumentally useful and should only be regarded as useful, but not true, descriptions of the world. More radical antirealists, like Thomas Kuhn and Paul Feyerabend, have argued that scientific theories do not even succeed at this goal, and that later, more accurate scientific theories are not "typically approximately true" as Popper contended.
Realists often point to the success of recent scientific theories as evidence for the truth (or near truth) of our current theories Antirealists point to either the history of science, epistemic morals, the success of false modeling assumptions, or widely termed postmodern criticisms of objectivity as evidence against scientific realisms. Some antirealists attempt to explain the success of our theories without reference to truth while others deny that our current scientific theories are successful at all.
1. Scientific explanation
In addition to providing predictions about future events, we often take scientific theories to offer explanations for those that occur regularly or have already occurred. Philosophers have investigated the criteria by which a scientific theory can be said to have successfully explained a phenomenon, as well as what gives a scientific theory explanatory power. One early and influential theory of scientific explanation was put forward by Carl G. Hempel and Paul Oppenheim in 1948. Their Deductive-Nomological (D-N) model of explanation says that a scientific explanation succeeds by subsuming a phenomenon under a general law.[21] Although ignored for a decade, this view was subjected to substantial criticism, resulting in several widely believed counter examples to the theory
2. Analysis and reductionism
Analysis is the activity of breaking an observation or theory down into simpler concepts in order to understand it. Analysis is as essential to science as it is to all rational enterprises. For example, the task of describing mathematically the motion of a projectile is made easier by separating out the force of gravity, angle of projection and initial velocity. After such analysis it is possible to formulate a suitable theory of motion.
Reductionism in science can have several different senses. One type of reductionism is the belief that all fields of study are ultimately amenable to scientific explanation. Perhaps a historical event might be explained in sociological and psychological terms, which in turn might be described in terms of human physiology, which in turn might be described in terms of chemistry and physics.
Daniel Dennett invented the term greedy reductionism to describe the assumption that such reductionism was possible. He claims that it is just 'bad science', seeking to find explanations which are appealing or eloquent, rather than those that are of use in predicting natural phenomena. He also says that:
There is no such thing as philosophy-free science; there is only science whose philosophical baggage is taken on board without examination. —Daniel Dennett, Darwin's Dangerous Idea, 1995.
Arguments made against greedy reductionism through reference to emergent phenomena rely upon the fact that self-referential systems can be said to contain more information than can be described through individual analysis of their component parts. Examples include systems that contain strange loops, fractal organization and strange attractors in phase space. Analysis of such systems is necessarily information-destructive because the observer must select a sample of the system that can be at best partially representative. Information theory can be used to calculate the magnitude of information loss and is one of the techniques applied by Chaos theory

D. GROUNDS OF VALIDITY OF SCIENTIFIC REASONING
1. Empirical Verification
Science relies on evidence to validate its theories and models. The predictions implied by those theories and models should be in agreement with observation. Ultimately, observations reduce to those made by the unaided human senses: sight, hearing, etc. To be accepted by most scientists, several impartial, competent observers should agree on what is observed. Observations should be repeatable, e.g., experiments that generate relevant observations can be (and, if important, usually will be) done again


2. Induction
It is not possible for scientists to have tested every incidence of an action, and found a reaction. How is it, then, that they can assert, for example, that Newton's Third Law is universally true? They have, of course, tested many, many actions, and in each one have been able to find the corresponding reaction. But can we be sure that the next time we test the Third Law, it will be found to hold true?
One solution to this problem is to rely on the notion of induction. Inductive reasoning maintains that if a situation holds in all observed cases, then the situation holds in all cases. So, after completing a series of experiments that support the Third Law, one is justified in maintaining that the Law holds in all cases.
Explaining why induction commonly works has been somewhat problematic. One cannot use deduction, the usual process of moving logically from premise to conclusion, because there is simply no syllogism that will allow such a move. No matter how many times 17th century biologists observed white swans, and in how many different locations, there is no deductive path that can lead them to the conclusion that all swans are white. This is just as well, since, as it turned out, that conclusion would have been wrong. Similarly, it is at least possible that an observation will be made tomorrow that shows an occasion in which an action is not accompanied by a reaction; the same is true of any scientific law

3. Test of an isolated theory impossible
According to the Duhem-Quine thesis, after Pierre Duhem and W.V. Quine, it is impossible to test a theory in isolation. One must always add auxiliary hypotheses in order to make testable predictions. For example, to test Newton's Law of Gravitation in our solar system, one needs information about the masses and positions of the Sun and all the planets. Famously, the failure to predict the orbit of Uranus in the 19th century led, not to the rejection of Newton's Law, but rather to the rejection of the hypothesis that there are only seven planets in our solar system. The investigations that followed led to the discovery of an eighth planet, Neptune. If a test fails, something is wrong. But there is a problem in figuring out what that something is: a missing planet, badly calibrated test equipment, an unsuspected curvature of space, etc.
One consequence of the Duhem-Quine thesis is that any theory can be made compatible with any empirical observation by the addition of suitable ad hoc hypotheses.
This thesis was accepted by Karl Popper, leading him to reject naïve falsification in favor of 'survival of the fittest', or most falsifiable, of scientific theories. In Popper's view, any hypothesis that does not make testable predictions is simply not science. Such a hypothesis may be useful or valuable, but it cannot be said to be science. Confirmation holism, developed by W.V. Quine, states that empirical data are not sufficient to make a judgment between theories. In this view, a theory can always be made to fit with the available empirical data. However, the fact that empirical evidence does not serve to determine between alternative theories does not necessarily imply that all theories are of equal value, as scientists often use guiding principles such as Occam's Razor.
One result of this view is that specialists in the philosophy of science stress the requirement that observations made for the purposes of science be restricted to intersubjective objects. That is, science is restricted to those areas where there is general agreement on the nature of the observations involved. It is comparatively easy to agree on observations of physical phenomena, harder for them to agree on observations of social or mental phenomena, and difficult in the extreme to reach agreement on matters of theology or ethics (and thus the latter remain outside the normal purview of science).

4. Theory-dependence of observations
When making observations, scientists peer through telescopes, study images on electronic screens, record meter readings, and so on. Generally, on a basic level, they can agree on what they see, e.g., the thermometer shows 37.9 C. But, if these scientists have very different ideas about the theories that supposedly explain these basic observations, they can interpret them in very different ways. Ancient "scientists" interpreted the rising of the Sun in the morning as evidence that the Sun moved. Later scientists deduce that the Earth is rotating. While some scientists may conclude that certain observations confirm a specific hypothesis; skeptical co-workers may yet suspect that something is wrong with the test equipment, for example. Observations when interpreted by a scientist's theories are said to be theory-laden.
Observation involves both perception as well as cognition. That is, one does not make an observation passively, but is also actively engaged in distinguishing the phenomenon being observed from surrounding sensory data. Therefore, observations depend on our underlying understanding of the way in which the world functions, and that understanding may influence what is perceived, noticed, or deemed worthy of consideration. More importantly, most scientific observation must be done within a theoretical context in order to be useful. For example, when one observes a measured increase in temperature, that observation is based on assumptions about the nature of temperature and its measurement, as well as assumptions about the way the instrument used to measure the temperature functions. Such assumptions are necessary in order to obtain scientifically useful observations (such as, "the temperature increased by two degrees").
Empirical observation is used to determine the acceptability of some hypothesis within a theory. When someone claims to have made an observation, it is reasonable to ask them to justify their claim. Such justification must include reference to the theory – operational definitions and hypotheses – in which the observation is embedded. That is, the observation is framed in terms of the theory that also contains the hypothesis it is meant to verify or falsify (though of course the observation should not be based on an assumption of the truth or falsity of the hypothesis being tested). This means that the observation cannot serve as an entirely neutral arbiter between competing hypotheses, but can only arbitrate between the hypotheses within the context of the underlying theory.


5. Coherentism
Induction attempts to justify scientific statements by reference to other specific scientific statements. It must avoid the problem of the criterion, in which any justification must in turn be justified, resulting in an infinite regress. The regress argument has been used to justify one way out of the infinite regress, foundationalism. Foundationalism claims that there are some basic statements that do not require justification. Both induction and falsification are forms of foundationalism in that they rely on basic statements that derive directly from immediate sensory experience.
The way in which basic statements are derived from observation complicates the problem. Observation is a cognitive act; that is, it relies on our existing understanding, our set of beliefs. An observation of a transit of Venus requires a huge range of auxiliary beliefs, such as those that describe the optics of telescopes, the mechanics of the telescope mount, and an understanding of celestial mechanics. At first sight, the observation does not appear to be 'basic'

6. Ockham's razor
“ William of Ockham (c. 1295–1349) … is remembered as an influential nominalist, but his popular fame as a great logician rests chiefly on the maxim known as Ockham's razor: Entia non sunt multiplicanda praeter necessitatem ["entities must not be multiplied beyond necessity]. No doubt this represents correctly the general tendency of his philosophy, but it has not so far been found in any of his writings. His nearest pronouncement seems to be Numquam ponenda est pluralitas sine necessitate [Plurality must never be posited without necessity], which occurs in his theological work on the Sentences of Peter Lombard (Super Quattuor Libros Sententiarum (ed. Lugd., 1495), i, dist. 27, qu. 2, K). In his Summa Totius Logicae, i. 12, Ockham cites the principle of economy, Frustra fit per plura quod potest fieri per pauciora [It is futile to do with more things that which can be done with fewer]. (Kneale and Kneale, 1962, p. 243)”.
The practice of scientific inquiry typically involves a number of heuristic principles that serve as rules of thumb for guiding the work. Prominent among these are the principles of conceptual economy or theoretical parsimony that are customarily placed under the rubric of Ockham's razor, named after the 14th century Franciscan friar William of Ockham who is credited with giving the maxim many pithy expressions, not all of which have yet been found among his extant works

7. Objectivity of observations in science
It is vitally important for science that the information about the surrounding world and the objects of study be as accurate and as reliable as possible. For the sake of this, measurements which are the source of this information must be as objective as possible. Before the invention of measuring tools (like weights, meter sticks, clocks, etc) the only source of information available to humans were their senses (vision, hearing, taste, tactile, sense of heat, sense of gravity, etc.). Because human senses differ from person to person (due to wide variations in personal chemistry, deficiencies, inherited flaws, etc) there were no objective measurements before the invention of these tools. The consequence of this was the lack of a rigorous science

E. PHILOSOPHY OF PARTICULAR SCIENCES
In addition to addressing the general questions regarding science and induction, many philosophers of science are occupied by investigating philosophical or foundational problems in particular sciences. The late 20th and early 21st century has seen a rise in the number of practitioners of philosophy of a particular science
1. Philosophy of physics
Philosophy of physics is the study of the fundamental, philosophical questions underlying modern physics, the study of matter and energy and how they interact. The main questions concern the nature of space and time, atoms and atomism. Also the predictions of cosmology, the results of the interpretation of quantum mechanics, the foundations of statistical mechanics, causality, determinism, and the nature of physical laws. Classically, several of these questions were studied as part of metaphysics (for example, those about causality, determinism, and space and time).
2. Philosophy of biology
Philosophy of biology deals with epistemological, metaphysical, and ethical issues in the biological and biomedical sciences. Although philosophers of science and philosophers generally have long been interested in biology (e.g., Aristotle, Descartes, and even Kant), philosophy of biology only emerged as an independent field of philosophy in the 1960s and 1970s. Philosophers of science then began paying increasing attention to developments in biology, from the rise of Neodarwinism in the 1930s and 1940s to the discovery of the structure of Deoxyribonucleic acid (DNA) in 1953 to more recent advances in genetic engineering. Other key ideas such as the reduction of all life processes to biochemical reactions as well as the incorporation of psychology into a broader neuroscience are also addressed.
3. Philosophy of mathematics
Philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics.

F. EDUCATION FACILITATION
1. Adjustment
To settle or to bring to a satisfactory state, so that the parties are agreed in the result; as, to adjust accounts. When applied to a liquidated demand, the verb "adjust" has the same meaning as the word "settle" in the same connection, and means to pay the demand. When applied to an unliquidated demand it means to ascertain the amount due or to settle. In the latter connection, to settle means to effect a mutual adjustment between the parties and to agree upon the balance. Example :
a. General Debt
• Debtor and creditor adjustment: As the term appears in an assignment for the benefit of creditors, "Creditor" means one who has a definite demand against the assignor, or a cause of action capable of adjustment and liquidation at trial.
• Adjustable Rate Loan: Loan arrangement which permits the lender to change the interest rate based on a specific factor such as the prime lending rate charged by banks.
• Adjusting agency: In one sense, a collection agency; in another sense, an agency representing a debtor in making an arrangement with his creditors for the settlement of his obligations by modification of the indebtedness. .
• Adjusted Balance Method: Method used by a credit card issuer to compute the balance on which a debtor must pay interest. The adjusted balance method determines the outstanding balance at the beginning of the current billing cycle and then deducts payments made during that cycle

b. Insurance
• Insurance adjustment, the settlement of an insurance claim; the determination for the purposes of a settlement of the amount of a claim, particularly a claim against an insurance company, giving consideration to objections made by the debtor or insurance company, as well as the allegations of the claimant in support of his claim. Adjustment of claims is not confined to claims against insurance companies. An allowance made by a creditor, particularly a storekeeper, in response to a complaint by the debtor respecting the accuracy of the account or other claim, or a reduction in the claim or account made to induce a prompt payment, is in a proper sense an adjustment.
• Public adjuster One whose business is the adjustment of claims for insurance, employed, not regularly for full time by one person or company, but by members of the public, insureds or insurers, as their need of an adjuster arises.
• Adjuster: A person who makes a determination of a claim, especially a claim against an insurance company, and objections made thereto by the debtor or insurance company, for the purpose of arriving at an amount for which the claim will be settled
c. Principles of Law
• Equity delights in amicable adjustments A maxim of equity; a maxim addressed to the judicial conscience and intended to govern the court in the determination of disputes between litigants.
• Settlement in pais: A settlement or adjustment of differences between the parties themselves, out of court.
• Composition, the adjustment of a debt, or avoidance of an obligation or liability, by some form of compensation agreed on between the parties". This noun corresponds to the verb to compound, q.v., and often means merely "a compounding." E.g., "If a slave killed a freeman, he was to be surrendered for one half of the composition to the relatives of the slain man, and the master was to pay the other half." O.W. Holmes,

2. Personal of philoshopy
John Locke considered personal identity (or the self) to be founded on consciousness (viz. Memory), and not on the substance of either the soul or the body. Chapter XXVII "On Identity and Diversity" in An Essay Concerning Human Understanding (1689) has been said to be one of the first modern conceptualization of consciousness as the repeated self-identification of oneself. Through this identification, moral responsibility could be attributed to the subject and punishment and guilt could be justified, as critics such as Nietzsche would point out.
According to Locke, personal identity (the self) "depends on consciousness, not on substance" nor on the soul. We are the same person to the extent that we are conscious of our past and future thoughts and actions in the same way as we are conscious of our present thoughts and actions. If consciousness is this "thought" which "that goes along with the substance ... which makes the same person", then personal identity is only founded on the repeated act of consciousness: "This may show us wherein personal identity consists: not in the identity of substance, but... in the identity of consciousness". For example, one may claim to be a reincarnation of Plato, therefore having the same soul substance. However, one would be the same person as Plato only if one had the same consciousness of Plato's thoughts and actions that he himself did. Therefore, self-identity is not based on the soul. One soul may have various personalities.
Neither is self-identity founded on the body substance, argues Locke, as the body may change while the person remains the same. Even the identity of animals is not founded on their body: "animal identity is preserved in identity of life, and not of substance", as the body of the animal grows and changes during its life. On the other hand, identity of humans is based on their consciousness. Take for example a prince's mind which enters the body of a cobbler: to all exterior eyes, the cobbler would remain a cobbler. But to the prince himself, the cobbler would be himself, as he would be conscious of the prince's thoughts and acts, and not those of the cobbler. A prince's consciousness in a cobbler's body: thus the cobbler is, in fact, a prince.
But this interesting border-case leads to this problematic thought that since personal identity is based on consciousness, and that only oneself can be aware of his consciousness, exterior human judges may never know if they really are judging - and punishing - the same person, or simply the same body. In other words, Locke argues that you may be judged only for the acts of your body, as this is what is apparent to all but God; however, you are in truth only responsible for the acts for which you are conscious.

3. Moral
Moral philosophy is the area of philosophy concerned with theories of ethics, with how we ought to live our lives. It is divided into three areas: metaethics, normative ethics, and applied ethics.

a. Metaethics
Metaethics is the most abstract area of moral philosophy. It deals with questions about the nature of morality, about what morality is and what moral language means. This section of the site contains material on cognitivism and noncognitivism, and on moral relativism.
• Moral Realism and Antirealism
Perhaps the biggest controversy in metaethics is that which divides moral realists and antirealists. Moral realists hold that moral facts are objective facts that are out there in the world. Things are good or bad independent of us, and then we come along and discover morality. Antirealists hold that moral facts are not out there in the world until we put them there, that the facts about morality are determined by facts about us. On this view, morality is not something that we discover so much as something that we invent.
• Cognitivism and Noncognitivism
Closely related to the disagreement between of moral realists and antirealists is the disagreement between cognitivism and noncognitivism. Cognitivism and noncognitivism are theories of the meaning of moral statements. According to cognitivism, moral statements describe the world. If I say that lying is wrong, then according to the cognitivist I have said something about the world, I have attributed a property wrongness to an act lying. Whether lying has that property is an objective matter, and so my statement is objectively either true or false. Noncognitivists disagree with this analysis of moral statements. According to noncognitivists, when someone makes a moral statement they are not describing the world; rather, they are expressing their feelings or telling people what to do. Because noncognitivism holds that moral statements are not descriptive, it entails that moral statements are neither true nor false. To be true is to describe something as being the way that it is, and to be false is to describe something as being other than the way that it is; statements that aren’t descriptive can’t be either
b. normative ethics
Normative ethics is the attempt to provide a general theory that tells us how we ought to live. Unlike metaethics, normative ethics does not attempt to tell us what moral properties are, and unlike applied ethics, it does not attempt to tell us what specific things have those properties. Normative ethics just seeks to tell us how we can find out what things have what moral properties, to provide a framework for ethics
c. applied ethics
To give an example, then, suppose that a man bravely intervenes to prevent a youth from being assaulted. The virtue theorist will be most interested in the bravery that the man exhibits; this suggests that he has a good character. The deontologist will be more interested in what the man did; he stood up for someone in need of protection, and that kind of behaviour is intrinsically good. The consequentialist will care only about the consequences of the man’s actions; what he did was good, according to the consequentialist, because he prevented the youth from suffering injury.

TO UNCOVER THE PHENOMENA

TO UNCOVER THE PHENOMENA
In our life one day’s, we have found some occurence which abstraction and real. A occurence named by abstraction of if that occurence is difficult in understanding or comprehended by others. While visible occurence of real is event occurence which can be comprehended by others without old time need to comprehend
In congeniality of to uncover the phenomena of there are various type of is nature of human being which is because of above occurence. Between : trauma, readiness, motivate the, prediction, feeling, attitude and determinant.
Trauma can be interpreted by fearsome one to an occurence which have faced of like at lecturing psykologi learn the mathematics of two week ago. lecture intentionally do the emotion game of so that can submit the items by student is claimed to earn the fell of how to uncover the phenomena.
Readiness is an somebody behaviour which is in context of to uncover the phenomena is the readiness of arising out of effect of inplus which is in giving by somebody causing our x'self ready to by what will be submitted by the somebody.
Motivation earn in interpreting something that make the us wish to do something matter or something matter pushing somebody to more impetous in working. Ordinary such as those which in doing by many lecture in UNY which always give the motivation to its student in each every lecturing
Prediction can be interpreted by that human being earn the prediction of an occurence by what have experienced of empirically owned of, like student of mathematics education which always earn the prediction of what will in facing the student.
Felling can be interpreted to feel an matter which natural medium of. Feeling directly is bitter what is called race, sweet, sour, and its his crispy is world. As does child - child which is learn, they have to can feel directly what medium learning of.
Matter - above matter is some of glimpse or effect from what we mention the to uncover the phenomena. Still a lot of matter - other matter becoming effect from to uncover the phenomena. This problem of vital importance for student of because matter - matter the above is true which can develop the spirit from the student