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Gadis itu duduk di depan jendela. Manis wajahnya tak pernah pudar, meski tak lagi berhias senyum dan tawanya yang khas. Celotehannya tak pernah lagi terdengar sejak empat bulan yang lalu. Tubuhnya kini hanya tinggal tulang berbalut kulit. Seorang wanita 40tahunan membuka pintu kamarnya, mendekap gadisnya yang termenung di depan jendela. Wanita itu mengecup kening gadisnya, lalu menyuapkan sesendok nasi, meski si gadis tak kunjung membuka mulutnya, bahkan saat ujung sendok itu telah menyentuh bibirnya. Wanita 40tahunan itu Ipah, ibu si gadis yang kini tengah menggigit bibirnya, tak kuasa melihat keadaan sang putri. Baginya, terkena stroke mungkin masih lebih melegakan daripada harus melihat Zizi dalam keadaan seperti ini.

Kurang lebih 4 bulan yang lalu, Mak Ipah menerima telpon dari Jogja. Pemilik kost yang ditempati Zizi menyampaikan keluhan anak-anak kost yang lain tentang keanehan perilaku Zizi selama beberapa hari terakhir. Mereka tak melihat Zizi keluar kamar, juga tak mendengar suara Zizi. Yang sampai ke telinga mereka hanyalah suara musik yang disetel yang terlalu keras, yang tak kunjung memelan sejak matahari terbit, hingga bulan muncul menggantikannya. Mereka sudah mengetuk, bahkan menggedor pintu kamar Zizi. Tapi, tak pernah ada jawaban, tak pernah ada suara pintu terbuka, atau sekedar langkah kaki menuju ke arah daun pintu yang bergetar karena ketukan yang terlampau keras.

Sejak saat itu, Mak Ipah akhirnya mengurus cuti kuliah Zizi, dibantu Kiky, adik Zizi yang sedang menikmati semester keempatnya di salah satu perguruan tinggi negeri di Jogja. Bukan karena ingin memaksakan sebuah toga wisuda bagi putrinya, tapi untuk menenangkan dan menyenangkan hatinya sendiri, dengan menciptakan harapan dan illusinya tentang kesembuhan Zizi. Entah kenapa dan bagaimana ceritanya Zizi sampai bisa seperti ini, mungkin hanya Zizi dan Tuhan yang tau.

Air mata Mak Ipah menyusut saat Fafa, adik Zizi yang tengah duduk di bangku SD mengucap salam dan terdengar derit pintu dibuka. Langkah-langkah mungil Fafa mendekat, dan terhenti persis di depan pintu kamar Zizi. Bocah tujuh taun itu, entah karena mengerti kondisi kakak kesayangannya atau lantaran melihat mata sembab Mak Ipah, tiba-tiba butiran bening meluncur dari bola matanya yang jernih. Fafa mengambil dan mencium tangan Mak Ipah, lalu mendekat pada Zizi. Mak Ipah bangkit, membiarkan Fafa meluapkan kerinduannya pada sang kakak yang seolah membatu bak arca sejak empat bulan yang lalu.

“Mbak, mau Empah entuk biji 100 ulangan matematika.” Zizi tetap mematung, seolah kata-kata Fafa terkalahkan oleh suara langkah kaki semut-semut yang berada di bingkai jendelanya.

“Mbaaaakkkk…,” Fafa, entah karena kesal atau putus asa, mulai berteriak. Batiran bening jatuh tetes demi tetes dari bola mata bulatnya. Mak Ipah hanya mampu menahan pilu menyaksikan pemandangan di depan matanya. Mak Ipah sadar bahwa Zizi adalah kakak yang sangat dicintai semua adiknya. Kepulangan Zizi dari Jogja selalu menjadi hal yang paling dinantikan oleh Fafa dan Nuna. Setiap si sulung pulang, Fafa selalu yang paling antusias membuka tas Zizi, mengaduk semua isinya dan mengambil apapun yang membuatnya tertarik. Berbeda dengan Fafa yang suka tas Zizi, Nuna lebih suka merentangkan tangannya dan berlari ke arah Zizi, lalu bergelayut dalam gendongannya. Betapa semuanya adalah gambaran sempurna sebuah kehidupan. Atau hanya topeng bahagia diantara sekian banyak luka dan kepedihan? Hanya Zizi dan Tuhan yang tau jawabannya.

Sore itu, semua keluarga berkumpul kecuali Kiky, yang entah sedang melakukan aktivitas apa di antara hiruk pikuk kota Jogja. Seperi hari-hari sebelumnya, mereka berkumpul di depan tivi. Bedanya, selama empat bulan terakhir sejak kepulangan Zizi, keramaian dan keonaran di rumah sederhana itu berkurang volume dan frekuensinya. Malam itu semua menonton tivi dalam diam, tapi semua isi kepala mereka kurang lebih sama, hanya tentang Zizi. Suara tivi yang dinyalakan tak lebih dari sebuah sandiwara untuk membungkus kebisuan mereka semua.

Dua jam berlalu, duo kurcaci Fafa dan Nuna sudah tergeletak di atas karpet. Mak Ipah dan Pak Jali mengangkat dua tubuh mungil itu dan memindahkannya ke kamar. Sesaat Mak Ipah memandangi keduanya dan tersenyum getir. Entah sudah sampai dimana khayalan kedua kurcaci kecil ini. Fafa yang cerdas dan cerewet mungkin sedang menata kepingan mimpinya bersama Zizi. Anak itu kadang berpikir lebih dewasa dari usianya. Nuna, si pipi chubby dan maniak kamera itu pun mungkin telah sampai entah di negeri dongeng mana.

Kini tinggal Mak Ipah dan Pak Jali yang duduk dalam kebisuan di depan layar cembung berukuran 14’ tersebut. Yaya sudah masuk ke kamarnya, yang juga kamar Zizi. Sebenarnya, remaja 14 taun itu keberatan saat ibunya bersikukuh agar dia tetap satu kamar dengan Zizi. Baginya, Zizi yang sekarang terbaring di sisinya dengan tatapan kosong itu bukan lagi kakaknya. Zizi yang dikenalnya tidak akan pernah bisa sediam dan setenang ini di sampingnya.

“Pak, sampai kapan kita akan membiarkan Zizi seperti ini? Apa tidak sebaiknya kita mencari tau penyebabnya? Atau setidaknya memulai berikhtiar untuk kesembuhan Zizi.”

“Itu yang sedang aku pikirkan. Besok kita coba telpon semua teman-teman terdekatnya. Atau kita undang mereka kesini, sekadar untuk menyapa Zizi. Mungkin itu bisa membantu Zizi tersenyum.”

“Iya, Pak. Rasanya aku sendiri tidak kuat jika harus melihat Zizi terus-terusan seperti ini.”

Pak Jali memeluk istrinya. Pelukan itu bukan sekadar usaha untuk menenangkan Mak Ipah, tapi juga semacam usaha mencari kekuatan untuk menenangkan batin Pak Jali sendiri.

Pagi yang mendung. Awan kelabu tergantung di atas jajaran rumah mungil di kompleks perumahan sederhana itu. Seorang laki-laki berumur 30an keluar dari salah satu pintu rumah yang berjajar rapi itu. Perempuan berjilbab ikut keluar, lalu menyalami laki-laki tadi dan mencium tangannya dengan khidmat. Sungguh pemandangan jum’at pagi yang luar biasa. Dari bola mata Syifa, perempuan berjilbab yang berdiri dengan anggun itu, mengalir cinta yang deras untuk sang suami, laki-laki yang baru saja pergi dengan motornya untuk mencari nafkah bagi keluarga kecil mereka.

Syifa kembali masuk ke rumah mungilnya untuk melakukan aktivitas hariannya sebagai ibu rumah tangga. Syifa masuk ke kamar untuk mengambil pakaian suaminya yang tergantung di balik pintu, hingga gendang telinganya disentil oleh dering hp sang suami yang tergeletak di meja samping tempat tidur mereka. Dua belas digit angka tampak di layar hp suaminya. Tak ada nama untuk nomor itu, namun Syifa memberanikan diri untuk mengangkat panggilan itu. Aku istrinya. Jadi, aku juga berhak mengangkat telpon ini.

“Assalamu’alaikum…”

“Wa’alaikumussalam wa rahmatullah. Mbak, bisa bicara dengan Mas Agung?”

“Maaf, ini dengan siapa, ya?”

“Ini ibunya Zizi. Apa saya bisa berbicara dengan Mas Agung?”

“Maaf, Bu. Tapi, Mas Agung sedang keliling. Boleh saya tau keperluannya? Nanti biar saya sampaikan ke Mas Agung.”

“Terima kasih banyak, Mbak. Barokallahulakum. Tolong sampaikan pada Mas Agung, Zizi sakit dan sekarang ada di rumah Pekalongan. Kami sangat berharap Mas Agung dan Mbak Syifa bisa datang untuk membantu Zizi. Tolong sampaikan itu pada Mas Agung, Mbak. Terimas kasih sebelumnya. Assalamu’alaikum…”

Mak Ipah menutup telpon setelah mendengar jawaban salam dari Syifa. Sementara Syifa, hatinya panas dan wajahnya memerah karena amarah dan cemburu yang tak mampu dibendungnya. Zizi, adalah satu-satunya ancaman bagi kebahagiaan rumah tangganya. Zizi adalah sosok yang Syifa yakin sampai kini pun, tak mampu dihapus dari ingatan Agung. Syifa dengan susah payah membangun rumah tangganya dengan Agung di Bekasi, menjauh sebisa mungkin dari bayang-bayang nama itu. Syifa tau, Agung tak akan pernah bisa benar-benar mengenyahkan Zizi dari benaknya, dari lembaran-lembaran kehidupannya, dari daftar orang-orang yang dikhawatirkannya. Sekali nama itu muncul ke permukaan dan sampai ke telinga Agung, dinding yang Syifa bangun untuk menyekat Agung dan Zizi akan runtuh seketika.

Syifa mulai mencuci baju, mengusir jauh-jauh nama Zizi dari pikirannya, dan bersikap seolah pembicaraan via telpon tadi tak pernah terjadi. Syifa telah menghapus bukti adanya panggilan tadi. Syifa benar-benar tidak ingin Zizi mengusik rumah tangganya dengan Agung, apalagi dengan kehadiran si kecil dalam rahimnya.

Kalaupun Zizi benar sakit, kenapa harus Mas Agung yang mereka hubungi? Apa playgirl itu sudah kehabisan stok sampai harus menghubungi Mas Agung yang jelas-jelas sudah beristri.

                                                                        ***

Di rumah Zizi, satu per satu temannya datang menjenguk. Dea, sahabat Zizi sejak kelas 2 SMA, menangis sesenggukan di ruang tamu rumah Zizi. Dea datang bersama pacarnya. Sepanjang perjalanan mereka ke rumah Zizi, Dea dengan bangga menceritakan tentang sosok Zizi, sahabat teraneh sekaligus yang paling mengagumkan itu, pada mas pacar yang kini ia pinjam bahunya sebagai sandaran untuk menuangkan air matanya.

Di dalam kamar Zizi, ada Mbak Santi, sahabat Zizi sejak kelas 1 SMA, yang dulu sempat perang dengan Dea karena berebut menjadi orang penting bagi seorang pemain sepak bola andalan sekolah mereka. Masih ada Prisna, yang dulu selalu mengandalkan Zizi sebagai penyangga saat dirinya patah hati. Ada laras, teman sekaligus adik yang selalu menganggap selalu menganggap Zizi sebagai tempat yang tepat untuk menumpahkan beban di pundaknya sekaligus meminta nasehat.

“Ibuk, sejak kapan Zizi seperti ini?” Dea memberanikan diri bertanya pada Mak Ipah, disusul tatap mata seisi ruangan yang menanti jawaban Mak Ipah.

“Empat bulan yang lalu, dek. Adek-adek ini ada yang tau kenapa Zizi seperti ini? Apa Zizi pernah cerita atau mengeluhkan sesuatu pada kalian?”

“Mboten, Bu. Terakhir Zizi Cuma cerita tentang seseorang bernama Zaky. Zizi mengenalkannya pada saya lewat facebook, tapi saya justru merasa kalo Zizi yang suka sama orang bernama Zaky ini.”

“Waktu KKN, Zizi memang sempat cerita kalo dia lagi seneng sama orang. Tapi anak itu tidak menyebutkan namanya. Mungkin si Zaky itu yang dia maksud. Adek punya nomor hp-nya?”

“Mboten, Bu. Kulo nggeh dereng natih kepanggih tiyange. Tapi nanti coba saya carikan kontaknya, atau saya coba hubungi sekalian.”

Air mata Mak Ipah tak terbendung lagi. Entah karena terharu, atau karena terlalu mengharapkan kesembuhan Zizi. Pak Jali yang baru pulang dari sawah, menyalami teman-teman Zizi.

“Bu, apa nggak ada yang tau password hape, laptop atau facebooknya?” Laras nyeletuk dalam keheningan ruangan itu.

“Kami bahkan tidak tau di mana Zizi menaruh hp dan laptopnya. Mencari nomor adek-adek ini saja sudah sulit sekali.”

“Jadi, waktu Zizi dibawa pulang dari Jogja…”

“Kami tidak menemukan laptop dan hapenya. Teman-teman di kosnya juga tidak ada yang tau. Yang mereka yakini, laptop Zizi masih ada, hanya entah dititipkan dimana. Karena Zizi pasti akan cerita pada mereka kalau dia kehilangan barang berharganya.”

Percakapan terus berlanjut tentang hari-hari Zizi di SMA, hingga perjalanan awal kuliahnya. Hanya saja, tak ada cerita yang bisa dikaitkan dengan kondisi Zizi sekarang.

Adab dan Tata Cara Berfilsafat

Refleksi Mata Kuliah Filsafat Pendidikan Matematika

(Pertemuan ke-1)

By: Anniltal Manzilah (09301241028)

Sebelum mempelajari tentang filsafat pendidikan matematika, kita perlu mengetahui tentang filsafat. Filsafat adalah olah pikir yang refleksif, sehingga mata kuliah filsafat pendidikan matematika juga dilaksanakan dengan metode refleksif, yaitu mahasiswa diminta untuk membuat refleksi dari satiap pertemuan. Dalam mempelajari filsafat, kita harus mengetahui adab-adab dalam berfilsafat. Seperi halnya dalam beribadah, dalam berfilsafat pun, kita harus mengikuti adab atau tata caranya. Orang yang beribadah, harus melakukan adab-adab dan mematuhi tata cara yang telah ditentukan. Contohnya ketika seorang muslim akan melakukan sholat, maka adab atau tata caranya adalah harus berwudlu lebih dulu. Jika ibadah dilakukan tanpa mematuhi adab dan tata caranya, maka ibadah yang dilakukan tidak akan diterima atau hanya akan sia-sia. Begitu juga halnya dengan berfilsafat. Orang yang berfilsafat tanpa mengetahui adab dan tata caranya, maka berfilsafat yang dia lakukan hanya akan sia-sia.

Adab berfilsafat yang pertama adalah bahwa setinggi-tingginya filsafat, tetap tidak boleh melebihi spiritual. Filsafat harus selalu berada di bawah spiritual atau keyakinan. Karena filsafat adalah olah pikir dan olah pikir letaknya di pikiran. Sedangkan spiritual atau keyakinan letaknya adalah di hati. Sehingga setinggi-tinggi filsafat, jangan sampai melebihi spiritual, karena bisa menyeret kita menjadi orang yang sesat. Selain itu, untuk berfilsafat kita juga perlu memahami tentang konsep ketuhanan, agar kita tidak tersesat. Sebelum berfilsafat pun, kita perlu berdoa pada Tuhan, agar kita tidak tersesat dalam berfilsafat. Sehingga, kita perlu mengenal Tuhan sebelum berfilsafat. Untuk mengenal Tuhan, kita menggunakan hati, bukan pikiran. Sehingga kedudukan spiritual itu berada di atas filsafat.

Kemudian, adab berfilsafat yang kedua adalah bahwa filsafat itu hidup. Untuk bisa berfilsafat, kita harus hidup sehat. Hidup sehat disini artinya hidup yang sesuai dengan aturan yang berlaku, sesuai dengan nilai-nilai kehidupan yang baik, dan sejalan dengan hati nurani. Orang yang hidup sehat diartikan sebagai orang yang beradab. Sedangkan hidup yang tidak sehat contohnya seperti menghilang secara tiba-tiba tanpa kabar, dating tiba-tiba tanpa pemberitahuan, melakukan sesuatu dengan terpaksa, memaksa, dan lain sebagainya. Makna hidup yang tidak sehat juga bisa dikaitkan dengan kondisi fisik, contohnya seperti sakit atau cacat. Hakikat dari cacat ini adalah kurang atau tidak lengkap. Untuk berdoa dan beribadah, maka kita memerlukan kondisi yang sehat. Selain itu, hidup yang sehat juga memiliki makna hidup yang seimbang atau harmoni. Contohnya seimbang antara pemasukan dan pengeluaran dalam hal keuangan. Orang yang pengeluarannya lebih banyak dari pemasukan atau defisit bisa dikategorikan ke dalam hidup tidak sehat. Selain keseimbangan dalam keuangan, contoh keseimbangan hidup yang harus dipenuhi juga adalah seimbang antara kehidupan dunia dan akhirat. Orang yang hanya memikirkan kehidupan dunia tanpa menghiraukan akhirat dikatakan tidak seimbang, karena kehidupan yang kekal adanya di akhirat, bukan di dunia. Namun jika kita hanya memikirkan akhirat tanpa memedulikan dunia, maka hal tersebut juga tidak seimbang, karena kita sebagai manusia memiliki kebutuhan-kebutuhan biologis seperti makan, minum, dan lain sebagainya yang merupakan urusan duniawi.

Filsafat adalah olah pikir. Maka, dalam berpikir itu kita menggunakan referensi. Satu tingkat diatas filsafat adalah spiritual atau keyakinan. Dalam berkeyakinan, kita menggunakan kitab suci. Lalu, di bawah filsafat ada yang disebut ilmu-ilmu bidang. Ilmu-ilmu bidang ini memiliki buku pintar sebagai pedomannya. Sedangkan di tingkat paling bawah, ada yang kita sebut kegiatan. Dalam kegiatan-kegiatan yang kita lakukan, semua selalu ada petunjuk teknisnya. Selain itu, dalam berfilsafat, kita menggunakan metode yang disebut terjemah-menterjemahkan, atau dalam hermeneutika. Dalam tatanan dewa-dewa Yunani, ada yang disebut Dewa Hermen, yaitu Dewa yang dianggap sebagai pembawa bisikan Tuhan. Yang dimaksud membawa bisikan Tuhan ini adalah bahwa Dewa Hermen menterjemahkan petunjuk dari Tuhan agar dapat dimengerti dan dilaksanakan ileh umat manusia saat itu.

Selanjutnya, setelah mengetahui dua adab berfilsafat di atas, kita juga perlu mengetahui alat untuk berfilsafat. Alat yang digunakan dalam berfilsafat adalah bahasa analog. Karena filsafat adalah olah pikir, maka jika kita menggunakan tulisan, olah pikir kita akan sulit mencapai maksimal. Jadi, dalam berfilsafat, alat yang kita gunakan adalah bahasa analog.

Obyek dalam berfilsafat dibagi menjadi dua, yaitu hal yang ada dan hal yang mungkin ada. Hal yang ada adalah segala sesuatu yang sudah ada di pikiran kita. Sedangkan hal-hal yang mungkin ada adalah hal-hal yang belum ada di pikiran kita. Hal yang da bisa kita teukan dalam pikiran kita. Sedangkan untuk hal yang mungkin ada, bisa menjadi ada jika kita mau mencari dari berbagai referensi, baik buku maupun internet atau bisa juga melalui narasumber.

Adab berfilsafat yang terakhir adalah berpikiran jernih. Berpikiran jernih ini maknanya adalah bahwa dalam berfilsafat, kita harus terbebas dari hal-hal yang membebani diri dan pikiran kita. Untuk dapat berpikiran jernih, maka kondisi fisik juga perlu diperhatikan. Jika fisik kita dalam keadaan sakit, maka kita tidak akan mampu berpikir jernih. Contohnya jika kita digigit kutu kemudian menggaruk kepala atau menahan sakit, maka konsentrasi kita dalam berpikir akan terganggu. Selain itu, berpikiran jernih juga diartikan bahwa kita memerlukan konsentrasi penuh. Jika perasaan kita tidak tenang, was-was, panik, dan lain sebagainya, maka kita tidak akan mampu berpikir jernih, sehingga kegiatan berfilsafat juga akan sulit dilakukan. Karena filsafat ini adalah olah pikir, maka kejernihan dan konsentrasi dalam berpikir adalah tata cara yang harus dipenuhi dalam berfilsafat. Selain itu, berpikiran jernih sangat penting dalam berfilsafat, yaitu agar kita tidak tersesat. Karena jika kita tidak mampu berpikiran jernih, berfilsafat ini bisa menjadi berbahaya.  Jangan sampai dengan berfilsafat, kita kemudian justru menyombongkan diri dan mulai mengusik tentang kitab suci apalagi tentang konsep ketuhanan. Jadi, adab-adab atau tata cara dalam berfilsafat ini harus dipenuhi agar kita dapat berfilsafat dengan benar dan tidak tersesat. Kejernihan berpikir di sini juga bisa diartikan kejernihan dalam memandang kedudukan filsafat.

Jadi, hakikat filsafat adalah olah pikir dan obyek dari berfilsafat cenderung hal-hal atau benda-benda yang sangat sederhana atau bahkan hal-hal sepele yang mungkin tidak pernah terlintas di pikiran kita.

Nak, Ibu sayang padamu

Anakku...bagaimana harimu?

Adakah kau bahagia hari ini?

Ibu begitu merindukanmu, Nak...
Ibu merindukan tawamu...
Ibu merindukan tangismu...
Ibu merindukan saat-saat bersamamu...

Anakku...
Sembilan bulan engkau berada dalam kandungan ibu...
ibu mengerti sedihmu...
ibu memahami bahagiamu...
setiap hari, tanpa lelah dan tanpa mengeluh,  ibu berusaha memenuhi semua keinginanmu...

Anakku...
jangan pernah lupakan ibu, Nak...
meski ibu tak dapat berada di sisimu lagi...
meski ibu tak mampu mendampingimu lagi, ibu tetap menyayangi dan mencintaimu...
cinta ibu untukmu takkan pernah berkurang,
meski kita terpaut oleh jarak, meski kita terpisah oleh ruang, ibu akan tetap mencintaimu...

Anakku...
hentikan tangisanmu, Nak...
tak mampu ibu melihatmu menangis...
tak sanggup ibu menyaksikanmu berurai air mata...
ingin rasanya ibu berada di sisimu untuk menghapus tetesan-tetesan kesedihan dari matamu yang dulu selalu berbinar...

Anakku...
Ibu masih ingat bagaimana saat pertama kali mengantarmu ke sekolah...
kau pakai seragam barumu dengan bangga,
kau berjalan menggandeng tangan ibu dengan penuh semangat,
Senyummu adalah pelipur lara ibu...
tawamu adalah sumber kebahagiaan ibu...

Anakku...
Dimanapun engkau, seperti apapun rentang jarak dan ruang memisahkan kita,
mata indahmu akan selalu ibu ingat...
senyum nakalmu akan selalu terbayang dalam benak ibu...
canda tawamu akan menjadi kenangan tak terlupakan di hati ibu...

Jangan menangis, anakku...
karena takkan putus cinta ibu untukmu...
takkan lapuk kasih ibu padamu...

Jangan bersedih, Nak...
Seandainya Tuhan memberi ibu satu hari lagi, takkan ibu biarkan kau jauh dari pandangan...
Seandainya Tuhan memberi ibu satu jam lagi, hanya tawamu yang ingin ibu dengar...hanya senyummu yang ingin ibu lihat...
Seandainya Tuhan memberi ibu satu menit lagi, ibu akan berikan pelukan terhangat untukmu...hingga takkan hilang kehangatan itu, meski tak ada lagi ibu di sisimu...
dan jika Tuhan hanya memberi ibu satu detik lagi, maka biarkan ibu menghapus air matamu, Nak...
Biarkan ibu jauhkan kesedihan darimu...
karena hanya bahagiamu yang ingin ibu lihat...

Tapi tak ada satu hari itu, tak ada satu jam tambahan itu, tak ada semenit dan sedetik itu...Hingga kini ibu hanya mampu menatapmu menangisi jasad ibu yang terkulai lemah di hadapanmu...

Jasad yang kini hanya bernilai seonggok daging dan tulang-belulang, yang tak mampu lagi menemanimu...

Selamat tinggal, Anakku...
Nak, Ibu sayang padamu...

  

How  to Promote International Level of Schooling if I were Agency Head of Education

By Anniltal Manzilah

09301241028 (P. Matematika Subsidi 2009)

(akkudifferent.blogspot.com)

If I were Agency Head of Education, I will promote International level of schooling by make any changes to increase the school quality so that the International level schools in Indonesia such as :

1.      Improve the curriculum

Curriculum is the main part of education. So, if we want to increase the schhol quality, we must develop and make some changes in the curriculum. Because curriculum is so important in teaching-learning activities. In our country, implementation of the curriculum is not as good as the curriculum yet. At this moment, our curriculum is called KTSP. KTSP is a curriculum that more specific than the before ones. The curriculums before KTSP is generalize every school in every province, so that they have just little chance to develop their culture and their natural sources in education aspect. Also, in KTSP, the students must be an active learner, because the teachers i only  facilitator, so that they only have to facilitate and motivate the students to be more active, to be more competitive. Beside implement KTSP optimally, we also should adapt curriculums from the other countries, such as United States of America, Japan, Singapore, etc. And to be underlined, if we adapt other country’s curriculum, we have to sort, not only adapt and implement. We have to sort the other country’s curriculum and take just the right and good values. Before, we employ other country’s curriculu, we also have to compare and set the curriculum so that it’s match with our cultures and traditions.

We need a curriculum that can make the students more active, make the teachers more creative, maximize the useful of school and teaching-learning facilities, etc.  If we have changed or improved the curriculum, we must implement it well in teaching-learning process. To do this step, we need good attitude persons. People with good attitude will make the curriculum to be perfect with the maximal implementation.

2.      Complete school facilities

Beside we have to improve the curriculum, we also have to complete the school with the good quality of facilities. School with good and complete facilities will be able to support well the teaching-learning process. The facilities that should be there is divide to some parts, those are the facilities to make the students feel comfort in learning process, teaching-learning aids, and school facilities.

Facilities that be able to make the students feel comfort in learning activities is like a fan or air-conditioner, a comfort class, a good design of the seats, cleaning utilities, etc. we have to make the class as comfort as we can. Because a succeed teaching-learning process is also depend on the class facilities.

Teaching-learning aid is the aids that we can use in teaching a lesson. Teaching-learning aids will make the students easier in understanding the lessons. For example, if we want to teach the students about geometry, we can use a useless-box as a model of cube and pipe as a model of tube.

School facilities is also should be completed to support the students to study well. The school facilities is like school yard, laboratory, a good design of library, etc.

So, if I were agency head of education, I will give an enough fund so that every interntional school is able to compete with the other interntional school in other countries.

3.      Develop teachers quality

Teachers is a key of teaching-learning process. So, to increase the quality of International level of schooling, we must develop and increase the teachers quality. It’s not like make a test such sertifikasi. We must increase the teachers quality by treat and train them to be modern teachers, faclitators for the students. Teachers in International school have to know that they aren’t the main player in class, but the students. Teaching-learning process must be student-centered.  Teachers only need to give them hints and let them find the formulas by themselves.  Students need to built and construct their knowlwdge, because they are who need it in future. The purpose of teaching-learning activities is to make the students understand about the lessons and can implement it in daily life.

Sudents have to be active, because  the teachers is only facilitators. They won’t lecture the students, read and explain everytimes. The teachers only need to supervise and control the students in class, in the process of finding the formulas or in discussion in a small group.

The teachers is also have to employ various method to help the students in understanding the lessons. In our curriculum, there is written that students must be active in teaching-learning activities. But in the implementation, students only have to listen to the teachers. It’s not good because students won’t know the steps to get formulas, to find a value, etc. the teacher only a facilitator and the conclusion of learning activities is the student’s rights.

MATHEMATICS TEACHING ACROSS MULTICULTURAL CONTEXT

By: Anniltal Manzilah

Introduction

Since 1968/1969, a more systematic approach to develop education in Indonesia has begun to be evident. Since that time up to the late of 1990, the approach to develop education has designed under the assumption that curricular objectives could be logically derived from national and system-wide goals and then broken down into a precise hierarchy of instructional objectives, and that learning could be made individualized and ‘teacher-proof’ so that students could learn what they needed to learn with minimal assistance from teachers (Shaeffer, 1990, pp.22). However, in 1984, evidences indicated that the approach was perceived not to able to mobilize resources and to embark the model to the nationwide application.

Mathematics teaching system is different in almost every countries or may be in every city. It’s because every country have a different culture, so that they use or employ a method, teaching aid, curriculum, etc which match with their culture. For example in our country. Indonesia not only have a culture, but there are so many culture in our country. That’s why the president make a KTSP curriculum. By employ KTSP, our country just make one model or standard for all schools in every grade. And that is the minimum standard, so that the favorite or best-quality school can improve the curriculum to reach the best achievements. The others countries is also have a foreigh to optimalize their Mathematics teaching system to get the best achievements and to produce the best human resources by give the best education. They optimalize their educational system appropriate by their own culture so that they can get the best human resources to develop their natural resources.

Mathematics Teaching Across Multicultural Context

There are some differences of mathematics teaching system in every country because of the differences of their culture. For example, we can make a comparison of the mathematics teaching system in some countries, such as Philippines, Thailand, Japan, and our country, Indonesia. We will find a differences the teaching system because of the culture differences, and the human resources quality.

              ­­­­­First, we will go to Japan. In this country,  the purpose of mathematics education in Japan is to study how to think, the point of view of every thing, and better human being formation through learning of mathematics; to study mathematical practical use, utility through learning of mathematics; and to enjoy and develop the wonderful cultural heritage of mathematics through learning of mathematics (Nishitani, 2002). Further he stated that the characteristics of the new course of study in Japan consist of: (a) reduction of the learning contents, (b) decrease of the number of classes, (c) comprehensive five-day school week, (d) integrated study mathematical activities, (e) practical and operational activities and problem-solving activities and so on, (e) basis points of active learning, (f) have the purpose of learning clearly, (g) have interest in the subject, (h) have an perspective to solve the problem, (i) have a feeling of satisfaction and joy, and (j) acquire the way of learning.

Beside that, the Japanese educational system is characterized as centralized in which at the regional level, the prefectures or district has its own board of education. Marsigit, in his article, Math Programs for International Cooperation in Indonesia (2002) said that generally, it’s like the KTSP in Indonesia, but we don’t bring about it well yet. In Japan, the schools are established by the national government, a local government or an educational cooperation. The board of education carries out the educational functions of the local government. Teachers are encouraged to be more flexible and to recognize that children need to be active. Teachers encourage their students involving in classical discussion. It seems that teachers more emphasize on teaching with understanding than stressing on calculating. However, some teachers implement a series of drills to master the skills.

In Japan, some of the students by their own initiations , complete the books by buying from the bookstores. At our country, we know it’s too impossible to act, because as we know, not of all students in a school is from a good economical family.The teachers use the textbooks for developing their mathematics problems. The students are instructed to bring the textbook to their home. At class, the students use both textbooks and book of collection of problems. Calculators are to be used but only a little; some of the teachers perceive that calculator has a little value in education. However, teachers introduce abacus for laying the basic skill of computation. Most of primary schools employ worksheets in their teaching. Worksheets in Japanese education is not like in our country. In Japan, worksheets contains anythings the students have to do, not so many questions to do like we always found in almost everyschool in our country.

To improve the quality of mathematics and sciences education, in a certain occasion, Japanese educational expert suggested the followings: (a) implementing open class teaching, (b) encouraging the teachers to make their own teaching material (textbook), (c) evaluating teaching learning processes by their students, (d) analyzing students’ mistakes and errors, (e) encouraging the teachers to have good and strong will (spirit) to develop their competences, (f) implementing good balance of old and new method in teaching, (g) promoting good collaboration between university and school, (h) teachers should have their own original method in teaching, (i) teachers should continue to develop their teaching ability, (j) teachers always ask how to make their own class better, and (k) the role of teacher is similar to doctor; rescue the children.

Next, we will go to Philippines and compare how far the differences of their mathematics education system and ours. In Philippines, a students will pass six years in elementary school, four years in second level, and four or five years in third level. Its not like in our country or Japanese one. In Japan, the level division is like in our country. The purpose of the Phillipines mathematics education is almost same as the Japanese one. Both of them try to give the students various experiences will increase their capability to thinking logically and to be creative in using mathematics problems according to the fact in their daily life.

Philippines have give more times to the students to learn mathematics than Japan. For example, in first grade, Philippines students learn mathematics more than the students in Japan. And beside that, Pihilippines is also use English in introduction, but Japan use their own language, Nihongo. In Phileppines, the students textbooks should used and will be improved in every five years. That’s not like in Japan, because in Japan, the textbooks will be improved in every three or four years. The Philippines textbooks give many exercise to the students to drill their ability in calculating. Philippines is looks not so different with our country. They give too many lessons, so that the students will forget the lesson quickly. Because it’s over than their capacity in receiving knowledge. Japanese students try to enjoy their mathematics, not coerced to learn over their capacity.

And then, we will look at the mathematics teaching system in Singapore. In this country, every subject will teached by three teachers, that is a master teacher, and his/her two assistents. They said it’s just to make the students learn mathematics easier. Further, in Singapore, the education system is based on the thoughts that every students have a unique talent and interests. Singapore employs a simple method and flexible one to develop the students capability. Evaluation of the students did continuous, even since the students still in elementary school. The students’s six years in elementary school divide to two categories. For first four years, the students learn English, Malay language, and mathematics. Singapore teach the students mathematics since elementary school so that the students can develop their ability in thinking logically, thinking critically, and be accustomed to solve any problem. But there are other subjects to develop the students’s talent like music, art, sport, etc. And then, the students’s two years will be used to prepare them to pass final examination.

Singapore curriculum has been international curriculum and has used to be a model to the others, espescially in mathematics teaching.

In our country, The current picture of teaching practice in Indonesia is generally extensive teacher directed explaining and questioning in the context of whole class instruction followed by students working on paper and pencil assignments at their places. The teacher functions as the central figure in determining activities and conducting instruction; and, the students rarely actively engage in learning directly from one another or in initiating processes of interaction with others. Most teachers observed spend most of the time conveying information to children; the blackboard is by far the commonest visual aid but was often used as the teachers' scribbling pad rather than for presentation of a logical sequence of ideas. The challenge for educators in the next decade is to improve students' learning of higher order skills in mathematics; teachers should organize instruction to involve children so that they actively construct their own knowledge with understanding (Peterson in Grouws, et al., 1988).

The condition of Mathematics education in Indonesia have the indication that children’s achievement in the subjects of mathematics and Science is low, as indicated by the result of the National Leaving Examination (EBTANAS) year by year both in Primary and Secondary School. Children’s mastery on Mathematics and Science concepts and Science process skills is still low. This fact may be as the results of: (a) the shortage of laboratory activities; (b) lack of teachers having mastered science process skill approach; (c) contents on Mathematics and Science curriculum too crowded; (d) too many time consuming administration stipulation for teachers; (e) lack of laboratory equipment and laboratory human resource. The studies also indicates that mismatch among the objectives education, curriculum, and evaluation system which can be identified by the following: (a) National Leaving Examination assess the children’s ability cognitively only; (b) Streaming in Senior Secondary School starting at grade 3. It is argued that the implementation of this system is late and consider individual differences inappropriately; (c) University Entrance Examination (UMPTN) System is considered to trigger Elementary and Secondary School teachers apply goal oriented rather than process oriented in teaching Mathematics and Science.

Indonesia have a curriculum called KTSP. KTSP is a minimum standard of Indonesia’s curriculum for every school for each grade. This curriculum adapt to the school of isolated regional, so that the good-quality school can make improvisation so that the curriculum is match with the culture in every province in Indonesia.

Conclusion

There are some differences of mathematics teaching system in every country because of the differences of their culture. For example, we can make a comparison of the mathematics teaching system in some countries, such as Philippines, Thailand, Japan, and our country, Indonesia. We will find a differences the teaching system because of the culture differences, and the human resources quality.

The characteristics of the new course of study in Japan consist of: (a) reduction of the learning contents, (b) decrease of the number of classes, (c) comprehensive five-day school week, (d) integrated study mathematical activities, (e) practical and operational activities and problem-solving activities and so on, (e) basis points of active learning, (f) have the purpose of learning clearly, (g) have interest in the subject, (h) have an perspective to solve the problem, (i) have a feeling of satisfaction and joy, and (j) acquire the way of learning.

In Philippines, a students will pass six years in elementary school, four years in second level, and four or five years in third level. The purpose of the Phillipines mathematics education is almost same as the Japanese one. Both of them try to give the students various experiences will increase their capability to thinking logically and to be creative in using mathematics problems according to the fact in their daily life.

In Singapore, every subject will teached by three teachers, that is a master teacher, and his/her two assistents. They said it’s just to make the students learn mathematics easier. Further, in Singapore, the education system is based on the thoughts that every students have a unique talent and interests. Singapore employs a simple method and flexible one to develop the students capability.

            In Indonesia, there are a curriculum called KTSP. KTSP is a minimum standard of Indonesia’s curriculum for every school for each grade. This curriculum adapt to the school of isolated regional, so that the good-quality school can make improvisation so that the curriculum is match with the culture in every province in Indonesia.

How to Develop Teaching Learning Process of Mathematics in Junior and Senior High School

By Anniltal Manzilah

09301241028

Mathematics Education of 2009

I.    Introduction

As we know, in Indonesia, teacher prefer employing traditional method to a modern one. It’s not so good because in traditional method, the teacher always explain, explain and explain the students about the matter. This is not so good because by employ this method, the teacher have killed the student’s creativity. The students just have to listen and write what the teacher said, and the teacher treat the students like an empty vessel so that teacher can fill them more and more. It will make the student be a passive participant. The student is not too dare to ask some questions or ask clearer explanation.

To improve this condition, we have to reform all of the teaching learning components. We can make changes in the lesson plan, student’s worksheet, use small group discussion method, employ various interaction, implement various teaching methods, ask students to make a reflection everyday, understanding the cognitive schema, let the student to make a conclusion, understanding the apperception, assessment, and start using various media and teaching aids. We can make the students understanding the matter easily if wecan make a nice and fun condition of teaching learning process.

II.     How to Develop Teaching Learning Process of Mathematics in Junior and Senior High School

1.    Lesson plan

Lesson plan is the planning made by the teachers contains about standard competency, basic competency, indicator, the matter will be tought, the method will be employed, the assessment or evaluating system, etc. Lesson plan is made individually by each teacher, so that every teacher have a different lesson plan that will be used or will be implemented in their class.

Lesson plan is made everyday, so the teacher can evaluate the teaching-learning process to improve the quality of teaching-learning activities. There are standard competency and basic competency in lesson plan. Standard competency is chapter or an achievement that the teacher or maybe goverment want the students to mastered. Well, and basic competency is not the same as. Basic competency is more specific than standard competency. The steps that can be taken in making lesson plan are:

1.         Take a unit of learning that will be tought

2.         Make and determine standard and basic competency

3.         Determine the indicators

4.         Organize the time allocation

5.         Formulate learning objectives

6.         Determine and learn the materials

7.         Organize the methods that will be employed

8.         Arrange the learning activities that will be run

9.         Determine the assessment techniques and evaluating system

Beside that, lesson plan contains indicator and the matter will be tought too. Indicator is the ability that should be reached by the studets. Then, the matter is what subject or chapter that will be tought by the teacher in the class. To make it seems easier for you, I’ll give you an example. For example, a teacher make a lesson plan for mathematics subject. The standard competency is about Logic, that is how to use mathematical logic in problem solving that related to complex pronouncements. The basic competency can you make is: students understand about mathematics pronouncement and it’s negation, students can determine the propriety value of the pronouncement, etc. And then, the teacher must determine the indicators, it’s like students understand mathematical pronouncements and can make example of it. The matter that able to write in this lesson plan is about the definition of mathematics pronouncements, conjunction, disjunction, implication, biimplication, etc. And the last step, the teacher should plan about tha method and evaluating system that will be employd in his class. Tha teacher can employed more than just one method. The teacher may start his class with a short introduction employ expository method, and the use problem based learning, or perhaps he can employ discussion method for the next. The evaluating system is different for each method. In discussion method, the teacher should appraise student’s active, the question from each students, how the discussion going on, etc. After the teacher  did their lesson plan, they have to evaluate if the lesson plan run well or otherwise. If the lesson plan didn’t run well, may be the teacher should change the teaching method, or teaching strategy. By this way, teachers will understand how far their students understand the subject, and the difficulties that had to the students to improve the quality of learning activities.

2.    Student’s Worksheet

Student’s worksheet, usually called LKS in Indonesia, is a worksheet for students to measure hhow far they understand the matter tought by the their teachers. As we know, student’s worksheet usually given to students as a long list of tasks. I think that it’s not too effective to know how far the student’s understanding. Till the day, teachers always give a theory about mathematics, give their students some examples, and last, give them a lot of tasks. It’s exposition method. But our students is not like an empty vessel. We can’t treat them like an empty glass and fill more and more. How many teachers in Indonesia that understand this problem? Especially for elementary school’s teacher. They are the determinator of the characteristic of students. If we always employ this method, we don’t ever get a creative students or a smart one. We just produce machines. And our students is not machines. Why don’t we give them a chance, an opportunity to develop their ability? Why don’t we give them a problem and just look how they solve it?

It’s much better to make them more creative. If we always train them to be craeive in problem solving, although they forget the subject, they will always employ the way of thinking, that is critical, logic, and creative. I have a little example how to give a good student’s worksheet to train their creativity. For example, we are the teachers will be start the class. We enter the class, give a short introduction, in this case is about triangle. We can make or bring a picture of a triangle and show that to the students. We can asking the students to make a paper or the simpler one about the picture. Let them make and show up their perception about the picture. Let them construct their knowledge about triangle. The thing that we should do is just moving around and controlling the students or maybe we can help the students if they found a problem in making a perception. After they make and write their perception about the picture, we can ask some students to show up and present their perception in front of class. Let the other students enjoy the show. Don’t ever stop the show before it’s over. Ask 5 or more students to show up, and then let the other students to give a comment or maybe a question about their friend’s perception. In this moment, we can answer and straighten the perception if it’s not right. In other meeting, ask the other students to show up. We have to give a same chance for all students. If the students is cannot to work individually, we can split them to a small groups. Let them discuss the picture we gave, or in other case, we can give them a problem. It will train them to be creative and critical.

Beside that format of student’s worksheet, there are another format that could develop the student’s ability. I will explain in a simple example. This worksheet’s format is a reflection. After we end the teaching-learning process, we can ask our students to write a reflection about the subject and anything they got that day. It will help them to focus of attention along the class. So, student’s worksheet is not only a list of question given to the students, buat it can be given in many format to develop our student’s creativity, to make them critically, to train them to find a strategy in solving a problem. By this way, we can train their mind better.

3.    Small Group Discussion

Small Group discussion is a kind of interaction in class. Small group discussion run by split the students in a small group of some students to discuss a problem or a task that given by the teacher. Small group discussion is good to run if we employed problem solving learning or problem based learning. Because in this case, students need to discuss to their friends to find the best way or the simple strategy to solve the problem. Small group discussion will trai our students how to working in group, how to help each other in finding solutions of the problem, etc. The goal of employing small group discussion are:

1.      To provide an opportunity forour students to take their initiation in solving the problems. Small group discussion give the students more chance to improve their character, to develop their imagination to solve the problems.

2.      To deepen the student’s understanding. By discuss with their small group, students will more understand the matter.

3.      To give the students an opportunity to think and determine a strategy to solve the given problems.

In the implementation of this small group discussin, we need an active students. But at the fact, our students is almost passive ones. So, the obstacles of small group discussion’s implementation are:

a.       Teacher’s perception about this method is less. The teachers usually employ the traditional method because they don’t wanna to make difficulties to their selves to learn more about the modern methods.

b.      Small group discussion requires additional time. Of course, that’s right. In small group discussion, we will ask the students to discuss thw given problem with their small group, and then show up and present their discussion result in front of class.

c.       Small group discussion method usually dominated by brilliant students. That’s right too. To employ this small group method, we need active students, so the passive ones will be covered by the active and smart students. But it’s can be solved. We can give a little question to each member of the small group to make certain that al of the member in the group is understanding well about the matter.

d.      Evaluating system of small group discussion is more complex. This is the reason why almost teacher don’t employ this method. The teacher find a simple evaluating format, and find it in exposition method. In small group discussion, teachers sholed know and understanding the characteristic of each students to make the evaluating easier.

4.    Various Interaction

     There are three interaction can be run in class, that are whole class, small group discussion, and individually one. Whole class is interaction of the students or a students to all of the class. For example, in exposition method, the teacher stand up in front of class and explain more and more about the matter. It’s a whole class interaction. But, whole class interaction is can employ not only in exposition methods. We can combinate the methods to make a fun and nice learning so that the students will not feel bored in class. Although we employ discussion method, we still allowed to run whole class interaction, maybe in introduction, or when we straighten the student’s perception. The goal of whole class interaction are:

1.      To covered all of the students. For example, when the teachers gonna to give a problem to solve by all of the students. Before split the students in small groups, the teacher can run whole class interaction to explain what the problem is and how to make a small group discussion.

2.      Take a short time. If the teacher explained the problem in each small group, it will spend many times. So that, teacher sould run whole class iinteraction.

The next interaction is small group discussion. Small group discussion run by split the students in a small group of some students to discuss a problem or a task that given by the teacher. Small group discussion is good to run if we employed problem solving learning or problem based learning. Because in this case, students need to discuss to their friends to find the best way or the simple strategy to solve the problem. Small group discussion will trai our students how to working in group, how to help each other in finding solutions of the problem, etc. The goal of employing small group discussion are:

1.      To provide an opportunity forour students to take their initiation in solving the problems. Small group discussion give the students more chance to improve their character, to develop their imagination to solve the problems.

2.      To deepen the student’s understanding. By discuss with their small group, students will more understand the matter.

3.      To give the students an opportunity to think and determine a strategy to solve the given problems.

The last interaction is individually one. In this interaction, teacher or a student only talk or meking interaction to another one. For example when there is a student that give a question to the teacher or to another student that presenting his/her presentation. The goal of individual interaction is to make certain that all of the students understood the matter. If there is a student that don’t undrestanding about a presentation, we have to train him/her to give a question, so that all of the class can understand the matter well. Individual interaction will make teacher understanding deepen about the characteristic of each student. For this three various of class interaction, we cannot employ an interaction only, but we have to combine all of the varians to increase the learning quality.

5.    Various Teaching Method

There are so many teaching methods in teaching-learning process, such as:

1.      Exposition Method

This is a traditionnal or convention method in teaching-learning. The characteristics of this method are:

a.       The students are passive, it’s causes that the students just listen. Listen and listen to the teacher’s explanation

b.      The teacher treat their students as an empty vessel, so that they fill them more and more

c.       The class is very formal. The teacher standing in front of class and never stop of talk and the students sit to listen the teacher’s explanation

d.      The teacher is one and the only one sources of learning. The students must listen and record or make a note waht the teacher explain

e.       The teacher always talk and chalk only

f.       The structure are to explain, give students examples and finally give them tasks

g.      The teacher tends to be otoritarian

This method is not compatible to employ without combination with the other method. Exposition is good only to make a whole class interaction, so that the information can covered all of the students.

2.      Discussion Method

Discussion method is a way to organize, to manage learning activities with problem solving or problem based learning. Discussion method is participate by all of the students, and it’s good to develop colaboration each other. Small group discussion run by split the students in a small group of some students to discuss a problem or a task that given by the teacher. Small group discussion is good to run if we employed problem solving learning or problem based learning. Because in this case, students need to discuss to their friends to find the best way or the simple strategy to solve the problem. Small group discussion will trai our students how to working in group, how to help each other in finding solutions of the problem, etc. the characteristics of discussion method is the role of teacher is to facilitate the student’s need to learn mathematics.

3.      Ask and Answer Method

Ask and answer method is a way to manage learning process by produce and giving students some questions to help them to think critically in understanding the matter. This method will be run effectively if the matter is amazing and make the students interested to solve and learn more.

4.      Giving task method

Giving task method is a step to teach or present the matter by giving the students task. But it is better if we give the students task in front, so it’s like a student’s worksheet. Before we explain about the matter, we can ask the students to make a paper about the matter that will be tought, so that the students have a knowledge about what’the matter that will be learn. This task can be give in groups, so that the teacher can employ small group discussion and train their students about colaboration.

Beside the methods above, there are still many others, like games method, experimental method, etc.

6.    Student’s Reflection

Student’s refelection is like a resume or a summary of the day. So, after the teacher close his/her presention that day, let them to follow us in all, but give them a chance to make hers/his refelection as the evaliauion of teaching processs. Teacher can’t manipulate the student’s refelection. Because this reflection is a tool to evaluate how the teaching-learning run, and how to improve it.

The implementation of student’s reflection is to: give the student a chance for meking improvotation in teaching-learning process. By write the reflection honestly, they can show up their difficulties, what’s the matter that they can’t understand, etc. the teachers is also can understand the student’s difficulties so that teachers can help the student to solve their difficulties. For example, I got an English subject on my third semester. My lecturer is teach well. In every meeting, after the class closed, he always asking us to make a reflection and give them at the next week. By this way, he can understand our difficulties in learning English and know the students that have a good English.

7.    Cognitive Schema

Cognitive Schema- the organization of knowledge about a particular concept. The schema contains the features or attributes that are associated with a category membership. (Sims & Lorenzi, 1992). The Types of schema include:

1.      Person Schema. Schema about the attributes (skills, competencies, values) of a particular individual. This often takes the form the personality we attribute to that person.

2.      Event schema (cognitive scripts). These are processes, practices, or ways in which we typically approach tasks and problems. They are the programs we call upon when faced with a certain stimulus. These are behaviorally oriented

3.      Role schema. These schema contain sets of role expectations, that is, how we expect an individual occupying a certain role to behavior.

4.      Self-schema. Generalizations about the self abstracted from the present situation and past experiences. This is essentially one's self concept which is in essence perceptions of oneself in terms of traits, competencies, and values (see Laura's notes on Self Concept Based Motivation). Self-efficacy is a type of self schema that applies to a particular task.

The functions of cognitive schema are:

1.      To evaluate. When we evaluate individuals occupying a certain role (e.g., doctor, accountant, actor, artist), we compare their behavior to our culturally derived role schema for that role.

2.      Role playing. In assuming a certain role, the role schema often becomes our scripts as to how to behave.

3.      To identify. We often identify and categorize individuals by the role they assume. We use these role schema to help us place individuals into a certain category by matching their observed behavior with our role schema.

4.      To predict. Once an individual is placed into a category (role) we tend to assume he or she will behave in accordance with the role schema and use this as basis to predict future behavior of this person.

8.    Student’s Conclusion

Student’s conclusion is the conclusion of every student about a matter. This conclusion is mean a concluson about a subject, or teaching-learning process. The subject’s conclusion is student’s right. So the teacher can’t determine and just fill them like an empty vessel, because they have rights to make their conclusion about the matter. They can sort by theirselves what’s the matter that important for them, what’s the solving strategy that looks easier to do, etc. If a teacher give the students problem to solve, let them make and create their strategy to solve the problem. Even if the way, the steps or the strategy is complicated, just let them. Because how complicated the strategy is, the strategy is found by their selves, so that they can understand the steps well.

For example, in small group discussion, after the students discuss the problem with their grouup, we will ask some groups to present their result, their strategy in solving the problems. From the groups that presented their solving strategy, I’m sure that there are differences in each group. The teachers can’t judge a strategy is complicated or wrong, even if the teachers have a simpler one. Because the conclusion is the student’s right. So, let them look and pay attention to the presenter group and give them a chance to choose and determine which strategy that they think they can do well.

As same as like a solving strategy, the conclusion of teaching learning process is the student’s right too. The students should be given a chance to evaluate how good the teaching-learning process, and let them speak up about their conclusion, so that the teachers can make improvitation anytime the students find a difficulties about a teaching method.

9.    Apperception

Apperception  is any of several aspects of perception and consciousness in such fields as psychology,philosophy and epistemology.

In psychology, apperception is "the process by which new experience is assimilated to and transformed by the residuum of past experience of an individual to form a new whole. In short, it is to perceive new experience in relation to past experience. It originally means passing the threshold into consciousness, i.e., to perceive. But the percept is changed when reaching consciousness due to the contextual presence of the other stuff already there, thus it is not perceived but apperceived.

Apperception is a general term for all mental processes in which a presentation is brought into connexion with an already existent and systematized mental conception, and thereby is classified, explained or, in a word, understood; e.g. a new scientific phenomenon is explained in the light of phenomena already analysed and classified. The whole intelligent life of man is, consciously or unconsciously, a process of apperception, in as much as every act of attention involves the appercipient process.A rich child and a poor child walking together come across the same ten dollar bill on the sidewalk. The rich child says it is not very much money and the poor child says it is a lot of money. The difference lies in how they apperceive the same event – the lens of past experience through which they see and value (or devalue) the money. But it’s in psychology. There some differences about apperception in psychology, philosophy, and epistemology. In philosophy, Leibniz introduced the concept of apperception into the more technical philosophical tradition,although he used the word practically in the sense of the modern attention, by which an object is apprehended as "not-self" and yet in relation to the self. And last, in epistemology, apperception is "the introspective or reflective apprehension by the mind of its own inner states.

10.     Assessment

Assessment is include how to evaluate, how to record, how to uncover the student’s understanding about the matter. The goals of assessment are:

1.      To help the teacher making a standard value for student’s achievement

2.      To help the teacher to know the good students

3.      To help the teacher to determine or employ better teaching-learning strategy

4.      To help the teacher identifying what’s the student need in learning process

The instruments that can be used in assessment process are:

1.      Group Discussion

In discussion, the students will be asked to discuss each other(or maybe teacher can split the students in small groups) to discuss about the solutions of the problems given.

2.      Problem Analysis

In this instrument, the students will be given a problem and asked to analyze the problem in their perception and then find or create strategy to solve the problem.

3.      Presentation

The students (in a small group or individual) asked to show up their minds and their perception or maybe solutions about a given problem.

4.      Test of creative thinking

In this instrument, students are given some questions contains problems and then they asked to determine r create a strategy to solve. It is not about the solutions, but the strategy students create.

5.      Individual test

It is like an examination, but the format is not multiple choise. The teacher give some writen questions contains problems to solve, or asked the student to make a writing about a matter.

11.    Various Media

In teaching learning process, the teacher should use various media. To learning mathematics, students can’t only use a textbook. They need another sources. As same as teaching activities. The teacher can’t only talk and chalk, because it will make the students feel so bored about mathematics. So, teacher must use various media in teaching learning acivities, such as whiteboard, or sometimes can use LCD projector, and etc. It head for:

1.      Provide variety activities

2.      Provide various teaching methods

3.      Provide various context and learning atmosphere

4.      Make the learning activities to be nice and fun

5.      To deepen the student’s understanding

6.      Make the matter easier to understood by the the students

But it is not as easy as the theory to implement various media in teaching-learning process. That’s cause:

1.      Using various media requires a lot of time

2.      Need creative and professional teacher

3.      It requires more costs

It’s why the various media is cannot implemented yet. Because some schools is not too dare to give additional expence to increase teaching learning quality. And we also don’t have many creative teachers yet. The teachers in our country prefer employing exposition methods to try another one.

12.     Various Teaching Aids

Beside various media, there is various teaching aids. Teaching aids is the aids that teacher use to make students understand the matter easily. It can forms a model of cube, tube and the others, or picture about the matters. For example, we can use marbles to make the elementary students in understanding about operating systems such as addition, substraction, etc. To be underlined, teachers should use a familiar things so that the students can understand easily, especially for elementary students. In junior or senior high school, teacher don’t need to use marbles because it’s not appropriate with the matters in senior or junir high school. For high school students, teacher can use a picture of something related to the matter and ask the students to explain about the picture. For example, teacher will give a matter about triangle and rectangle. Taecher can use a palm leaf rib, or pipe and then ask the students to make a design of triangle and rectangle. By this way, teaching learning activities will be niceand funnier so that the students can understand the matter easily because the enjoy their learning activities.

The obstacles of implementing various teaching aids are:

1.      It’s spend more times

2.      It’s requires a creative teachers

3.      And it’s need additional costs to set aside the aids

But, it still can run. Even if there are no additional costs from the school, teacher still can run this method, but teachers must be more creative to make aids from unuseful things.

III.      Conclusion

From the explanation above, they know that to increase the teaching learning quality, we must take changes of learning components, from the lesson plan till the teaching learning activities. The teacher should be more creative in teaching activities and facilitate the student’s need to learn mathematics. Beside, the teacher must employs various methods of teaching and use various media and aids in teaching activities. But, the changes is not easy to do, because there are some obstacles in practicing the changes. Those are:

1.      The changes requires creative and professional teacher. It means that we should give training to the teachers so that they can take the changes and handle the class better.

2.      The changes spend more times in teaching learning process. For example in discussion and presentation. Discussion method is good, but it’s take more time. The teachers must be find the solution how to employ discussion method in short time.

3.      The changes need more costs. Using various media and aids will take more costs, but it can be solved by using unuseful things and recycle its to be reused.

4.