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AN ANALYSIS OF THE NEW ELEMENTARY MATHEMATICS TEACHER
EDUCATION CURRICULUM IN TURKEY
Disusun Guna memenuhi Tugas Mata Kuliah Penelitian Pendidikan Matematika
Prof. Dr. Sutama, M.Pd.
Disusun Oleh :
ANNISA IKA CAHYANI
A 410 080 169
FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN
UNIVERSITAS MUHAMMADIYAH SURAKARTA
2011
KATA PENGANTAR
Assalamu’alaikum Wr.Wb.
Alhamdulillahirobbil ‘alamin, Puji syukur kehadirat Illahi Robbi yang telah melimpahkan
rahmat dan karunia–Nya sehingga penulis dapat menyusun dan menyelesaikan review dengan
judul ”An Analysis of the New Elementary Mathematics Teacher Education Curriculum in
Turkey ”
Review jurnal ini disusun guna memenuhi tugas mata kuliah Penelitian Pendidikan
Matematika. Selama mereview jurnal ini, penulis tidak lepas dari bantuan berbagai pihak. Pada
kesempatan ini, penulis ucapkan terimakasih kepada:
1. Bapak Prof.Dr.Sutama,M.Pd selaku dosen mata kuliah Penelitian Pendidikan Matematika
yang telah memberikan pemikiran, pengarahan, dan bimbingan sehingga memperlancar
dalam penyelesaian review jurnal ini.
2. Orang tua yang selalu memberi motovasi.
3. Teman-teman VI D yang selalu memberi motivasi.
Penulis menyadari bahwa review jurnal ini masih jauh dari sempurna, untuk itu penulis
mengharapkan kritik dan saran untuk perbaikan dan kesempurnaan hasil yang telah didapat.
Harapan penulis semoga review jurnal ini dapat bermanfaat khususnya bagi penulis dan
bagi pembaca pada umumnya.
Wassalamu’alaikum Wr.Wb.
Surakarta, 26 April 2011
Penulis
ii
DAFTAR ISI
Halaman
HALAMAN JUDUL ...................................................................................
i
KATA PENGANTAR .................................................................................
ii
DAFTAR ISI................................................................................................
iii
BAB I
BAB II
BAB III
PENDAHULUAN
A. Latar Belakang Masalah ......................................................
1
B. Rumusan Masalah ................................................................
3
C. Tujuan Review .....................................................................
4
D. Manfaat Review ...................................................................
4
KAJIAN TEORI
A. Pengertian Pendidikan .........................................................
5
B. Fungsi dan Tujuan Pendidikan.............................................
5
C. Pengertian Kurikulum ..........................................................
6
D. Pengertian Guru ...................................................................
6
ISI
A. Gambaran sistem pendidikan guru di Negara-negara
berkembang. .........................................................................
B. Karakteristik
guru
Matematika
sebelum
7
kurikulum
direvisi………......................................................................
8
C. Kebutuhan kurikulum perlu direvisi/diperbaharui…………
9
D. Karakteristik
guru
matematika
setelah
kurukulum
direvisi………………………………………………………
iii
13
BAB IV
PEMBAHASAN
A. Gambaran sistem pendidikan guru di Negara-negara
berkembang ... ......................................................................
B. Karakteristik
guru
Matematika
sebelum
kurikulum
direvisi………......................................................................
17
C. Kebutuhan kurikulum perlu direvisi/diperbaharui…………
20
D. Karakteristik
guru
matematika
setelah
kurukulum
direvisi………………………………………………………
BAB V
15
26
KESIMPULAN, IMPLIKASI ,DAN SARAN
A. Kesimpulan ..........................................................................
30
B. Implikasi ..............................................................................
32
C. Saran ....................................................................................
33
DAFTAR PUSTAKA
LAMPIRAN
iv
BAB I
PENDAHULUAN
A. LATAR BELAKANG
Pendidikan merupakan investment yang paling utama bagi setiap bangsa yang
sedang berkembang dan giat membangun negaranya. Jalan pendidikan itu sendiri adalah
suatu proses untuk membantu manusia dalam mengembangkan dirinya sendiri sehingga
mampu menghadapi segala perubahan dan permasalahan yang bersifat terbuka serta
pendekatan kreatif tanpa kehilangan identitas diri.
Untuk mewujudkan pembangunan dibidang pendidikakn diperlukan peningkatan dan
penyempurnaan penyelenggaraan satu sistem pendidikan nasional, yang disesuaikan
dengan perkembangan ilmu pengetahuan dan teknologi, perkembangan masyarakat serta
kebutuhan pembangunan. Apalagi situasi dewasa ini dimana kemajuan ilmu pengetahuan
dan teknologi sudah mencapai taraf yang tinggi dimna pada saat ini dikuasai oleh negaranegara maju dan industry. Secara tidak langsung perkembangan ilmu pengetahuan dan
teknologi menyebabkan timbulnya problem-problem baru dalam masyarakat yang
menuntut pemecahan dengan pengetahuan, kemampuan dan keterangan baru yang
dikembangkan dalam pendidikan. Untuk mewujudkan kualitas pendidikan yang sesuai
dengan ilmu pengetahuan dan teknologi. Untuk mencapai tujuan tersebut, diperlukan
adanya para pendidik yang berkualitas yang didukung adanya kurukulum pendidikan
yang sesuai.
Pembangunan kurikulum Matematika menjadi sangat penting untuk dilakukan
oleh guru-guru sebagai tugas di lapangan. Untuk itu guru-guru harus pandai menguasai
Matematika yang mampu mendukung peningkatan kemampuan berfikir kritis, logis,
cermat dan disiplin serta menghargai kegunaan Matematika. Dengan semakin berat tugas
guru, sering kita dengar keluhan dari guru dalam penguasaan materi ajar. Maka guru
sebaiknya memahami dan menguasi materi ajar agar siswa dapat memahami apa yang di
ajarkan oleh guru tersebut.
Pendidikan di era reformasi menghadapi dua tuntutan. Pertama adalah tutuntan
masyarakat terhadap mutu pendidikan yang rendah dan belum relevan dengan
1
perkembangan masyarakat. Kedua, problema dalam meningkatkan kualitas manusia
manusia sebagai sumber daya yang berkualitas dan professional. Posisi guru merupakan
hal yang sangat penting dalam dunia pendidikan. Bidang pengajaran juga merupakan
salah satu bagian yang integral dari system pendidikan di sekolah yang menjadi tanggung
jawab guru.
Keberadaan guru bagi suatu bangsa amatlah penting, apalagi bagi suatu bangsa
yang sedang membangun, terlebih-legih bagi keberlangsungan hidup bangsa di tengahtengah lintasan perjalanan zaman dengan teknologi yang kian canggih dan segala
perubahan serta pergeseran nilai yang cenderung memberi nuansa kepada kehidupan
yang menuntut ilmu dan seni dalam kadar dinamik untuk dapat mengadaptasi diri.
Semakin akurat para guru melaksanakan fungsinya, semkin terjamin tercipta dan
terbinanya kesiapan dan keandalan seseorang sebagai manusia pembangunan. Dengan
kata lain, potret dan wajah diri bangsa di masa depan tercermin dari potret diri para guru
masa kini, dan gerak maju dinamika kehidupan bangsa berbanding lurus dengna citra
para guru di tengah-tengah masyarakat. Sejak dulu, dan mudah-mudahan sampai
sekarang, guru menjadi panutan masyarakat. Guru tidak hanya diperlukan oleh para
murid di ruang-ruang kelas, tetapi juga diperlukan oleh masyarakat lingkungannya dalam
menyelesaikan aneka ragam permasalahan yang dihadapi masyarakat.
Maka, Guru hendaknya menjadi pendidik yang dapat dijadikan tokoh, panutan,
dan identifikasi bagi para peserta didik dan lingkungannnya. Oleh karena itu, guru harus
memiliki standar kualitas pribadi tertentu. Seperti, bertanggung jawab, berwibawa,
mandiri, dan disiplin. Tanggung jawab seorang guru tercermin dari sikap mengetahui dan
memahami nilai, norma, dan social, serta berusaha berbuat sesuai dengan nilai dan norma
tersebut. Guru harus mempunyai wibawa. Hal ini dapat dilihat dari kelebihan dalam
merealisasikan nilai spiritual, emosional, moral, social, dan intelektual pribadinya, serta
memiliki kelebihan dalam pemahaman ilmu pengetahuan, teknologi, dan seni sesuai
dengan bidang yang dikembangkan. Ketika mengambil suatu keputusan guru harus
mandiri (indefendent), terutama yang berkaitan dengan pembelajaran dan
pembentukan kompetensi, serta bertindak sesuai dengan kondisi peserta didik dan
lingkungan.
2
Guru juga harus disiplin. Dalam arti mereka harus mematuhi berbagai peraturan dan tata
tertib secara konsisten, atas kesadaran professional, karena mereka bertugas untuk
mendisiplinkan para peserta didik, terutama dalam pembelajaran. Peranan guru sebagai
pendidik dapat dilaksanakan apabila guru memenuhi persyaratan kepribadian. Guru akan
mampu mendidik apabila dia mempunyai kestabilan emosi, memiliki rasa tanggung
jawab yang besar untuk memajukan peserta didik, bersikap realistis, jujur, terbuka, dan
peka terhadap perkembangan, terutama terhadap inovasi pendidikan. Guru sebagai
pendidik harus mempunyai kepribadian yang baik. Seperti berperilaku yang terpuji,
memiliki kestabilan emosional dan spiritual. Dengan kata lain, pendidik harus berakhlak
yang mulia dalam memberikan contoh kepada peserta didiknya.
Untuk menunjang itu semua perlu adanya kualifikasi akademik yaitu ijazah
jenjang pendidikan akademik yang harus dimiliki oleh guru sesuai dengan jenis, jenjang,
dan satuan pendidikan formal di tempat penugasan. Karena ketika seorang guru sudah
mempunyai kualifikasi dalam akademik, hendaknya guru memiliki kompetensi,
kemudian kualifikasi dan kompetensi tersebut diukur atau dinilai dari sertifikasi yang
dilakukan oleh pemerintah. Proses yang telah dilalui oleh guru dan dosen tersebut akan
menghasilkan tenaga yang professional.
Dengan berpijak pada beberapa persoalan yang ada, maka hal itulah yang
mendorong penulis untuk melakukan review tentang kurikulum pendidikan dan
karakteristik guru matematika meliputi peran dan tanggungjawab sebagai guru
matematika.
B. Rumusan Masalah
1. Bagaimana gambaran sistem pendidikan guru di negara-negara yang sedang
berkembang?
2. Bagaimana karakteristik guru matematika sebelum kurukulum
direvisi/diperbaharui?
3. Bagaimana kebutuhan kurikulum perlu direvisi/diperbaharui?
4. Bagaimana karakteristik guru matematika setelah kurukulum revisi/diperbaharui?
3
C. Tujuan Penelitian
Tujuan Umum
1. Menggambarkan sistem pendidikan guru.
2. Mengetahui karakteristik guru sebelum kurikulum direvisi/diperbaharui.
3. Mengetahui kebutuhan kurikulum perlu direvisi/diperbaharui.
4. Mengetahui karakteristik guru setelah kurikulum direvisi/diperbaharui.
Tujuan Khusus
1. Menggambarkan sistem pendidikan guru di negara-negara yang sedang
berkembang.
2. Mengetahui
karakteristik
guru
matematika
sebelum
kurikulum
direvisi/diperbaharui.
3. Mengetahui kebutuhan kurikulum perlu direvisi/diperbaharui.
4. Mengetahui
karakteristik
guru
matematika
setelah
kurukulum
direvisi/diperbaharui.
D. Manfaat Penelitian
1. Manfaat Teoritis
Secara teoritis review ini diharapkan dapat memberikan sumbangan kepada
pembelajaran matematika terutama pada prngetahuan tentang kurikulum yang
baik dan karakteristik dari guru matematika.
2. Manfaat Praktis
a. Sebagai masukan bagi guru dan sekolah untuk menerapkan kurikulum
yang baik.
b. Sebagai masukan bagi guru untuk menerapkan karakteristik guru yang
sesuai dengan peran dan tanggungjawab dalam mengajar.
c. Sebagai bahan pengetahuan bagi teman-teman yang belum mengetahui
kurikulum yang baik dan peran guru matematika serta tanggungjawab
sebagai guru matematika.
4
BAB II
KAJIAN TEORI
A. Pengertian pendidikan
“Pendidikan adalah usaha sadar untuk menyiapkan peserta didik melalui kegiatan
bimbingan, pengajaran, dan / atau latihan bagi peranannya di masa yang akan datang”
(pasal 1 ayat (1) UU No. 2 Tahun 1989)
“Pendidikan adalah usaha sadar dan terencana untuk mewujudkan suasana dan
proses pembelajaran agar peserta didik secara aktif mengembangkan potensi dirinya
untuk memiliki kekuatan spiritual keagamaan, pengendalian diri, kepribadian,
kecerdasan, akhlak mulia, serta ketrampilan yang diperlukan dirinya, masyarakat, bangsa,
dan Negara”. (pasal 1 ayat 1 UU No. 20 Tahun 2003).
B. Fungsi dan tujuan pendidikan
Menurut Pasal 3 UU No. 2 Tahun 1989 “Pendidikan nasional berfungsi untuk
mengembangkan kemampuan serta meningkatkan mutu kehidupan dan martabat manusia
Indonesia
dalam
rangka
upaya
mewujudkan
tujuan
nasional”
Pasal 3 UU No. 20 tahun 2003, tertulis : “Pendidikan nasional berfungsi mengembangkan
kemampuan dan membentuk watak serta peradaban bangsa yang bermartabat dalam
rangka mencerdaskan kehidupan bangsa”
Pasal 4 UU No. 2 Tahun 1989 “Pendidikan nasional bertujuan mencerdaskan
kehidupan bangsa dan mengembangkan manusia seutuhnya, yaitu manusia yang beriman
dan bertakwa terhadap Tuhan Yang Maha Esa dan berbudi pekerti luhur, memiliki
pengetahuan dan ketrampilan, kesehatan jasmani dan rohani, kepribadian yang mantap
dan mandiri serta rasa tanggung jawab kemasyarakatan dan kebangsaan”
Menurut UU No. 2 Tahun 1989 sasaran fungsi pendidikan nasional lebih luas,
yaitu : “terwujudnya tujuan nasional”.
5
Sedangkan dalam UU No. 20 Tahun 2003 sasarannya lebih menjurus yaitu
“dalam rangka mencerdaskan kehidupan bangsa”, melalui berkembangnya kemampuan
dan terbentuknya karakter serta peradaban banga.
C. Pengertian kurikulum
Pengertian kurikulum 1975 Surat Keputusan Menteri P dan K No : 008 c/v(1975),
kurukulum diartikan : “ Sebagai sejumlah pengalaman belajar yang diberikan di bawah
tanggung jawab sekolah dalam usaha untuk mencapai tujuan pendidikan tertentu .“
Menurur Soedijarto “ Kurikulum adalah segala pengalaman dan kegiatan yang
direncanakan dan diorganisir aleh para siswa atau mahasiswa untuk mencapai tujuan
pendidikan yang telah ditentukan bagi suatu lembaga pendidikan
( H. Soetopo,
N.Soemanto, 1986:13 ) .“
“Kurikulum berurusan dengan apa yang harus diajarkan kepada siapa, kapan, dan
bagaimana (Eisner dan Vallance 1974:2).”
D. Pengertian guru
Di Indonesia guru dan dosen termasuk dalam kelompok pendidik berdasarkan
Undang-Undang Sistem Pendidikan Nasional No. 20 Tahun 2003 pada Bab I tentang
Ketentuan Umum, yang berbunyi : “Pendidik adalah tenaga kependidikan yang
berkualifikasi sebagai guru, dosen, konselor, pamong belajar, widyaiswara, tutor,
instruktur, fasilitator, dan sebutan lain yang sesuai dengan kekhususannya, serta
berpartisipasi dalam menyelenggarakan pendidikan.”
Kemudian dalam Undang-Undang Guru dan Dosen pada Bab I pasal 1 ayat 1 dan
2, telah dijelaskan bahwa: “ Guru adalah pendidik professional dengan tugas utama
mendidik, mengajar, membimbing, mengarahkan, melatih, menilai, dan mengevaluasi
peserta didik pada pendidikan anak usia dini jalur pendidikan formal, pendidikan dasar,
dan pendidikan menengah.
“ Dosen adalah pendidik professional dan ilmuwan dengan tugas utama
mentransformasikan, mengembangkan, dan menyebarluaskan ilmu pengetahuan,
teknologi, dan seni melalui pendidikan, penelitian, dan pengabdian kepada masyarakat.”
6
BAB III
ISI
A. Gambaran sistem pendidikan guru di negara-negara yang sedang berkembang
Turki merupakan salah satu negara yang sedang berkembang,yaitu sejak dari
dasar Republik Turki pada tahun 1923, Turki bertujuan untuk meningkatkan standarnya
di arena ekonomi, sosial, politik, dan pendidikan dengan negara-negara maju melalui
berbagai upaya reformasi. Reformasi di bidang pendidikan termasuk di antara perubahan
yang paling penting di tahun 1920. Pada tahun 1924, sistem pendidikan di Turki terpusat
dan semua lembaga pendidikan yang diletakkan di bawah kendali Departemen
Pendidikan Nasional (MNE). Mengubah sistem pendidikan guru negara itu merupakan
fokus reformasi. Sebelum tahun 1980, guru-guru lulus dari berbagai lembaga dengan
beragam pengalaman, namun pada tahun 1981, semua lembaga pendidikan guru berada
di bawah kewenangan HEC . Untuk sistem yang terintegrasi dilakukan dengan pelatihan
guru. Kemudian, pada tahun 1989 Dewan mengamanatkan bahwa calon guru harus
melakukan pendidikan di perguruan tinggi selama empat tahun untuk memenuhi
persyaratan mendapatkan sertifikat mengajar (Binbasioglu, 1995).
Gelombang reformasi dalam pendidikan guru Turki cukup kuat di akhir 1990-an.
Pada tahun 1998, dengan dukungan dari Bank Dunia, guru HEC direstrukturisasi dengan
program pendidikan untuk meningkatkan kualitas, ini merupakan bagian dari proyek
empat tahun yang melibatkan perubahan di semua primer dan sekunder program
pendidikan guru di perguruan tinggi. Sebelum perubahan tahun 1998, ada 26 departemen
atau divisi pendidikan matematika yang memberikan lisensi untuk mengajar matematika
sekunder. Sebagai hasil dari perubahan ini, program yang ada ditutup dan diganti dengan
28 dasar dan 12 sekolah tinggi guru matematika program pendidikan. Sebagai bagian dari
perubahan kurikulum pendidikan guru, termasuk kurikulum pendidikan guru matematika
secara substansial perlu direvisi. Kurikulum itu diberlakukan mulai dari musim gugur
semester Tahun 1998.
7
B. Karakteristik guru matematika sebelum kurukulum direvisi/diperbaharui
Selama delapan tahun dari 1998-2006, dalam berbagai akademik dan publik
platform, termasuk simposium, panel, lokakarya dan konferensi, kualifikasi dari
preservice guru di kurikulum sebelumnya dipertanyakan. Ada konsensus tentang
kekurangan yang meliputi pengetahuan materi pelajaran, konten pedagogis pengetahuan,
dan keterampilan para guru preservice dalam menghadapi tuntutan masyarakat dan
teknologi saat ini. Ini disimpulkan bahwa kurikulum pendidikan guru ikut bertanggung
jawab atas masalah dalam pendidikan guru matematika. Dalam rangka untuk mencari
solusi untuk masalah yang ada, HEC berkolaborasi dengan fakultas dan dekan dari
perguruan tinggi dan memutuskan untuk merevisi kurikulum yang ada. Lulusan SMA
memperoleh program pendidikan guru melalui ujian masuk universitas. Beberapa fokus
sekolah tinggi di akhir pendidikan adalah mereka mengikuti sekolah tinggi dengan
kurikulum nasional tetapi menawarkan program pendidikan profesional, misalnya,
pengantar pendidikn dan psikologi pendidikan. Calon guru matematika juga diperlukan
untuk mengambil berbagai kuliah pedagogi. Calon guru matematika SD juga terlibat
dalam pengalaman lapangan sebagai bagian dari pendidikan mereka. Siswa mengambil
146 SKS untuk lulus dari program ini. Matematika dan fisika biasanya diajarkan dalam
cara yang sangat tradisional melalui ceramah. Pada umumnya ada dua ujian tengah
semester dan satu ujian akhir untuk menilai kinerja siswa kuliah. Metode pengajaran
kuliah matematika diharapkan diajarkan di non-tradisional, dengan format teori dan
praktek dicampur untuk membantu calon guru memahami aplikasi teori dan mendapatkan
pengalaman melalui berbagai kegiatan. Kuliah pedagogi diajarkan dalam berbagai cara.
Sedangkan kuliah umum, mahasiswa melakukan presentasi, presentasi video, kelompok
kecil kerja, diskusi kelompok besar dan non-metode tradisional yang digunakan untuk
menyampaikan materi pedagogi. Program pendidikan seluruh guru mengambil empat
tahun, setara dengan gelar sarjana reguler. Sertifikat yang diberikan oleh universitas
adalah permanen dan berlaku di seluruh negara. Guru diwajibkan untuk lulus Staf
Pemerintah Seleksi Ujian (KPSS) untuk bekerja di sekolah umum. Hanya 2% dari semua
sekolah SD (757 sekolah dari 34656) dioperasikan oleh organisasi swasta dan merekrut
guru berdasarkan kriteria mereka sendiri.
8
C. Kebutuhan kurikulum perlu direvisi/diperbaharui
Ada empat motivasi utama bagi revisi kurikulum pendidikan guru.
1. Persiapan untuk mengintegrasikan dengan Eropa Union
Secara umum Turki, bisa memperoleh manfaat dalam banyak hal dari
keanggotaan Uni Eropa (UE). Secara khusus, Turki berharap dapat menjadi lebih
terintegrasi, lebih makmur, lebih otonom, dan lebih demokratis sebagai seorang
anggota Uni Eropa. Selain reorganisasi di bidang politik, ekonomi dan sosial,
pendidikan dianggap sebagai komponen penting dari integrasi proses dengan Uni
Eropa. Turki yang lama berdiri ingin menjadi anggota Uni Eropa sehingga guru
termotivasi dan pengembang kurikulum untuk merevisi program pendidikan guru
dan memperbaiki tingkat standar pengajaran.
2. Perubahan dalam Kurikulum Matematika Sekolah Dasar
Pada tahun 2003, Departemen Pendidikan Nasional Turki diselenggarakan tim
pengembangan kurikulum untuk merevisi kurikulum matematika sekolah dasar
yang ada. Kurikulum baru ini dirancang sebagai bagian dari inisiatif reformasi
kurikulum yang lebih besar-besaran yang termasuk lima bidang yaitu:
matematika, ilmu pengetahuan, ilmu sosial, ilmu hidup dan bahasa Turki. Salah
satu tujuan utama dari reformasi kurikulum adalah untuk mempromosikan
pengajaran dan pembelajaran lingkungan di mana siswa bisa berbagi ide mereka
dan secara aktif berpartisipasi. Kurikulum baru ditempatkan suatu penekanan
yang berat pada pengembangan kognitif anak-anak, emosi, sikap, minat,
kepercayaan diri, keyakinan, kecemasan, pengaturan-diri, pengembangan
psikomotorik dan sosial keterampilan. Selain itu, kurikulum dipromosikan
mahasiswa melalui diskusi, penyelidikan, dan rasa ingin tahu tentang apa yang
sedang terjadi di dalam keluarga mereka, sekolah, dan masyarakat. Untuk
meningkatkan partisipasi siswa, guru didorong untuk mengatur siswa berpusat di
lingkungan kelas. Selain itu, adalah dalam tujuan kurikulum untuk mendorong
siswa untuk bekerja sama, untuk berkomunikasi secara efektif tentang ide-ide
mereka dan untuk mencerminkan pembelajaran mereka. Kurikulum mendorong
guru untuk mempertimbangkan unsur-unsur kontekstual luar, seperti gaya hidup
9
dan faktor-faktor geografis, sambil merancang tugas kelas. Guru diharapkan
untuk menunjukkan varietas keterampilan dan karakteristik agar dapat secara
efektif menerapkan kurikulum sekolah baru di SD. Mereka harus percaya bahwa
semua siswa dapat belajar matematika. Karakteristik tertentu sangat penting
dalam
mempromosikan
ekuitas
dalam
pembelajaran
matematika.
Guru
menghormati dan mengikuti semua aspek hak asasi manusia dan nilai-nilai etika
matematika dalam ruang kelas. Guru juga diharapkan untuk bekerja ke arah
membantu siswa mengembangkan sikap positif tentang matematika. Selain itu,
guru perlu membimbing dan memotivasi siswa dalam belajar matematika. Mereka
juga harus memotivasi siswa untuk mengajukan pertanyaan, terlibat dalam
kondisi kritis, negara berpikir dan ide dukungan, dan menanyakan tentang materi
pelajaran. Untuk mencapai tujuan tersebut, guru harus mengenal murid mereka,
orang tua, dan masyarakat di mana mereka tinggal. Selain itu, secara eksplisit
dinyatakan dalam kurikulum baru bahwa guru matematika harus menikmati
mengajar matematika. Pengajaran tanggung jawab guru sekolah dasar
matematika. Selain itu, di beberapa sekolah guru matematika ditugaskan kelas
advisees. Seperti semua guru lainnya, guru matematika juga bertanggung jawab
untuk mengatur dan memimpin kegiatan sosial seperti kegiatan olahraga, upacara
nasional, dan kegiatan ekstrakurikuler. Kurikulum menyatakan bahwa guru harus
mengembangkan dan melaksanakan kegiatan pembelajaran yang mempromosikan
pemahaman matematis, secara teratur memonitor dan evaluasi belajar siswa,
secara efektif mengelola waktu pembelajaran, dan mendorong siswa untuk
mengevaluasi mereka sendiri dan kemajuan rekan-rekan mereka. Guru juga
diharapkan dapat menggunakan hasil penilaian dan evaluasi untuk meningkatkan
kualitas pengajaran. Selanjutnya, guru matematika harus berkolaborasi dengan
orang tua, personil sekolah lainnya, dan masyarakat luar meningkatkan kualitas
sekolah. Mengingat di atas harapan untuk para guru, sudah pasti penting bahwa
guru mengembangkan kepercayaan diri dan peraturan keterampilan. Akhirnya,
mereka perlu untuk terus meningkatkan pengetahuan profesional dan pengalaman
melalui berbagai aktivitas, termasuk mengikuti penelitian ilmiah literatur dan
melakukan skala kecil proyek penelitian.
10
3. Kebutuhan untuk lebih baik kualifikasi guru
Salah satu faktor kunci dalam meningkatkan dan instruksi pemahaman siswa
dalam kelas matematika adalah peran guru . Pengajaran matematika secara efektif
adalah suatu usaha yang kompleks, dan tidak ada resep mudah untuk sukses.
Efektif guru harus mengetahui dan memahami mengajar matematika, dan mereka
fleksibel harus menarik bahwa pengetahuan. Sementara menantang dan
mendukung siswa, guru perlu mengetahui kesenjangan antara apa yang siswa
mereka tahu dan apa yang mereka butuhkan untuk belajar. NCTM (1991)
menekankan bahwa " guru harus membantu setiap siswa mengembangkan
konseptual dan prosedural pemahaman angka, operasi, geometri, pengukuran,
statistik, probabilitas, fungsi, dan aljabar dan hubungan di antara ide-ide ".
Dengan demikian, dalam rangka untuk mengembangkan konseptual dan
prosedural pemahaman siswa, guru harus memahami isi pada kedua tingkat ini.
Guru Matematika tidak hanya perlu memiliki isi cukup pengetahuan tentang
matematika, tetapi juga konten pedagogis pengetahuan. Guru perlu tahu mengapa
laporan matematika adalah benar, bagaimana untuk mewakili ide-ide matematika
dalam berbagai cara, apa yang merupakan definisi yang tepat dari suatu istilah
atau konsep, dan metode untuk menilai dan mengevaluasi metode matematika,
representasi, atau solusi . Pokok pengetahuan dan isi pengetahuan pedagogik
sangat penting dalam pengajaran matematika yang efektif dan di persiapan guru
matematika. Tirosh (2000) menyatakan bahwa tujuan utama dalam guru program
pendidikan harus untuk berkontribusi pada pengembangan pengetahuan
preservice guru dari umum cara anak-anak berpikir tentang sekolah matematika
topik. Pengalaman yang diperoleh dalam program pengajaran adalah utama, tetapi
bukan satu-satunya, sumber pengetahuan guru konsepsi umum siswa dan
kesalahpahaman. guru Preservice 'pengalaman sendiri sebagai pembelajar,
bersama dengan keakraban mereka dengan yang relevan penelitian perkembangan
dan kognitif, dapat digunakan dalam program pendidikan guru untuk
meningkatkan mereka pengetahuan umum cara berpikir di antara anak-anak.
Singkatnya, matematika isi dan isi pengetahuan pedagogi merupakan faktor
penting
dalam
efektivitas
guru
11
matematika.
Kurikulum
sekolah
baru
mengharuskan para guru untuk memperluas pengetahuan teoretis mereka dan
siswa berpusat pengalaman mengajar. HEC bertujuan untuk meningkatkan
kuantitas dan kualitas program studi di guru kurikulum pendidikan untuk
membantu
preservice
guru
meningkatkan
pengetahuan
profesional
dan
keterampilan untuk mengajarkan matematika SD. Turki, dalam program
pendidikan guru mengalami beberapa tantangan dalam mencapai tujuan-tujuan,
termasuk sejumlah anggota fakultas khusus dalam pendidikan guru, universitas
tidak memadai kemitraan sekolah, kurangnya lapangan cukup dan siswa
pengalaman mengajar, dan masalah dengan kuantitas dan kualitas kursus metode
pengajaran.
4. Masalah dengan sebelumnya kurikulum
Masalah utama dan bagaimana mereka mengatasi dalam kurikulum direvisi. Ini
masalah masuk ke dalam dua kategori utama: (a) isi dan pedagogi dan (b)
kebijakan. Pada kurikulum sebelumnya, ada 27 isi dan pedagogi kursus, termasuk
matematika, ilmu pengetahuan dan metode pengajaran program .Calon guru
matematika dasar juga diwajibkan untuk mengambil 9 program konten luar
mereka utama daerah, seperti biologi, fisika, dan kimia, dalam rangka
membangun interdisipliner hubungan antara ilmu pengetahuan dan matematika.
Siswa juga diharapkan untuk mencapai tingkat yang sama kemahiran dalam ilmu
sebagai ilmu pengetahuan yang diperlukan guru. Ketidakseimbangan antara
jumlah ilmu pengetahuan dan kursus matematika menjadi salah satu perhatian
utama pendidik guru dan spesialis lain karena revisi kurikulum pendidikan.
Keprihatinan lain tentang isi guru kurikulum pendidikan adalah jumlah terbatas
kursus pendidikan umum. Dalam program sebelumnya studi, ada sepuluh
program dirancang untuk umum pendidikan guru preservice, termasuk sejarah,
Bahasa Turki, bahasa asing, dan prinsip-prinsip dari Kemal Ataturk, pendiri
republik . Program tersebut bertujuan untuk meningkatkan guru kandidat
kesadaran sosial, budaya, dan sejarah isu (HEC, 2006). Dengan demikian, pada
akhir kursus ini, guru preservice harus memiliki pengalaman yang sesuai
bertujuan untuk meningkatkan pemahaman mereka tentang konten dan pedagogi
12
matematika. Permasalahan lain yang berkaitan persiapan guru adalah penekanan
terbatas pada perencanaan instruksional dan penilaian. Sebelumnya, hanya ada
satu program yang meliputi perencanaan dan penilaian, namun menangani semua
tujuan tentu saja dalam satu semester sulit. Akhirnya, guru calon tidak diberikan
cukup pengalaman dalam bekerja dengan siswa dari beragam populasi, termasuk
siswa dengan kebutuhan khusus kebutuhan. Terkait dengan persoalan ini,
pendidikan guru kursus tidak dirancang untuk membantu guru preservice
mengajarkan materi pelajaran untuk semua siswa.
D. Karakteristik guru matematika setelah kurukulum revisi/diperbaharui
Kurikulum adalah penekanan diberikan kepada umum melalui kursus pendidikan.
Kurikulum pengembang diharapkan masa depan guru matematika untuk mempelajari
lebih lanjut tentang budaya Turki, sejarah pendidikan Turki sistem, filsafat ilmu, dan
sejarah dan filsafat matematika. Guru dengan cukup latar belakang dan keterampilan
dalam studi umum dan informasi teknologi, pengalaman yang cukup dalam melakukan
penelitian, dan multidimensi perspektif mungkin lebih efektif dalam kelas mereka
praktek. Dalam kursus tertentu, mereka diharapkan untuk bekerja dengan pemerintah dan
non- organisasi pemerintah untuk terlibat dalam berbagai proyek, misalnya, membantu
orang dalam kemiskinan, membantu perpustakaan lokal, dan bekerja dengan siswa di
pedesaan daerah. Tujuan dari program ini adalah untuk memotivasi calon guru untuk
berpartisipasi dalam kesempatan relawan dan meningkatkan rasa empati dan kesadaran
sosial. Kurikulum pendidikan membutuhkan guru baru menyelesaikan kursus metode
penelitian. Penelitian tentu saja akan memberikan kesempatan belajar bagi preservice
guru untuk meningkatkan keterampilan dan penelitian praktek. Ide ini berasal dari
Harrison, Dunn, dan Coombe (2006) yang berpendapat bahwa penelitian kelas akan lebih
efektif jika di kelas guru aktif praktisi mengajar. Untuk melaksanakan kurikulum baru,
guru perlu dilengkapi dengan sesuai pengetahuan, keterampilan, dan pengalaman. Guru
kurikulum pendidikan baru menempatkan cukup tingkat penekanan pada sukses
pemanfaatan kurikulum sekolah dasar. Ini termasuk memotivasi siswa untuk mengajukan
pertanyaan, menarik siswa dalam berpikir kritis, dan menggunakan matematika
13
penyelidikan dalam praktek matematika di kelas mereka. Kurikulum pendidikan guru
baru juga bersangkutan dengan mengatasi mengatasi kurikulum sebelumnya. Masalahmasalah ini didasarkan pada konten, pedagogi dan isu-isu kebijakan terkait. Dengan
meningkatkan jumlah mengajar kursus matematika metode, calon guru diharapkan
memiliki pemahaman lebih mendalam tentang matematika dan prosedur dan pengetahuan
konten pedagogi. Kurikulum pengembang bertujuan untuk meningkatkan kualitas
pendidikan guru matematika untuk bahwa dari standar internasional, namun untuk
merevisi kurikulum tidak cukup untuk mencapai tingkat yang diinginkan. Pelaksanaan
program kurikulum baru akan dipantau dan terus dievaluasi untuk meningkatkan kualitas
guru untuk tingkat tertinggi. Pelaksanaan kurikulum akan diawasi oleh Dewan
Pendidikan Tinggi Turki melalui umpan balik yang berkesinambungan dari pendidik
guru. Lebih lanjut upaya pemantauan dapat dilakukan oleh individu program pendidikan
guru untuk mengeksplorasi kekuatan dan kelemahan dari kurikulum yangdirevisi.
14
BAB IV
PEMBAHASAN
Pembahasan dari Jurnal Internasional dengan Judul ” An Analysis of the New Elementary
Mathematics Teacher Education Curriculum in Turkey “ atau
Sebuah analisis
matematika oleh guru SD tentang Kurikulum baru di Turki, hal ini sebagai upaya untuk
meningkatkan pemahaman tentang kurikulum yang menjadi dasar mengajar serta
kualifikasi yang harus dimiliki guru sebagai pengajar.
Adapun permasalahan yang akan dicari jawabannya dalam review jurnal ini adalah :
A. Permasalahan I : Bagaimanakah gambaran sistem pendidikan guru di nerara-negara
berkembang ?
Dari hasil review dari Jurnal dan dari beberapa buku serta artikel ada beberapa
gambaran sistem pendidikan guru yang dapat diambil dan dapat dijadikan acuan serta
gambaran agar sistem pendidikan lebih maju lagi. Beberapa gambaran sistem
pendidikan guru di nerara-negara berkembang diantaranya :
1. Dari Jurnal Internasional dengan judul” An Analysis of the New Elementary
Mathematics Teacher Education Curriculum in Turkey “ yaitu tentang
gambaran sistem pendidikan guru di nerara Turki.
Turki merupakan salah satu negara yang sedang berkembang,yaitu sejak
dari dasar Republik Turki pada tahun 1923, Turki bertujuan untuk
meningkatkan standarnya di arena ekonomi, sosial, politik, dan pendidikan
dengan negara-negara maju melalui berbagai upaya reformasi. Reformasi di
bidang pendidikan termasuk di antara perubahan yang paling penting di tahun
1920. Pada tahun 1924, sistem pendidikan di Turki terpusat dan semua lembaga
pendidikan yang diletakkan di bawah kendali Departemen Pendidikan Nasional
(MNE). Mengubah sistem pendidikan guru negara itu merupakan fokus
reformasi. Sebelum tahun 1980, guru-guru lulus dari berbagai lembaga dengan
beragam pengalaman, namun pada tahun 1981, semua lembaga pendidikan guru
berada di bawah kewenangan HEC . Untuk sistem yang terintegrasi dilakukan
dengan pelatihan guru. Kemudian, pada tahun 1989 Dewan mengamanatkan
bahwa calon guru harus melakukan pendidikan di perguruan tinggi selama
15
empat tahun untuk memenuhi persyaratan mendapatkan sertifikat mengajar
(Binbasioglu, 1995). Gelombang reformasi dalam pendidikan guru Turki cukup
kuat di akhir 1990-an. Pada tahun 1998, dengan dukungan dari Bank Dunia,
guru HEC direstrukturisasi dengan program pendidikan untuk meningkatkan
kualitas, ini merupakan bagian dari proyek empat tahun yang melibatkan
perubahan di semua primer dan sekunder program pendidikan guru di perguruan
tinggi. Sebelum perubahan tahun 1998, ada 26 departemen atau divisi
pendidikan matematika yang memberikan lisensi untuk mengajar matematika
sekunder. Sebagai hasil dari perubahan ini, program yang ada ditutup dan
diganti dengan 28 dasar dan 12 sekolah tinggi guru matematika program
pendidikan. Sebagai bagian dari perubahan
kurikulum pendidikan guru,
termasuk kurikulum pendidikan guru matematika secara substansial perlu
direvisi. Kurikulum itu diberlakukan mulai dari musim gugur semester Tahun
1998.
2. Dalam buku “ Dari KBK sampai MBS “ karangan J. Drost, SJ tentang gambaran
sistem pendidikan di Indonesia yaitu :
Mulai tahun 2004 Kurikulum Berbasis Kompetensi (KBK) diterapkan di
Indonesia. Secara singkat dengan KBK mau ditekankan agar siswa yang
mengikuti pendidikan di sekolah memperoleh kompetensi yang diinginkan.
Dengan demikian siswa bukan hanya menghafal, mengingat dan mengerti
teori,tetapi sungguh menguasai bidang yang dikuasai.
Namun diberbagai sekolah , terlebih di pelosok yang jauh dari fasilitas dan
ahli, banyak guru tidak siap. Mereka mendengar, tetapi belum mengerti. Dalam
praktiknya mereka masih bingung bagaimana mengajar dengan model KBK itu.
Maka tidak mengherankan bahwa di berbagai tempat, banyak guru yang mengajar
dengan cara lama, yang menekankan pada banyaknya isi bahan. Bahkan di
beberapa tempat guru meski dengan nama KBK, tetapi mengajar dengan cara
lama. Akibatnya siswa malah menjadi makin berat karena harus menekuni dua
cara yang berbeda.
16
Salah satu sebab kualitas pendidikan di Indonesia agak rendah di berbagai
tempat adalah karena mutu guru yang memang cukup rendah. Memang di stu sisi
kita melihat adanya banyak guru di sekolah-sekolah bermutu di kota besar yang
sungguh tinggi dan mereka menjalankan tugas mereka sebagai pendidiksecara
profesional. Namun di samping itu di berbagai tempat, terlebih di daerah pelosok,
tenaga pendidik ternyatabanyak kualitasnya yang kurang.
B. Permasalahan II : Bagaimana karakteristik guru matematika sebelum kurukulum
direvisi/diperbaharui?
Dari hasil review dari Jurnal dan dari beberapa buku serta artikel ada beberapa
karakteristik guru matematika sebelum kurukulum direvisi/diperbaharui dari negaranegara yang sedang berkembang, diantaranya adalah :
1. Dari Jurnal Internasional dengan judul” An Analysis of the New Elementary
Mathematics Teacher Education Curriculum in Turkey “ yaitu tentang
karakteristik guru matematika sebelum kurukulum direvisi/diperbaharui.
Selama delapan tahun dari 1998-2006, dalam berbagai akademik dan
publik platform, termasuk simposium, panel, lokakarya dan konferensi,
kualifikasi dari preservice guru di kurikulum sebelumnya dipertanyakan. Ada
konsensus tentang kekurangan yang meliputi pengetahuan materi pelajaran,
konten pedagogis pengetahuan, dan keterampilan para guru preservice dalam
menghadapi tuntutan masyarakat dan teknologi saat ini. Ini disimpulkan bahwa
kurikulum pendidikan guru ikut bertanggung jawab atas masalah dalam
pendidikan guru matematika.
Dalam rangka mencari solusi untuk masalah yang ada, HEC berkolaborasi
dengan fakultas dan dekan dari perguruan tinggi dan memutuskan untuk merevisi
kurikulum yang ada. Lulusan SMA memperoleh program pendidikan guru
melalui ujian masuk universitas. Beberapa fokus sekolah tinggi di akhir
pendidikan adalah mereka mengikuti sekolah tinggi dengan kurikulum nasional
tetapi menawarkan program pendidikan profesional, misalnya, pengantar
pendidikn dan psikologi pendidikan. Calon guru matematika juga diperlukan
17
untuk mengambil berbagai kuliah pedagogi. Calon guru matematika SD juga
terlibat dalam pengalaman lapangan sebagai bagian dari pendidikan mereka.
Matematika dan fisika biasanya diajarkan dalam cara yang sangat tradisional
melalui ceramah. Pada umumnya ada dua ujian tengah semester dan satu ujian
akhir untuk menilai kinerja siswa kuliah. Metode pengajaran kuliah matematika
diharapkan diajarkan di non-tradisional, dengan format teori dan praktek
dicampur untuk membantu calon guru memahami aplikasi teori dan mendapatkan
pengalaman melalui berbagai kegiatan. Program pendidikan seluruh guru
mengambil empat tahun, setara dengan gelar sarjana reguler. Sertifikat yang
diberikan oleh universitas adalah permanen dan berlaku di seluruh negara. Guru
diwajibkan untuk lulus Staf Pemerintah Seleksi Ujian (KPSS) untuk bekerja di
sekolah umum.
2. Dalam artikel yang berjudul “Analisa Kebijakan Peningkatan Kualitas
Pendidikan” terdapat karakteristik guru matematika sebelum kurukulum
direvisi/diperbaharui yaitu :
Dunia pendidikan di Indonesia mengalami perubahan yang sangat besar
baik swasta maupun pemerintah. Hal ini dapat dilihat dari berbagai fasilitas
layanan dan mutu yang ditawarkan sekolah, Setiap institusi pendidikan akan
berusaha memaksimalkan jasa layanan dan meningkatkan mutu kepada
masyarakat dengan tujuan untuk memuaskan pelanggan dalam hal ini orang tua
dan siswa itu sendiri. Kemajuan zaman dalam era globalisesi seperti sekarang ini,
menuntut kesiapan yang lebih matang dalam segala hal terutama bidang yang
terkait dengan dunia pendidikan. Bidang pendidikan merupakan salah satu
andalan untuk mempersiapkan sumber daya manusia yang dibutuhkan dalam
menghadapi tantangan zaman. Kualitas pendidikan di Indonesia saat ini sangat
mengawatirkan, ini terbukti antara lain dengan data UNESCO pada tahun 2000
tentang peringkat Indekpembangunan manusia ( Human Develelopmant Indeks)
yaitu komposisi dari peringkat pencapaian pendidikan, kesehatan, penghasilan
perkepala yang menunjukan bahwa indek pembangunan Indonesia ( Human
Develelopment Indeks) makin menurun.
18
Permasalah utama pendidikan ada dasarnya adalah disparitas mutu
pendidikan khususnya yang berkaitan dengan (1) ketersediaan pendidik dan
tenaga kependidikan yang belum memadai baik secara kuantitas dan kualitas
maupun kesejahteraannya, (2) prasarana sarana belajar yang belum tersedia atau
belum memadai, (3) pendanaan pendidikan yang belum memadai untuk
menunjang mutu pembelajaran, (4) proses pembelajaran yang belum efisien dan
efektif, dan penyebaran sekolah yang belum merata, ditandai dengan belum
meratanya partisipasi pendidikan antara kelompok masyarakat, seperti masih
terdapatnya kesenjangan antara penduduk kaya dan miskin, kota dan desa, lakilaki dan perempuan, antar wilayah. Dua permasalahan tersebut diatas menjadi
bertambah parah karena tidak didukung dengan komponen-komponen utama
pendidikan seperti kurikulum, sumberdaya manusia pendidikan yang berkualitas
sarana dan prasarana, pembiayaan. Masalah sarana pendidikan yang dihadapi
sekolah, dimana sarana penunjang pendidikan belum sepenuhnya dimiliki oleh
sekolah dan belum sepenuhnya berada dalam kondisi yang memadai. Hal ini
dapat dilihat dari sarana belajar seperti peralatan olah raga, praktikum serta
beberapa sekolah masih belum memiliki lab. bahasa, sehingga kondisi ini akan
sangat berpengaruh pada proses belajar baik pada guru dan siswa serta akan
berdampak pada kualitas hasil pembelajaran. Manajemen sarana pendidikan
sangat penting agar sarana pendidikan dapat berfungsi dengan baik dimana
berkaitan dengan penentuan kebutuhan, proses pengadaan, pemakaian, pencatatan
dan pertanggung jawaban. Dalam hal pengadaan sarana pendidikan juga sering
terjadi masalah tentang kebutuhan sarana pendidikan tetapi sarana tersebut tidak
ada, dimana hal ini akan menghambat proses belajar mengajar serta akan
mempengaruhi motivasi
guru dalam mengajar sehingga kualitas hasil
pembelajaran menjadi tidak optimal. Sistem penyelenggaraan pendidikan, dimana
tanpa mengecilkan peran pendidikan lainnya, harus diakui bahwa guru sebagai
salah satu komponen pendidikan merupakan faktor utama dalam proses
pendidikan. Meskipun fasilitas pendidikannya lengkap dan canggih, namun
apabila tidak ditunjang oleh keberadaan guru yang berkualitas maka mustahil
akan menimbulkan proses belajar mengajar yang maksimal. Oleh karena itu
19
permasalahan tentang mutu pendidikan tidak akan pernah terlepas dari
permasalahan kinerja guru sebagai tenaga pendidik.
C. Permasalahan III : Bagaimana kebutuhan kurikulum perlu direvisi/diperbaharui?
Dari hasil review dari Jurnal dan dari beberapa buku serta artikel ada beberapa
kebutuhan kurukulum direvisi/diperbaharui dari negara-negara yang sedang
berkembang, diantaranya adalah :
1.
Dari Jurnal Internasional dengan judul” An Analysis of the New Elementary
Mathematics Teacher Education Curriculum in Turkey “ yaitu tentang
kebutuhan kurukulum direvisi/diperbaharui.
Ada empat motivasi utama bagi revisi kurikulum pendidikan guru.
a) Persiapan untuk mengintegrasikan dengan Eropa Union
Secara umum Turki, bisa memperoleh manfaat dalam banyak hal dari
keanggotaan Uni Eropa (UE). Secara khusus, Turki berharap dapat
menjadi lebih terintegrasi, lebih makmur, lebih otonom, dan lebih
demokratis sebagai seorang anggota Uni Eropa. Selain reorganisasi di
bidang politik, ekonomi dan sosial, pendidikan dianggap sebagai
komponen penting dari integrasi proses dengan Uni Eropa. Turki yang
lama berdiri ingin menjadi anggota Uni Eropa sehingga guru termotivasi
dan pengembang kurikulum untuk merevisi program pendidikan guru dan
memperbaiki tingkat standar pengajaran.
b) Perubahan dalam Kurikulum Matematika Sekolah Dasar
Pada tahun 2003, Departemen Pendidikan Nasional Turki diselenggarakan
tim pengembangan kurikulum untuk merevisi kurikulum matematika
sekolah dasar yang ada. Kurikulum baru ini dirancang sebagai bagian dari
inisiatif reformasi kurikulum yang lebih besar-besaran yang termasuk lima
bidang yaitu: matematika, ilmu pengetahuan, ilmu sosial, ilmu hidup dan
bahasa Turki. Salah satu tujuan utama dari reformasi kurikulum adalah
untuk mempromosikan pengajaran dan pembelajaran lingkungan di mana
siswa bisa berbagi ide mereka dan secara aktif berpartisipasi. Kurikulum
20
baru ditempatkan suatu penekanan yang berat pada pengembangan kognitif
anak-anak, emosi, sikap, minat, kepercayaan diri, keyakinan, kecemasan,
pengaturan-diri, pengembangan psikomotorik dan sosial keterampilan.
Selain
itu,
kurikulum
dipromosikan
mahasiswa
melalui
diskusi,
penyelidikan, dan rasa ingin tahu tentang apa yang sedang terjadi di dalam
keluarga mereka, sekolah, dan masyarakat. Selain itu, adalah dalam tujuan
kurikulum
untuk
mendorong
siswa
untuk
bekerja
sama,
untuk
berkomunikasi secara efektif tentang ide-ide mereka dan untuk
mencerminkan pembelajaran mereka. Kurikulum mendorong guru untuk
mempertimbangkan unsur-unsur kontekstual luar, seperti gaya hidup dan
faktor-faktor geografis, sambil merancang tugas kelas. Kurikulum
menyatakan bahwa guru harus mengembangkan dan melaksanakan
kegiatan pembelajaran yang mempromosikan pemahaman matematis,
secara teratur memonitor dan evaluasi belajar siswa, secara efektif
mengelola waktu pembelajaran, dan mendorong siswa untuk mengevaluasi
mereka sendiri dan kemajuan rekan-rekan mereka. Guru juga diharapkan
dapat menggunakan hasil penilaian dan evaluasi untuk meningkatkan
kualitas pengajaran. Selanjutnya, guru matematika harus berkolaborasi
dengan orang tua, personil sekolah lainnya, dan masyarakat luar
meningkatkan kualitas sekolah.
c) Kebutuhan untuk lebih baik kualifikasi guru
Salah satu faktor kunci dalam meningkatkan dan instruksi pemahaman
siswa dalam kelas matematika adalah peran guru . Pengajaran matematika
secara efektif adalah suatu usaha yang kompleks, dan tidak ada resep
mudah untuk sukses. Efektif guru harus mengetahui dan memahami
mengajar matematika, dan mereka fleksibel harus menarik bahwa
pengetahuan. Sementara menantang dan mendukung siswa, guru perlu
mengetahui kesenjangan antara apa yang siswa mereka tahu dan apa yang
mereka butuhkan untuk belajar. NCTM (1991) menekankan bahwa " guru
harus membantu setiap siswa mengembangkan konseptual dan prosedural
pemahaman angka, operasi, geometri, pengukuran, statistik, probabilitas,
21
fungsi, dan aljabar dan hubungan di antara ide-ide ". Dengan demikian,
dalam rangka untuk mengembangkan konseptual dan prosedural
pemahaman siswa, guru harus memahami isi pada kedua tingkat ini. Guru
Matematika tidak hanya perlu memiliki isi cukup pengetahuan tentang
matematika, tetapi juga konten pedagogis pengetahuan. Kurikulum
sekolah baru mengharuskan para guru untuk memperluas pengetahuan
teoretis mereka dan siswa berpusat pengalaman mengajar. HEC bertujuan
untuk meningkatkan kuantitas dan kualitas program studi di guru
kurikulum pendidikan untuk membantu preservice guru meningkatkan
pengetahuan profesional dan keterampilan untuk mengajarkan matematika
SD. Turki, dalam program pendidikan guru mengalami beberapa
tantangan dalam mencapai tujuan-tujuan, termasuk sejumlah anggota
fakultas khusus dalam pendidikan guru, universitas tidak memadai
kemitraan sekolah, kurangnya lapangan cukup dan siswa pengalaman
mengajar, dan masalah dengan kuantitas dan kualitas kursus metode
pengajaran.
d) Masalah dengan sebelumnya kurikulum
Masalah utama dan bagaimana mereka mengatasi dalam kurikulum
direvisi. Ini masalah masuk ke dalam dua kategori utama: (a) isi dan
pedagogi dan (b) kebijakan. Pada kurikulum sebelumnya, ada 27 isi dan
pedagogi kursus, termasuk matematika, ilmu pengetahuan dan metode
pengajaran program .Calon guru matematika dasar juga diwajibkan untuk
mengambil 9 program konten luar mereka utama daerah, seperti biologi,
fisika, dan kimia, dalam rangka membangun interdisipliner hubungan
antara ilmu pengetahuan dan matematika. Permasalahan lain yang
berkaitan persiapan guru adalah penekanan terbatas pada perencanaan
instruksional dan penilaian. Sebelumnya, hanya ada satu program yang
meliputi perencanaan dan penilaian, namun menangani semua tujuan tentu
saja dalam satu semester sulit. Akhirnya, guru calon tidak diberikan cukup
pengalaman dalam bekerja dengan siswa dari beragam populasi, termasuk
siswa dengan kebutuhan khusus kebutuhan.
22
2. Dalam buku “ Menjadi Guru Unggul “ karangan Ahmad Barizi dan dalam artikel
yang berjudul “Analisa Kebijakan Peningkatan Kualitas Pendidikan” terdapat
beberapat kebutuhan kurukulum direvisi/diperbaharui diantaranya adalah :
a) Masalah tentang kualitas pendidikan di Indonesia
Untuk memecahkan masalah tersebut maka Pemerintah dengan Dinas
Pendidikan menyusun melakukan beberapa upaya perbaikan diantaranya
sarana dan prasarana pendidikan .Kebijakan Publik yang dikeluarkan
pemerintah berupa ,Peraturan pemerintah No. 19 tahun 2005 tentang
Standar Nasional Pendidikan, sebagai upaya meningkatkan kualitas
Pendidikan di Indonesia. PP No. 19 Tahun 2005, tentang standar Nasional
pendidikan pada penjelasan pasal 11 ayat (2) dan (3), Dengan berlakuknya
Standar Nasional Pendidikan, maka Pemerintah memiliki Kepentingan
untuk memetakan sekolah/madrasah menjadi sekolah/madrasah yang
sudah
hampir
memenuhi
Standar
Nasional
Pendidikan
dan
Sekolah/Madrasah yang belum memenuhi Standar Nasional Pendidiakan.
Terakait
dengan
hal
tersebut
Pemerintah
mengkategorikan
sekolah/madrasah yang telah memenuhi atau hampir memenuhi Standar
Nasional Pendidikan kedalam Kategori Mandiri, dan sekolah/madrasah
yang belum memenuhi sdardar Nasional Pendidikan ke dalam ke dalam
Kategori Standar. Sekolah tersebut dapat dikategorikan SKM/SSN
karakteristiknya
adalah
sudah melaksanakan
8 standar
Nasional
Pendidikan yaitu (1) Standar isi dan standar Kelulusan, (2) Standar Proses,
(3) Standar Pendidikan dan Tenaga Kependidikan, (4) standar sarana dan
Prasarana, (5) Standar Pengelolaan, (6) Standar Pembiayaan, (7) Standar
Penilaian (8)Kesiapan Sekolah dan Dukumen Eksternal. Perdiknas RI No.
13 Tahun 2007 Tentang Standar Kepala sekolah/Madrasah, dengan
demikian tugas dan fungsi kepala sekolah dapat lebih optimal karena
berdasarkan kompetensi (kemampuan) yang mereka miliki benar-benar
telah terkualifikasi dengan baik. Sehingga diharapkan dapat menjalankan
manajeman pembelajaran dengan baik.
23
b) Menyiapkan sumber daya manusia yang bermutu
Guru merupakan salah stu pilar atau komponen utama yang dinamis dalam
mencapi tujuan pendidikan serta untuk mewujudkan pendidikan yang
bermutu. Salah satu faktor penyebab adalah guru tidak siap untuk
memanfaatkan fasilitas yang diberikan oleh berbagai macam proyek yang
ditujukan kesekolah tersebut, Oleh karena itu pencapaian standar
kopetensi guru merupakan keharusan. Sebab tanpa ada standar maka
jaminan kepada stakholder tidak mungkin terpenuhi secara optimal. Upaya
peningkatan kualitas pendidikan untk mengangkat dari keterpurukan tidak
mungkin terlaksana dengan baik apabila tidak dibarengi dengan upaya
penegagak standar penyelenggaraan pendidikan, standar pelayanan
pendidikan,
standartenaga
serta
standarkompetensi
kependidikan
lainnya.
guru,
Upaya
standar
lulusan
pencapaian
dan
standar
kompetensi guru tersebut diantaranya adalah dapat dilakukan Pendidikan
Profesi dan Sertifikasi Guru.
c) Persoalan Kualitas Guru
Kurangnya rasa bangga akan mempengaruhi motivasi kerja dan citra
masyarakat terhadap profesi guru. Akibatnya, sulitnya mencari guru yang
sesuai dengan bidangnya (keahlian/profesionalitasnya) adalah suatu hal
yang lumrah terjadi. Dalam banyak kasus lapangan, banyak sekali
ditemukan guru yang “salah kamar”, banyak guru di suatu sekolah
memegang suatu mata pelajaran yang bukan vaks-nya. Persoalan ini
merupakan rangkaian dari kurangnya penghargaan pada profesi guru.
Profesi guru seharusnya diisi oleh orang-orang besar, berpengetahuan luas,
dan memiliki keahlian yang bermutukarena akan mencetak SDM yang
unggul. Ada banyak kritik yang dialamatkan kepada problematika
defesiensi guru yang salah ruang ini, khususnya yang berkaitan dengan
kualitas pembelajaran di sekolah, yaitu :
 Pembelajaran lebih berkonsentrasi pada persoalan-persoalan
teoritis yang bersifat kognitif.
24
 Metodologi pembelajaran tidak kunjung berubah, berjalan secara
konvensional, tradisional, dan monoton.
 Kegiatan pembelajaran kebanyakan bersifat menyendiri, kurang
berinteraksi dengan yang lain.
 Pendekatan pembelajaran cenderung normatif, tanpa ilustrasi
konteks budaya yang melatarinya.
 Guru lebih bernuansa guru spiritual/moral dan kurang diimbangi
dengan nuansa intelektual dan profesional.
Berbagai
kritik
mendiskreditkan
menggugah
guru,
bagaimana
tersebut
tetapi
bukanlah
lebih
bertendensi
untuk
mengembangkan
meningkatkan
guru
sehingga
untuk
dan
lebih
professional dan menjadi guru yang unggul.
3. Dalam buku “ Dari KBK sampai MBS “ karangan J. Drost, SJ tentang kebutuhan
kurukulum direvisi/diperbaharui yaitu :
Persoalan pendidikan dasar dan menengah di Indonesia dewasa ini sangat
komleks. Beberapa permasalahan yang besar antara lain menyangkut soal kualitas
pendidikan, proses pembelajaran dan evaluasi, kualitas guru, dan pemerataan
pendidikan.
a) Kualitas pendidikan
Banyak majalah dan jurnal pendidikan mengungkapkan bahwa mutu
pendidikan di Indonesia adalah rendah, termasuk rangking bawah
dibandingkan pendidikan di beberapa negara di Asia Tenggara. Dalam
pada itu, berbicara tentang mutu pendidikan di Indonesia kiranya perlu
dilihat beberapa unssur yang mempengaruhinya, seperti : kurikulum, isi
pendidikan, proses pembelajaran dan evaluasi, kualitas guru, sarana dan
prasarana sekolah dan buku ajar.
b) Proses pembelajaran dan evaluasi
Penyebab utama dari mutu pendidikan yang belum tinggi adalah karena
proses pembelajaran yang belum lancar dan baik di banyak sekolah. Di
banyak sekolah proses pembelajaran masih banyak terganggu karena
situasi sekolah yang tidak memungkinkan pembelajaran berjalan lancar
25
seperti sekolah yang rusak berat, tidak ada sekolah di beberapa tempat
bencana, tidak banyak peralatan belajar mengajar, dan di beberapa tempat
kekurangan guru.
c) Kualitas guru
Kualitas guru yang rendah disebabkan oleh beberapa hal yaitu :
 Di daerah itu memang tidak ada guru yng sesuai dengan bidang
studi yang dibutuhkan.
 Kualitas guru juga dipengaruhi oleh kualitas para calon guru.
 Mutu pendidikan calon guru yang mencintai dan memperhatikan
profesinya.
d) Pemerataan pendidikan
Alasan mengapa pemerataan itu belum terjadi, perkiraan memang
disekitar masalah dana dan soal otonomo daerah.
 Soal dana pendidikan
Kebanyakan anak tidak dapat sekolah karena memang tidak
mempunyai biaya untuk membayar sekolah, entah karena orang
tuanya miskin atau karena ada persoalan lain.
 Otonomi daerah
Daerah yang penghasilannya kecil, pendidikan jelas tidak
mendapatkan dana yang cukup. Hal ini menyebabkan semakintidak
meratanya pendidikan di negra Indonesia.
D. Permasalahan IV : Bagaimana karakteristik guru matematika setelah kurukulum
revisi/diperbaharui?
Dari hasil review dari Jurnal dan dari beberapa buku serta artikel ada beberapa
karakteristik guru matematika setelah kurukulum revisi/diperbaharui diantaranya
adalah :
1. Dari Jurnal Internasional dengan judul” An Analysis of the New Elementary
Mathematics Teacher Education Curriculum in Turkey “ yaitu tentang
karakteristik guru matematika setelah kurukulum revisi/diperbaharui.
26
Kurikulum adalah penekanan diberikan kepada umum melalui kursus pendidikan.
Kurikulum pengembang diharapkan masa depan guru matematika untuk
mempelajari lebih lanjut tentang budaya Turki, sejarah pendidikan Turki
sistem, filsafat ilmu, dan sejarah dan filsafat matematika. Dalam kursus tertentu,
mereka diharapkan untuk bekerja dengan pemerintah dan non-organisasi
pemerintah untuk terlibat dalam berbagai proyek, misalnya, membantu orang
dalam kemiskinan, membantu perpustakaan lokal, dan bekerja dengan siswa di
pedesaan daerah. Tujuan dari program ini adalah untuk memotivasi calon guru
untuk berpartisipasi dalam kesempatan relawan dan meningkatkan rasa empati
dan kesadaran sosial. Kurikulum pendidikan membutuhkan guru baru
menyelesaikan kursus metode penelitian. Penelitian tentu saja akan memberikan
kesempatan belajar bagi preservice guru untuk meningkatkan keterampilan dan
penelitian praktek. Untuk melaksanakan kurikulum baru, guru perlu dilengkapi
dengan sesuai pengetahuan, keterampilan, dan pengalaman. Guru kurikulum
pendidikan baru menempatkan cukup tingkat penekanan pada sukses pemanfaatan
kurikulum sekolah dasar. Ini termasuk memotivasi siswa untuk mengajukan
pertanyaan, menarik siswa dalam berpikir kritis, dan menggunakan matematika
penyelidikan dalam praktek matematika di kelas mereka. Dengan meningkatkan
jumlah mengajar kursus matematika metode, calon guru diharapkan memiliki
pemahaman lebih mendalam tentang matematika dan prosedur dan pengetahuan
konten pedagogi. Kurikulum pengembang bertujuan untuk meningkatkan kualitas
pendidikan guru matematika untuk bahwa dari standar internasional, namun untuk
merevisi kurikulum tidak cukup untuk mencapai tingkat yang diinginkan.
Pelaksanaan program kurikulum baru akan dipantau dan terus dievaluasi untuk
meningkatkan kualitas guru untuk tingkat tertinggi.
2. Dalam buku “ Menjadi Guru Unggul “ karangan Ahmad Barizi terdapat
karakteristik guru matematika setelah kurukulum revisi/diperbaharui yaitu :
Guru bukan hanya sekedar orang yang berdiri di depan kelas untuk
menyampiakan materi pengetahuan (mata pelajaran) tertentu, akan tetapi guru
adalah anggota masyarakat yang harus ikut dan berjiwa bebas serta kreatifdalam
27
mengarahkan perkembangan anak didiknya untuk menjadi anggta masyarakat
sebagai orang dewasa. Untuk itu tugas guru dibagi menjadi tiga bagian yaitu:
1) Guru sebagai orang yang mengkomunikasikan pengetahuan.
Tugas ini mengharuskan seorang guru memiliki penetahuan yang
mendalam bahan yang akan diajarkannya. Guru juga perlu menyediakan
berbagai
fasilitas
hidupnya,
memperbaiki
nasib
hidupnya
dan
meningkatkan kesejahteraan hidupnya sehingga dapat melaksanakan
profesi keguruannya dengan baik.
2) Guru
sebagai
model
berkaitan
dengan
bidang
studi
yang
diajarkannyasebagai sesuatu yang berdaya guna dan bisa dipraktikan
dalam kehidupan sehari-hari.
Guru harus menjadi model atau contoh nyata dari mata pelajaran yang di
ampunya.
3) Guru harus menampakkan model sebagai pribadi yang berdisiplin, cermat
berfikir, mencintai pelajarannya, penuh idealisme, dan luas dedikasi.
Sebagai tenaga pendidik yang memiliki kemampuan kualitatif, guru harus
menguasai ilmu keguruan dan mampu menerapkan strategi pembelajaran
untuk mengantarkan siswanya pada tujuan pendidikan.
3. Dalam buku “ Dari KBK sampai MBS “ karangan J. Drost, SJ tentang
karakteristik guru matematika setelah kurukulum revisi/diperbaharui yaitu :
Seorang pelajar harus mengenal para pelajar lebih dahulu. Dianjurkan,
pengajar berkenalan baik dengan pelajar, dan mempelajari kecakapan, bakat,
kekurangan, dan implikasi perilaku pelajar di kelas.
Ada beberapa cara yang dapat dipakai dalam pengajaran yaitu :
a) Bila suasana sekolah tertib, tidak sukar menentukan dengan cepat tujuan
akademis terbatas untuk tiap kelas. Pengajar menyiapkan dengan baik para
pelajar untuk kegiatan mereka sendiri, yaitu belajar. Hanya dengan cara
demikian, dapat dihasilkan proses belajar yang baik dan pembentukan
kebiasaan-kebiasaan yang kuat.
28
b) Tujuan belajar harus disesuaikan dengan para pelajar. Mereka mampu
belajar banyak, asal tidak dihujani banyak bahan pada waktu yang sama.
Jadi, perhatian akan cakupan dan urutan menjadi amat penting sesuai
kemampuan setiap pelajar.
c) Asas giat diri dari pihak pelajar disalurkan lewat ulangan harian,
mingguan, bulanan, dan tahunan. Ulangan-ulangan tidak dimaksudkan
sebagai perulangan yang membosankan dari bahab hafalan, tetapi sebagai
kesempatan pelajar untuk mendapat refleksi guna menyerap apa yang
membingungkan atau menggugahnya dalam mengikutim pelajaran.
d) Waktu belajar paling lama dalah dua jam. Sesudah itu harus beristirahat.
Perlu juga ada keanekaragaman dalam kegiatan di dalam kelas. Terlalu
banyak bahan dari satu macam hal akan mematikan semangat. Sejauh
mungkin,belajar menjadi kegiatan yang menyenangkan baik secara batin
maupun secara lahir.
29
BAB V
KESIMPULAN, IMPLIKASI, DAN SARAN
A. Kesimpulan
Dari hasil review Jurnal Internasional dengan Judul ” An Analysis of the New Elementary
Mathematics Teacher Education Curriculum in Turkey “, beberapa artikel dan beberapa
buku maka dapat disimpulkan sebagai berikut :
1. Setelah melakukan review Jurnal Internasional dengan Judul ” An Analysis of the
New Elementary Mathematics Teacher Education Curriculum in Turkey “,
beberapa artikel dan beberapa buku ternyata masih banyak di negara-negra
berkembang yang mempunyai kurikulum pendidikan yang kurang, baik dari segi
kualitas gurunya maupun kurukulum yang diterapkan di negara tersebut.
2. Kurikulum pendidikan kurang tersebut mempengaruhi karakeristik gurunya. Jadi
guru yang belum memiliki kualitas yang baik untuk mengajar diharapkan untuk
memperbaiki kualitasnya dengan berbagai cara baik meneruskan kuliah
selanjutnya atau mengikutu berbagai macam seminar. Permasalah utama
pendidikan ada dasarnya adalah disparitas mutu pendidikan khususnya yang
berkaitan dengan (1) ketersediaan pendidik dan tenaga kependidikan yang belum
memadai baik secara kuantitas dan kualitas maupun kesejahteraannya, (2)
prasarana sarana belajar yang belum tersedia atau belum memadai, (3) pendanaan
pendidikan yang belum memadai untuk menunjang mutu pembelajaran, (4) proses
pembelajaran yang belum efisien dan efektif, dan penyebaran sekolah yang belum
merata, ditandai dengan belum meratanya partisipasi pendidikan antara kelompok
masyarakat, seperti masih terdapatnya kesenjangan antara penduduk kaya dan
miskin, kota dan desa, laki-laki dan perempuan, antar wilayah.
3. Di negara-negara berkembang masih banyak kurikulum yang perlu diperbaiki
diantaranya :
a) Menyiapkan sumber daya manusia yang bermutu
Salah satu faktor penyebab adalah guru tidak siap untuk memanfaatkan
fasilitas yang diberikan oleh berbagai macam proyek yang ditujukan
30
kesekolah tersebut, Oleh karena itu pencapaian standar kopetensi guru
merupakan keharusan. Sebab tanpa ada standar maka jaminan kepada
stakholder tidak mungkin terpenuhi secara optimal.
b) Persoalan Kualitas Guru
Kurangnya rasa bangga akan mempengaruhi motivasi kerja dan citra
masyarakat terhadap profesi guru. Akibatnya, sulitnya mencari guru yang
sesuai dengan bidangnya (keahlian/profesionalitasnya) adalah suatu hal
yang lumrah terjadi.
c) Pemerataan pendidikan
Alasan mengapa pemerataan itu belum terjadi, perkiraan memang
disekitar masalah dana dan soal otonomo daerah.
 Soal dana pendidikan
Kebanyakan anak tidak dapat sekolah karena memang tidak
mempunyai biaya untuk membayar sekolah, entah karena orang
tuanya miskin atau karena ada persoalan lain.
 Otonomi daerah
Daerah yang penghasilannya kecil, pendidikan jelas tidak
mendapatkan dana yang cukup. Hal ini menyebabkan semakintidak
meratanya pendidikan di negra Indonesia.
4. Setelah adanya perbaikan kurikulum diharapkan bisa meningkatkat kulitas
pendidikan di negra-negra tersebut sehingga bisa bersaing dengan negara yang
lebih maju. Perubahan-perubahan tersebut antara lain :
a) Guru sebagai orang yang mengkomunikasikan pengetahuan.
Tugas ini mengharuskan seorang guru memiliki penetahuan yang
mendalam bahan yang akan diajarkannya. Guru juga perlu menyediakan
berbagai
fasilitas
hidupnya,
memperbaiki
nasib
hidupnya
dan
meningkatkan kesejahteraan hidupnya sehingga dapat melaksanakan
profesi keguruannya dengan baik.
b) Guru harus menampakkan model sebagai pribadi yang berdisiplin, cermat
berfikir, mencintai pelajarannya, penuh idealisme, dan luas dedikasi.
31
c) Tujuan belajar harus disesuaikan dengan para pelajar. Mereka mampu
belajar banyak, asal tidak dihujani banyak bahan pada waktu yang sama.
Jadi, perhatian akan cakupan dan urutan menjadi amat penting sesuai
kemampuan setiap pelajar.
d) Bila suasana sekolah tertib, tidak sukar menentukan dengan cepat tujuan
akademis terbatas untuk tiap kelas. Pengajar menyiapkan dengan baik para
pelajar untuk kegiatan mereka sendiri, yaitu belajar. Hanya dengan cara
demikian, dapat dihasilkan proses belajar yang baik dan pembentukan
kebiasaan-kebiasaan yang kuat.
B. Implikasi
Kesimpulan butir pertama memberikan implikasi bahwa banyak negara-negra
berkembang yang memiliki kurikulum pendidikan yang kurang. Maka negara-negara
tersebut selalu berusaha untuk memperbaiki kurukulum pendidikannya baik dari kualitas
gurunya sampai kurikulum pendidikan yang diterapkan di negra tersebut.
Kesimpulan butir kedua memberikan implikasi bahwa kurikulum pendidikan yang
kurang akan mengakibatkan munculnya berbagai nmasalah dalam pendidikan dan
mempengaruhi karakteristik pengajar atau guru.
Kesimpulan butir ketiga memberikan implikasi bahwa masalah-masalah yang
diakibatkan kurikulum pendidikan yang kurang maka akan lebih memunculkan masalahmasalah yang lebih berat di dunia pendidikan dan mempengaruhi segala sesuatu yang
menyangkut pendidikan seperti kualitas pendidikan, kualitas guru, proses pembelajaran
dan evaluasi,pemerataan pendidikan dan lain-lain.
Kesimpulan butir keempat memberikan implikasi bahwa setelah kurikulum
pendidikan yang kurang tersebut diperbaiki ternyata dapat merubah kualitas pendidikan
serta dapat memperbaiki kualitas pengajar atau guru. Sehingga pendidikan di suatu
negara tersebut mampu bersaing dengan negara yang lebih maju.
32
C. Saran
Berdasarkan hasil review Jurnal Internasional dengan Judul ” An Analysis of the New
Elementary Mathematics Teacher Education Curriculum in Turkey “, artikel dan
beberapa buku, diajukan sejumlah saran sebagai berikut :
1. Terhadap negara atau pemerintah
Hendaknya melakukan perbaikan kurikulum yang benar-benar bisa membuat
pendidikan yang lebih baik, serta melakukan perbaikan kurikulum harus merata dari
kota hinggga pelosok desa agar kurikulum pendidikan bisa merata dengan baik.
2. Terhadap guru terutama guru matematika
a. Hendaknya guru memiliki kualitas yang baik untuk mengajar, seperti mengerti
profesinya sebagai guru, menguasai bahan ajar, mamapu munguasai kelas dan
tau tanggung jawab sebagai guru.
b. Kepada guru yang belum mencapai syarat mengajar hendaknya melakukan
kursus atau menempuh kuliah minimal 4 tahun untuk mencapai syarat mengajar .
3. Bagi pereview selanjutnya
Mengingat dalam review ini masih banyak kekurangannya, maka review perlu
dilaksanakan lebih teliti lagi dalam mereview dan lebih mendalami jurnal tersebut
sehingga lebih menguasai masalah-masalah yang trdapat dalam jurnal tersebut.
Review hendaknya dilaksanakan dengan membaca berulang-ulang serta memahami
isi dari jurnal tersebut.
33
DAFTAR PUSTAKA
Barizi, Ahmad. 2009. Menjadi Guru Unggul. Jogjakarta : Ar-Ruzz Media
Drost, J. 2005. Dri KBK sampai MBS. Jakarta : PT Kompas Media Nusantara
LAMPIRAN
 JURNAL 1
Leung,
2003;
Darling-Hammond
&
Bransford, 2005). Among other disciplines
An Analysis of the New Elementary
mathematics teacher education has been
Mathematics
at
Teacher
Education
the
focus
of
reform
in
teacher
Curriculum in Turkey
education (Lin & Cooney, 2001). The
Mine Isiksal Yusuf Koc Safure Bulut
curriculum
for the
Tulay Atay-Turhan
mathematics
teachers
2007, Vol. 17. No 2. 41-51
considered a very crucial aspect of the
education
has
of
also
been
mathematics teacher education enterprise
The purpose of this paper is to describe and
(Grossman, Schoenfeld, & Lee, 2005). In
reflect on the changes in the new elementary
Turkey,
mathematics teacher education curriculum
revised the existing curriculum for the
in Turkey. It is our goal to share the
education
revised teacher education curriculum with
mathematics teachers as part of a larger
the outside mathematics teacher education
scale
community.
curricula (Higher
The
paper
is
organized
policy
makers
of
have
elementary
revision
of
recently
school
teacher
education
Education
Council
around four major sections: An overview
[HEC], 2006). In this paper, our purpose
of
is to describe and reflect on the changes
the
teacher
education
system
in
Turkey, the characteristics of the previous
in
mathematics teacher education curriculum,
teacher education curriculum in Turkey.
the
We
need
for
the
revisions,
and
the
new
will
elementary
discuss
mathematics
the history
of
characteristics of the revised curriculum.
mathematics teacher education in Turkey,
All over the world, there has been
the major motivations for revising the
increased attention
previous curriculum
education
of
on
teachers
the
professional
at all
levels
(Bishop, Clements, Keitel, Kilpatrick, &
of
elementary
mathematics
teacher education programs,
and
development
the
characteristics
of
process
the
and
revised
curriculum.History of Mathematics Teacher
support from the World Bank, the HEC
Education in Turkey Beginning from the
restructured teacher education programs to
foundation of the Republic of Turkey in
enhance quality; this was part of
1923, Turkey has aimed to raise its
year project
standards in economical, social, political,
primary and secondary teacher education
and educational arenas to that of the
programs in colleges of education (Bulut,
developed countries through a wide range of
1998). Prior to the 1998 changes, there
reform efforts. Reforms in the field of
were
education were among the most important
mathematics education awarding licenses
changes
for
in
the
1920s (Cakiroglu &
involving
26 departments
a four-
changes
or
in
all
divisions
secondary mathematics
of
teaching
Cakiroglu, 2003). In 1924, the Turkish
(grades 6 thru 11). As a result of these
education system was centralized and all
changes,
educational institutions were put under the
closed and replaced by 28 elementary and
control of
the Ministry of
12
Education
(MNE) (Binbasioglu,
National
high
the existing
programs
school mathematics
were
teacher
1995).
education programs (Center for Student
Changing the country’s teacher education
Selection and Placement, 1998). As part
system was another
of the change, teacher education curricula,
Before
focus
1980, teachers
of
reform.
were graduating
including
the
mathematics
teacher
from a variety of institutions with diverse
education curriculum, were substantially
experiences (see Cakiroglu & Cakiroglu,
revised. The 1998 curriculum was put in
2003 for
place starting from the fall semester of 1998;
details); however, in 1981, all teacher
the details of
education institutions were placed under the
Appendix A. For additional details of the
authority of the HEC for a unified system of
1998 curriculum, see Bulut’s 1998 article.
teacher training. Later, in 1989, the Council
The
mandated
be
teacher education curriculum was in use for
educated in four-year colleges in order to
eight years, from 1998 to 2006. During
be
certificate
this time, in various academic and public
(Binbasioglu, 1995). The reform wave in
platforms, including symposiums, panels,
Turkish
workshops
that
eligible for
teacher
teacher candidates
a
teaching
education
was
quite
strong in the late 1990s. In 1998, with a
previous
the program are given in
elementary
and
mathematics
conferences,
the
qualifications of the preservice teachers in
the previous curriculum were questioned.
introduction to education and educational
There was a consensus on the inadequacy
psychology.
of
knowledge,
Because graduates of these high schools
pedagogical content knowledge, and skills
are given extra points on the university
of the preservice teachers in the face of
entrance exams, most of the teacher
current
education majors have graduated from such
the
subject matter
societal
demands.
It was
and
technological
concluded
that
the
high schools.
responsible for such problems in the
courses, general education courses, and
education of mathematics teachers. In
pedagogy courses (Appendixes A & B).
order
Mathematics courses, science courses, and
to
existing
major areas:
take
courses
find solutions
three
teachers
teacher education curriculum was partly
to
in
Preservice
content
problems, the HEC collaborated with the
mathematics
faculty and deans of the colleges of
constitute
education and
General education courses, referred to in
decided
to
revise
the
teaching methods
the
content
area
courses
courses.
existing curriculum. In this article, as a
the
continuation of Bulut’s (1998) discussions,
provide preservice teachers with necessary
the characteristics of the 2006 elementary
background in technology, social, cultural
mathematics teacher education curriculum
and historical topics such as computer
are discussed and compared with the 1998
literacy, foreign
curriculum.
History
Currently,
elementary
in
Turkey,
mathematics teachers
are
United States as a core curriculum,
language,
and
required to
mathematics; yet, they mainly teach sixth,
courses. These are
seventh and eighth grades. High school
topics
graduates
educational
admitted
to teacher
Language.
Preservice
elementary mathematics teachers are also
certified to teach 4th through 8th grade
are
and Turkish
in
take a number of pedagogy
general
mainly
devoted
to
pedagogy, including
psychology,
classroom
education programs via the university
management and counseling. Preservice
entrance exam. Some high schools focus
elementary mathematics
on careers in education; they follow the
engage in field experiences and student
national
teaching
high
professional
school curricula but offer
education
courses,
e.g.,
activities
as
teachers also
part
of
their
education. These students take 146 credit
hours
of courses to graduate from the
program.
It is always hard to characterize
degree. The two academic semesters, fall
an entire education system, but we will try
and spring, each
to portray what happens in these three
Teaching
certificates
categories of courses. Mathematics and
universities
are
physics are usually taught in a very
throughout the country. Certified teachers
traditional way, through lecture. There are
are required to pass the Government Staff
generally two midterms and one final
Selection Exam (KPSS) in order to work
examination to assess student performance
in
in such
elementary schools (757 schools out of
courses.
The
mathematics
public
last about
weeks.
awarded
permanent
schools.
by
and
Only
2%
of
all
34,656)
taught in a non-traditional format where
organizations. They recruit teachers based
theory and practice are blended to help
on their own criteria. Motivations for the
the
Revision
teachers
understand
of
operated
valid
teaching methods courses are expected be
preservice
are
14
the
by private
Teacher
Education
applications of theories and earn first-hand
Curriculum We will discuss four major
experience
motivations for the revision of the teacher
through
various
activities.
General education courses are taught by
education
faculty with diverse backgrounds; as a
preparation
result,
prefer
European Union, (b) the changes in the
lecturing, others promote more student
elementary school mathematics curriculum,
participation.
(c) the need for better qualified teachers,
while some
In
of
them
addition
to
regular
curriculum.
for
These
integrating
paper-pencil tests, projects are used to
and
assess
curriculum (HEC, 2006).
student performance
in
those
(d) problems with
are
(a)
with
the
the previous
Integration With
courses. The pedagogy courses are taught
the European Union Turkey, in general,
in
could
various ways. While
common,
is
benefit
in
many
ways from
presentations,
video
European Union (EU) membership.
presentations, small group work,
whole
particular, we expect to become more
group
student
lecture
discussions
and
other
non-
integrated,
more
prosperous,
In
more
traditional methods are used to deliver
autonomous, and more democratic as an EU
pedagogy courses. The
member.
education
program
equivalent
to
a
entire
takes
regular
teacher
four years,
undergraduate
In addition to reorganizations
in political, economical and social areas,
education
is considered
a
critical
component of the integration process with
curiosity about what is going on in their
the EU. Turkey’s long-standing wish to
families, schools, and society (MNE, 2004).
be a member of the EU motivated teacher
Researchers
educators and curriculum developers
memorization
revise
teacher education programs
to
suggest
replacing
rote
with
learning
for
and
understanding (Hiebert, Carpenter, Franke,
improve the level of teaching standards
et al., 1997). In order to address this
(HEC, 2006). This reform is not limited
and
to the K-12 curriculum. Changes in the
teachers were
Elementary School Mathematics Curriculum
student-centered classroom environments.
In 2003, the Turkish Ministry of National
Furthermore, it was within the goals of
Education
thecurriculum to encourage students to
organized
a
curriculum
to
increase student
participation,
encouraged
set up
development team to revise the existing
work
elementary school mathematics curriculum.
effectively about their ideas and to reflect
The new curriculum was designed as part of
on their learning. Research suggests that
a larger-scale curriculum reform initiative
this will
that included
express
five
content
areas:
collaboratively,
to
give
their
to communicate
students
ideas
a
chance
to
and increase self-
mathematics, science, social sciences, life
confidence (Bandura, 1986).
science
solving, a critical aspect of understanding
and
Turkish
language (Koc,
Problem
Isiksal, & Bulut, 2007). One of the
(Polya, 1957), was
major objectives
of
integral aspect of all subject areas in the new
reform
promote teaching
was
to
this
curriculum
and
introduced
as an
curriculum. For meaningful student learning,
learning environments in which students
the curriculum encouraged teachers to
can
consider the outside contextual elements,
share
participate
their
ideas
actively
new
such as lifestyle and geographical factors,
curriculum placed a heavy emphasis on
while designing classroom tasks. Finally,
children’s
assessment was regarded as an essential
emotions,
confidence,
(MNE, 2006).
and
cognitive
attitudes,
beliefs,
The
development,
interests,
anxiety,
self
self-
part of the classroom instruction (Irish
National
Council
1999;
for
Curriculum
United
and
regulation, psychomotor development and
Assessment,
Kingdom
social skills. Additionally, the curriculum
Qualifications and Curriculum Authority,
promoted student discussion, inquiry, and
1999; National Council of Teachers of
Mathematics
[NCTM],
Romberg, 2004).
1995,
Expected
2000;
to teach 15 class hours per week. They
teacher
are paid for every extra hour above 15
dispositions in the new school curriculum.
hours.
Teachers are expected to exhibit a variety of
mathematics teachers are assigned a class of
skills
advisees. Like
and
characteristics
in
order
to
Additionally,
in
all
some
other
schools,
teachers,
effectively implement the new elementary
mathematics teachers are also responsible
school curriculum. First of all, they should
for organizing and leading social activities
believe
such
that
all
students
can
learn
as
sporting
events,
national
mathematics. This particular characteristic
ceremonies, and extracurricular activities.
is
There
essential in
mathematics
promoting
equity
in
learning. Aligned with this,
are
at
least
two department
meetings and two general faculty meetings
teachers are to respect and follow all aspects
in elementary schools. Additionally, some
of human rights and ethical values in
teachers organize after school and weekend
mathematics classrooms. Teachers are also
courses for students willing
expected to work toward helping students
extra mathematics
develop
minimal fee.
positive
attitudes
mathematics. Additionally,
about
teachers need
instruction
instructional
mathematics.
mathematical
receive
for
a
The curriculum states that
teachers should develop and
to guide and motivate students in learning
They should also motivate
to
activities
implement
that
promote
understanding,
students to ask questions, engage in critical
monitor
thinking, state and support ideas, and inquire
effectively manage instructional time, and
about the subject matter. To accomplish
encourage students to evaluate their own
these goals, teachers must know their
and their peers’ progress. Teachers are
students, parents, and the community in
also expected
which
is
evaluation results to improve the quality
explicitly stated in the new curriculum
of instruction. Furthermore, mathematics
that mathematics teachers should enjoy
teachers should collaborate with parents,
teaching
other school personnel, and the outside
they
responsibilities
mathematics
live.
Additionally,
mathematics.
of
Teaching
elementary
teachers.
In
it
school
and evaluate
regularly
to
use
community to improve
student
learning,
assessment
the
and
quality of
elementary
schooling. Given the above expectations
schools, mathematics teachers are required
for the teachers, it is definitely important
that teachers develop self-confidence and
functions,
self-regulation skills. Finally, they need
connections among ideas” (p. 21). Thus,
to continuously improve their professional
in order to develop the conceptual and
knowledge and experiences through
procedural
a
and algebra
and
understanding
of
the
students,
variety of activities, including following
teachers should understand the content on
scientific research literature and conducting
both of these levels.Mathematics teachers
small-scale research projects. The Need for
not only need to have sufficient content
Better-Qualified Teachers One of the key
knowledge
factors in improving instruction and student
pedagogical
understanding
1990). Teachers need
in
the
mathematics
of
mathematics,
content
but
knowledge
to
also
(Even,
know
why
classroom is the role of the teacher (Hiebert
mathematical statements are true, how to
et al., 1997). The above discussions indicate
represent mathematical ideas in multiple
that there is a need for qualified teachers
ways, what constitutes an appropriate
to
definition of a
be
able
to
implement
the
new
term or concept,
and
elementary mathematics school curriculum
methods for appraising and evaluating
effectively.
mathematics
mathematical methods, representations, or
effectively is a complex endeavor, and
solutions (Hill, Schilling, & Ball, 2004).
there are no easy recipes for success.
Subject matter knowledge and pedagogical
Effective teachers must
and
content
are
effective mathematics teaching and in the
understand
Teaching
the
know
mathematics
they
knowledge
preparation
that knowledge (Hill, Schilling, & Ball,
(NCTM, 2000). Tirosh (2000) states that
2004). While challenging and supporting
a
students, teachers need to understand the
programs should be to contribute to the
gap between what their students know and
development
what they need to learn (NCTM, 2000).
knowledge
NCTM (1991) emphasizes that “teachers
think about school mathematics topics.
must
She
help
every student
develop
goal
of
mathematics
in
teaching, and they must flexibly draw on
major
of
are essential
in
conjectures
teacher education
preservice
of common
that
teachers
ways
teachers’
children
the experience
conceptual and procedural understandings
acquired in the course of teaching is the
of
main, but not
numbers,
measurement,
operations,
statistics,
geometry,
probability,
the only,
source of
teachers’knowledge of students’ common
conceptions and misconceptions. Preservice
courses.Problems
teachers’ own experiences as learners,
Curriculum The developers of the new
together
with
teacher
relevant
developmental
their
familiarity
and
with
cognitive
With
the
Previous
education curriculum
identified
major handicaps of the content
research, could be used in teacher education
and implementation of the curriculum that
programs to enhance their knowledge of
had been in place during the previous
common
ways
among
eight years. Teacher education programs
children.
In
mathematics
experienced a number of challenges in
content
and
pedagogical
content
achieving these goals, including a limited
knowledge
are
critical
in the
number of faculty members specialized
of
thinking
summary,
factors
effectiveness of mathematics teachers.
in teacher education, inadequate university-
The
school partnerships, lack of enough field
new
teachers
school
curriculum
to expand
their
requires
theoretical
and student
teaching experiences, and
knowledge and student-centered teaching
issues with the quantity and quality of the
experiences. These
teaching methods courses. Here,
Turkish
revise
Higher
needs motivated the
Education
the teacher
Council
education
we
to
mention the major problems and how they
programs.
were overcome in the revised curriculum.
The HEC aimed to increase the quantity
These problems
and quality of the courses in the teacher
categories: (a) content and pedagogy and
education curriculum to help preservice
(b) policy.In
teachers
professional
there were 27 content mathematics, science
knowledge and skills to teach elementary
and teaching methods courses (Appendix
school mathematics. In Turkey, teacher
A). Among these 27 courses, only 13 of
education programs experience a number
them
of challenges in achieving these goals,
Preservice
including a limited number of faculty
teachers were also required to take 9
members specialized in teacher education,
content courses outside their major area,
inadequate university-school
such as biology, physics, and chemistry,
increase
their
partnerships,
the
were
order
fit
into
previous
two main
curriculum,
mathematics
elementary
to
build
courses.
mathematics
lack of enough field and student teaching
in
interdisciplinary
experiences, and issues with the quantity
connections
between
and quality of the teaching methods
mathematics.
These students were also
science
and
expected
to
level of
through community services and university-
proficiency in science as that required of
community partnerships. Also missing were
science teachers.
opportunities for the preservice teachers
elementary
required
reach
In
the same
fact,
preservice
mathematics teachers
to
obtain
a
were
supplementary
to learn more about the history of Turkish
education
and
the
cultural
teaching certificate in elementary science.
philosophical roots
Interestingly, they were only required to
teaching. Thus, during the
complete 13 courses in their major area,
curriculum
revision
mathematics. This imbalance between the
educators
and specialists agreed on
number
increasing the number of general education
of
science
and mathematics
of
and
mathematics
process,
courses became one of the major concerns
courses to fill these needs.
of teacher educators and other specialists
teacher education curriculum,
as
they revised the teacher education
two teaching methods courses (Appendix
curriculum. Another concern regarding the
A). The first one was devoted to general
content
education
teaching methodologies and philosophies,
number of
in which the preservice teachers were
general education courses. In the previous
involved in more theoretical aspects of
program of study, there were ten courses
pedagogy.
designed
for general education of the
students were
preservice
teachers,
history,
and practical applications of the teaching
Turkish language, foreign language, and
methodologies in mathematics teaching.
the principles of
They
of
the teacher
curriculum was
founder
of
the
limited
including
Kemal
Ataturk,
the
the republic (Appendix A).
In the
the
were provided
the
to more specific
experiences
relationships
in
among
Such courses aimed to increase teacher
mathematical
candidates’ awareness of social, cultural,
and processes. Thus, at the end of these
and historical issues
courses, preservice teachers should have
(HEC,
2006).
concepts,
old
there were
second course,
exposed
constructing
In
teacher
However, there was no specific course
had
designed for the preservice teachers to
improving
develop awareness of social, cultural, and
content and
historical
However, two courses devoted to the
issues
in
their
local
communities, which could be accomplished
appropriate
representations,
content
and
experiences aimed at
their understanding of
pedagogy
pedagogy
the
of mathematics.
of
elementary
school mathematics were not sufficient for
science
and
the need
for
addressing
elementary mathematics
teachers,
the
should
be
all
elementary
school
teachers
mathematics concepts. Thus, a suggestion
double licensure
was made to increase the number of
rethought
mathematics teaching methods courses for
Development
preservice
teachers.
Curriculum At
concerning
teacher
limited
Another
issue
preparation was the
emphasis
on
instructional
system
during
the revision process.
Process
the
of
the
beginning
New
of
the
reform process, the HEC asked some of
the colleges of education to review the
planning and assessment. Previously, there
1998 program, identify weaknesses and
was
strengths
only one
planning
course covering
and
assessment;
both
however,
suggestions
of the
for
program,
and
give
improvement. Then,
a
addressing all objectives of the course in
program revision group was formed with
one semester was difficult. For example,
25 faculty members from various teacher
instructors could not spend enough time on
education programs. This group met for a
developing
Finally,
week in March 2006 to form the blueprint
preservice teachers were not provided
of the revised curriculum. The blueprint
enough
experience
with
was distributed to colleges of education
students
from
diverse
populations,
around the country for feedback. Based on
including
students
with
special needs.
the received feedback, the final version of
classroom
tests.
in
working
Related with this issue, teacher education
the
courses were
help
Higher Education Council in July 2006.
preservice teachers teach the subject matter
What’s “New” in the New Mathematics
for all students. There were also issues
Teacher Education Curriculum? The new
related to the policy of double licensure.
mathematics teacher education curriculum
As
preservice
changes are detailed in Appendixes B and
elementary mathematics teachers were also
C. First of all, as seen in Table 1, the
certified to teach
science
in elementary
number and percentages of courses in the
school. Officials
from
the teacher
content area, pedagogy courses, and general
not
previously
designed
mentioned,
to
curriculum
was approved
by
the
education department of the Ministry of
education courses are different.
National Education decided that, due to
Table 1 Number and Percentages of the
the adequate supply of elementary school
Course Types in the Previous and Current
Curricula Type of courses
Number and
dual licensure requirement was
removed
percentages of the courses in the previous
from the teacher education programs due
curriculum Number and percentages of the
the ineffectiveness of the process.One of
courses in the current curriculum Content &
the
Content Teaching Methods (C) 27 (56%) 22
curriculum is the emphasis given to the
(44%) Pedagogy (P) 11 (23%) 13 (26%)
general education
General
developers
Education (GE) 10 (21%)
15
(30%) Total 48 (100%) 50 (100%)
As
indicated
number
in
of courses
Table
in
1,
the
significant
changes
in
the
new
courses.
Curriculum
expected future
mathematics
teachers to learn more about the Turkish
the
total
elementary
culture,
history
of
the
Turkish
educational system, philosophy of science,
mathematics teacher education curriculum
and
increased from 48 to 50. In particular,
mathematics.
while the percentages of content and content
background and skills in general studies
teaching methods courses decreased (from
and information
56% to 44%), the percentages of pedagogy
experiences in performing research, and a
courses and general education courses
multidimensional perspective may be more
increased (P: from 23% to 26%; GE: from
effective in their classroom practices. Yet,
21% to 30%). In sum, the number of
these history and philosophy courses are
mathematics,
teaching
only recommended, not required, for the
methods, general education and pedagogy
teacher education programs because there
courses increased; whereas, the number of
are not enough faculty members to teach
science
the courses in some universities. A new
and
mathematics
science
teaching methods
history
and
philosophy
Teachers
with
technologies,
sufficient
sufficient
courses decreased from nine to two in
teaching
the revised curriculum (see Appendixes).
Service Practice, helps teacher candidates
For instance, the 13 mathematics (C)
become more aware of current social
courses
problems
in
the
previous
curriculum
profession
of
and
course, Community
develops university-
increased to 16 in the revised curriculum.
community partnerships. As mentioned
Also, the number of general education
earlier, preservice teachers were not given
(GE) courses increased from 10 to 15, and
enough
the number of pedagogy (P) courses
community-related projects in the previous
increased from 11 to 13. In addition, the
curriculum. In this particular course, they
opportunities
to
work
on
are expected to work with governmental
School
and
to
preservice teachers will learn about the
engage in a wide range of projects, e.g.,
structure and philosophy of the Turkish
helping people in poverty, assisting local
educational system. Also, students will have
libraries, and working with students in
a
rural areas. The goal of this course is to
administration
motivate preservice teachers to participate
instruction.
in volunteer opportunities and increase
blueprint of the curriculum for the teacher
theirsense of empathy and awareness to
education programs, but the schools
social issues. They will be encouraged to
educations have flexibility in utilizing the
participate in professional activities, such
curriculum. That is, they can remove,
as panels, conferences, symposiums and
add, and revise the name and content of up
workshops
the Community
to 30% of the total courses; however, they
Service Practice course. The new teacher
are not allowed to remove any pedagogy (P)
education curriculum requires completion
courses (HEC, 2006). This flexibility will
of a research methods course. The research
give the colleges of education a chance
course will provide learning opportunities
to organize their own teacher education
for the preservice teachers to improve their
programs
research skills and practices. In particular,
capabilities.
the course will be the main vehicle for
Recommendations Reform efforts in the
promoting
Turkish
non-governmental organizations
throughout
teachers’
own teaching
via
studying
scientific
of
their
research
Management
chance
to
course
see
how
contributes
The
HEC
based
on
in
which
the
school
to
quality
developed
their
needs
Discussions
education
the
of
and
and
system focused
on
increasing the quality of education from
methods, as in action research. This idea
kindergarten to university in all content
comes from Harrison, Dunn, and Coombe
areas (Binbasioglu, 1995). The change in
(2006) who argue that classroom research
the
will be
education curriculum is part of this larger
more
effective
if
classroom
elementary mathematics
teachers, active practitioners of teaching,
scale reform agenda.
are involved in conducting the research.
major
Another
makers,
addition
to
the
elementary
factors
teacher
There were four
that
motivated policy
educators
the
other
specialists
is
elementary mathematics teacher education
Turkish Educational System and
revise
and
mathematics teacher education curriculum
the
to
teacher
previous
curriculum: integration with the European
the
Union, changes in the elementary school
curriculum, the number of mathematics and
mathematics curriculum,
for
mathematics
teaching
and
education,
and
more
qualified
dissatisfaction
the
need
teachers,
with
the
previous
new mathematics teacher education
methods, general
pedagogy
courses
increased in order to provide preservice
curriculum. Turkey’s goal of becoming a
elementary
permanent
the European
previously lacking learning opportunities.
Union (EU) catalyzed their efforts to meet
Additionally, with the increased number of
European
educational
mathematics teaching methods courses,
is believed that with the
the preservice teachers are expected to
successful implementation of the new
have a more in-depth understanding of
elementary school curriculum and the
mathematical relationships and procedures
teacher education programs, Turkey will
and
reach
Furthermore, the introduction of more
member
Union
standards.
It
of
countries’
the educational levels of other
European Union countries.
mathematics teachers
pedagogical
content
with
knowledge.
To implement
general education courses will provide
the new elementary school curriculum,
preservice teachers with more experiences to
teachers
increase their awareness of social, cultural,
need
appropriate
to
be
equipped
with
skills,
and
knowledge,
and historical issues.
The
teacher
has
been
experiences. The new teacher education
education
curriculum places a considerable degree
implemented nationwide since Fall 2006.
of emphasis on a successful utilization of
The transition from the previous curriculum
the elementary school curriculum. This
to the new one has been challenging for
includes
ask
the programs because the students in the
critical
same cohort do not progress at the same
thinking, and using mathematical inquiry
pace; although most of the students are
in their mathematics classroom practices.
able to follow their program successfully,
The new teacher education curriculum is
there are others who repeat courses or fall
also concerned with overcoming problems
behind their peers. Curriculum developers
in
aimed
motivating
students
questions, engaging students
the
problems
in
previous curriculum.
were
based
on
to
These
curriculum
new
to
increase the quality of
content,
mathematics teacher education to that of the
pedagogy and policy-related issues. In
international standards; however, revising
the curriculum is not sufficient to reach
Educator, 9(2), 30–33. Cakiroglu, E., &
the desired level. Implementation of the
Cakiroglu, J. (2003). Reflections on teacher
new curriculum program will be monitored
education in Turkey. European Journal of
and continuously evaluated in order to
Teacher Education, 26, 253–264. Center for
enhance the quality of teachers to the
Student Selection and Placement. (1998).
highest level. The implementation of the
Öğrenci seçme ve yerleştirme sınavı ikinci
curriculum
the
basamak kılavuzu [Student selection and
Turkish Higher Education Council through
placement examination manual for the
continuous
teacher
second level]. Ankara, Turkey: Author.
educators, preservice teachers and K-12
Darling-Hammond, L., & Bransford, J.
institutions.
attempts
(2005). Preparing teachers for a changing
may be carried out by individual teacher
world: What teachers should learn and be
education
the
able to do. San Francisco: Jossey-Bass.
strengths and weaknesses of the revised
Even, R. (1990). Subject-matter knowledge
curriculum.
for teaching and the case of functions.
will
be monitored
feedback
from
Further monitoring
programs
by
to
explore
International
Journal
of
Mathematics
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 JURNAL 2
Researching Mathematics Education
and empirical work will point to the
and Language in Multilingual South
significance of language as power in
Africa .
mathematics education settings and thus
demonstrate the need forresearching the
Mamokgethi Setati This paper explores
relationship
between
language
policy, practice, and research issues that
theteaching
and
learning
relate to the teaching and learning of
mathematics
in
mathematics in multilingual classrooms
classrooms
from
of South Africa. The paper begins with
perspective.The history of language-in-
a brief history of language-in-education
education policy in South Africa The
policy in South Africa to showhow such
history of language-in-education policy
policy is driven by political as well as
in
educational interests. Thus the paper
particularly regarding the language of
sets up what will be the main argument:
learning
Language-use
multilingual
African2 schools. This history has been
educational context like South Africa is
interwoven with the resistance and
as much, if notmore, a function of
affirmation (African National Congress
politics1 as it is of communicationand
[ANC], 1994). The LoLT history in
thinking.
between
African education can be traced back to
language and mathematical learning is
the policies of missionary education
considered from a range ofperspectives,
during the 19th century. In mission
drawing from a range of literature in
schools English featured strongly as a
thefield not confined to South Africa. I
LoLT as well as a school subject. This
will
code-
English as LoLT policy in missionary
switching in multilingual mathematics
schools was continued by government-
classrooms, as it is this practice that has
aided African education following the
been the object of recent research in
Union of South Africa in 1910 (Beukes,
South Africa. This review of theoretical
1992). The importance of learning in
in
The
focus
a
relationship
specifically
on
South
Africa
and
South
a
is
teaching
and
of
African
political
controversial,
(LoLT)
in
the main language gradually came to be
recognized in Natal and also in the
Eiselen report closely, largely because
Cape
of its concern with protecting and
Province
(Hartshorne,
1987).
Between 1910 and 1948 the language in
expanding
education policy was flexible, and
Afrikaans language in the system
different provinces made their own
(Hartshorne). In 1953 the government
decisions about languages of learning.
passed the Bantu Education Act which
For instance, in Natal the LoLT in
stipulated that mother tongu instruction
African schools was Zulu for the first
be phased in across all primary school
six years of schooling (i.e., up to and
Grades in African primary schools, with
including
1948
English and Afrikaans as compulsory
(Hartshorne). Language in education
subjects from the first year of schooling.
during Apartheid When the Nationalist
At the time, English and Afrikaans were
government came into power in 1948,
the only two official languages. The
African schools were removed from
latter language had developed out of
provincial administrations and placed
Dutch settlement. In addition, both
under the National Department of Bantu
English and Afrikaans were also to be
Education. In 1949 the Nationalist
used as languages of learning and
government appointed a Commission
teaching on a 50/50 basis when transfer
on National Education, chaired by Dr.
from main language3 learning took
Eiselen. At the end of two years, the
place in the first year of secondary
commission
school
Grade
6)
until
recommended
a
rigid
the
influence
(Hartshorne,
of
1987).
the
The
mother tongue instruction policy in the
educational interests of the pupils
name of Christian National Education
became subordinate to ideological and
(Hartshorne, 1987). The commission
political factors. The government’s
recommended that all education should
greatest concern at the time was that the
be through the medium of the mother
constitution of South Africa required
tongue for the first four years, and that
equality in treatment of the two official
this principle should be progressively
languages. These policies were centered
extended year by year to all eight years
on fears that the Afrikaner language,
of primary schooling (p.68). However,
culture, and tradition Mamokgethi Setati
the government did not follow the
recently completed her Ph.D. at the
University
of
the
Witwatersrand,
medium of their main language in both
Johannesburg, South Africa, and is now
primary
a
mathematics
Hartshorne (1987) has argued that the
education at the same university. Her
language policy in African education in
main research interest is in discursive
South Africa since the 1948 election
practices in mathematics teaching and
(and
learning in multilingual settings. She is
Education Act) has centered on two
the
the
major issues: mother tongue instruction
Association for MathematicsEducation
and the establishment of the primacy of
of South Africa (AMESA). Vol. 12 No. 2,
Afrikaans as the preferred LoLT in
Fall 2002 7 might be overwhelmed by
secondary school. The majority of the
the
African people rejected both these
senior
lecturer
national
older,
in
president
more
of
internationally
and
particularly
since
the
Bantu
issues.
and tradition (Reagan & Ntshoe, 1992).
orashamed of African traditions per se,
Alongside these policies for African
mainstream African nationalists have
learners, white, so-called “coloured”,
generally viewed cultural assimilation
and Indian schools were also segregated
as a means by which Africans could be
along apartheid racial lines but came
released from a subordinate position in
under different legislation. Learners in
a common, unified society (Reagan &
these schools were required to take both
Ntshoe, 1992). Therefore, they fought
English and Afrikaans throughout the
against the use of African languages in
12 years of school, one at a first
schools, since their use was seen as a
language level, and the other at either
device to ensure that Africans remain
first
level.
“hewers of wood and drawers of water”
Depending on department and location,
(p. 249). The LoLT issue became a
the LoLT in these schools was either
dominating factor in opposing the
English or Afrikaans, or in some cases
system of Bantu Education during the
dual medium. As English and Afrikaans
apartheid era. African opinion never
were the main languages of white,
became reconciled to the extension of
coloured, and Indian learners, these
first language learning beyond Grade 4
learners were able to learn through the
nor the dual medium policy (of English
second
language
not
schools.
established English language, culture
or
Though
secondary
unmindful
and Afrikaans) in secondary school
1990 the Nationalist government passed
(Hartshorne, 1987). Many analysts trace
an amendment to the 1979 Act giving
the 1976 uprising, which began in
parents the right to choose whether their
Soweto and spread all over the country,
child would be immediately exposed to
to rather belated attempts by the
a second language (e.g., English) as the
Nationalist government to enforce the
LoLT (from Grade 1), or would
controversial
contested
experience a more gradual transfer.
50/50 anguage policy for African
While there is no systematic research
learners that was first promulgated in
evidence, it is widely held that many
1953. This policy prescribed that all
schools with an African student body
African children at secondary school
adopted English as the LoLT from
should learn 50% of their subjects in
Grade 1 (Taylor & Vinjevold, 1999).
Afrikaans and the other 50% in English.
The unbanning of liberation movements
African teachers were given five years
and the release of Nelson Mandela in
to become competent in Afrikaans. In
February
1979, in the wake of the 1976 revolt,
beginning of a new era for South Africa.
the government introduced a new
The ANC was voted into power in 1994
language policy. This
and multiple policy initiatives began
emphasized
and
initial
highly
new policy
main
of
1990
signalled
the
language
across all social services. In terms of
learning with an eventual shift in the
language policy, a process to fully
LoLT to English or Afrikaans. As a
recognize the rich multilingual nature of
general rule, the African child began his
South
or her schooling in the main language,
constitution adopted in 1996 for a
which remained the LoLT through the
postapartheid South Africa recognizes
fourth year of schooling (Grade 4).
11 official languages. For the first time
During these first four years both
nine
English and Afrikaans were studied as
Sepedi, Setswana, Tshivenda, Xitsonga,
subjects. Beginning in the fifth year of
IsiNdebele,
schooling (Grade 5), there was a shift in
IsiZulu—received official status, in
the LoLT to either English or Afrikaans,
addition to English and Afrikaans. In
the official languages of the country. In
1997
Africa
African
a
was
The
anguages—Sesotho,
IsiXhosa,
new
initiated.
IsiSwati
and
language-in-education
policy that
recognizes
11
official
the
8
The
Mathematics
Educator
languages was introduced. Language in
language of power and the language of
education in the new South Africa
educational
According to this policy, not only can
advancement, thus it is a dominant
South African schools and learners now
symbolic resource in the linguistic
choose their LoLT, but thereis a policy
market (Bourdieu, 1991) in South
environment supportive of the use of
Africa.
languages other than one favored LoLT
embodied by and enacted in the many
in school, and so too of language
key situations (e.g., educational settings,
practices like code-switching. While
job situations) in which
this new language-in-education policy
resources,
is widely acknowledged as “good”, it is
linguistic skills, are demanded of social
already meeting
actors if they want to gain access to
significant
on-the-
and
The
socio-economic
linguistic
like
market
certain
symbolic
types
valuable
suggests that most schools are not
eventually
material
opting to use learners’ main languages
(Bourdieu).
Various
as LoLTs in both policy and practice
arrangements and government policies
(Taylor & Vinjevold, 1999). This
continue to produce the dominance of
situation is not unexpected; as described
English in the linguistic market. First,
earlier, main language as LoLT policy
the
or mother tongue instruction has a bad
institutions
image among speakers of African
Afrikaans, and it seems that this policy
languages.
with
will continue for many more years since
apartheid and hence inferior education.
it has not yet been challenged in higher
While the new language policy in South
education circles. Second, there is an
Africa is intended to address the
English/Afrikaans-language
overvaluing of English and Afrikaans
requisite for anyone aspiring to become
and
a professional in South Africa. Students
the
is
associated
undervaluing
of
African
LoLT
to
educational,
of
ground constraints. Recent research
It
social,
is
in
is
resources
institutional
higher
either
pass
education
English
or
pre-
languages, in practice English continues
need
to dominate. Even though English is a
examination in English as a first or
main language of a minority, it is both
second
language,
a
and
school-leaving
in
addition
to
mathematics, to enter and succeed in
administrative,
the Englishmedium training programs
professional arenas of South Africa, a
in professional fields such as medicine
symbolic market has been formed
and engineering and in order to earn
where English constitutes the dominant,
qualifications to enter high-income
if not exclusive, symbolic resource. It is
professions. “The symbolic market is
a prerequisite for individuals aspiring to
therefore not a metaphor but one with
gain a share of the socio-economic,
transactions that have material, socio-
material resources enjoyed by an elite
economic consequences for individuals”
group. Recognizing the historically
(Lin, 1996, p. 53). Third, there are still
diminished use and status of the nine
policies upholding English as an official,
African languages of the people of
legal, and government language. The
South Africa, in December 1995 the
nine African languages spoken by the
Minister of Arts, Culture, Science and
majority of South Africans are still
Technology
secondary to English in reality; for
establishment of a Language Plan Task
example, most of the policy documents
Group (LANGTAG). Its role was to
are written in English only. Fourth,
identify South Africa’s language-related
there
is
imposition
Englishlanguage
of
an
needs
and
requirement
for
LANGTAG
educational,
and
announced
priorities.
has
the
Since
then,
articulated
a
individuals aspiring to join the civil
multilingual policy for South Africa. It
service.
to
proposed a widespread use of the nine
communicate in English is one of the
African languages in all spheres. This
requirements for anyone willing to train
proposal was challenged by some
for police or military service. The fact
members of the division of Applied
remains that English is the most
English
important criterion for selection for
University of the Witwatersrand, who
high-ranking officials; knowledge of an
believe that the widespread use of the
African
nine
For
instance,
language
is
ability
seen
as
an
Language
African
Studies
languages
at
will
the
not
additional asset but not an essential one.
necessarily alter the status and power of
With these institutions and policies
English (Granville, et al., 1998). They
well-entrenched
proposed that all learners be guaranteed
in
the
various
access to the language of power
context of South Africa In 1995 the
(English), while at the same time
Minister of Education announced the
ensuring redress for African languages.
introduction of the new curriculum.
They maintain that this redress will
This curriculum was intended “to
enable teachers to teach English as a
overturn the legacy of apartheid and
subject without guilt and to help
catapult South Africa into the 21st
learners understand that all languages
century” (Chisholm, et al., 2000, p. 8).
are valuable and are a national treasure
It would bring together education and
(Granville, et al.). The issue of the
training, content and skills, values and
dominance of English in South Africa is
knowledge.
not easy to resolve. As Sachs, a
curriculum was launched and became
constitutional court judge, pointed out,
known as Curriculum 2005 (National
in South Africa “all language rights are
Department
rights against English” (1994, p. 1). The
1997).According to Curriculum 2005 a
above discussion highlights the link
minimum of two languages should be
between language and politics in South
offered;
Africa. It is clear that in South Africa,
prescription as to what these languages
change in language-in-education policy
should
has been linked to change in political
recognized as a valuable resource.
power. Thus if “mathematics education
According to the official document, The
begins in language, [it] advances and
advancement of multilingualism as a
stumbles because of language” (Durkin,
major resource affords learners the
1991), then the politics of changing
opportunity to develop and value: their
language policies must impact on
home languages, cultures and literacies;
mathematical teaching and learning
other languages, cultures and literacies
practices particularly in multilingual
in our multilingual country and in
classrooms. Just like the language-in-
international contexts; and a shared
education policy, changes in the school
understanding of a common South
curriculum in South Africa have been
Africa (Department of Education [DoE],
preceded by changes in political power.
1997). A focus on an integrated and
The school mathematics curriculum
non-disciplinary
In
of
March
Education
however,
be.
1997
there
this
[NDE],
is
Multilingualism
no
is
division of knowledge in Curriculum
“use
2005 led to an introduction of eight
communicate
learning areas that replaced school
concepts, generalisations and thought
subjects. The understanding here was
processes.” In the elaboration of this
that learning areas would promote
outcome, the policy documents states
strong integration of what is learned
that Mathematics is a language that uses
both academically and in everyday life
notations,
(Chisholm, et al., 2000). The official
conventions, models and expressions to
description of the mathematics learning
process and communicate information.
area
the
The branch of mathematics where this
construction of knowledge that deals
language is mostly used is algebra and
with
quantitative
learners should be developed in the use
relationships of space and time. It is a
of this language. Curriculum 2005 was
human activity that deals with patterns,
reviewed during the year 2000. As a
problem solving, logical thinking etc.,
result of the review, a task team was
in an attempt to understand the world
appointed
and make use of that understanding.
curriculum statement for mathematics.
This
Language
is
that
Mathematics
qualitative
and
understanding
developed
and
language,
symbols
is
is
expressed,
contested
and
through
social
mathematical
language
mathematical
symbols,
to
develop
and
to
ideas,
terminology,
a
national
communication
of
mathematics are again emphasized in
the
national
curriculum
statement.
interaction (DoE, 1997). The above
Learning outcome 2 that focuses on
description emphasizes the role that
patterns, functions and algebra states,
language
“the learner should be able to recognise,
plays
in
the
expression,
development,
and
contestation
mathematics.
This
view
of
highlights
describe and represent patterns and
relationships,
and
solves
problems
language as a tool for communication,
using algebraic language and skills”
thinking and politics in mathematics.
(Chisholm, et al., 2000). As the above
The role of language in mathematics is
discussion shows, there is an explicit
also
focus
highlighted
in
the
specific
on
multilingualism
and
the
outcomes for mathematics. Outcome 9
communication of mathematics in the
states that learners should be able to
present mathematics school curriculum.
purposes….We
should
This focus raises questions about the
mathematical
language used for communication and
not think of a mathematical register as
how
a
constituting solely of terminology, or of
language
the development of a register as simply
choices in their multilingual classrooms,
a process of adding new words (p. 76).
advancing
Part
mathematics
balance
between
initiating
teachers
find
making
multilingualism,
learners
into
and
learning
mathematics
is
of
acquiring control over the mathematics
communicating mathematics. In the
register—learning to speak, read, and
remainder of the paper I explore the
write
complex relationship between language
mathematics register includes words;
and mathematics, drawing on research
phrases; symbols; abbreviations; and
in South Africa and elsewhere. As
ways of speaking, reading, writing and
stated above, I develop an argument for
arguing that are specific to mathematics.
the centrality of the political for both
Since mathematics is not a language
research and practice in language and
like French or Xhosa, speaking or
mathematics education. Without such a
writing it requires the use of an ordinary
focus we will fail to understand and so
language,
work with the demands that teachers
mathematics is taught and learned. As
face. The relationship between language
discussed earlier, a majority of learners
and mathematics In his seminal work,
in South Africa learn mathematics in a
Pimm (1987) explored some of the
language that is not their main language.
connections
Thus communicating mathematically in
between
ways
of
language
and
like
a
the
mathematician.
language
in
The
which
mathematics He argues that one way of
multilingual classrooms in South
describing the relationship between
Africa follow :
mathematics and language is in terms of
· ordinary English and mathematical
the linguistic notion of register. The
English.
mathematics
· formal and informal mathematics
register
is
a
set
of
meanings that belong to the language of
language.
mathematics (the mathematical use of
· procedural and conceptual discourses.
natural language) and that a language
· learners’ main language and the LoLT.
must
express
if
it
is
used
for
The
interaction
between
ordinary
“any”, and so on (Rowland). These
English (OE) and
words from the language of predicate
mathematical English (ME)
logic can be confusing when used in
As Pimm (1987) argues, speaking like a
mathematical conversations (spoken or
mathematician does not just involve the
written) because they can appear to
use of technical terms, but also phrases
belong to ordinary English when in fact
and characteristic modes of arguing that
they have been redefined for logical
are
reasons. Pimm uses the following
consistent
Mathematics
register.
with
Educator
Mathematical
the
10
The
mathematics
example
speech
difficulties
and
to
highlight
with
the
one
word
of
the
“any”.
writing have a variety of language types
Consider the following two questions:
that learners need to understand in order
a) Is there any even number which is
to participate appropriately in any
prime?
mathematical conversation. These types
a) Is any even number prime?
are ordinary and mathematical English,
According to Pimm (1987), question a)
or logical language and meta-language
is clear and the response to it is “yes, 2
(Pimm; Rowland, 1995). Mathematical
is an even number and it is also prime”.
English can be described as the English
Question b), however, is not clear and
mathematics register, in the same way
can be interpreted in two conflicting
that we can have mathematical French,
ways:
or mathematical Swahili. One of the
· Is any (i.e., one specific) even number
difficulties
prime?
of
learning
to
use
mathematical English is that in its
Answer: Yes, 2 is an even number and
spoken (sometimes also in its written)
it is alsoprime.
form it is blended with ordinary English
· Is any (i.e., every) even number
(natural language), and the distinction
prime?
between the two languages is often
Answer: No, almost all are not prime.
blurred.
is
The source of the difficulty in the above
embedded in the language of predicate
example is the mathematical meaning
logic, which includes items such as
of the word “any”. While the word “any”
“and”, “or”, “if…then”, “some”,
is used widely in mathematics at all
Mathematical
English
levels, it is ambiguous. It may be used
usually
to mean every or some. For example the
settings like schools. Considering the
question “is any rectangle a rhombus?”
above example of a “half”, in formal
can legitimately be answered both “yes,
mathematics
a square is” and “no, unless it happens
inappropriate to talk about a whole
to be a square”. According to Pimm
being divided into three halves. If any
(1987), mathematicians tend to use
whole is divided into three equal parts,
“any” to mean “every”, and on occasion,
the result is”thirds”. The valued goal in
their meaning conflicts with ordinary
school
usage. However, it is clear from the
formal written mathematical language
above examples that the word “any” is
(Setati & Adler, 2001). Pimm (1991)
not used consistently in mathematical
suggests two possible routes to facilitate
English. The same can be said of other
movement
from
informal
spoken
logical connectors such as “if…then”.
language
to
formal
written
Mathematics words can also mean
mathematical language. The first is to
different things depending on whether
encourage learners to write down their
they are used informally or in a formal
informal utterances and then work on
mathematical conversation. Formal and
making the written language more self-
informal mathematics language In most
sufficient. The second is to work on the
mathematics classrooms both formal
formality and self-sufficiency of the
and informal language is used, in either
spoken language prior to writing it
written
down. I have previously argued that in
or
spoken
form.
Informal
developed
within
language
mathematics
formal
it
is
classrooms
is
language is the kind that learners use in
multilingual mathematics classrooms
their everyday life to express their
where learners learn mathematics in an
mathematical
For
additional language, the movement
example, in their everyday life, learners
from informal spoken language to
may refer to a “half” as any fraction of
formal written language is complicated
a whole and hence can talk about
by the fact that the learners’ informal
dividing a whole into “three halves”.
spoken language is typically not the
Formal mathematical language refers to
LoLT (Setati & Adler, 2001; Setati,
the standard use of terminology that is
2002).
understanding.
Figure
1
shows
that
the
movement from informal spoken to
mathematics teachers in multilingual
formal
in
classrooms in South Africa would not
multilingual classrooms occurs at three
work on formalising spoken and written
levels: from spoken to written language,
mathematics in the main language:
from main language to English, and
· The mathematics register is not well
from informal to formal mathematical
developed in most of the African
language. The different possible routes
languages.
are represented in Figure 1 by different
· Due to the dominance of English this
lines. For instance, one route could be
work would generally be seen or
to encourage learners to write down
interpreted as a waste of time.
their informal utterances in the main
Procedural and Conceptual Discourses
language, then write them in informal
In addition to both spoken and written
mathematical English, and finally work
modes
on making the written mathematical
mathematics, mathematics in school is
English more formal. In this case the
carried out by distinctive mathematics
teacher works first on learners writing
discourses. For example, Cobb (Sfard,
their informal mathematical thinking in
Nesher, Streefland, Cobb, & Mason,
both
thereafter on
1998) has distinguished calculational
formalizing and translating the written
from conceptual discourses in the
mathematics into the LoLT. Another
mathematics classroom. He defines
possibility is to work first on translating
calculational discourse as discussions in
the
mathematical
which the primary topic of conversation
language into spoken English and then
is any type of calculational process, and
on
the
conceptual discourse as discussions in
mathematics. Of course there are other
which the reasons for calculating in
possible routes that can be followed. As
particular ways also become explicit
can be seen in Figure 1, while formal
topics of conversations (Sfard, et al.).
written mathematics in the learners’
Previously I have referred to procedural
main language(s) is a possibility, there
and
are no routes to or from it. There are a
procedural discourse focuses on the
variety
procedural steps to be taken to solve the
written
mathematics
languages, and
informal
spoken
formalizing
of
and
reasons
writing
why
most
of
formal
conceptual
and
discourses
informal
where
problem. I have argued for the use of
in part determining the patterns of
the term procedural discourse rather
communication in the classroom, but
than Cobb’s calculational discourse
also serving as a role model of a “native
because
speaker” of mathematics (Pimm, 1987).
“procedural”
is
self-
explanatory (Setati, 2002). To give an
As
example, in the problem 28 + 18,
interactions with the teacher, students
learners can enter into discussions
learn the range of accepted ways in
focusing
which
on
calculational
the
procedure
processes)
to
(or
follow
a
consequence,
mathematics
communicated
from
is
and
their
to
be
discussed.
The
without focusing on why the procedure
teacher models the accepted ways of
works (e.g., why they do not write 16
actinginteracting-
under the units). Another possibility is
speaking-reading-writing
that learners can solve this problem by
mathematically.
engaging in discussions about the
encourage
problem and also about why a particular
allowing learners to speak informally
procedure works (conceptual discourse).
about
mathematics—exploring,
In conceptual discourse, the learners
explaining,
and
articulate, share, discuss, reflect upon,
interpretations and ideas. The challenge
and refine their understanding of the
here is for the teacher to know when
mathematics that is the focus of the
and how to lead learners from their
interaction or discussion. It is the
informal
responsibility of the teacher to arrange
mathematics. If the teacher intervenes
classroom situations in which these
prematurely, she could unintentionally
kinds of interactions are possible—
discourage learners from expressing and
classroom situations where conceptual
exploring their conceptions regarding
discourse is not just encouraged but is
the mathematics that is being discussed.
also
This
valued.
“discourse
The
guide”
teacher,
(Mercer,
as
a
thinking-valuing-
Teachers
conceptual
talk
kind
of
to
can
discourse
arguing
formal
exploratory
by
their
spoken
talk
is
1995),
important for learners to develop Figure
conveniently acts to a considerable
1. Alternative routes from informal
extent as an intermediary and mediator
spoken (in main language) to formal
between the learners and mathematics,
written
(in
English)
mathematics
language. Informal spoken mathematics
same time intervening so as to work
main language Formal spoken
with the learners to develop their
mathematics main language Informal
mathematical
spoken
LoLT
competence (Adler, 2001, p. 3). This
Formal spoken mathematics English
dilemma of mediation highlights a key
LoLT Informal written mathematics
challenge in the context of Curriculum
main
written
2005, where learner participation is
mathematics main language Informal
valued and teachers strive for inclusion,
written
LoLT
voice, and greater mathematical access.
Formal written mathematics English
This challenge is exacerbated by the
LoLT 12 The Mathematics Educator
“dilemma of transparency where the
ideas and concepts in a comfortable
tension is between implicit and explicit
environment. It is also important for
teaching of the mathematics language”
enabling teachers to listen to learners’
(Adler, 2001, p. 4, italics added). As
ideas and conceptions so that these can
Adler has noted, these dilemmas are a
be worked with and built upon (Setati,
challenge for all teachers. They are not
Adler, Reed, & Bapoo, 2002). It is in
specific to a multilingual classroom.
this
informal
But as this paper will show, these
exploratory talk that learners begin to
dilemmas are more complex in a
acquire conceptual discourse. Therefore
multilingual classroom where informal
the teacher is faced with the challenge
spoken mathematics is not in the LoLT.
of keeping a balance between informal
In
and formal spoken language and of
acquiring
making sure that the learners explore
mathematics. Adler’s description of the
their ideas sufficiently in informal ways
dilemmas is crucial and highlights the
in order to acquire fluency in formal
fundamental pedagogic tensions that
conceptual discourse. Adler refers to
cannot be resolved once and for all.
this challenge as the dilemma of
However, she does not explain in
mediation: The dilemma of mediation
specific detail why teachers experience
involves the tension between validating
these dilemmas in the way that they do.
diverse learner meanings and at the
This focus was not her project. She
mathematics
language
Formal
mathematics
environment
English
English
of
these
communicative
classrooms
English
learners
while
are
learning
posits an explanation that the dilemmas
Teaching and learning mathematics in
are at once personal and contextual. For
bi/multilingual classrooms The effects
instance, one of the teachers in Adler’s
of bi/multilingualism on learners have
study experienced the dilemma of
been the focus of research for decades. I
mediation because of changes in her
will not rehearse the arguments here as
classroom and because of her personal
they have been described in detail
commitment to her learners. In this
elsewhere (e.g., Saunders, 1988; Setati
paper I argue that the dilemmas that the
2002). Instead, the discussion below
multilingual
focuses on the complex relationship
experience
mathematics
are
also
teachers
political.
The
between
bi/multilingualism
and
complex and competing demands on
mathematics learning as well as on
mathematics teachers in multilingual
code-switching as a common learning
classrooms in South Africa are evident
and
from the above discussion. Teachers
bi/multilingual classrooms in South
have to ensure learners’ access to
Africa
English, to the language of mathematics,
Bi/multilingualism
and
learning
to
a
range
of
mathematical
teaching
resource
and
The
in
many
elsewhere.
and
complex
mathematics
relationship
discourses. In particular, they need to
between bilingualism and mathematics
assist learners in developing formal
learning has long been recognized.
spoken and written mathematics. These
Dawe (1983), Zepp (1989), Clarkson
competing
(1991),
demands
can
affect
and
Stephens,
Waywood,
classroom practices in contradictory
Clarke, and Izard (1993) have all
evidenced
Adler’
argued that bilingualism per se does not
identification of two teacher dilemmas.
impede mathematics learning. Their
In the remainder of this paper I explore
research used Cummin’s (1981) theory
the implications of policy and the
of the relationship between language
growing understanding of the complex
and cognition. Cummins distinguished
role
different
ways,
as
of
language
in
in
mathematical
levels
kinds
of
also
showed
a
learning as I examine research on the
bilingualism.
teaching and learning of mathematics in
relationship between learning and level
bi-
of proficiency in both languages on the
and
multilingual
classrooms.
He
and
one hand and the additive or subtractive
students in a South African university
model of bilingual education used in
who were learning mathematics in
school on the other. Secada (1992) has
English, which was not their main
provided an extensive overview of
language. This field of research has
research on bilingual education and
been criticized because of its cognitive
mathematics achievement. He pointed
orientation and its inevitable deficit
to findings of a significant relationship
model of the bilingual learner (Baker,
between the development of language
1993). The argument is that school
and achievement in mathematics. In
performance
particular, oral proficiency in English in
mathematics
the
tongue
determined by a complex set of inter-
instruction was negatively related to
related factors. Poor performance of
achievement
bilingual
absence
of
mother
in
mathematics.
(and
by
implication,
achievement)
learners
thus
is
cannot
be
Rakgokong (1994) has argued that
attributed to the learners’ language
using English only as a LoLT in
proficiencies in isolation from the wider
multilingual
mathematics
social, cultural, and political factors that
classrooms in South Africa where
infuse schooling. While I agree with the
English is not the main language of the
above
learners has a negative effect on the
cognitively-oriented
learners’ meaning making and problem
implicit argument in support of the
solving. His study showed that, in
maintenance
of
classrooms where English, was the only
language(s),
and
language used for teaching and learning,
benefits of learners using their main
learners were able to engage in neither
language(s) as a resource in their
procedural nor conceptual discourse.
mathematics
Varughese and Glencross (1996) found
(1991) has argued, bilingualism is
that students at the university level had
becoming the norm rather than the
difficulty
understanding
exception in urban classrooms. Hence
mathematical terms such as integer,
the need in mathematics education
perimeter, and multiple. Their study
research to examine classroom practices
involved
where the bilingual speaker is not only
primary
in
first-year
mathematics
criticism,
I
read
into
research
learners’
of
learning.
the
As
this
an
main
potential
Secada
treated as the norm, but where his or her
compare a high hurdler to a sprinter or
facility across languages is viewed as a
to a high jumper, even though the
resource rather than a problem (Baker,
former blends certain characteristics of
1993). In an article entitled “The
the latter two. In many ways the
Bilingual as a Competent Specific
bilingual is like the high hurdler (p.
Speaker-hearer”,
(1985)
471). In Grosjean’s terms, language
argues for a bilingual (or holistic) view
practices in multilingual classrooms
of bilingualism in any consideration of
will not be the same as in any other
bilinguals. This view is different from
classroom. For example, an important
the monolingual view, which always
aspect of multilingualism, one which
compares
makes
the
Grosjean
linguistic
ability of
the
multilingual
person
an
bilinguals with that of monolinguals in
integrated whole, is code-switching. As
the languages concerned. Bilinguals
indicated earlier, code-switching is now
have a unique and specific language
encouraged
configuration and therefore they should
education policy. In the section below I
not be considered as the sum of two
present a review of research on code-
complete or incomplete monolinguals:
switching in bilingual and multilingual
The
classrooms
coexistence
and
constant
by
in
the
South
language-in-
Africa
and
interaction of the two languages in the
elsewhere. Code-Switching in bilingual
bilingual has produced a different but
and
complete language system. An analogy
classrooms
comes from the domain of athletics.
when an individual alternates between
The high hurdler blends two types of
two or more languages. Codeswitches
competencies: that of high jumping and
can be deliberate, purposeful, and
that of sprinting. When compared
political. There are important social and
individually with the sprinter or the
political aspects of switching between
high jumper, the hurdler meets neither
languages,
level of competence, and yet when
switching between discourses, registers,
taken as a whole, the hurdler is an
and
athlete in his or her own right. No
switching in South Africa has had an
expert in track and field would ever
inferior status (Setati, 1998). As a result,
multilingual
mathematics
Code-switching
as
dialects.
there
are
Historically,
occurs
between
code-
many people still regard it as a
than one language, rather than a defect
grammarless mixture of languages.
arising from insufficient knowledge of
Some monolinguals see it as an insult to
one or the other. Some researchers see
their own rule-governed language. It is
code-switching as an important means
generally believed that people who
of conveying both linguistic and social
code-switch know neither language well
information. For instance, Gumperz
enough to converse in either one alone.
cited in Grosjean (1982) maintains that
Grosjean (1982) points out that it is
code-switching is a verbal strategy,
because of these attitudes that some
used in the same way that a skilful
bi/multilinguals prefer not to code-
writer might switch styles in a short
switch,
their
story. For instance, a teacher can use
switching to situations in which they
learners’ main language as a code for
will not be stigmatized for doing so. For
encouragement.
instance, in a multilingual classroom
main language in this manner, the
learners may choose to switch only
teacher may implicitly be saying to
when interacting with other learners and
learners “I am helping you; I am on
not with the teacher. Why code-switch?
your side”. In most classrooms code-
Even
has
switching seems to be motivated by
from
cognitive and classroom management
purists, there are researchers who see it
14 The Mathematics Educator factors
as a valuable communication resource.
(Adendorff, 1993; Merritt, et al., 1992):
On the basis of their ethnographic
Usually it helps to focus or regain the
observation of classroom interaction in
learners’
three primary schools in Kenya, Merrit,
enhance, or reinforce lesson material.
Cleghorn, Abagi, & Bunyi (1992) argue
Determinants of code-switching in the
that
mathematics
while
though
received
others
code-switching
substantial
code-switching
additional
restrict
resource
criticism
provides
attention,
using
or
learners’
to
classroom
clarify,
are
only
meeting
partially dictated by formal language
classroom needs. Poplack cited in
policy. Even if official policy exists,
Grosjean
teachers make individual moment-to-
(1982)
for
an
By
argues
that
codeswitching is a verbal skill requiring
moment
decisions
about
language
a large degree of competence in more
choice that are mostly determined by
the need to communicate effectively:
· to quote someone,
Multilingual teachers do not only teach
· to interject in a conversation, or
lessons and inculcate values having to
· to exclude someone from an episode of
do wit conservation of resources. They,
conversation. Thus code-switching has
perhaps unconsciously, are socialising
more than just linguistic properties; it can
pupils into the prevailing accepted
also be used for political purposes.
patterns of multilingualism (Merritt, et
Researching
al., p. 118). As pointed out earlier, the
multilingual
language-in-education policy in South
code-switching in multilingual classrooms
Africa
in South Africa reveals that it is used for a
recognizes
eleven
official
code-switching
classrooms.
in
Research
on
languages and is supportive of code-
variety of reasons. A study undertaken in
switching as a resource for learning and
primary
teaching in multilingual classrooms.
classrooms in the Eastern Cape, South
Within this policy environment that
Africa, has shown that codeswitching is
encourages switching, it is important
used to enable both learner-learner and
that research focus not only on whether
learner-teacher interactions (Ncedo, Peires,
code-switching is used or not in the
& Morar, 2002). Adendorff (1993), who
teaching and learning of mathematics
observed nonmathematics lessons in the
but also on how and why it is used or
Kwazulu-Natal province of South Africa,
not used. According to Baker (1993),
found that an English teacher switched to
mathematics
and
science
code-switching can be used to describe
Zulu in order to advance his explanation
changes which are relatively deliberate
of the meaning of a poem. The same
and have a purpose. For example,
teacher also used codeswitching as a
codeswitching can be used:
language of provocation—he used it to
· to emphasize a point,
raise
· because a word is not yet known in
bi/multilingual persons switch when
both languages,
they cannot find an appropriate word or
· for ease and efficiency of expression,
expression or when the language being
· for repetition to clarify,
used does not have the necessary
· to express group identity and status or
vocabulary
to be accepted by a group,
translation (Grosjean, 1982). This kind
controversial
item
issues.
or
Most
appropriate
of
switching
would
occur
a
2001; Arthur, 1994; Khisty, 1995;
mathematics
Merritt, et al., 1992; Moschkovich,
conversation. For instance, if learners
1996, 1999; Ncedo, Peires, & Morar,
can hold a mathematical conversation in
2002; Setati, 1996, 1998; Setati & Adler,
Setswana,
the
2001). These studies have presented the
mathematical terms will be in English,
learners’ main languages as resources
because
well-
for learning mathematics. They have
developed register in English but not in
argued for the use of the learners’ main
Setswana. While some of the technical
languages in teaching and learning
mathematics terms are available in
mathematics as a support needed while
Setswana, they are not widely known
learners continue to develop proficiency
and used. For instance while the
in the LoLT while learning mathematics.
Setswana
equilateral
All of these studies have been framed
triangle is “khutlotharo- tsepa”, this
by a conception of mediated learning,
term is usually not used in mathematical
where language is seen as a tool for
conversations in Setswana. There are
thinking and communicating. In other
instances
multilingual
words, language is understood as a
knows
a
social thinking tool (Mercer, 1995).
mathematics word in both English and
Therefore it is not surprising that
her main language (e.g., Setswana), but
problems arise when learners’ main
the
more
languages are not drawn on for teaching
mathematical
and learning. Arthur (1994) conducted
conversations. This phenomenon can be
her study in Botswana primary schools
understood because, as indicated earlier,
where the main language of the learners
a majority of African language speakers
is Setswana. English as the LoLT starts
in South Africa learn mathematics in
from standard six. Her study of the use
English. Code-switching as a learning
of English in standard six mathematics
and teaching resource in bi/multilingual
classrooms revealed that the absence of
mathematics classrooms has been the
learners’ main language (Setswana)
focus of research in the recent past (e.g.,
diminished
Addendorff, 1993; Adler, 1996, 1998,
exploratory talk, and thus for meaning-
bi/multilingual
it
possible
mathematics
word
English
has
for
where
mathematics
available
is
an
the
learner
word
during
in
that
a
becomes
the
opportunities
for
making. The form and purposes of the
for learners to acquire the English
teaching and learning interaction in
language
these classrooms were constrained by
classroom.
the use of English only. As Arthur
infrastructure
explains, communication was restricted
supportive of English as the LoLT.
to what she referred to as “final draft”
There is more environmental print (e.g.,
utterances in English, which were
advertising billboards) in English, and
seemingly devoid of meaning. This
teachers and learners have greater
dominance of English is not unique to
access
Botswana. As discussed earlier, English
magazines
as the LoLT continues to dominate in
speakers of English. Setati, et al. (2002)
multilingual classrooms in South Africa
found greater use of code-switching in
despite the new progressive language-
ALLEs.
ineducation policy (Taylor & Vinjevold,
observed as a “main linguistic feature in
1999). In describing the code-switching
classrooms where the teacher and the
practices
school
learners share a common language, but
mathematics teachers in South Africa,
ha[ve] to use an additional language for
Setati and Adler (2001) observed the
learning…the learners’ language is used
dominance of English in non-urban
as a form of scaffolding” (National
primary schools. They argued that in
Centre for Curriculum and Research
these schools English is only heard,
Development, 2000, p. 68). Adler (1996,
spoken, read, and written in the formal
1998, 2001) identified codeswitching as
school context, thus teachers regard it
one of the dilemmas of teaching and
as their task to model and encourage
learning mathematics in multilingual
English. Setati, Adler, Reed, and Bapoo
classrooms. Adler observed that in
(2002) described these school contexts
classrooms where the main language of
as
learning
the teacher and learners is different
They
from the LoLT, there are ongoing
additional
dilemmas for the teacher as to whether
environments
or not she should switch between the
(ALLEs), where there are opportunities
LoLT and the learners’ main language,
of
foreign
environments
primary
language
(FLLEs).
distinguish
FLLEs
language
learning
from
informally
to
outside
the
The
English
language
of
ALLEs
is
English
and
newspapers,
television,
Code-switching
more
and
has
to
been
particularly in the public domain.
mathematics in their main language(s)
Another issue is whether or not she
to a stage where they can use the formal
should encourage learners to use their
language of mathematics in the LoLT
main language(s) in group discussions
(English), and can engage in procedural
or
and conceptual mathematics discourses
whole-class
discussion.
These
dilemmas are a result of the learners’
in
need to access the LoLT, as critical
demonstrates that there is a growing
assessment will occur in this main
amount of theoretical and empirical
language. Adler’s study suggests that
work related to mathematics teaching
the dilemmas of code-switching in
and
multilingual mathematics classrooms
classrooms. The unit of study in early
cannot necessarily be resolved. They do,
research
however,
managed.
bilingual learner. It is my view that this
Moschkovich (1996, 1999) argues that
location of the problem in the learner
bilingual
the
was based on an underlying assumption
mathematics classroom different ways
of inferiority—that there is something
of talking about mathematical objects
wrong with the bilingual or multilingual
and
on
learner. Recent studies have moved
She
from focusing on the bi/multilingual
emphasizes that a discourse approach
learner to the bi/multilingual classroom.
can also help to shift the focus of
This change in focus drew attention to
mathematics instruction for additional
the significance of the teacher as a
language
language
discourse guide in the bi/multilingual
development to mathematical content.
classroom, and to code-switching and
In Mercer’s (1995) terms, the teacher in
the dilemmas that emerge with its use.
Moschkovich’s study was a discourse
All of the studies referred to have been
guide. As Figure 1 shows, the role of
framed by a conception of mediated
the teacher as a discourse guide in a
learning, where language is seen as a
multilingual
tool for thinking and communication. A
have
to
learners
different
mathematical
be
bring
points
of
situations.
learners
from
mathematics
into
view
classroom
English.
The
learning
on
above
in
bi/multilingual
bilingualism
perspective
discussion
on
was
the
involves moving learners from a stage
different
language.
where they can talk informally about
Language is much more than a tool for
communication and thinking; it is
switch between English and Setswana)
always political (Gee, 1999). Decisions
they 16 The Mathematics Educator
about which language to use, how, and
must be “careful”, as students will be
for what purpose(s), are political. This
denied access to English and being able
political role of language is not dealt
to “improve” (p. 3). Adler (2001)
with
on
describes the language practices of a
bi/multilingualism and the teaching and
teacher in her study (Thandi) as
learning of mathematics. My own
follows: Thandi’s actions, including
experience as a multilingual teacher and
reformulation and repetition, were not
researcher in multilingual mathematics
tied simply to her pedagogical beliefs,
classrooms suggests that we cannot
but also to her social and historical
describe and explain language practices
context and her positioning within it,
in a coherent and comprehensive way if
including
we stop at the cognitive and the
working mathematically in English. In
pedagogic aspects. We have to go
particular, in the South African context,
beyond these aspects and explore the
where
political aspects of language use in
powerful,
multilingual mathematics classrooms.
and practices were constrained by the
Research so far does not capture this
politics of access to mathematical
complexity. As mentioned earlier, Adler
English. Thandi might value using
(2001) points to the complexity by
languages other than English in her
describing dilemmas as personal and
mathematics classes to assist meaning-
contextual, and more particularly by
making.
exploring
code-
understanding interacts with strong
switching. According to Adler, teachers
political goals for her learners, for their
in
access,
in
the
the
multilingual
literature
dilemma
of
classrooms
face
a
her
own
English
is
Thandi’s
But
through
confidence
dominant
of
and
decision-making
this
pedagogical
mathematics
and
continual dilemma of whether to switch
English, to further education and the
or not to switch languages in their day-
workplace. In addition, her decision-
to-day teaching: If they stick to English,
making on code-switching inter-related
students often don’t understand. Yet if
in complex ways with the mathematics
they “resort” to Setswana (i.e., they
register on the one hand and its
insertion
in
school
mathematical
participate in the lesson. It is clear from
discourses on the other (p. 85). In my
the above discussion that there are a
view, Adler partially explains Thandi’s
growing number of studies that have
dilemma.
focused
Thandi
experienced
the
on
language
use
in
dilemma of codeswitching not only
bi/multilingual classrooms. But none of
because of her learners and because of
the studies focused on language as a
the pedagogical and political contexts
political tool. How is language used “to
but also because of who she is: an
enact
African
identities”
mathematics
teacher
who
activities,
(Gee,
perspectives
1999,
p.
and
?)
in
shares a main language with her
bi/multilingual
additional language learners. In addition
classrooms? The main argument of this
Thandi saw her role not only as a
paper is that research on the use of
mathematics
as
language(s) in multilingual mathematics
someone who is supposed to make sure
classrooms needs to embrace language-
that her learners are prepared for higher
in-use as a political phenomenon. The
education in English and the outside
political
world. Thandi’s language practices
teaching and learning of mathematics In
were tied up with her pedagogy,
South Africa, mathematics knowledge
identity, and understanding of the
and the English language are social
power of English. Thandi’s dilemma of
goods. They are perceived to be a
code-switching
is
only
source of power and status. Both of
pedagogic
also
The
them provide access to higher education
political and the pedagogic are in
and jobs. The fact that English is a
tension. This dilemma manifests itself
language of power and socioeconomic
in the multiple identities that teachers
advancement in South Africa makes
take on. For instance, politically Thandi
English a valued linguistic resource in
wanted her learners to have access to
multilingual mathematics classrooms.
English, and therefore she did not use
Even though the nine African languages
code-switching; however,pedagogically
now enjoy an official status, they still
she knew that she needed to switch so
do not enjoy the same kind of status as
that her learners could understand and
English. Gee (1999) argues that when
teacher
but
but
thus
also
not
political.
role
mathematics
of language
in
the
people speak or write they create a
seeing as a condition for qualifying
“political”
use
them to act as subjects. That is,
language to project themselves as
institutions impose certain identities on
certain kinds of people engaged in
people.
certain kinds of activity. Words are thus
mathematics teacher one is expected to
never just words; language is not just a
master the discursive (ways of talking)
vehicle to express ideas (a cultural or
and ideological (ways of “seeing”)
communicative
a
norms which the teaching profession
political tool that we use to enact (i.e.,
attaches to that subject position. That is,
to be recognized as) a particular “who”
one
(identity) engaged in a particular “what”
mathematics teacher and see things (i.e.,
(situated activity). Thus a mathematics
things like learning and teaching) like a
teacher who is also a cultural activist
mathematics teacher. These ways of
wil have an identity that shifts and takes
talking and seeing are inseparably
different shapes as she enacts her
intertwined in the sense that in the
multiple identities in and through
process of acquiring the ways of talking
language. Her decisions about what
which are associated with a subject
language to use, how, when, and why
position, one necessarily also acquires
will be informed by the activity and
its ways of seeing (ideological norms).
identity she wants to enact. The point
Any social
here is that mathematics teachers, like
regarded as a speech and ideological
all people, have multiple identities.
community. Mathematics teaching is a
Research that considers the use of
speech and ideological community. To
language in multilingual mathematics
be part of this social practice you need
classrooms only as a pedagogic and
to
cognitive
mathematics
perspective;
tool
tool),
does
they
but
not
also
attend
For
must
talk
example,
learn
to
practice
and
see
to
be
talk
like
can
thus
things
teacher.
like
Any
a
a
be
a
social
sufficiently to the multiple identities of
practice imparts ways of talking and
multilingual teachers. Fairclough (1995)
seeing that are relevant for that practice.
refers
People
to
institutional
and
social
need
this
kind
of
shared
identities. He argues that institutions
knowledge in order to participate in that
impose upon people ways of talking and
social
practice.
In
the
case
of
mathematics teaching, a mathematics
unconsciously and treat some of them
teacher needs this kind of knowledge in
as if they depict prototypical (what we
order to say acceptable things in an
take to be “normal”) people, objects,
appropriate way. Since this shared
and events. Cultural models do not
knowledge is rooted in the practices of
reside in people’s heads. They are
socio-culturally
of
available in people’s practices and in
people, Holland and Quinn as cited in
the culture in which they live—through
D’Andrade and Strauss (1992) refer to
the
it as culture. When talking about culture
through interaction with others in
in this way, they do not refer to
society. In a recent study focusing on
people’s customs, artifacts, and oral
language
traditions, but to what people must
mathematics classrooms in South Africa
know in order to act as they do, make
I have considered language practices in
the things they make, and interpret their
multilingual mathematics classrooms
experience in the distinctive ways they
from
do. Thus, they would argue that to be a
attending to the multiple identities of
mathematics teacher, one needs more
multilingual teachers. In the study I
than mathematics content knowledge—
used the notion of cultural models as an
one also needs the cultural knowledge
analytic tool to explore and explain the
of mathematics teaching. According to
language practices of six teachers in
Holland
cultural
multilingual mathematics classrooms
knowledge is organized into schemas
(Setati, 2002). Since cultural models are
that are called cultural models. Cultural
not only inferred from what people say,
models are taken-for-granted models of
but also from how they act, think, value,
the world that guide people’s actions
and interact with others (in Gee’s terms,
and their expression of values and
their “Discourses”), these teachers were
viewpoints. Gee (1999) argues that
interviewed and observed in practice.
cultural models are like tapes of
Three categories of cultural models
experiences we have had, seen, read
emerged from the analysis of the
about, or imagined. People store these
interviews and lesson transcripts in that
tapes
study. Hegemony of English cultural
and
either
defined
Quinn,
groups
this
consciously
or
media,
a
written
use
political
in
materials
and
multilingual
perspective,
thus
models
reflect
the
dominance
of
institutional
English in the teaching and learning of
government
mathematics in multilingual classrooms.
discussed earlier, have achieved the
The Policy cultural models revealed the
formation of an English-dominated
teachers’
linguistic
understanding
language-in-education
of
the
policy.
The
English
tensions
language
accompany
teaching
policies
market.
In
and
which,
an
as
in-depth
analysis of one of the lessons observed,
Pedagogic cultural models mirrored the
that
arrangements
emerged
of
as
a
legitimate
communication during
mathematics to learners whose main
teaching, and thus was the language of
language is not the LoLT. These
mathematics, of learning and teaching
multiple cultural models reveal the
and
multiple identities that teachers enact in
dominance of English produced a
their multilingual classrooms to make
dominance of procedural discourse,
both mathematics and English, and
mainly because the learners were not
mathematics in English, accessible to
fluent
learners. Through these three categories
English. Thus whenever the teacher
of cultural models, the pedagogical and
asked a conceptual question, they
the political were deeply intertwined.
responded in procedural discourse in
English is International emerged as the
English, or remained silent until she
“master model” (Gee, 1999). The
changed the question into a procedural
emergence of this master model was is
one. This dynamic is mainly due to the
not
surprising. The dominance of
differing linguistic and mathematical
English in politics, commerce, and the
demands of procedural discourse and
media in South Africa is well known.
conceptual discourse. In conceptual
English is seen as a key to academic
discourse learners are not only expected
and economic success, and therefore
to know the procedure that needs to be
being fluent in it opens doors that are
followed to solve a problem, but also
closed to vernacular speakers (Friedman,
why, when, and how that procedure
1997).
English
works. Procedural discourse, on the
cultural models that emerged in this
other hand, focuses on the procedural
study
steps that should be followed in the
The
form
Hegemony
part
of
of
the
various
of assessment. However, this
in
conceptual
discourse
in
solution of a problem. These steps can
giving instructions to and reprimanding
be memorized without understanding.
learners.
Unlike conceptual discourse, procedural
language was a voice of solidarity while
discourse does not require justification.
English was the voice of authority. This
It is therefore not surprising that in an
study has moved the dominance of
additional
English from a common-sense position
language
environment
like
the
learning
multilingual
to
a
Thus
the
rigorous
learners’
and
main
theoretical
classrooms in the study, procedural
understanding of this dominance, and of
discourse
how
would
mathematical
dominate
conversation
when
was
in
it
plays
itself
out
in
the
multilingual mathematics classroom in
English. As illustrated earlier in Figure
terms
1, the journey from informal spoken
opportunities for learners. This study
mathematics (in the main language) to
has also revealed how the power of
fluency in formal spoken and written
mathematics and English can work
procedural and conceptual mathematics
together in multilingual mathematics
discourses in English is complex in
classrooms to reduce the mathematical
multilingual classrooms. What is more
opportunities for procedural discourse.
interesting is that the teacher whose
Further, it appears that for substantial
lesson was analyzed was convinced that
teaching and learning and engagement
she was promoting multilingualism in
in conceptual discourse to occur, the
her teaching. The 18 The Mathematics
learners’ main languages are required.
Educator analysis shows that she used
However, given the master model of
the
for
English is International, it is not always
regulation and solidarity. While she was
possible to fulfill this requirement. The
regulating the learners’ behavior, she
issue
also showed her support and unity with
language learners learn mathematics in
them. Her utterances in the learners’
a language that is not their main one,
main language were encouraging and
but that the various languages used will
motivating
privilege
learners’
to
main
the
language
learners.
Her
of
is
creating
not
mathematical
only that
different
additional
discourses
Conclusion
of
regulatory utterances in English, on the
mathematics.
The
other hand, were more authoritative,
theoretical elaboration in this article has
shown that to describe and explain
teaching
language
complex
practices
in
multilingual
dilemmas:
Unlocking
multilingual
the
secondary
mathematics classrooms, we need to go
mathematics
beyond the pedagogic and cognitive
Learning of Mathematics, 18, 24-33.
aspects. All language practices occur in
Adler, J. (2001). Teaching mathematics
contexts where language is a carrier of
in multilingual classrooms.
symbolic power. This aspect shapes the
Dordrecht:
selection and use of language(s) and
Publishers. African National Congress,
mathematical discourses. The different
(1994).
ways in which teachers and learners use
education and training. Johannesburg:
and produce language is a function of
Education Department, The African
the
National Congress.
political
structure
and
the
classroom.
For
Kluwer
A
policy
the
Academic
framework
for
multilingual settings in which they find
Arthur, J. (1994). English in Botswana
themselves.
primary classrooms:
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teacher’s
a
of
Functions and
multilingual
constraints. In C. M. Rubagumya (Ed.),
mathematics class is therefore not
Teaching and researching language in
simply cognitive or pedagogic, but is
African
also a social product arising from that
Clevedon: Multilingual Matters Ltd.
particular political context.
Baker, C. (1993).
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 JURNAL 3
particularly interesting cases: Mathematics,
as a discipline, has a long reputation for
Mathematicians’Religious
providing truth and certainty. Though more
Affiliations and Professional
recently this reputation has been called into
Practices: The Case of Charles
question (Kline, 1980), there is something
Anderson Norton III
about the context-free, abstract nature of
mathematics that makes the subject seem
This paper reports on the second of
incontrovertible. Yet religion is often
three cas studies, all intended to explore
considered as an avenue to Truth. In fact, I
the
recall
implications
of
religious
one
of
my
undergraduate
affiliationin the professional lives of
mathematics professors proclaiming that
mathematicians. These case studies
“mathematics is the only truth with the
yield implication for various topics
possible exception of theology.” Well then,
within
mathematics
how might these two truths co-exist? In a
education. For example, each of the
previous paper (Norton, 2002), I reported
first two cases has revealed a religious
on the first of the three case studies
influence on the participant’s childhood
concerning
decision
mathematicians’
the
to
field
of
study
mathematics.
the
relationship
religious
beliefs
and
From
my
Naturally, we might conclude that such
professional
an influence exists for many school-
experiences with that participant—a Jewish
aged, religious mathematics students.
man named Joseph—I concluded that
Other implications range from the
mathematicians
mutual
influence
of
students’
practices.
between
must
reconcile
their
practices with their life philosophies or
mathematical and religious practices to
religions
in
order
the religious value of teaching and
mathematical practice meaningful. This
researching mathematics. In this spirit, I
reconciliation
report on my experience with Charles,
mathematical thought and religious beliefs
the second of the three mathematicians
(and values) are viewed as contradictory. In
of my study. One might find religious
fact, such a view is the case for Charles. “If
implications for various professions, but
the scientific community concedes even
professional mathematics provides
one miraculous event, then how can it
is
to
make
difficult
their
when
credibly contest the view that the world
department:
(and all its fossilized relics) was created in
Buddhist. Here I will abbreviate my report
one instant just 6,000 years ago?” (Singham,
on the methods of the larger study, which
2000, p. 428). Singham’s short statement
can be found in Norton (2002), and focus
summarizes the ongoing conflict between
on the case of Charles. Like myself,
religious belief (especially Judeo-Christian
Charles is a Christian but our views are
beliefs) and scientific thought. Nord’s reply
somewhat different because I am a Catholic
to such questions, on the other hand,
and he is a Protestant. Charles is a full
anticipates one possible resolution by
professor in a large southern university’s
noting
other
mathematics department and is expected to
scientifically defined processes may just be
do mathematical research and teach classes.
“God’s way of doing things” (1999, p. 30).
However, he also has a long list of
The purpose of this paper is to analyze the
additional duties that are described in the
similar conflict and resolution experienced
background section. Data collection for
by Charles so that
we might draw
Charles’ case was similar to the other cases.
conclusions for mathematics education
I conducted a single, one-hour interview
from his struggle. Indeed, an emergent
and was able to collect additional data from
theme from this case—the paucity of value
archival sources. These documents included
for
the
his online vita and a booklet describing the
devaluation of many scientific branches
faculty of their department. I used this data
that seem to contradict Biblical truth)—
in addition to some of the interview data for
may have important implications for the
background information about Charles.
work of mathematics teachers in secondary
After transcribing, reading, and rereading
schools in the United States. Methods In
the interview transcript, I coded, grouped,
order to study the implications of religious
and identified concepts from the data.
affiliations in the lives of professional
These concepts were then developed in
mathematicians, I conducted interviews
narrative form. First I developed Andy
with
mathematics
Norton is currently working on his doctoral
professors. I identified three religious
dissertation in mathematics education and
groups
master’s
that
secular
three
evolution
study
(and,
university
representing
the
and
indeed
diversity
of
religious beliefs in their mathematics
University
Jewish,
degree
of
in
Christian,
mathematics
Georgia.
His
and
at
research
interests include students’ mathematical
story consists of three parts: background,
conjectures and their role in learning.
narrative,
paragraphs from the concepts. Then I
Background
identified the major themes relating the
American man, about fifty years of age. He
participant’s religion and profession and
was raised in his mother’s church, the
restructured the narrative section around
United Church of Christ, in Montana. His
these themes. The final narrative is the
mother and two sisters were very devoted
central component of the analysis of
Christians,
Charles’ case. In order to relate Charles’
struggled with many of the Christian
case and build on emergent themes, I
doctrines, such as the deity of Jesus, for
recount a few histories in the discussion
much of his life. The tension between him
section that I will use as a backdrop Since
and his sisters led him to renew his faith
the narratives are made up of my own
during graduate school, but he continued to
words, I wanted to include something
wrestle with many church doctrines years
additional to capture Charles’ words and
later. Charles was never a very social
phrases.
poetic
person. Even as a child his extracurricular
transcription (Glesne, 1999), restructuring
activities were restricted to band and
words from the transcripts into a poem. I
church. At a very young age Charles also
began with a list of phrases and organized
became aware of his mathematical talent.
them into stanzas centered on particular
He was set apart from his peers in public
themes or concepts. The stanzas began to
school mathematics classes, often working
take form as I shuffled and reduced quotes.
alone or with a small group of other gifted
In forming the stanzas, I was careful to stay
students on higher-level mathematics. His
close to my interpretations of their meaning.
mathematical
While I used only Charles’ literal phrases
attention of his professors in college and
and words in this section, their order and
eventually led to his graduate studies at
concatenation may be very different from
Princeton. Charles is now married and a
the literal transcriptions. I hope that the end
father of three. He describes his profession
result gives the flavor of the participant’s
as one of teaching, advising, serving on
voice and language that is missing from the
committees,
and
narratives. Thus my presentation of Charles’
departmental
decisions.
So
I
incorporated
and
Charles’
poem.
Charles
was
talent
is
a
European-
agnostic.
also
story
Charles
caught
helping
His
to
the
make
research
(mostly in Number Theory) must be
was not the same as their mother’s. This
squeezed in whenever other commitments
difference led to tensions between Charles’
taper off, such as at the beginning of the
mother and sisters. Eventually, his mother
school year. This situation is very different
came to peace with his sisters’ decisions,
from the one he imagined for himself when
but his sisters’ strong faiths continued to
he decided to become a mathematics
cause tension for Charles who, in contrast,
professor. Though he seems to enjoy
had not become comfortable with his
teaching, research is his main interest and
Christianity. Throughout his life Charles
he considers many other duties subsidiary
has attended church regularly, though he
to that. Narrative Struggle followed by
has struggled with many doctrinal issues. In
peace. In describing hisreligious beliefs and
particular, he seemed to share his father’s
mathematical interests, Charles talked a lot
view
about his childhood and the frequent
evolutionism. As a high school class
conflict he experienced in his family. He
assignment, he wrote a rebuttal to the
described his mother as a very strong
theory of creationism; his sisters had
person who worked in the church. In fact,
written in favor of it in similar assignments.
his parents both signed the original
The tension between his scientific views
covenant of their Congregationalist church
and his sisters’ faith in religious doctrine
in Montana. However, Charles’ father
remained throughout Charles’ graduate
perceived contradiction between Biblical
school studies. Charles noted that while
inerrancy and theories of evolution, which
growing up he was not part of a church
made religion problematic for him. These
youth group and that he had been quite shy.
perceptions led to quarreling between
Although he had attended church through
Charles’ parents, quarreling that ended
graduate school, it wasn’t until he began
when the father stopped attending church.
post-doctoral work in Cambridge that he
The theme of conflict followed by peace
found a group of young Christians with
creationism
is
inferior
to
story.
which he could identify. At that time, he
Charles’ two sisters were both very
renewed his own Christian beliefs. He said
involved with Protestant Christian churches.
that it was the tension with his sisters that
Both went on religious missions, and one
brought him to the point of renewal.
became a pastor. However, their church
Though he continued to struggle with many
continues
throughout
Charles’
that
other doctrinal issues, he founded his
he enjoyed the competitiveness involved in
beliefs on three main doctrines: “I believed
it. At the same time, he was careful “not to
that God answered prayer… that if Jesus
show out”, though he was “inwardly very
were alive I would follow him… and that I
proud.” While he had a great deal of
couldn’t be justified before God on my own
mathematical talent and a strong desire to
merits.” 30 The Mathematics Educator
develop that talent, Charles felt he needed
When he moved to the South in 1981,
to find religious meaning for pursuing such
Charles began attending a Presbyterian
a profession. When Charles was about eight
Church. There, a friend questioned him
years old, he prayed for his sick parakeet to
about the doctrine of Jesus’ deity, and
get better, promising that in return he
Charles resisted the provision of pat
would find the best way to serve God. The
answers to these questions. “I wasn’t going
parakeet got better and ever since Charles
to be steam-rolled into any doctrinal
struggled with finding the best way to serve.
confessions at the start without thinking
By the end of his undergraduate years, he
about things,” he said. The tension that
was “in a knot” trying to decide what career
ensued between him and his friend led to a
he should pursue to serve God. Though he
distancing between them. Only years later,
was never gifted socially, for a time
after meeting and marrying his Christian
Charles thought about becoming a pastor.
wife, did Charles come to a peace about
“I used to think that being a pastor was the
that issue and other religious beliefs. He
only thing
had needed time to resolve such issues for
God]…but I can see that I am not gifted to
himself. During the period of his life that
do that kind of work.” He was clearly
he was struggling with doctrinal issues,
gifted in mathematics, but felt he needed to
Charles
do
was
trying
to
reconcile
his
you
could
do
[to
serve
would directly benefit man. He
mathematical interests with his Christianity.
considered
As early as seventh grade, Charles knew
engineering,
that he was gifted in mathematics. His
problems. However, upon graduating, he
teachers knew it too. He was the best
chose to continue doing the work he
mathematics student his college professors
enjoyed; he began a graduate program in
had
liked
pure mathematics at Princeton. Once again,
mathematics because he was good at it and
Charles came to peace—this time about his
seen
at
their school. He
professions
tackling
in
physics
or
environmental
choice of careers: “It’s okay to have been a
he orchestrates everything else. In all of the
mathematician.”
mature
sciences, mankind is “wavering toward a
judgment, he sees that everyone plays a
truth.” Though individual theories may fail,
part in God’s plan. He cannot expect to
better ones replace them. So though people
produce the key idea in solving pollution
sometimes take the wrong path in their
problems
theories, there is a general trend toward
or
With
any
more
other
social
or
environmental problem. People work one
Truth.
step at a time on small, technical aspects of
knowledge contributes to that Truth as well.
problems.
in
Charles feels like an explorer in his own
mathematics. God orchestrates. Charles
search for mathematical knowledge. In a
believes that “God orchestrates everything
way, mathematics actually stands out from
that happens in history.” This belief
all
resolves the conflict between evolution and
“Mathematics is the most certain of all of
creationism because, as Charles explains,
the sciences.” Charles seems bothered by
God created the world through evolution.
the fact that, historically, there has been a
The industrial revolution, evolution and
lot of vagueness in mathematics: “People
other scientific developments are part of
would just do things [in mathematics]
God’s plan. He works through people so
because they worked.” Since then, people
that they find Truth. However, “it takes the
have tried to re-establish solid grounding
eyes of faith… to see God’s hand [in it].”
for mathematics. There are still problems
As for Biblical inerrancy, Charles does not
such as the existence of undecidable
believe that God wrote the Bible, but that
statements, but Charles says that shouldn’t
God inspired the authors. He feels that God
stop
was present to Isaiah, Paul, and the other
Historically, new developments shed light
Christian prophets. He reveres them as “the
on problems so that they are resolved in
greatest souls that ever were”, and respects
new
them as the “giants of another domain.”
approaching Truth. Looking back, Charles
Because of their importance in that domain,
feels at peace with his decision to pursue
Charles compares them to Newton and
mathematics and feels that God has blessed
Gauss of mathematics. God orchestrates
his career. He feels he is a channel used by
ideas in the domain of mathematics, just as
God to bring mathematical knowledge to
This
is
just
as
true
Every
other
one
ways.
piece
of
scientific
from
working
This process
mathematical
knowledge:
on
is
them.
part
of
the world. In fact, Charles can recall at least
about his Christianity, and as a result some
four instances when that channel was quite
have developed stronger personal and
direct. Each time, he was completely stuck
professional relationships with him. “I’ve
on a mathematical problem. Each time, he
had
prayed for an idea, and each time God gave
verymany,”
him one. Though others may argue the idea
Toward a Truth It takes the eyes of faith to
would have come anyway, the certainty and
see God’s hand; I’m probably not as
immediacy of the ideas have made Charles
conscious of it as I should be. Church was
believe his prayers were answered. At the
part of her life, all of her life, but biblical
time he decided to become a mathematician,
truth Was his tremendous stumbling block.
Charles anticipated a career centered on
So my parents quarreled constantly, until
research, developing new mathematics.
the break point. My sisters were youth with
However, he finds himself occupied with a
a mission, off in some crazy left field. My
lot of busy work. There are committee
tension, my struggle, my mother’s heart
meetings,
anxiety, We eventually became at peace
departmental
duties,
and
impact
it.
on
a
he
concluded.
Montana,
few
students—not
Boston,
Wavering
subsidiary tasks such as grading papers and
with
Princeton,
meeting with students. His mathematical
Georgia. Straight as an arrow, Easily miles
research must be “squeezed around the
beyond the closest of my classmates, I kept
corners,” when the pressure of seeing
my pride Hidden (secret, inward, non-godly
students is not so great. While he would
motives) and continued on a reasonable
like to focus more on his research, Charles
path. I’m not going to be steam-rolled into
does try to build relationships with his
any doctrinal confessions—not at the start,
students as well. In the classroom, Charles
Not without thinking about things. But if
identifies himself as a Christian on the first
Jesus were alive now I would trust Him.
day of each semester. He feels that this
And eventually I came to a peace about the
openness has had a positive influence on
deity of Christ. The ongoing enterprise of
many of his students, though any more
Mathematics—I see that as my calling My
mention of it in the classroom might be
parakeet got sick. I prayed. My parakeet got
“inappropriate.” Students often approach
better. I was just in a knot, but would serve
him after class that first day to let him
God the best way I could. Should we do
know that they appreciate his openness
this? Should we do that? Time, time, very
busy, very busy time: You get 30 unhappy
I begin by placing him within the historical
undergraduates beating down your door,
spectrum on views of mathematical truth.
And research gets squeezed in the corners
Situating him historically is important
of whatever time is left. It’s okay to have
because Charles’ views of mathematical
been a mathematician: explorer of non-
truth were eventually embedded in religious
physical world. You can see this rock up
truth, and this larger truth gives meaning to
ahead of you. It’s not like reaching into fog.
his practice. Next, in order to highlight the
You reach up for it, and in the fullness of
void that Charles was attempting to fill,
time Truth will be found. They say the
Charles’ search for meaning can be
universe is contracting; the next day it’s
compared to Joseph’s built-in meaning for
expanding. Science goes in fads (and
mathematics. Finally, I draw on Charles’
pastors decry it as the work of the devil).
search and resolution to reveal implications
Now they think there’s lots of dark matter.
for mathematics classrooms. In particular,
So we bumble along, but truth will be
mathematics educators need to demonstrate
found. You can either put up or shut up,
the usefulness of mathematics in solving
you can take it as I do (I think it’s rather
important social problems and invoke
unique): I prayed for an idea, God cared
students’
about that piece of work, and An idea came
classroom so that students are motivated to
into the world. The idea came into the
develop meaning for mathematics. Working
world. Seeing the immense amount of
Toward Reconciliation Charlotte Methuen
vagueness, what can one person do? One
(1998)
small step at a time, you shouldn’t give up
relationships between mathematics and
on the restoration of rigor. And what
religion: conflict, independence, dialogue,
surfaces at the end—that’s God’s. 32 The
and integration. These ideas can be useful
Mathematics Educator
in discussing Charles’ relationship to his
Discussion
religion and mathematics profession. In the
What can mathematics educators learn from
previous paper about Joseph (Norton, 2002),
the case of Charles? Charles’ approach to
I suggested that he seemed to hold an
mathematical meaning lies at the heart of
independent
the answer. In order to frame his approach
mathematics and his Jewish religion. For
and final stance on mathematical meaning,
Charles, I argue that the relationship is one
natural
identified
curiosities
four
relationship
in
the
historical
between
his
of
conflict
followed
by
integration.
human
service,
such
as
tackling
Methuen identified the relationship for 16th
environmental issues as an engineer. But
century mathematician Philip Melanchthon
later Charles found religious value in
as one of integration as well, though
bringing Truth to the world, even
without the preceding conflict. That is,
believes that God orchestrates everything
while Philip Melanchthon’s philosophy that
that happens in the Universe. This belief
“the study of mathematics offers a vehicle
holds for both mathematical advancement
by which the human mind may transcend
and religious prophecy. In this way,
its restrictions and reach God,” (Methuen,
Charles can serve God by helping to bring
1998, p. 83) makes mathematician and
mathematical Truth to the world, so that
pastor
see
“it’s ok” for him to be a mathematician.
mathematics serving such a distinguished
However, the domain of mathematics does
role. Charles’ struggle for mathematical
not stand out in importance fromother
meaning
mathematical
secular studies, and the path toward Truth
practice began in childhood. When he
in these fields is not a direct one. In all
prayed to God to save his parakeet and God
domains of study, we are “wavering toward
responded, Charles was committed to
a truth.” The ideas we hold today were
keeping his promise of serving God in the
brought to the world by God and through us,
best way that he could. Initially this
but they can still be proved false in the
promise
his
future. That is, by continually developing
mathematical career. He knew very early in
new ideas (with God’s help), we are getting
his life that he wanted to do research in
closer to Truth. In sum, Charles’ view
mathematics and his teachers continually
helped
recognized his talent. But he felt that in
practice and religious beliefs. Like the
order to fill his promise he might have to
twentieth-century
become a pastor because it was difficult for
Erdös (Hoffman, 1998), Charles believes
him to find religious meaning for his
that there is absolute mathematical Truth.
mathematical activity. However, he seemed
Erdös imagined a book in which all
to value doing things to help others, as a
mathematical truths were written and
way of serving God. At first his view of
jealously guarded by “the Supreme Fascist.”
efficacious service was restricted to direct
Hardly a religious man, Erdös explained
one,
and
stood
Charles
value
in
doesn’t
of
the
way
of
to
integrate
his
Charles
mathematical
mathematician
Paul
that “you don’t have to believe in God, but
mathematical
you should believe in the Book” (p. 26).
conflict with his religious beliefs. On the
For Charles, on the other hand, the Book is
contrary, his mathematical pursuits were
held by God and the ideas that we are able
encouraged and possibly motivated by his
to bring to the world may only be leading
religious beliefs. In fact, Joseph approached
toward the Truth. Though Charles singles
mathematical study in much the same way
out mathematics as the most certain of the
he approached his religious study of the
sciences, he does not feel that God’s book
Talmud. The case is very different for
is limited to this domain. Like the Hindu
Charles who had to struggle for many years
mathematician,
(Hoffman,
in search of mathematical meaning. His
1998), Charles believes that God’s method
mathematical talents and interests remained
of dissemination is often very direct.
at odds with his religious beliefs throughout
Ramanujan
great
most of his youthas he tried to reconcile the
mathematical ideas were delivered to him
two domains. While Christianity certainly
in his sleep, by the goddess Namagiri.
does
Charles’ connection to divine ideas is based,
mathematical thought, we have seen how
instead, on one of his central religious
one
tenets: God answers prayer. The immediate
mathematician struggled in coming to
relevancy of the ideas he receives in reply
peace with his profession. The difficulty
to prayer has convinced Charles that God
derives from the absence of value for
often participates in Charles’ mathematical
secular
activity in a very direct way. This belief is
communities. Whereas this value was
the strongest suggestion that Charles’
embedded in Joseph’s Jewish religion,
mathematics and religion are integrated.
Charles had to undergo the arduous task of
Also in this way, he feels that his career has
building it up on his own. His somewhat
been
in
reclusive childhood may have aggravated
Mathematical Activity In the paper about
the task. Perhaps if he could have engaged
Joseph, I pointed out the meaningfulness of
in
Joseph’s
a
mathematicians about their perspectives, he
mathematician. Joseph was raised with a
might have been spared some of the anxiety.
religious value for secular study so that his
Herein lies the important message of
Ramanujan
claimed
blessed.
that
Finding
“meritorious
his
Value
activity”
as
not
pursuits
preclude
particularly
studies
dialogue
were
scientific
bright
in
with
never
many
other
in
and
Christian
Christian
Christian
Charles’ story. If students hold religious
those
beliefs that do not value mathematical
mathematics are not only safe, but more
study, they are not likely to be motivated to
aligned
overcome many of the cognitive struggles
mathematics
they experience in learning mathematics.
perception of mathematics as “the vehicle
As teachers in secular schools, we cannot
to God” (Methuen, 1998, p. 83) or Erdös’
foster a community for them to share
lofty regard for “the Book” (Hoffman, 1998,
religious perspectives and build religious
p. 26). Morris Kline’s Loss of Certainty
meaning for mathematical study. However,
(1980)
we can strive to help them to find, in their
demonstrate that mathematics is a human
Christian lives, a need for mathematics and
and fallible endeavor. On the other hand,
a
religious
mathematics should still provoke a sense of
conflict—in which to practice it. Charles
amazement for its power to model and
experienced conflict between scientific
predict events and for the beauty of its
Truth and religious Truth very early in life,
interconnectedness. Both of these aspects
over
of mathematics allude to the need for it, but
safe
the
place—i.e.,
debate
on
without
creationism
and
fields.
These
with
perceptions
modern
philosophy
than
provides
Melanchthon’s
ample
evidence
sense that it need not make any claims
circumvented if one perceives that religion
about Truth at all, much less ones that
offers a priori answers for all of life’s needs.
might
Truth.
What need do students (Christian or
Mathematics, in one sense, is a game
otherwise) have for solving mathematical
played with logical rules and based on a
problems if everything we need to know
few initial assumptions—none of which
can be found in a religious text or through
make any claims about the physical world
divine
or the nature of the spirit. In another sense,
mathematics is not an initially satisfying
mathematics is a tool that can be applied in
activity for students (unlike Charles), why
various fields that operate on additional
should they seek its meaningfulness or
assumptions in order to draw logical
necessity as
conclusions. If the conclusions within these
problems, mathematics educators should try
other fields contradict one’s religious
to appeal to students’ curiosity and sense of
beliefs, one can dismiss the assumptions of
wonder. If mathematical problems appeal
intervention?
Charles
need
may
to
this
religious
of
of
evolutionism. Mathematics is safe in the
contradict
perception
of
Moreover,
did?
In
be
if
posing
to students, as they did to Charles, we have
Methuen, C. (1998). Kepler’s tübingen:
a nice start. However, this appeal was not
Stimulus to a theological mathematics.
enough for Charles. He needed to know
Sydney, Australia: Ashgate.
that his activity served a greater purpose. If
Nord, W. A. (1999). Science, religion, and
mathematics is not “the vehicle to God”
education. Phi Delta Kappan, 1, 28-33.
that Melanchthon imagined, maybe it is the
Norton,
A.
application of mathematics in helping
religious
affiliations
and
people to solve worldly problems that
practices:
The
of
makes it a worthwhile and meritorious
Mathematics
activity. Finally, as Charles concluded, it
Singham, M. (2000). The science and
may be that we are all doing our part to
religion wars. Phi Delta Kappan, 2, 425-
bring God’s truth to the world. While
432. 34 The Mathematics Educator Figure
Biblical Truth will be most essential to
2 is another way of acknowledging that
many Christians, it is possible to attribute
there are many factors that affect student
all knowledge to an omniscient God, and
learning
whatever parts people play in sharing that
acheivement gap between students from
knowledge, it contributes to the whole.
different ethnic and socio-economic groups.
Charles’ assumption that mathematics is the
The student/teacher/mathematics triangle is
most certain of all sciences may explain
located in a classroom, in a school, in a
why mathematics is so central to the
district, in a community that is situated in a
development
why
larger society. People in this community
mathematics serves a key role in so many
and in the larger society hold beliefs,
of the parts we play.
attitudes, values, and often deep emotions
REFERENCES
about
Glesne, C. (1999). Becoming qualitative
learning,
researchers: An introduction (2nd ed.).
mathematics, the nature of schools in a
New York: Addison Wesley Longman.
democratic society, race, class, gender,
Hoffman, P. (1998). The man who loved
sexual orientation, culture, and language—
only numbers. New York: Hyperion.
to name a few. In this article I will pose
Kline, M. (1980). Mathematics: The loss of
some questions and offer some thoughts
certainty. Oxford: Oxford University Press.
about how some of these beliefs, attitudes,
of
knowledge
and
(2002).
case
Educator,
and
a
Mathematicians’
variety
the
of
assessment,
professional
Joseph.
12(1),
The
17-23.
well-publicized
issues—teaching,
the
nature
of
values, and emotions affect inequity in
mathematics education.1 The first question
concerns mathematics
mathematics
and
culture. Is