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Web-Based Lesson : Wrapping A Box Gift

Web-based Lesson Plan

Date: 26/12/2012


Teacher:
Wahid Yunianto
College student of Mathematics Ecucation Master Program, Sriwijaya University


Class/Level: Elementary students Grade 5


Topic: Geometry 3D shapes


Objectives (Learning Goals): 
  1. Find things which have the same shape with a rectangular polyhedron 
  2. Draw a net / nets of rectangular polyhedron (prism) 
  3. Find the surface area of rectangular prism 
  4. Students will see that the Internet is user-friendly in the process 
Web Sites used

Name of Web site: Great Atlantic and Pacific Tea Co., American Stores Company

Rationale for selecting this site: It is an interactive Web site where students can learn about three-dimensional shapes, calculate surface area and volume, and discover some of the mathematical properties of shapes. 

Other materials:
Variety of Boxes, paper, wrapping paper gift, rulers, scissors, cutters, and pencils.



Teacher Preparation:
Bookmark sites. Put addresses on the board as well. Optional- create worksheets to use while on -line and change scenario cards.
Steps for learners:


Description of pre-computer/classroom activities (preparation):
  1. Review through class discussion the 3D shapes (polyhedrons)around us how they look like. Discuss where those shapes are found and used. 
  2. Go around the class and find 3D shapes you can find. 
  3. Students list the same 3D shapes they find at home 
  4. Use all the material, let them experience in wrapping a box gift and find the surface area of polyhedrons by using this activity. 
  5. Go on-line to Interactives Geometry 3D shapes to practice. 

Description of computer/online activities:
  1. See the tutorial here
  2. At Interactives Geometry 3D shapes, students explore how to find a net of a rectangular polyhedron or other polyhedrons. 
  3. At Interactives Geometry 3D shapes, students find the surface area, by filling the net with the area of each blanks and adds up those areas . 
  4. At Interactives Geometry 3D shapes, students try other prisms and find their surface area. 

Description of follow up activities:
Take home: 
  1. Students use activity of wrapping a box gift to make a connection to wrapping a tube. 
  2. Students are challenged to find surface area of a tube or cylinder. 
  3. Students are challenged to use the surface area of other cylinders.


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Tutorial: Interactive Geometry 3D Shapes

Bagaimana cara menggunakan manipulative "interactive Geometry 3d Shapes"  dalam membantu siswa meemahami materi luas permukaan bangun ruang khususnya yang berbentuk prisma segi empat atau balok.
Berikut ini adalah langkah-langkah yang bisa dipelajari melalui video.


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Virtual Manipulatives for Mathematics Education

Sometimes, it is hard to teach some materials without using any tools when we teach in our classes or it is hard to make any media for teaching. It impacts also to students in getting the material's concept and deep understanding.
I use manipulatives from National Library of Virtual Manipulatives (NLVM) and you should believe in me that this manipulatives are so cool. I take this articles and it gives me a such great inspiration to teach mathematics in my classrooms. 
IT-based manipulatives are an important supplement to and/or replacement for certain types of hands-on "concrete" manipulatives often used in math education. 

Manipulatives (blocks, rods, bean sticks, etc.) are commonly used in mathematics education. In recent years, a number of websites have been developed that contain "virtual" versions of some of these manipulatives. The references given below provide information about some of these websites. 

It appears that there may be a fine dividing line between a concrete manipulative and a virtual manipulative. For example, does it make any difference in student learning whether a physical spinner is used to generate data, or whether a computerized spinner (that may well look the same) is used? 

One of the most important general developments in science in recent years has been the idea of Computational Science. Thus, we now have Computational Biology, Computational Chemistry, etc. (The same idea applies to other disciplines, and these other disciplines have had varying levels of success in incorporating IT within their basic fabric.) And, as might be expected, Computational Mathematics is now an important branch of mathematics. 


For full article, you may visit this website : http://otec.uoregon.edu/virtual_manipulatives.htm 


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Integrating the Internet into Mathematics Classroom

Nowadays, the internet is spreading fast even in the village, people can access internet trough hand phone. So it's good news right, isn't it? We can use the internet to improve and integrate students' knowledge since many resources can be accessed though it easily.

In mathematics, it helps students to get deep understanding about materials they learn. For teachers or educator, this article (slide show) below may help you to try applying the internet into your classroom. I am so happy when i found this slide. You may try it now...HAPPY TEACHING....:-)





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Realistic Mathematics Education

What is Realistic Mathematics Education or known as RME? It is said as a promising approach to improve the quality of mathematics education in Indonesia.




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IELTS for IMPoME Students

English as an international language makes it very important for all people around the world to communicate to others especially for students who want to study abroad in  European countries or  English speaking countries.

Scholarships offering scholars to study to such countries require English competence or skills in order to minimize the barrier of non-native English. What students need to do is to learn English, have good English skills (Reading, Writing/ Grammar, Speaking, and Listening). 

One of English certificates usually need to have is IELTS (International English Language Testing System) certificate. Some universities have different minimum IELTS score for its requirement so it depends on the countries or universities.

That's the reason why IMPoME students is facilitated by an English course before studying to Utrecht University. For IMPoME students now should acquire minimum band score 6.5 overall and writing minimum score is 6.0.

Do you want to know more about IELTS? learn by yourself by files below. I hope it will help you.


Cambridge IELTS 1http://letitbit.net/download/7174.79a3fb7fb5f26e8c1ec6a50c0/Cambridge_IELTS_1.rar.htmlCambridge IELTS 2http://letitbit.net/download/9179.f9fcf53b0959cddcbfee37657/Cambridge_IELTS_2.rar.htmlCambridge IELTS 3http://letitbit.net/download/4160.f4e7ba45e935e57313d6489f6/Cambridge_IELTS_3.rar.htmlCambridge IELTS 4http://letitbit.net/download/9133.f95f508acdc5dfcd6477c4498/Cambridge_IELTS_4.zip.htmlCambridge IELTS 5http://letitbit.net/download/4155.49ab8d33328771d3add0f1951/Cambridge_IELTS_5.rar.htmlCambridge IELTS 6http://letitbit.net/download/4157.43dcf52606c34e3be75eeb066/Cambridge_IELTS_6_Book.rar.htmlhttp://letitbit.net/download/6168.f60013e02709e4712c727b3b6/Cambridge_IELTS_6_listening.rar.htmlCambridge IELTS 7http://letitbit.net/download/3159.cb3f5439d12dca918750e47ed/Cambridge_IELTS_7.rar.html
Read more at http://ebookee.org/Cambridge-IELTS-1-2-3-4-5-6-7_808905.html#8H5peTj27A494k1H.99 



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Abstract Algebra

One of courses for IMPoME students is Abstract Algebra. The book reference used is Mathematical Thinking and Writing by Randall B. Maddox


Here is the book. 


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What is a Web-based lesson?

What is a Web-based lesson? Considering to World Education Literacy Division in 2005, a web-based lesson is  simply a lesson that in some way incorporates a Web site or many Web sites. A web-based lesson can be conducted entirely online or it can be a traditional classroom lesson with an online component. It can be used in a lesson for variety of purposes, including research, reading, writing, publishing, communication and collaboration with teachers and learners around the world.

For more information and details related to web-based lesson, read or download file below.



Web-based lessons and e-portfolios from Evelyn Izquierdo

We can create a web-based lesson for mathematics education, though. Lets make it fun.


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Mengajarkan Konsep Pengurangan Meminjam dengan PMRI

Bagaimana supaya siswa kelas 2 SD bisa memahami konsep pengurangan meminjam? Dengan menggunakan pendekatan PMRI, konteks membeli di warung bisa digunakan lho. Membeli di warung merupakan aktivitas yang wajar dan sering dilakukan oleh siswa saat di rumah.

Untuk lebih jelasnya bisa dilihat pada presentasi berikut ini. Selamat mencoba dan berkreativitas sesuai dengan konteks yang dapat digunakan dilingkungan sekitar anda.


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How to Teach Subtraction with Borrowing

Hiii all mathematics teachers....Do you get stuck when you deal with teaching subtraction with borrowing to your pupils at second grade?
It's a good news for you.. Are you ready?
Here we go....I hope and wish, pupils will get a deep understanding about subtraction with borrowing. last but not least, i hope you can develop your own teaching and learning design which is suitable in your contexts chosen.


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Tutorial 3 end: "Fraction Pieces"


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Tutorial 2: "Fraction Pieces"


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Tutorial 1 : "Fraction Pieces"


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Belajar Pecahan Sederhana Secara Interaktif

Mengajarkan materi pecahan memang sedikit sulit untuk siswa kelas 3SD. Namun hal ini bisa lebih menarik dan mudah dengan pendekatan PMRI yang dikombinasikan menggunakan  alat peraga (manipulative) "National Library of Virtual Manipulatives" yaitu "Fraction Pieces". Siswa akan berkreasi sendiri menggunakan manipulative ini.Manipulative ini bisa di download gratis selama 60 hari ataupun anda bisa membelinya. Jika tidak anda bisa menggunakan secara online di website-nya di nlvm.usu.edu.

Dengan pendekatan PMRI konteks  yang digunakan adalah membagi kue secara adil, dalam hal ini kue berbentuk lingkaran dan persegi.

Kue berbentuk lingkaran dan persegi


Potongan Kue

Dalam membagi kue, masing-masing orang mendapatkan bagian yang sama besar. Bagaimana jika kue dibagi untuk 2 orang, 3 orang, 4 orang? Manakah bagian potongan kue yang lebih besar antara kue yang dibagi untuk 2 orang dan kue yang dibagi untuk 3 orang?

Untuk lebih jelasnya, lihat pada penjelasan file dibawah ini. 



Web Based Lesson PMRI: Pembelajaran Pecahan Sederhana


Jika ingin mengetahui bagaimana menggunakan manipulative "Fraction Pieces" bisa dilihat disini.
Selamat mencoba...:-)


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Ada Apa dengan Kurikulum 2013?

Bagaimanakah pendapat anda tentang kurikulum 2013 yang sedang hangat diperbincangkan saat ini? Mungkin ada sebagian dari anda yang setuju ataupun tidak setuju dengan perubahan kurikulum yang baru ini.  Berikut ini adalah salah satu postingan salah satu dosen pendidikan matematika saya waktu saya menempuh S1 di Universitas Negeri Yogyakarta. Sungguh menarik sekali apa yang disampaikan oleh beliau. 


Masukkan untuk Perbaikan Draft Kurikulum 2013_ Oleh Marsigit

Yogyakarta, 9 Desember 2012


Masukkan untuk Perbaikan Draft Kurikulum 2013


Kepada Yth:
Tim Pengembang Draft Kurikulum 2013, Kemdikbud, 
Jakarta


Dengan hormat,


Bersama ini perkenankanlah saya , Marsigit atas nama pribadi ingin memberikan kontribusi untuk perbaikan Draft Kurikulum 2013.



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Cara Menampilkan PDF di Blog

Jika anda memilik suatu blog, pastinya anda akan berusaha membuat blog anda menarik bukan? Contohnya, jika anda ingin membuat suatu posting dan memuat file, pastinya anda akan berusaha bagaimana supaya file pdf tersebut bisa tampak dan tampil menarik di blog.

Berikut ini adalah salah satu cara yang bisa anda lakukan jika anda menggunakan blogspot.com


  • Anda bisa menggunakan account di docstoc.com, jika belum punya account, silahkan sign up terlebih dahulu.
  • Jika anda sudah memiliki account di docstoc.com, klik> upload> share document


  • Kemudian pilih file pdf yang akan diupload: klik > Select Files



  • Setelah proses upload complete, maka anda bisa menambahkan diskripsi file anda agar mudah dicari oleh pengunjung yang mencari di search engine.
  • Kemudian klik > save and publish 
  • Setelah berhasih dipublish, maka disamping dokumen / file anda akan ada keterangan dan embed pada sisi file. Klik > embed.



  • Anda bisa meletakkan embed file ini ke dengan cara klik> copy code dan paste ke Post yang anda buat pada HTML.



  • Sebelum anda publish postingan anda, anda bisa melakukan preview untuk melihat tampilan file pdf anda. Untuk menagtur tinggi dan lebar file pdf yang ditampilkan, anda bisa mengaturnya dengan mengganti pada isian "width" dan :height" sesuai kebutuhan anda.
  • Kemudian publish postingan anda yang sudah memuat file yang di embed di HTML blogspot anda,


Selamat Mencoba.....HAPPY BLOGGING......! :-)


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Membagi Buah Strawberry Sebagai konsep FPB

Pendidikan karakter memang harus diberikan kepada anak sejak dini baik dirumah maupun disekolah. Salah satu karakter yang berbudi baik adalah berbagi dengan teman. Jika kita memiliki suatu barang bisa berupa makanan, kue, buah, dsb  dan bisa dibagikan dengan teman yang lain. Hal ini bisa mengajarkan untuk peduli dengan sesama dan menjadikan diri kita tidak individualis / egois.
Dalam pembelajaran matematika, pendidikan karakter dapat ditanamkan pada pembelajaran FPB. Kontek yang digunakan adalah berbagi buah. Bagaimana cara mebagi buah dengan adil dan dapat diberikan kepada banyak teman. Dengan menggunakan bantuan media flash, siswa tidak harus membagi buah-buah secara nyata, namun dapat digambarkan pada animasi flash yang telah didesain untuk pembelajaran ini. Dengan flash siswa diharapkan lebih tertarik dalam belajar matematika dan meningkatkan antusias siswa. 
Siswa sedang menggunakan laptop di depan kelas untuk mengerjakan soal FPB


Hasil dari pembelajaran ini telah dilakukan di SD IBA Palembang seperti pada hasil laporan observasi berikut:
Laporan Materi Pemecahan masalah yang berkaitan dengan FPB di SD IBA _indo_


Berikut perangkat yang digunakan pada pembelajaran FPB ini.

Perangkat Pemecahan masalah yang berkaitan dengan FPB di SD IBA


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Desain Pembelajaran PMRI: Meghitung Volume Kubus dan Balok

Bagaimana menemukan rumus volume kubus dan balok?
Dengan pendekatan PMRI siswa kelas 5 SD dapat mengalami suatu pengalaman dalam menemukan rumus volume kubus dan balok dengan kegiatan yang dilakukan dikelas.Kontek yang digunakan adalah memasukkan kotak snack makana ke dalam kardus dan membandingkan kardus mana yang bisa memuat koata snack lebih banyak.

Siswa sedang memperkirakan volume balok dengan beberapa kubus satuan



Untuk lebih jelasnya kegiatan yang dilakukan bisa di download laporan tentang pembelajaran ini.
Download file lengkapnya disini


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Kok bisa ya?

Dalam matematika, luas suatu bangun jika diptong-potong menjadi beberapa potong dan disusun kembali dengan bentuk yang lain maka bangun baru tersebut mempunyai luas yang sama dengan luas bangun awal.


Ada hal yang menarik yang saya dapat dari posting di FB teman mengenai masalah luas seperti penjelasan diatas. 

Jika anda tertarik, silahkan mencoba untuk menyelesaikan permasalahan ini (lihat gambar).

  


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Problem Solving Strategies

We can solve a problem or some problems using some strategies. In mathematics, to solve mathematics problems a student can learn some strategies suiting him or her in order to get the solution.

Here two strategies that my friend and i compiled from a book reference. 


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Bermain Lompat Kelinci

Bermain sambil belajar atau belajar sambil bermain? Beberapa orang beranggapan bahwa pernyataan tersebut memiliki makna yang berbeda. Ada yang bilang kalau bermain sambil belajar itu hanya lebih banyak bermainnya daripada belajarnya, tetapi ada juga yang beranggapan bahwa belajar sambil bermain itu lebih banyak belajar dan diselingingi bermain. Tapi menurut Dr. Ratu Ilma Indra Putri, M.Si dalam workshop PMRI di SDN 1 Palembang, itu sama saja. Menurut saya, belajar untuk anak-anak memang dapat dilakukan saat bermain, dan tidak bisa dihindari bahwa masa anak-anak adalah masa bermain.

Dalam pembelajaran PMRI, permainan dapat digunakan sebagai kontek ataupun batu pijakan dalam belajar matematika yang memang berhubungan dengan kehidupan sehari-hari bagi anak-anak. Permainan apa ya yang bisa digunakan untuk belajar nilai tempat, penjumlahan dan pengurangan? Salah satu permainan yang digunakan dalam buku "Matematika untuk Kelas II Sekolah Dasar / MI yang disusun oleh Tim PMRI"  adalah Loncat Kelinci. Berikut penjelasan pembelajaran PMRI tentang nilai tempat, penjumlahan dan pengurangan dengan "Bermain Lompat Kelinci"


a. Tujuan Pembelajaran: mengenal nilai tempat secara informal, melakukan penjumlahan dan pengurangan

b. Konsep Matematika: nilai tempat, penjumlahan dan pengurangan.

c. Alat / Sumber Belajar: manipulative "Blocks Addition"

d. Pokok-pokok Kegiatan Guru:

   1.Jelaskan peraturan permainan lompat kelinci berikut:
  • Jika satu kali melompat, siswa mendapatkan nilai 100.
  • Jika satu kali melangkah, siswa mendapatkan nilai 10.
  • Jika satu kali berjalan setapak, siswa mendapatkan nilai 1.
  • Jika melompat, melangkah dan berkalan setapak maju maka nilainya ditambah dan jika mundur nilainya dikurangi.
  2. Minta salah seorang siswa untuk memperagakan permainan lompat kelinci di depan kelas dengan                                                 meminta siswa untuk melompat satu kali , melangkah dua kali, dan berjalan setapak tujuh kali.

  3. Tanyakan kepada siswa yang lain berapa nilai siswa tersebut.

  4. Minta siswa tadi meneruskan langkah tiga kali.

  5. Tanyakan kepada siswa yang lain, berapa nilai yang diperoleh sekarang.

  6. Minta kembali siswa untuk berjalan setapak lima kali.

  7. Tanyakan kepada siswa yang lain, berapa nilai siswa pada posisi terakhir.

 8. Lakukan langkah 2-7 beberapa kali dengan bilangan yang berbeda-beda, dan divariasikan dengan melangkah mundur, dan siswa yang berbeda.

  9. Minta siswa mengerjakan sola latihan di buku siswa.

 10. Diskusikan  jawaban siswa.

e. Bahan Pengayaan: minta siswa mendiskusikan berbagai kemungkinan cara berbeda yang dapat dilakukan  untuk mendapatkan suatu nilai tertentu, misalnya 82 dalam permainan lompat kelinci. Menggunakan manipulative "Block Addition" untuk melakukan penjumlahan dengan menggunakan aktivitas permainan siswa. Misalnya, melompat maju 2 kali dan melangkah maju 3 kali, dan berjalan setapak maju 7 kali, dengan menggunakan "blok addition", kemudian melompat maju lagi 1 kali, melangkah maju 1 kali, dan berjalan setapak  maju 2 kali.


lihat pula cara menggunakan manipulative "Base Blocks Addition"
f. Bahan Remedi:-
g. Alternatif Penilaian: Penilaian proses dapat dilakukan pada saat siswa melakukan atau mengikuti lompat kelinci, menyelesaikan latihan, mencari laternatif penyelesaian soal., berdiskusi, dan berargumentasi. Penilaian hasil dilakukan terhadap pekerjaan siswa dalam mengerjakan soal latihan yang ada dibuku siswa.


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How to use NLVM "Base Block Addition"


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Tangram


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Desain Pembelajaran PMRI menggunakan Tangram

Bermain sambil belajar memang menarik dan menyenangkan bagi anak-anak maupun siswa. Salah satu permainan yang dapat digunakan dalam pembelajaran PMRI adalah tangram. Permainan ini dapat melatih    kreativitas anak-anak dan dapat mengenalkan bentuk-bentuk bangun datar kepada siswa.

Permainan ini sekarang sudah bisa dimainkan melalui komputer, salah satunya adalah dengan NLVM, sehingga akan lebih menarik jika siswa dapat mengekplorasi kreativitas mereka dengan menggunakan virtual manipulative ini. Sebagai slah satu contoh, lihat video permainan tangram dengan manipulative "tangram" berikut



Berikut adalah desain pembelajaran Tangram di kelas PMRI untuk siswa kelas 2 SD/MI yang dirancang oleh TIM PMRI. Klik disini untuk download.

Lihat juga Tangram di P4MRI Universitas Syah Kuala di Aceh,


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What is Tangram?

Tangram (Bahasa Mandarin : 七巧板 (qī qiǎo bǎn), secara harafiah berarti "tujuh papan keterampilan") adalah suatu puzzle yang terdiri dari tujuh keping bangun datar (disebut ‘tans’) : Dua segitiga siku-siku sama kaki (besar) Dua segitiga siku-siku sama kaki (kecil) Satu segitiga siku-siku sama kaki (sedang) Satu bujursangkar (kecil), dan Satu jajaran genjang Tujuan dari permainan Tangram adalah untuk menyusun ketujuh kepingan itu (tanpa tumpang tindih) menjadi suatu bentuk - entahkah itu bentuk yang hanya ada dalam imajinasi kita, menyerupai binatang, orang, barang tertentu atau apa saja yang dapat kita pikirkan. 


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StuNed and DIKTI Scholarships for 20 Young Indonesian Lecturers to study in the Netherlands


Today, the Directorate General of Higher Education (DIKTI) and the Netherlands Education Support Office (Nuffic Neso Indonesia) signed an MOU to co-finance two more batches of the International Master Program on Mathematic Education (IMPoME) for a total of 20 young Indonesian lecturers. IMPoME started in 2009 and has so far produced 22 master-degree holders in Realistic Mathematic Education (RME) while currently there are 10 students still studying in the Netherlands at the Freudenthal Institute of the University of Utrecht. The two final groups of students will depart to the Netherlands in 2013 and 2014. From the Dutch side the financial contribution comes from the StuNed Scholarship programme.



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Impome 2012-2013 now is opened


Pendaftaran beasiswa IMPoME untuk periode 2012 telah dibuka, dengan syarat-syarat sebagai berikut:

1. Mengisi aplication form dengan lengkap, download di sini: stuned_form_impome_2012
2. Mengisi CV dengan lengkap, download di sini: cv-form-neso_2012
3. Fotocopy Kartu Tanda Penduduk (KTP)
4. Pas Photo 4 x6 (1 lembar)
5. Ijazah S1
6. Transkrip nilai dengan nilai IPK minimal 3, 00
7. Sertifikat TOEFL dengan score minimal 500
8. SK CTAB (Surat Keputusan Calon Tenaga Akademik Baru) dari Rektor


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GLAD TO BE A TEACHER


Stiill in National Teacher Day

‎"Ideal teachers are those who use themselves as bridges over which they invite their students to cross, then having facilitated their crossing, joyfully collapse, encouraging them to create bridges of their own." ~ Nikos Kazantzakis

Teachers: Thank you for being a “bridge” for your students! ~Heidi

Reference : http://www.uniqueteachingresources.com/


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Happy National Teacher Day
Every year on 25th November, Indonesian people celebrate the National Teacher Day. This event is to memorize teachers who dedicate their lives to help students become succeed and passionately lead us to be a good human being.  Teachers are our parents when we leave home to get school. Say thank to my teachers :-)



read also : unique teaching


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Problems?
Everyone has problems in his/her life, but do you know what a problem is? having a discussion with my lecturer and classmates, we referred a problem as something that differs between the results and expected goal, needs to be solved, encourages somebody to find out the solution or to do something dealing with the problems.


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PUSRI ELEMENTARY SCHOOL

Pre-Classroom Observation
One of required courses for IMPoME 2012 students at Sriwijaya University is classroom observation. The lecturer of this course is Mrs. Ratu Ilma Indra Putri. This course aims to implement Indonesian Realistic Mathematics Education (red. Pendidikan Matematika Realistik Indonesia / PMRI) in collaboration with teachers. Some elementary schools in Palembang, South Sumatra, Indonesia have been selected in order to be pioneer schools which allow IMPoME students as observers to carry out their PMRI material made by observers and teachers at those schools.

Before implementing PMRI materials, observers have to do pre-observation in order to know the school, school's environment, facilities, pupils, teachers, and other things relating to observations. My team and I have a chance to get a classroom observation at Pusri elementary school. Two classes are now being the classroom objects,classroom 2D and classroom 5C respectively.
For more detail, you can download PDF file of pre-observation at Pusri elementary school.
Classroom activity : The teacher guides a pupil to use a tool media.


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MY HERO, MY TEACHERS

HAPPY NATIONAL HEROES' DAY 
NOVEMBER 10, 2012

Every year on Nov. 10, people of Indonesia celebrate National Heroes Day. November 10, 1945 is the day where Battle of Surabaya appeared  in which pro-independence Indonesian soldiers and militia fought against British and Dutch troops as part of the Indonesian National Revolution. Do you still remember who our national heroes are? May be you have forgotten about them. Each day has its own hero, and everyone perhaps is a hero in his or her own way. I suggest you to choose your own hero since everyone has his/ her hero(s).Being a hero is not always to fight again enemies, a hero is just an ordinary people who can make mistake and he is not perfect human being. However, a hero is someone who has a great motivation to develop himself, others, and his country and gives the light in dark.


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Sharing Fairly a Cake

Lets Be Fair
There are six children want to slice a strawberry pan cake with chocolate topping, the cake’s shape is square. The rule is: each child gets the same part of cake that is the same topping and strawberry paste.


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Which one is more expensive?


It's the first day of my problem-solving  course with Mr. Ucup. I actually like his style of teaching and the course since I never got this course when i was at undergraduate.

Here is an example of problem solving in mathematics I got today;
Budi bought 3 pens and 2 books worth Rp. 30,000
Budi also bought 2 pens and 2 books worth Rp. 25,000

Then the question is which one is more expensive? pen or book?

Here is a simple answer without calculating each price,


We can see that both of them have 2 pens and 2 books, if we just add/buy one more pen it costs Rp. 30,000 and if we add/buy one more book, it costs Rp. 25.000.

Conclusion:
 It's clear that a pen is more expensive Rp. 5,000 than a book.


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A three-day workshop with Marteen Dolk


Thursday, 20 July 2012, students of International Master Program on Mathematics Education (IMPoME ) 2012 at Sriwijaya University, Palembang, had a three day workshop with Marteen Dolk, a head of mathematics education study program at Utrecht University in the Netherlands. Fifteen students coming from different cities in Indonesia should attend this workshop as one of compulsory requirements to study in Holland. This workshop was aimed to assess our ability skills-English, Mathematics, bravery, thinking, confidence, and team working.    

On the first day, we were warmly welcomed by Prof. Zulkardi, M.Sc who is the head of mathematics education department at post graduate degree of Sriwijaya University. There were also Prof. R.K Sembiring, one of Realistic Mathematics Education (RME) promoters and initiators in Indonesia who pays a lot of attention to education in Indonesia especially in mathematics education. We had to introduce ourselves to Marteen and he gave us a material about mathematics problem related to geometry. He showed a picture of building, a Spain church and our duty was to find the shape of the church if it is seen from above, is it six-sided (hexagonal) or eight-sided (octagonal)? We were divided into groups and aimed to solve this problem. Here, our mathematics skills were assessed by being asked by observers and convincing other member of group dealing with the church shape from above.  Having finished a group discussion we had to write down our result in a giant paper and embedded it into wall so other groups could see and compare to their results. In the end, individual report should be collected and Marteen gave us the answer which was "eight-sided" by giving a real design and structure of that Spain church, he also gave us homework of two articles to read and prepare  for tomorrow. The first day ended at 5 p.m. with a wonderful experience.

Friday, 21 July 2012, Let me tell you that it was the first day of fasting month Ramadan so it would be harder than yesterday and one of students did not come because she had to back to her city. After spending a whole night reading and preparing those articles I should be ready to talk about them in a group discussion. . Even though I was nervous and a little bit afraid of my understanding, I convinced myself to be brave and confident. Comparing and analyzing two different articles by Judith Sowder and Stanley Ocken with different point of views was difficult for me to cope with a question that could cover those papers. To have not only  a good understanding in reading books or references but also a good reasoning to convince others is very important for students especially who study abroad in order to get succeed.  Now i realize that i need to read a lot and build my critical thinking. The last session was about analyzing how 3rd grader did share sandwiches and get the most part of sandwiches by choosing which trip taking him/her to some tourism palces in the USA. There are five trips and here is the illustration, the first tour bus consisting of eight children and seven sandwiches goes to the Statue of Liberty and Ellis Island. The second one goes to Museum of Modern Art consisting five children and four sandwiches. A bus visiting Museum of National History carries four children and three sandwiches. The last bus heading to Planetarium has three sandwiches and carries five children. We should pretend as a 3rd grader to solve this problem through knowledge and thinking of a ten-year old child.

The last day of the workshop was so unforgettable day since we had an interview with Marteen and Mr. Zulkardi. Having trouble with English was not a big deal since this interview did not test us in English skills but it dealed with your submitted paper or task which you think the best for you and why you think so. Unfortunately, i got the last turn having interview with Marteen and Mr. Zulkardi and i felt so nervous. Finally, Marteen said that some of us could study to the Netherlands but we should study both mathematics and English and work hard in order to survive there. Hearing that two of us did not have that chance was so sad. An English course is waiting for us in order to learn English and to pass 6.5 IELTS score as the minimum score to study at Utrecht University. The moment of taking some pictures with Marteen is so nice and great. 

Those three days were so amazing, hopefully you will have that experience in IMPoME 2013, so sweat for it guys!!!.




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Realistic Mathematics Education

A brief overview of RME in Indonesia


Before we go to what RME is, let me remind you about your mathematics subjects when you were at elementary, secondary or high school; do you still remember who taught you math and can you solve some mathematical problems of elementary student’s level when your little brother or sister ask for your help to solve his or her homework? Did you hate mathematics or even do you still hate mathematics?

In Indonesia, not only was the problem of mathematics informed formally (Marpaung, 1995) that most pupils in a number of selected primary schools in Yogyakarta were afraid of mathematics, but also the result of mathematics education for 16 different urban and rural secondary schools in several provinces was very low based on finding from two diagnostic test carried out by Suryanto (1997) and Somerset (1996). He pointed out that mathematics teachers less confident and lack of smile so the classroom situation have no interaction and pupils have no chance to communicate their solution ( Zulkardi). Seeing mathematics like an evil or monster makes it difficult to learn mathematics due to the feeling of scary toward mathematics. However, lacking of understanding of teachers on the contents and pedagogic of mathematics is also one of factors that make pupils hard to learn mathematics. Too many exercises and homework to be solved, rules to be proved and lack of applications in their daily life get pupils had poor attitude toward mathematics. 
In an attempt to combat the low achievement and poor attitude toward mathematics, hence, a new approach in mathematics education that can overcome those problems is needed. one of the promising approaches toward the teaching and learning of mathematics thought to address these problems is realistic mathematics education (RME).

The philosophy of RME
Mostly determined by Freudenthal’s view on mathematics (Freudenthal, 1991), two of his points of views on RME are: mathematics must be connected to reality; and mathematics should be seen as human activity. Firstly, mathematics must be close to children and be relevant to everyday life situations. However, the word ‘realistic’ refers not only just to the connection with the real-world, but also to the problem situations which are real in students’ mind. Secondly, the idea of mathematics as a human activity is stressed. Mathematics education organized as a process of guided reinvention, where students can experience a similar process compared to the process by which mathematics was invented. Concepts of mathematization as a guide are used in this reinvention process and later it is categorized by Treffer (1991) into horizontal mathematization and vertical mathematization.
Principles and Characteristics of RME
 the characteristics of RME are historically related to three Van Hiele’s levels of learning mathematics (de Lange, 1996). Assuming that the process of learning process, it proceeds through three levels: (1) a pupil reaches the first level of thinking as soon as he or she can manipulate the known characteristics of a pattern that is familiar to him or her; (2) as soon as he or she learns to manipulate the interrelatedness of the characteristics,  he/she will have reached the second level; (3) he/she will reach the third level of thinking when he/she starts manipulating the intrinsic  characteristics of relations. Traditional instruction is inclined to start at second or third level, while realistic approach starts from first level. Then in order to start at the first level dealing with phenomena that are familiar to students, Freudenthal’s didactical phenomenology that learning should start from a contextual problem, is used. Furthermore, by the guided reinvention principle and progressive mathematizations, students are guided didactically and efficiently from one level to another level of thinking through mathematization.

The combination of three Van Hiele’s levels, Freudenthal’s didactical phenomenology and Treffer’s progressive mathematization result in five basic characteristics of realistic mathematics education or five tenets of RME (de Lange, 1987, Gravemejer, 1994). In brief those are:
  1.     Use of contextual problems (contextual problem figure as application and as starting points from which the intended mathematics can come out.
  2.    Use of model or bridging by vertical instruments (broad attention is paid to development models, schemes and symbolization rather than being offered the role or formal mathematics right away).
  3.    Use of student’s contribution (large contributions to the course are coming from student’s own constructions, which led them from their own informal to the more standard formal methods).
  4.     Interactivity (explicit negotiation, intervention, discussion, cooperation and evaluation among pupils and teachers are essential elements in a constructive learning process in which the student’s informal strategies are used as a lever to attain the formal ones).
  5.     Intertwining of learning stands (the holistic approach implies that learning strands cannot be dealt with as   separate entities; instead of intertwining of learning strands is exploited in problem solving.


Strategies for introducing RME in teacher education in Indonesia
In the country where RME originally has been developed and implemented for about 3 decades in the Netherlands, there are also positive results that can be used as indicators that RME might be promising to increase  the quality of mathematics education. For instance, the results of the Third International Mathematics and Science Study (TIMSS) showed that pupils in the Netherlands gained high achievement in mathematics education which was ranked 6th in 38 participating countries and the gap between smart pupils and weak ones was very small, while Indonesia, the achievement of pupils in mathematics education was ranked 34th out of 38 participating countries (Mullis et al., 2000). Thus, “mathematics for all’ which is only a slogan for some countries including Indonesia has been achieved in the Netherlands. Still, these positive results could be achieved not in short-term but in the long term endeavor.

Based on the explanation above, RME looks promising to be introduced and implemented in Indonesia because it could increase pupil’s understanding and motivation toward mathematics. For instance, RME content materials are developed using the contexts that are experimentally real to the pupils. Pendidikan Matematika Realistik Indonesia (PMRI) is an adapted RME founded by PMRI team promoted by Prof. R.K Sembiring and officially launched in 1998 to reform mathematics education in Indonesia. This team results in cooperation between Directorate General of Higher Education (DGHE) or DIKTI and NESO Indonesia that is an International Master Program on Mathematics Education (IMPoME). This program is under collaboration with between Freudenthal Institute Utrecht University and Sriwijaya University and Surabaya State University.

Reference : Zulkardi. Developing a 'rich' learning environment on Realistic Mathematics Education (RME) for student teachers in Indonesia. Matematika FKIP Unsri.


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