Mar 25, 2013

Dialog Internasional 5 Pendidikan Matematika

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Math, Math Education, Math Culture

Five Guiding Principles of Mathematics Education
It's high time we put grand ideas back into mathematics curricula.
Article link:

Zor Shekhtman:
@Marsigit: I'd like to suggest an approach to young students that might justify their efforts to study math. What if we suggest to them that math is gymnastics for their minds as much as pulling weights exercises their muscles? The concept of exercising is very much familiar to them. They also understand that real exercises might not be fun, but rather hard work. People in a gym don't usually have fun, they work hard on strengthening their muscles. Working hard solving math problem will strengthen their mind or, simply speaking, will make them smarter. I try to convey this idea in some introductory lectures on my Web site, but, obviously, have no idea whether this approach works or not.

Marsigit Dr MA:
@Zor and Natasha: My previous explanation indicated that teaching math for the younger is not as the simple as we expected. We should have a clear understanding of the NATURE of every aspect related to the learning activities. Teaching learning activities should have their appropriate foundations: psychologically, socially, or even anthropologically. What Zor's done is good example i.e. developing the concept of gym in math. However, it can be perceived as just partially in lying the educational foundation. In my perception, the most basic problem of the foundation of math educ is how the students are to construct their own math. What we need as adults people is to develop the scheme to facilitate them. Gym in math is good as far as the students be the actors of the game. Thank's.

Bradford Hansen-Smith:

@Marsigit: It is not apparent to students or to math educators what the principles of mathematics are. In my 1936 Webster dictionary the first definition of “principle” is "1. A source of origin, primordial substance: ultimate bases or cause. “ In other words what is principle is what comes first, not what we think is most important. These five ideas about math education that have been presented are just ideas out of many that one might believe to be more important over others. Principles are more universal than that; more than ideas about what we think.

What is principle comes first; all that follows is principled if there is alignment to what came first. When people talk about principles there is no reference to source or essential qualities and characteristics of origin. Isn’t that really what students are asking when they want to know why they have to learn math? They want to know the principles that underlie math that make it important to learn, the higher value inherent in mathematics that is worth their time and effort. We do not have a good answer for them.
Marsigit Dr MA:

@Bradford: I do agree with you Bradford. However I may say that your opinion is only small numbers (or even just one) aspects of the nature/principle of everything. As we know that every aspect of life is dimensional. Mathematics is also dimensional. People who learn math is also dimensional. The dimension of adult math is Formal Math/Axiomatix Math; and the dimension of younger math is School Math.

So the nature/principle is the generality in its dimension. The nature/principle of math for adults is different from that of younger. The nature/principle of adults' learn of math is also different with that of the younger. The best criteria for the nature/principle is about it's INTENSIVITY and EXTENSIVITY. A certain idea can be a principle in a certain dimension if it has the deepest and the widest aspect, in such a way that it will be un-debateble.

Further, we may need to differentiate between the Principle, the Concept/Meaning, and the Method. The very basic principle is that every OBJECT has its concept and method. I then found that the Principle is really a certain object. So the Principle has its own Concept and Method. So our discussion on the Principle of Math can not be separated with the discussion of Math Concept and Math Method. Especially, for younger student, the Principle of Younger Math (School Math) consist of the Concepts School Math and the Method of School Math. Without considering those two components then you will lose your meaning.


NCSM: Mathematics Education Leadership
Is it possible and advisable to have a global curriculum in Mathematics, where the best features of all existing curriculum can be incorporated?

V R:
Curricular development is no longer involves rational and incorporated course design. New courses are added based on faculty members’ expertise rather than students’ need. And typically, no one has a clue as to what is taught in other courses in the curriculum, and certainly no idea at all as to what has been learned in previous courses.

Anica Aleksova:

If we speak about primary education or grades 1 to 8, and about “prescribed curricula” (what is in the official documents) it is possible - see the TIMSS frameworks or mathematics international reports. There you can find that already more than 70% of the curricula for more than 50 different countries in the world the content is the same. The differences are in the approaches for teaching the students or in to “implemented curricula”.
Marsigit Dr MA:

Global curriculum is a crazy ideas. It's imaging to have similar and uniform people around the world. Even in a certain district, math teaching in one city should be differentiated with that of other city because of different context of learning math

Atiya Zaidi:
@Marsigit: Hi guys! This is a very important and interesting discussion that has caught my eye. In the light of your comments I have a few questions:
Can we categorise maths curriculum into stages to fit the education levels in every geographical region? For example: say Stage 1 refers to basic arithmetic and numeracy. Then, can we devise a Stage 1 curriculum to fit anywhere in the world where either teaching provision or student level fits this stage?
Can we devise enough stages to cover all possible levels of maths learning and teaching?
Can we devise the curriculum in English and translate it into all languages existing on the planet?

Marsigit Dr MA:

@Atiya: I perceive curriculum at least in two categories i.e first, the STAGE as you frequently stated, and second, the FORM, its content and approach. Stage is something in the vertical dimension of educational levels hierarchically existing in each educational context (a certain country or state). So there are many perspectives on how the a peoples from a certain educ system perceives educ curriculum. In the British context for example, a certain teacher can perceive that curriculum is in the level of classroom operational. So they talk about how to involve students' participation in their developing curriculum. They can do it starting form the very simple but fundamental question : " What do you expect from me as your teacher of math lesson next week? If the students are to expect some math activities and the teacher strive to fulfill their expectation, that is it that we can call it curriculum too.

However, in most countries, the situation may be very different. Even, in some countries which implement centralized curriculum, they have no ideas about the role of student in developing curriculum. So, before we talk everything about curriculum we should make sure about many things e.g. our philosophy of education and even ideology o education. Meanwhile, I really found that there are the similar philosophy and or ideology of education among the countries in the world i.e to liberate our younger generation from parental or adult generation misbehavior. We need to liberate our younger generation in order that they are able to have a free choices in each of educational event. As it was stated by the great philosopher Immanuel Kant that "free thinking" is everything and whatever to start to construct/build their knowledge/life/world.

The problem of developing curriculum on English subject as an international language is about its form, content and approach. The similarity in term of its form has no problem; however, we should put a concern in the similarity of the content and approach. As we know the the content and approach are something contextual. So they related to the foundation, ideology, philosophy up to the certain purpose of teaching English. Teaching English in Bali and Singapore will have different purposes. Teaching English in different places will have different resources potentialities.

Thank you.


  1. Fatmawati
    PM.D 2016
    Dalam sebuah proses pembelajaran terdapat siswa yang heterogen, siswa dengan berbagai karakteristiknya. Karakteristik yang berbeda-beda tersebut menjadi satu perhatian penting bagi guru untuk merencanakan sebuah proses pembelajaran, selain itu juga menjadi pertimbangan guru untuk menentukan materi yang perlu diajarkan kepada siswa nya.

    16709251056_PMC 2016
    Pendidikan Matematika-S2

    Menjadi guru yang efektif adalah idaman setiap guru, namun kembali lagi bagaimana kita bisa mengendalikan ruang kelas dengan peserta didiknya. Tidak sedikit peserta didik lebih bersemangat bila diajar oleh guru yang humoris namun selalu tepat sasaran dalam membangun konsep pengetahuan peserta didik. Maka sangat diperlukan kekuatan motivasi dengan hal-hal yang posotif dan mengena dengan tujuan pembelajaran.

  3. Sehar Trihatun
    S2 Pend. Mat Kelas C – 2016

    Mengajarkan matematika terhadap anak-anak yang lebih muda dari kita memanglah tidak mudah. Anak-anak tentunya memiliki taraf tingkat berpikir yang berbeda dengan orang dewasa. Sehingga salah satu yang harus dipertimbangkan kita sebagai orang yang lebih dewasa tentu harus memperhatikan tingkat perkembangan berpikir anak. Selain itu, berbagai aspek lain seperti tingkat emosional, psikologi anak dan lain sebagainya juga harus dipertimbangkan ketika kita akan mengajarkan atau menjalankan proses belajar mengajar dengan anak. Hal ini dilakukan agar anak senantiasa dapat memahami apa yang dikemukakan oleh guru dengan lebih baik karena proses pembelajaran terjadi sesuai dengan keadaan dan kondisi anak tersebut. Sehingga belajar matematika bukanlah hanya diberikan atau diberitahukan oleh guru, tetapi siswa lah yang harus mengkonstruksi dan membangun sendiri pemahaman mereka tentang matematika sesuai dengan taraf perkembangan anak tersebut.

  4. Sehar Trihatun
    S2 Pend. Mat Kelas C – 2016

    Kurikulum merupakan suatu pedoman bagaimana proses pendidikan itu akan dilaksanakan. Gagasan mengenai kurikulum yang berlaku global akan mencederai kondisi setiap subjek dan objek pendidikan yang pada hakikatnya belum tentu dapat disamakan. Hal ini sama halnya dengan seorang guru yang mengajar dengan metode tertentu tanpa memperhatikan kondisi siswanya. Untuk membentuk suatu kurikulum pendidikan haruslah juga memperhatikan ideologi dan filosofi suatu bangsa, setiap bangsa pasti memiliki ideologi dan filosofi yang berbeda-beda, maka dari itu gagasa kurikulum yang dapat berlaku secara global ini akan sangat sulit untuk diwujudkan.

  5. Eka Dina Kamalina
    S1 Pendidikan Matematika A 2014

    Salah satu komponen terpenting dalam pembelajaran adalah adanya guru. Guru memiliki peran penting selama proses pembelajaran, salah satunya adalah sebagai fasilitator. sebagai fasilitator, guru harus mampu untuk membuat skema yang baik untuk dapat memfasilitasi siswa belajar, khusunya disini adalah belajar matematika.

  6. Dimas Candra Saputra, S.Pd.
    PPs PMA 2017

    Assalamualaikum prof,
    Matematika pada dasarnya bersifat abstrak, formal, dan fondasional. Maka untuk membelajarkan pada siswa perlu alat komunikasi yang sesuai dengan siswa. Namun, dalam implementasinya tentu tidak akan semudah yang dibayangkan. Kita harus benar-benar memahami setiap hakikat yang terkait dengan proses belajar dan hakikat matematika itu sendiri. Pembelajaran juga harus memperhatikan aspek psikologi, sosial, dan yang lainnya. Pada dasarnya pembelajaran yang sesuai sampai sekarang ini adalah pembelajaran konstruktivisme, yaitu memberikan kesepatan pada siswa untuk berinteraksi dengan lingkungan dan orang-orang disekitarnya dalam mengkonstruk pengetahuannya sendiri.

  7. Maghfirah
    S2 Pendidikan Matematika A 2017

    Assalamualaikum Warohmatullah Wabarokatuh
    I strongly agree with "free choices in each of educational events". In nidonesia in particular, students are charged with so many subjects that they have to learn and get certain scores to pass even though they do not match their interests and preferences. this makes education less focused on developing students' talents and abilities.

  8. Auliaul Fitrah Samsuddin
    PPs P.Mat A 2017

    Thank you for sharing this, Sir. About global curriculum in Mathematics, i think it has no problem globalizing mathematics curriculum in terms of form but just like Prof Marsigit said it will be difficult to make the content and approach since every country has different value and ideology.

  9. I Nyoman Indhi Wiradika
    PEP B

    Terima kasih Prof, dialog yang sangat menarik sekali, selalu menambah gairah saya yang minim pengetahuan ini untuk selalu menempa diri dan belajar. Saya tertarik dengan konsep bermatematika seperti konsep dalam senam. Dalam senam, orang biasanya dengan giat atau rutin berolahraga demi dapat membentuk otot ditambah berdampak pada badan yang sehat. Sedangkan dengan bermatematika kita dapat melatih nalar untuk mendapatkan akal yang sehat. Terkait konsep gagasan pengembangan kurikulum di Inggris yang melibatkan siswa dalam mengembangkan kurikulm bagi saya merupakan hal yang menarik. Saya rasa hal tersebut sudah banyak dikembangkan oleh beberapa Negara, seperti contoh India dengan konsep Hole in The Wall, menariknya adalah program ini dijalankan di daerah kumuh dan pedalaman di India. Melalui Hole in The Wall, setiap anak dapat mempelajari segala hal yang menjadi kebutuhan mereka. Akan menarik kalau di Indonesia menggalakan sistem Swaajar, di mana tiap-tiap desa diberikan fasilitas komputer umum dengan berbagai macam teori praktis, sehingga anak-anak dapat mengembangkan kurikulum mereka sendiri yang dirasa menjadi kebutuhan anak-anak untuk hidup.

  10. Nama : Habibullah
    NIM : 17709251030
    Kelas : PM B (S2)

    Assalamualaikum wr.wb

    Pendekatan GYM merupakan suatu gagasan yang sangat bagus jika memang bisa diterapkan di dalam pembelajaran matematika. Umumnya setiap siswa sangat suka berolahraga karena menurut mereka sama seperti sedang bermain namun bermain dengan suatu aturan yang telah terstruktur. Dengan pendekatan GYM otak siswa akan lebih merasa segar, bugar, dan lebih termotivasi serta lebih bergairah dan bersemangat untuk mengikuti setiap step dalam pembelajaran matematika yang di ajarkan oleh guru di kelas. Namun yang paling penting adalah guru harus benar-benar bisa mengkondisikan waktu dan suasana kelas pada saat pembelajaran berlangsung agar tujuan yang diharapkan di dalam pembelajaran matematika tetap bisa tercapai.

  11. Nama: Hendrawansyah
    NIM: 17701251030
    S2 PEP 2017 Kelas B

    Assalamualaikum wr wb

    Terimakasih banyak Pak prof atas postingan ini, ada cendara mata yang menjadi pegangan buat diri saya pribadi untuk menambah pengetahuan baru buat saya.Mengutip kembali- pernyataan Bapak karena ini menurut saya merupakan hal penting.
    “In my perception, the most basic problem of the foundation of math educ is how the students are to construct their own math. What we need as adults people is to develop the scheme to facilitate them”
    Seorang guru mungkin harus memberikan peluang kepada siswa untuk lebih kreatif dalam menemukan berbagai pertanyaan dan gagasannya.Kemudian seorang guru tugasnya mengembangkan sebuah pendekatan untuk mengakomodir proses belajar mengajar tersebut.Di lain sisi terkait kurikulum saya sangat setuju jika siswa dilibatkan dalam pembuatan kurikulum.Berbagai macam sifat, karakter maupun pengetahuan siswa ikut menentukan kurikulum.Kalau dilihat sifat kurikulum sekarang benar adanya sifatnya global.Kesannya seolah-olah menggambarkan keadaan setiap anak memiliki kemampuan yang sama baik dari segi karakter maupun pengetahuannya.