Mar 25, 2013

Dialog Internasional 6 Pendidikan Matematika

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Math, Math Education, Math Culture

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The current issue for "Focus on Mathematics and Pedagogy" is now online.

Zor Shekhtman:
Marsigit, you are right. Students must be actors in the process of learning. The best I can do using Internet as a tool without personal contact with students is (1) present a lot of problems without solutions as notes to video lectures, (2) present solutions in my video that corresponds to notes, asking students to try to solve the problems themselves before and after watching the video and (3) had students to take exams for each topic scoring their answers. If there is any better way to get students involved via Internet, I'd appreciate any suggestion. Meanwhile, encouraging students to solve problems themselves before and after the corresponding lecture seems as a good idea and exams for registered students do force them to be actors.  I'd like to mention that Unizor was designed with a supervised study in mind. A parent in an environment of homeschooling or a teacher in a flipped classroom environment should supervise the process enforcing what I just said - solving problems before and after each lecture, where solutions are explained, and taking exams with comparing the score with theoretical maximum.

Marsigit Dr MA:

@Zor Shekhtman: Thanking for the response. I think you are right, and I also understand the limitation of such media using internet without personal contact with students. As I said before that your programs are very useful also to support the students' effort in learning math and they are also useful for the teachers and the parent as well. We may get some inspirations by employing or watching your on line VTR. Further, they also meet with the principles that education needs various resources of teaching and learning.

However, I may pose the very basic and latent mass spreading phenomena of not good teaching practice of math anywhere in the world that most of the teachers implement delivery method of teaching while usually the teachers themselves ultimately are the actors of activities. The students are perceived permanently to be the passive objects; they have no initiation. They are always expecting something that initiated by the adult/teacher. Ultimately, it forms a culture in which the students are always depend on the adult/teacher. That is why I purposely blow up the phenomena in order that people who have authority or skill in developing technology are aware about this situation and always find out the solutions.

So you may agree with me that at every single event of teaching learning of math, the most crucial problem is how to empower the students, to facilitate them in order they prepare their learning (aperseption), discuss actively in a certain small group, expose their ideas and find their conclusion by themselves. Hence, I still look at the important role of Unizor programs by improving its approach to be more students' oriented. Why should you yourself who are the actor in the video? Why don't you try the produce video in which e.g. there is a brilliant student who is trying to solve some math problems; or there are some younger students who are discussing how to find out math solution; or maybe you may produce such kinds of interactive programs in which the students may expects some response by employing the programs. Again, I wish to congratulate of your great efforts and apologize for my provocation. Thank you.

Dr. Narayan Ch Ghosh:
I have written number of article on Folk Mathematics. One of my student has done Ph.D. on Folk Mathematics. New methodology can be developed keeping ideas of Folk Mathematics. Do you believe it. Pl. see my articles on published in a journal of Kalyani University and another in a journal of Rabindra Bharati University. Using or you can see those.

G Donald Allen:
I do believe there is a lot of folk mathematics about. After all, the ancient Egyptians and Babylonians seemed to student mathematics this way, from an intuitive and practical viewpoint without the requirement of rigor. I had always thought of folk mathematics as expedient and transitory, before until correct and rigorous mathematics could be established. It would be most interesting to see the most advanced examples of correct folk math there are. This brings to fore another point. In your list of five basic topics in "FOLK-MATHEMATICS STUDY", i) Cultural basis, ii) Ways and means of presentation, iii) Duration of presentation, iv) Achieved knowledgeand its basis, v) Transfer process, where do you place "correctness?" The main problem I see with this informal mathematics is that once it becomes rooted in the consciousness of established procedure, it is most difficult to root it out.
Marsigit Dr MA:

@Narayan & Donald: Pure Mathematicians should do their best in Folk Mathematics. However, Folk Mathematics and Folk Math Education are totally different. The problem is when Pure Mathematician try to force to produce and employ Folk Math Educations. The cultural basis for Folk Math is the life of Pure Mathematician in the past; while the cultural basis of Folk Math Education is the life of students presently. Why Pure Mathematician strive to dominate and legitimate current practice of math educ? Because they use very simple logic " Mathematics first, and then everything - Mathematics first and then Education". This is the dangerous and very bad assumption that make very bad also in the practice of math teaching. The is actually the only one reason why the implementation of math teaching at school have always a problems. I wish to say "Stop from now on the domination of pure mathematician in primary and secondary math education". Let education practitioners speak about their math teaching. Let math teachers improve their own teaching without much intervening by University Professor or by Pure Mathematician. Let them discuss, communicate, interact, in their community independently. Thank's

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

Bradford Hansen-Smith:

Marsigit, of course any discussion of math is about concepts and methods, those are ideas fundamental to any educational objective. I am talking about principles that are inclusive of math and everything else (maybe you are too, I am unclear on that.) Math is not about anything if it is not about everything. Comprehensively there is no differentiation between math for adults and math for younger students except for the levels of increasingly abstract nature of the language, years of experience, and the tools. It then makes sense to differentiate levels of growth, the principles do not change. If we understood the principles by a logical tracing back of mathematical functions to origin we would find the same principles for all differentiated objects and for all levels of learning. This must include " INTENSIVITY and EXTENSIVITY" as a function of duality.

I do not understand what you have said, “the nature/principle is the generality in its dimension,” or how you are using the word dimension. The nature of an object is reliant on the principles underlying the generation of the object, regardless of how many imagined dimensions. I see nature and principle as different concepts. Before the discovery of math what gave direction to the nature of math? Is not pattern foundational to math that gives clarity to both young student and adult mathematician? Is pattern a principle or is it the nature of what is principled?

Marsigit Dr MA:
@Bradford: It seems we are agree on many things related with math educ./teaching. However may I smooth your notion "Comprehensively there is no differentiation between math for adults and math for younger students". I revise it as "It is not COMPREHENSIVELY but IDEALISTICALLY there is no differentiation between math for adults and math for younger students". It was Plato who has this ideas. However, your notion " except for the levels of increasingly abstract nature of the language, years of experience, and the tools", was related to Aristotelian notion. Again you posted the notions of Plato's school by saying " the principles do not change. If we understood the principles by a logical tracing back of mathematical functions to origin we would find the same principles for all differentiated objects and for all levels of learning."

Philosophically you look to be confused by mixing the existing school of Platonism and Aristotelianism.

As we know that pure math is in line with Platonism; and school math is in line with Aristotelian-ism. Both they have their own schools. The most important is that the educator should understand their position. Pure Mathematicians strive to legitimate Platonism at schools (although most of them do not aware of this); they just implement what they are able to do as mathematician. It is wrong; and from the early of history, Aristotelian was the first man who confront Plato. Socio-constructivist has tried to wake up all of us to start to move to develop math educ based on the nature of students learn math.

Bradford Hansen-Smith:
Marsigit, do not assume I have your knowledge, educational background or teaching experience because we have agreement. To say I am philosophically confusing Aristotle and Plato has no meaning for me. I have not read either and have no idea about the academic schools that have grown up around them. What I have expressed is my own understanding about math and education that comes from experience folding circles and working with student over the years. I feel no obligation to move through the present bringing along what belongs to the past. There are plenty of people doing that.

I do not think Aristotle or Plato folded circles, so you cannot use them or the difference between them to criticize my position. Please do not try to "smooth" over what I have said, or think that your words better reflect thoughts I have about my own experiences. The word “comprehensive” is exactly what I mean. Inclusive refers to syntheses and in referring to the whole I mean a process of revelation about relationships between parts. Whether my students are 5 yrs of 80 yrs we do the same folds and observe what is happening, discovering the patterns and principles that function throughout the mathematical spectrum. I understand the circle as a unit, and also as the only demonstration of unity, which belongs only to the Whole.

I do not know what socio-constructivist believe, but if understanding how the child learns math is based on the studies of scientific methods then we have learned nothing about how we learn. What information gained may be important, but it is not enough to make decisions about methods and curriculum for educating generations of children, particular when we are greatly in need of alternate ways of thinking about what is precariously in place.

Marsigit Dr MA:
@Bradford: I think your Wholemovement is amazing. I found some similarities principle both in your Wholemovement and students' constructing math concepts. Further I may add one more similarity i.e. in peoples' constructing their life. Although they have different scope or dimension. The first is the smallest and the last is the greatest scope. It means that your Wholemovement it is not enough to construct math concepts; and constructing math concepts is not enough to construct their life. You may say that I am talking about dimension of constructing life. Why do you have the smallest dimension here? And what happened? The reason is about REDUCTION and EXTENSION. Reduction consists of SIMPLIFICATION. And in the simplification there is ELIMINATION. Elimination is the most dangerous phenomena in (math) education. So that's why your Wholemovement has also limited access in contributing to math teaching except that you move to implement the principle. I see that you are talking with me is such kind of movement; so I am waiting for its extensive contribution. All of that is my ideal. As you also have your ideal.

There is a huge distance between Adults Math and Young's Math. If math educators do not see the distances, they surely have a pedagogic problems. According to Realistic-ism, the lowest level of math is Concrete Math and the highest math is Formal Math. Between the two there are the Model of Concrete Math and the Model of Formal Math. So there is a stage (dimension) for the students to learn math. Thank's


  1. Fatmawati
    PM.D 2016
    Pada dialog di atas kembali ditekankan bahwa matematika murni itu sangat berbeda dengan matematika sekolah untuk siswa, dan itu tidak dapat disamakan dalam penyajiannya. Bagaimana sebuah konsep matematika dapat tersajikan secara baik dan dapat dipahami dengan baik oleh siswa itu adalah tugas guru.

    16709251056_PMC 2016
    Pendidikan Matematika-S2

    Dalam pembelajaran dan pengajaran matematika pasti ada objek dan subjek. Sebab matematika merupakan suatu kegiatan. Dalam kegiatan pembelajaran, peserta didik merupakan subjek bukan objek yang hanya mendengarkan penjelasan gurunya. Dengan penerapan metode pembelajaran yang inovatif, siswa akan terbiasa untuk berpikir kritis dan mampu mengembangkan kreativitasnya. Maka guru berperan sebagai fasilitator dalam proses pembelajaran.

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

    Memanfaatkan teknologi untuk dijadikan suatu media pembelajaran matematika merupakan hal yang baik untuk dilakukan. Selain menambah variasi dalam kegiatan pembelajaran, hal ini juga memberikan pengetahuan baru bagi siswa disamping dia belajar matematika, mereka juga dapat belajar untuk menggunakan dan memanfaatkan teknologi sebagai sarana dalam belajar matematika. Hal ini juga dapat memudahkan guru untuk memberikan terobosan baru kepada siswa dalam kegiatan belajarnya. Siswa dapat lebih mandiri untuk beloajar matematika dan tidak hanya bergantung pada penjelasan-penjelasan dari guru. Fenomena-fenomena yang sering terjadi dalam pembelajaran matematika, siswa masih harus bergantung pada guru dalam belajar matematika, seakan-akan apabila guru tidak menjelaskan materi matematika siswa tidak tahu apa yang harus mereka pelajari, sehinggga apa yang siswa lakukan dalam belajar akan sangat tergantung dengan kegiatan guru. Padahal siswa harus dapat lebih mandiri dan aktif dalam mencari dan mempelajari pengetahuan. Dengan adanya pembelajaran berbasis teknologi seperti misalnya dengan menggunakan internet, siswa akan lebih leluasa untuk mencari sendiri materi pelajaran yang akan dipelajari maupun pengetahuan-pengetahuan lainnya yang akan bermanfaat bagi siswa tersebut.

  4. Eka Dina Kamalina
    S1 Pendidikan Matematika A 2014

    Pendidikan adalah usaha sadar. Sehingga, dalam pendidikan seharusnya siswa melakukan usaha untuk memeroleh pengetahuannya atau yang sering disebut student center. Dengan demikian, pengetahuan yang diperoleh akan bertahan lama, seperti teori Bruner tentang belajar bermakna apabila siswa menemukan sendiri pengetahuannya.

  5. Eka Dina Kamalina
    S1 Pendidikan Matematika A 2014

    Usaha yang telah dilakukan pemerintah patut dihargai, karena pemerintah selalu berusaha bagaimana untuk memperbaiki kulitas pembelajaran di Indonesia. Salah satunya adanya perbaikan dalam kurikulum yang digunakan. Saat ini kurikulum yang berlaku adalah kurikulum 2013 yang menitikberatkan pada keaktifan siswa selama pembelajaran.

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

    Assalamualaikum prof,
    Pembelajaran yang dilakukan oleh Zor dengan menggunakan internet tersebut banyak sekali manfaatnya. Terlebih di era sekarang ini, hampir semua siswa sudah memiliki HP yang mempermudahnya dalam mengakses internet. Pembelajaran melalui internet dapat membuat siswa belajar lebih mandiri, hal ini juga terkait dengan terbatasnya tatap muka di kelas. Internet yang digunakan semaksimal mungkin dengan menyediakan media pembelajaran mandiri seperti video, foto, dan recorder (VTR) akan dapat membantu siswa. Terlebih lagi bila dalam VTR tersebut ialah siswa yang menjadi aktornya.

  7. Assalamualaikum Warohmatullah Wabarokatuh
    the topic of "students must be actors in the process of learning" in my opinion still need effort in making it happen in indonesia. most teachers have not given the opportunity to students to be the center of learning process. this certainly needs to be a big government in promoting education in Indonesia as in developed countries.

  8. Auliaul Fitrah Samsuddin
    PPs P.Mat A 2017

    Thank you for sharing this, Prof. Just like you mentioned that students are not able to move on from concrete mathematics to abstract mathematics directly. They need process and time between. The process should be recognized by teachers and motivate their students.

  9. I Nyoman Indhi Wiradika
    PEP B

    Terima kasih prof, atas dialog-dialog yang sangat menarik, tawaran-tawaran konsep yang sangat mendalam dan mengupas secara matang konsep dari pendidikan matematika. Saya memiliki kesepemahaman dengan model matematika dengan menggunakan internet, namun hal tersebut tentu bukan yang utama. Pembelajaran matematika menggunakan internet memiliki kelebihan untuk dapat merealisasikan Folk Math Education karena memberi peluang yang luas untuk menumbuhkan long life learning, tidak hanya bagi para siswa, namun juga lingkungan siswa. Orangtua dari siswa dapat menjadikan internet sebagai rujukan untuk dapat membelajarkan konsep matematika kepada anak-anak. Sungguh menarik jika matematika dibangun mulai dengan konsep intuisi yang natural pada anak-anak.

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

    Assalamualaikum wr.wb

    Dengan membaca artikel di atas saya menarik suatu kesimpulan bahwa sebagai seorang guru matematika kita harus inovatif. Artinya kita harus mampu mendesain dan membuat suatu produk perangkat matematika yang di dukung oleh teknologi baik yang berbasis e-learning, android, maupun berbasis internet dengan bantuan program atau software matematika tertentu. Karena dengan begitu guru dapat membantu siswa dalam belajar matematika dengan membuat lingkungan yang menarik dan merangsang siswa untuk menemukan dan mengidentifikasi informasi apa yang mereka butuhkan untuk memecahkan masalah matematika serta mendorong siswa untuk berpikir logis, konsisten, dan bekerja secara sistematis.