Mar 25, 2013

Dialog Internasional 6 Pendidikan Matematika

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Math, Math Education, Math Culture

Follow G Donald
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. Sumandri
    S2 Pendidikan Matematika D 2016

    Saya setuju dengan gagasan dari Zor Shekhtman: yang mengatakan bahwa siswa harus menjadi aktor dalam pembelajaran. Namun menurut saya tidak semua tempat atau daerah bisa menerpakan gagasan itu, perlu dilihat situasi dan kondisi, letak suatu daerah itu. kalau siswa menjadi aktor dalam pembelajaran maka pemerintah harus mempersiapkan segala sesuatu yang bisa menjadikan siswa sebagai aktor dalam pembelajaran. Kalau untuk level kota menurut saya bisa namun juga tidak bisa 100%, apalagi di desa yang jauh dari jangakuan informasi. Dan menurut saya banyak faktor yang harus diperbaiki apalagi level Indonesia untuk menjadikan siswa sebagai aktor dalam pembelajaran.


  2. Yosepha Patricia Wua Laja
    S2 Pendidikan Matematika D 2016

    Masih menggunakan link yang sama Dalam membelajarkan matematika kepada anak-anak, kurikulum matematika SD mempertimbangkan beberapa hal diantaranya Penanaman Konsep Dasar, yaitu pembelajaran suatu konsep baru matematika, ketika siswa belum pernah mempelajari konsep tersebut, Pemahaman Konsep, yaitu pembelajaran lanjutan dari penanaman konsep, yang bertujuan agar siswa lebih memahami suatu konsep matematika., dan Pembinaan Keterampilan, yaitu pembelajaran lanjutan dari penanaman konsep dan pemahaman konsep. Pembelajaraan pembinaan keterampilan bertujuan agar siswa lebih terampil dalam menggunakan berbagai konsep matematika.

  3. Wahyu Lestari
    PPS P.Mat D

    perlu ditekankan bahwa matematika adalah kegiatan. Dimana siswalah yang melakukan kegiatan, bukan lagi guru yang mengisi kekosongan pengtahuan siswa. Adanya keaktifan di semua pihak, guru dan siswa. Di sinilah guru mulai belajar untuk menekan egonya dan membairkan siswa-siswanya memainkan kemampuan yang mereka punya untuk menemukan intuisinya sendiri.

  4. Ardeniyansah
    S2 Pend. Matematika Kelas C_2016

    Assalamualaikum wr. . wb.
    Belajar yang efektif hanya akan terjadi jika siswa turut aktif dalam merumuskan serta memecahkan berbagai masalah. Siswa salah satu komponen yang menempati posisi sentral dalam proses pembelajaran baik di kelas maupun di luar kelas dalam kegiatan pembelajaran siswa yang berperan sebagai subjek bukannya objek yang hanya mendengarkan gurunya. Siswa yang berperan aktif dalam belajar dan guru hanyalah memfasilitasi siswanya kaitannya dengan pembelajaran yang efektif maka siswa diberi kesempatan untuk berinteraksi dengan lingkungan dan benda-benda konkret yang ada dilingkupnya agar dapat mengembangkan pola pikir dan ide serta gagasannya sehingga dapat menemukan sendiri pola-pola yang akan mereka pelajari.

  5. Anwar Rifa’i
    PMAT C 2016 PPS

    Matematika akan menjadi ilmu jika dibangun dengan intuisi. Satu kalimat yang memegang makna sebenarnya dari ilmu matematika. Ilmu adalah bagian dari pengetahuan. Pengetahuan adalah sesuatu yang diketahui dari sumber atau referensi yang dapat dipercaya dan akuntabel. Kita bisa menerapkan pengetahuan untuk memecahkan masalah dalam kehidupan sehari-hari. Matematika adalah pengetahuan jika hanya sebatas diketahui bagaimana simbol-simbol, rumus, dan sebagainya. Namun, matematika akan menjadi ilmu jika kita menerapkan pengetahuan matematika dalam kehidupan sehari-hari. Tanpa perlu mendefinisikan pengetahuan matematika formal, maka kita telah berintuisi terhadap matematika dan dengan demikian kami telah membuat matematika menjadi pengetahuan matematika melalui intuisi yang kita miliki. Jadi dapat dikatakan bahwa intuisi adalah jembatan antara pengetahuan dan ilmu pengetahuan.

  6. Supriadi / 16709251048
    Kelas C 2016 Pendidikan matematika – S2

    Pembelajaran Berpusat Pada Siswa (Student Centred Learning) merupakan pendekatan Pembelajaran Kurikulum 2013 tertuang secara jelas dalam Permendikbud No. 81A tentang Implementasi Kurikulum 2013. Pada dokumen regulasi tersebut Pembelajaran Berpusat Pada Siswa (Student Centred Learning) sebagai ciri Pembelajaran Kurikulum 2013 perlu diikuti dengan penyempurnaan pola pikir (mindset) sebagai berikut (Permendikbud No. 70 Thn 2013) :
    1. perubahan dari pola pembelajaran satu arah (interaksi guru-peserta didik) menjadi pembelajaran interaktif (interaktif guru-peserta didik-masyarakat-lingkungan alam, sumber/ media lainnya) pada Pembelajaran Kurikulum 2013 ;
    2. pola pembelajaran terisolasi menjadi pembelajaran secara jejaring (peserta didik dapat menimba ilmu dari siapa saja dan dari mana saja yang dapat dihubungi serta diperoleh melalui internet) pada Pembelajaran Kurikulum 2013 ;
    3. pola pembelajaran pasif menjadi pembelajaran aktif-mencari (pembelajaran siswa aktif mencari semakin diperkuat dengan model pembelajaran pendekatan sains) pada Pembelajaran Kurikulum 2013 ;
    4. pola belajar sendiri menjadi belajar kelompok (berbasis tim) pada Pembelajaran Kurikulum 2013 ;
    5. pola pembelajaran alat tunggal menjadi pembelajaran berbasis alat multimedia pada Pembelajaran Kurikulum 2013 ;
    6. pola pembelajaran berbasis massal menjadi kebutuhan pelanggan (users) dengan memperkuat pengembangan potensi khusus yang dimiliki setiap peserta didik pada Pembelajaran Kurikulum 2013 ;
    7. pola pembelajaran ilmu pengetahuan tunggal (monodiscipline) menjadi pembelajaran ilmu pengetahuan jamak (multidisciplines) pada Pembelajaran Kurikulum 2013 ; dan
    8. pola pembelajaran pasif menjadi pembelajaran kritis pada Pembelajaran Kurikulum 2013 .


  7. Pendidikan matematika merupakan kesimbangan antara rasio dan empiris. Matematika dapat ditemukan dari realitas kemudian di cari idealnya atau sebaliknya dimulai dengan idealis kemudian diterapkan dalam kenyataan. Sebenar-benar matematika bermanfaat bagi kehidupan manusia, dan kehidupan manusia dapat digali untuk perkembangan ilmu matematika.

  8. Syaifulloh Bakhri
    S2 Pendidikan Matematika C 2016

    Assalamu’alaikum wr.wb.
    Matematika full rumus maupun full simbol, konsep baru terbentuk dari konsep-konsep sebelumnya. Menjadikan matematika bukan yang biasa-biasa saja sebagaimana sebatas pengetahuan, namun lebih kepada implementasi dalam kehidupan sehingga ilmu matematika itu berguna bagi kemaslahatan. Peserta didik itu ada karena berpikir serta adanya kegiatan mengembangkan kemampuan maupun kreatifitas dalam kehidupan.