Apr 6, 2013

Dialog Internasional 7 Pendidikan Matematika

LinkedIn Groups
Math, Math Education, Math Culture
The current issue for "Focus on Mathematics and Pedagogy" is now online. Please see http://distance-ed.math.tamu.edu/newsletter/newsletters_new.htm#current_issue Thanks. don

G Donald Allen:

Marsigit, Sorry to disagree, but pure mathematics and pure mathematicians have very little influence on math education, formal or informal. Of course mathematicians, not research mathematicians, often serve on curriculum revision and re-design committees, at both the state and federal levels. What they mostly recommend is an adherence to rigor and correctness in mathematics instruction. The curriculum is mostly fixed. What is changed from time-to-time is the set of priorities, the order and grade level for new topics, and the scope of the testing.

Most university math educators believe substantially on current pedagogical theories to educate their students. This is mollified by their personal and experiential beliefs on how best to engage and teach their students. This is where the idea of "Folk Math Education" resides. It would be an interesting research topic to determine just how this is done, and most importantly what math ed students take away from their instruction. After all, this is how they will teach. Another factor is to consider just how much educational theory teachers apply in their courses. Like many of us, I believe many experienced teachers use methods that they feel best resonate with their students and "Get The Job Done."

As well an important factor is to consider the constraints placed upon the teachers as to what curriculum they teach and how they teach it. This includes the use of calculators, group learning, the relative importance of high stakes testing, and student self-reliance.

Overall, pure mathematical considerations are out of the teaching game vis-a-vis methodologies used today.
Marsigit Dr MA:

Donald: That is. The problems of primary and secondary math teaching are coming substantially from the points containing in your notions " (pure) mathematicians often the serve on curriculum revision and re-design committees, at both the state and federal levels. What they mostly recommend is an adherence to rigor and correctness in mathematics instruction.".

My question to pure mathematician is about their legitimation to serve, revise, and recommend curriculum for primary and secondary math teaching? This is what I called as intervention to other subject. If they talk about their own math teaching in University, there will not be a problem. If they are doing research in primary and secondary math teaching, it will be good. As you know that such activities as you stated e.g. serving, revising and recommending the primary and secondary curriculum have very-very huge impacts at the implementation in primary and secondary math teaching learning processes. My Further question is, if they force to do so, then what is really their motive? I suspect that pure mathematician perceive primary and secondary math educ as the best area for doing their business.

Further, I also wish to say that most of pure mathematician lack of understanding on philosophical, theoretical, psychological ground of primary and secondary math education. As I also put a concern on your notions " The curriculum is mostly fixed. What is changed from time-to-time is the set of priorities, the order and grade level for new topics, and the scope of the testing. Most university math educators believe substantially on current pedagogical theories to educate their students. elements containing in your notions " These notions indicate a problematic understanding and vision of primary and secondary math. I totally disagree with your last notions.

Five Guiding Principles of Mathematics Education
It's high time we put grand ideas back into mathematics curricula.
Article link: http://www.eimacs.com/blog/2012/08/algebra-is-not-the-problem-part-2/.

Bradford Hansen-Smith:

Marsigit, I do not understand that you say "Wholemovement it is not enough to construct math concepts; and constructing math concepts is not enough to construct their life."  I agree that reduction to simplify is a problem. We usually eliminate context, thus removing meaning and limiting usefulness. Reduction creates missing-information. Are you saying because of the simplicity of the circle form it is limited in contribution, and what information is missing that is necessary to extend or construct mathematical concepts is also missing in math education to develop full math understanding? By saying " the smallest dimension" are you talking about the beginning levels of math education? Please explain.

The circle is indeed a simple figure. You can draw pictures of it or fold it. For at least 5000 years we have been drawing pictures, a reduction of information with intent to clarify. There is a huge bias to drawing the circle with no experience in folding. Until we have given serious time to explore folding circles we have no idea about the real contributions to math education. From a limited experience of 23 years of folding circles I would say there is less math contrivance, being more direct and accessible, than all the centuries of drawings. That is not to downplay human achievement in developing math concepts.

The circle image has origin in observations in the outline of spherical objects. The circle disc is the transformational compression of a spherical object; the only form that demonstrates undifferentiated unity, Wholeness. To start with less than Whole is to limit ourselves to a reduction. Reflected in the first fold of decompressing the sphere/circle is the action of compression itself, revealing seven qualities that are observable that I call principle since they happen first.

Starting with the WHOLE the first MOVEMENT creates DIVISION showing DUALITY forming TRIANGULATION. These five qualities refer to the mechanics having everything to do with fundamental pattern formation and development of symmetry. The next two are principles of relationship. There is CONSISTENCY between each part and the movement of the whole, and there is a DEPENDENCY of each part to the whole, which is the determination of the interrelationships between all parts.

Through observation I am constructing a set of principles based on the qualities inherent in the first movement of a form that displays complete self-referencing and self-organization. From that standpoint I would call these principles universal as they include fundamental aspects of every level of math concepts and life formation. They are quite different that the five principles first sighted in this discussion, and I can think of no greater "grand idea" to put back into math curricula than folding circles. I ask much of mathematicians in thinking about unity as the context that has been eliminated from the units use in constructing math.

I agree there are many stages of growth in understanding math from the concrete to formal to the imaginative theoretical. These universal principles do not change from level to level. The methods and tools we use at each level do change to accommodate difference in growth.
Marsigit Dr MA:

Bradford: Your explanation is wonderful. Inevitably, we both simultaneously are reflecting each of our works. Our reflections covers math, educ, and even philosophy. I also have experiences work with the circles; though it was in the case of doing math and not up to specifically learn it as wholemovement. I think your wholemovement is something more intensive and extensive. And they are useful for the learner to find out its principles.

As we know that, as I said before, in the epistemology of math, we have phenomenological approach consist of ABSTRACTION and IDEALIZATION. Abstraction is a double sided tool for human being to be able to survive. One side is the most powerful; and the other side is the most dangerous. It is the most powerful because no aspect of human being is free from abstraction. Why? Abstraction is reduction. Reduction is choices. So you are to be chosen by God to born in this world.

Meanwhile, abstraction is reduction. And reduction is simplification. And simplification consists of ELIMINATION. That I said to be very dangerous for us (math teachers) if they do not use it appropriately. You can imagine, how someone feel devastated if one or some aspects of her/his life to be eliminated. That's why I put a highly concern on this aspect in order that the adult peoples (math teachers) do not easily eliminate students' character in teaching math. So in order the learner do their best in learning math (also in your wholemovement) as well as in their life, they should have a highly skill in using abstraction.

The opposite direction of abstraction is EXTENSION and generalization (idealization). Life, math and your wholemovement, consists of abstraction and extension simultaneously. So I found, the ancient Greek prescription, that the best method to live, learn math and wholemovement is by employing abstraction and extension simultaneously. In a daily language, I say it as "to translate and to be translated"; in geometrical representation, it is as a CIRCLE i.e. your wholemovement.

Therefore I further found that a certain circle, with its characteristic you searched, has only related with a SPACE, as you have shown many forms of the results of folding the circles. This reflects only ONE HALF of the REAL WORLD. And the other one half is that your wholemovement should be related with TIME. May you feel strange to the last term; but if you are to communicate and interact with young students, it is inevitable that they are always related with TIME.

So then I have a suggestion for you that in order you are able to improve the dimension of your wholemovement, you should put in it the element of TIME. It will be very clear because there is no movement when there is no time. Ultimately, I then have a very clear picture on your future work to not just employ the CIRCLE; but also extent it into the WORLD OF SPIRAL. This is really the nature of HERMENEUTICS of life, hermeneutics of learning math, hermeneutics of wholemovement, and hermeneutics of EVERYTHING.

It is still related to the theme of this discussion, and so I proudly wish to say that THE PRINCIPLE OF MATHEMATICS EDUCATION IS THE HERMENEUTICS OF ITS ASPECTS.

Hope something to be clearer. Thank's


  1. Fatmawati
    PM.D 2016
    Salah satu hal yang terjadi dalam pendidikan matematika adalah bahwa yang membuat kurikulum, materi, dan lain-lain mengenai pendidikan matematika merupakan pure mathematician atau orang matematika murni. Sehingga hal tersebut tidak akan cocok jika diimplementasikan ke siswa sekolah, karena matematika murni bukanlah saatnya untuk dipelajari oleh siswa tingkat sekolah. Oleh karena itu perlu adanya pengkajian ulang mengenai sistem pendidikan matematika yang ada di Indonesia.

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

    Dalam dialog matematika ini, saya memahami apa yang dikemukakan oleh pak prof Marsigit bahwa prinsip dari pendidikan matematika adalah hermeneutika dalam segala aspeknya. Hal ini dikarenakan, bahwa dalam mempelajarai matematika kita tidak akan terlepas dari aktivitas menerjemahkan dan diterjemahkan. Matematika secara epistimologi memiliki dua pandangan yaitu abstraksi. Abstraksi ini memiliki dua sisi yang dapat mempengaruhi kehidupan manusia yaitu sisi yang pertama adaalah sisi yang paling kuat, karena abstraksi tidak terlepas dari kehidupan manusia, segala aspek yang ada dalam kehidupan manusia pasti mengandung abstraksi-abstraksi, sementara itu sisi yang berikutnya adalah sisi yang berbahaya bagi manusia. Abstraksi menjadi berbahaya, jika abstraksi merupakan suatu reduksi, reduksi merupakan penyederhanaan, dan penyederhanaan akan menimbulkan penghilangan atau eliminasi. Hal ini lah yang menjadikan abstraksi dapat berbahaya bagi manusia termasuk juga bagi guru matematika. Karena apabila kita selaku guru matematika tidak menggunakannya dengan tepat, maka dikhawatirkan bahwa seorang guru dapat membunuh atau menghilangkan karakter siswanya ketika mengajarkan matematika.

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

    Guru matematika tidaklah seharusnya menghalangi atau membunuh karakter siswanya dalam pembeblajaran matematika. Kegiatan guru dalam mengajarkan matematika yang tidak memberikan kesempatan kepada siswa nya untuk dapat secara aktif mempelajari matematika dengan caranya sendiri atau hanya mendoktrinisasi cara belajar matematika yang harus sesuai dengan apa yang diajarkannya. Bagi siswa yang pandai, mungkin akan dapat menyesuaikan dengan cara mengajar gurunya, tetapi siswa tersbut tidak dapat mengembangkan kemampuannya secara maksima, sementara bagi siswa yang kurang pandai, mereka mungkuin akan kesusahan dalam mengikuti cara belajar gurunya. Oleh karena itu, sangat penting bagi guru untuk menjadi fasilitator agar dapat memfasilitasi kegiatan belajar siswa nya sesuai dengan kemampuan mereka masing-masing.

  4. Angga Kristiyajati
    Pps UNY P.Mat A 2017

    Thanks a lot, Mr. Marsigit

    From this discussion I understand that it is very different between how to learn mathematics in University and how to learn mathematics in primary or secondary school. In primary or secondary schools, the student should do activities in learning mathematics such as finding the pattern, analyzing the phenomena, draw a picture, etc so they can build their own understanding about mathematics.

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

    Assalamualaikum prof,
    Kebanyakan yang terjadi adalah bahwa kurikulum pembelajaran matematika untuk siswa sekolah SD, SMP, dan SMA dirancang oleh para matematikawan murni. Prof. Marsigit dalam diskusi tersebut mempertanyakan tentang legitimasi matematikawan dalam menyajikan, merevisi dan merekomendasikan kurikulum untuk pembelajaran matematika di sekolah. Beliau mengatakan bahwa ini merupakan intervensi terhadap subyek yang lain. Hal ini memberikan dampak yang besar bagi pelaksanaan pembelajaran matematika di sekolah. Para matematikawan biasanya kurang memahami teori, filosofi, dan psikologi dari pendidikan matematika di sekolah. Jika para matematikawan berbicara tentang matematika di perguruan tinggi maka tidak ada maslah. Jika mereka mau melakukan penelitian di sekolah dasar dan menengah tentang pendidikan matematika akan lebih baik.

  6. Sofi Saifiyah
    S2 PEP B

    Matematika murni maupun matematika pendidikan, keduanya dua hal yang berbeda baik formal maupun informal. Penggunaan masing-masing matematika tersebut baik matematika murni maupun matematika pendidikan harus disesuaikan dengan ruang dan waktunya agar tidak terjadi kesalahan dalam penyampaian maupun penerimaan konsep. Pada pendidikan matematika lebih menekankan bagaimana matematika itu dapat dikenalkan kepada siswa untuk menjadi suatu kegiatan dalam belajar atau hermeneutika. Sedangkan matematika murni menekankan pada konsep yang abstrak dan struktur.

  7. Maghfirah
    S2 Pendidikan Matematika A 2017

    Assalamualaikum Warohmatullah Wabarokatuh
    thank you Prof, from the dialogue it can be understood that there is a very fundamental difference between university math and school math. school math learning process should be close to everyday life so that students can feel math close to them. Many students do not like mathematics because for them math is very abstract and difficult to understand.

  8. Auliaul Fitrah Samsuddin
    PPs P.Mat A 2017

    Thank you for sharing this article, Sir. I understand that pure mathematics is constructed from well defined, abstract and rigorous idea. While this idea is unknown in children world. They know Mathematics, and all sorts of knowledge, by experiencing activity related to the subject. That is why, teaching mathematics in primary school is not a small deal.

  9. Charina Ulfa
    PPs Pendidikan Matematika B

    dari tulisan diatas, saya jadi tau kenapa siswa di tingkat sekolah banyak yang membenci matematika. Matematika di sekolah berbeda dengan tingkat kampus, begitu juga dengan matematika pendidikan berbeda dengan matematika murni.
    Pembelajaran matematika di tingkat sekolah haruslah didekati dengan lingkungan hidup mereka, sehingga sebelum diajarkan matematika secara abstrak, akan lebih baik jiwa metematika itu dibawa ke konkrit terlebih dahulu. Dengan seperti itu, siswa akan merasa nyaman dan bertahap akan mempunyai tingkat abstrak yang tinggi sesuai dengan tingkat matematisnya.
    Pendidikan matematika lebih mengutamakan bagaimana matematika itu dapat dikenalkan dan dipelajari oleh siswa. Sedangkan matematika murni adalah suatu yang abstrak dan sistematis.

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

    Assalamualaikum wr wb

    Karena dalam dialog ini sedikit di bahas tentang kurikulum .Yang membingungkan bagi saya adalah apakah kurikulum yang membentuk karakter dan pengetahuan anak atau karakter dan pengetahuan anak yang menghadirkan kurikulum?Saya sangat terkesan dengan cerita pengalamannya Pak prof ketika melakukan wawancara terhadap guru di London dari postingan sebelumnya yang telah saya baca .Betapa menariknya seorang guru mampu membuat kurikulum sendiri berdasarkan hasil belajar yang dikelompokkan di dalam kelas.

    Saya menangkap bahwa dalam belajar matematika perlu berhermeutika untuk mengetahui dasar-dasar dari filosofi matematika itu sendiri.Kebanyakan matematika yang diterapkan selama ini berupa matematika murni.Khawatirnya jika penerapan matematika murni dilakukan pada bibit-bibit muda.Karena hal tersebut dapat menghilangkan sebagian kamampuan berpikir siswa.

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

    Assalamualaikum wr.wb

    Matematika merupakan salah satu ilmu pengetahuan yang mempunyai peranan penting dalam dunia pendidikan. Matematika berfungsi melatih seseorang berfikir dan bertindak logis, cermat, efisien, efektif dan sistematis. Matematika adalah pola pikir, pola mengorganisasikan, pembuktian yang logik, matematika itu adalah bahasa yang menggunakan istilah yang didefenisikan dengan cermat, jelas, dan akurat, representasinya dengan simbol dan padat, lebih berupa bahasa simbol mengenai ide daripada mengenai bunyi. Matematika merupakan mata pelajaran yang mempunyai peranan yang sangat penting dalam kehidupan manusia. Pentingnya matematika muncul dari kenyataan bahwa matematika perlu untuk dipelajari, dikuasai serta dikembangkan.

  12. Junianto
    PM C

    Dalam dunia pendidikan matematika, tentu tidak pernah terpelas dari dua jenis matematika yaitu matematika formal dan matematika sekolah. Di kalangan sekolah menengah ke bawah, matematika formal belum di ajarkan dan jangan diajarkan karena akan membuat siswa menjadi kesulitan karena matematikanya bersifat abstrak. Matematika sekolah yang diperuntukkan bagi pendidikan dasar dan menengah jangan sampai ditukar dengan matematika formal yang seharusnya di ajarkan di tingkat perguruan tinggi.

  13. Hari Pratikno
    Pendidikan Matematika S2 (Kelas B)

    Pos-pos strategis penentu kebijakan pendidikan nasional harus diisi oleh orang pendidikan. Sehingga paham berbagai aspek tentang kurikulum dan psikologi siswa dalam belajar. Tingkatan perkembangan siswa juga harus diperhatikan dalam menyusun kurikulum nasional, karena jika tidak maka siswa tidak akan belajar bermakna. Juga, karakter harus ditanamkan pada diri siswa, sehingga mereka tidak hanya pandai dalam pikiran saja namun moralnya juga baik.