Mar 10, 2013

Mathematics and Language 4

@ David:

There are many logical implications for separating mathematics and mathematics education: 1. It will be only the utterances of pure mathematicians about pure mathematics, 2. That mathematics educationist have their separate room for their utterances about both education and mathematics, 3. There will be a kind of demarcation that the pure mathematicians should not talk about primary and secondary education. and also 4. That mathematics education in university should be differentiated with that of primary and secondary schools.

From my above description, I agree with your notion for separating mathematics and mathematics education in the case of pure mathematics room and mathematics education in university. However, I do not agree if it means also for primary and secondary mathematics education room; because, for primary and secondary education, there should be a different nature of mathematics.

Agree or not agree, in my perception, at all level of education (primary, secondary and university) there are existing the ontology of constructivism. Even, for advance mathematicians, they should construct the world of mathematics in each of their math research. At the dimensions of constructivism, it is impossible to separate between your mind and your objects of mind; albeit, it is impossible to separate between your mind and your mathematics. Epistemologicaly, I wish to say that mathematics is ultimately you your self; mathematics is ultimately the students themselves.

David, if you expose your style of teaching, why you seemed not interested to expose the style of learning. For me, the last is more challenging. Again I still found your forcing to use pure mathematics criteria to judge School Mathematics; and I still did not find your interest in School Mathematics. I do not agree with the separation of mathematics and mathematics education if they want to speak about education. However, I agree to expel pure mathematics from primary and secondary teaching; it means that the expelling mathematics will be mathematics is for mathematics, mathematics is an art, mathematics is a King, mathematics is beautiful, mathematics is bla...bla...bla...up to the utterances of pure mathematicians. However, I wish to suggest to pure mathematician for not forcing their self-ego perceptions to the world of young learner. Let the young learners have their efforts to construct/build and get their own perceptions of mathematics.

I do not agree with your argument that because mathematics is partly uses methods which are no longer intuitive, nor which can be made to be so, to make an account and legalize pure mathematicians to organize primary and secondary math curriculum. I agree that in secondary education there should get away from the pure subjective approach; I perceive that is is as the transition stage of learning. It needs much more consideration both from educationist and from mathematicians.

Again I find your immanent "orthodoxy" approach i.e. by INTRODUCING the concepts; you still hard perceive the students as an object of teaching.

I do not agree with your introducing "logic" as a concept; rather I agree to facilitate them to learn it as a way of thinking (method), attitude and activities.

Again, I wish to claim that teaching learning of primary and secondary mathematics is not as simple as pure mathematics think. This is totally not about grounding down every single pure mathematics concepts into the lower level of mathematics education; rather this is about students' constructing of their mathematics.

If I and they have talked much in the same level of ontology and we still have many differences perception; I then have a question about their motivation. I wish to claim that motif is the ground below the truth.


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  2. Ilma Rizki Nur Afifah
    S2 Pendidikan Matematika A

    In university, mathematics and mathematics education are also be distinguished. Mathematics is talked about logic and intuitions are useful in life, such as: calculus, algebra, trigonometry, an so on. Mathematics education is more concern in the method to learn and teach mathematics. Mathematics is need for scientists to develop the mathematical sciences themselves and to set the primary and secondary level curriculum. We cannot underestimate the mathematics of mathematics education itself because many great teachers do not understand the important concepts of mathematics.

  3. iLania Eka Andari
    S2 P.Mat C 2017

    Dalam mempelajari matematika maupun pengajaran matematika, diperlukan konstruksi yang bertahap. Dengan kata lain, siswa sekolah dasar maupun sekolah menengah tidak bisa begitu saja diajarkan mengenai sintesis yang rumit seperti pembuktian rumus. Pembuktian memang merupakan hal yang mendasar. Karena merupakan hal yang mendasar, maka dibutuhkan dasar yang kuat pula untuk membangun pengetahuan dalam pembuktian, karena pembuktian-pembuktian akan mengiringi perjalanan perkembangan matematika seseorang.
    Mengajarkan atau memfasilitasi pengajaran matematika formal untuk siswa hanya dapat dilakukan di tahap operasional formal, yaitu ketika anak berusia 17 tahun ke atas. Pada tahap ini, kemampuan berpikir secara abstrak sudah mulai dibangun. Namun mengajarkan pembuktian kepada siswa SD atau SMP tidak akan efektif dan hanya akan membuat siswa tidak menyenangi matematika. Matematika yang cocok untuk siswa SD dan SMP adalah matematika konkrit dan kontekstual.