Proof as a practice of mathematical pursuit in a cultural, socio-political and intellectual context

Siu, Man‐Keung

doi:10.1007/s11858-008-0087-y

Cited by 8 publications

(2 citation statements)

References 11 publications

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“…-122 B.C.E.). [21][22][23][24][25][26][27][28] In Essay 3 entitled "Tianwenxun," one finds the following problem on measuring the height of heaven: "To find the height of heaven (i.e., of the sun) we must set up two 10-che gnomons and measure their shadows on the same day at two places situated exactly 1000 li apart on a north-south line. If the northern one casts a shadow of 2 che in length, the southern one will cast a shadow 1 and 9/10 che long.…”

Section: Daoismmentioning

confidence: 99%

Untitled

2021

AJMS

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There are various schools of mathematical philosophy. However, none of them can be founded on mathematics alone. At the same time, there are two types of mathematical proof styles: Dialectic and algorithm mathematical proof. The relationship between proof and philosophy is to study philosophical problems with mathematical models. This type of proof is important to Hong Kong Secondary education. In addition, teachers should explain the connection between mathematics-based subjects, such as physics, so that lessons are more interesting rather than technical. Mathematics relates to nearly all other subjects, and as such has the role of a "public servant" when it comes to serving them. One role of mathematics is to act as a "rational" instrument for various subjects. This can be shown in many ancient human activities, such as Daoism and Hiu, together with their symbolic representations. These examples are similar to Jewish culture; when discussing confidence, Abraham is often mentioned due to being the "Father of Confidence." Thus, it may be said that mathematics is more than just a servant -it is also a cultural subject that has been recorded throughout history. At the same time, in ancient China, what Daoism tried to do was a searching for the unity between human and nature. This is a kind of Taiwan philosophy. It tells us that there are always connection human and nature. Thus, man should follow strictly to the rule of nature so that one can finally achieve the harmony between man and nature. To conclude, other than mathematical proof, Hong Kong teachers should also allow students to learn the cultural context behind various topics and subjects.

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Section: Daoismmentioning

confidence: 99%

Untitled

2021

AJMS

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“…Secara historis, bukti adalah alat retoris untuk meyakinkan orang lain bahwa pernyataan matematika itu benar (Harel & Sowder, 2007;Krantz, 2007). Untuk meyakinkan, bukti harus selaras dengan norma-norma (misalnya, bentuk penalaran, aturan logis inferensi, mode argumentasi dan mode representasi argumen) dari komunitas yang disajikan (Harel & Sowder, 2007;Siu, 2008;Stylianides, 2007). Bukti yang diajarkan di sekolah saat ini mengkomunikasikan bahwa bukti lebih kepada membangun kebenaran daripada memvalidasi pernyataan berdasarkan pada aksioma yang disepakati (Jahnke, 2010).…”

Section: Bukti Yang Menjelaskanunclassified

Bukti yang Membuktikan dan Bukti yang Menjelaskan dalam Kelas Matematika

Hamdani

Junaidi

Novitasari

et al. 2020

Jurnal. Penelitian. Pengkajian. Pendidikan. e-Saintika

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Tujuan penelitian ini adalah mendeskripsikan secara komprehensif perbedaan bukti yang membuktikan dan bukti yang menjelaskan berdasarkan pertimbangan implikasi kedua bukti tersebut sebagai dasar konstruksi penalaran dan bukti dalam matematika. Kajian dijalani dengan kegiatan menguraikan perbedaan spesifik antara keduanya serta memberikan contoh kasus kedua bukti, dan memberikan justifikasi atas pentingnya pengenalan kedua bukti dalam kelas matematika. Kedua bukti digambarkan dengan permasalahan konsep barisan bilangan ganjil. Bukti yang membuktikan hanya menunjukkan dengan menggunakan induksi matematis, sementara bukti yang menjelaskan menunjukkan dengan bukti Gauss, representasi geometrik bangun titik, dan garis zig-zag. Perbedaan antara keduanya tampak pada pemberian alasan yang berasal dari bukti itu sendiri. Hasil kajian mengindikasikan bahwa peran bukti dalam kelas matematika pada tingkat perguruan tinggi adalah membuktikan/meyakinkan, pada tingkat menengah atas adalah membuktikan dan menjelaskan, dan pada tingkat sekolah menengah pertama dan dasar peran utamanya adalah menjelaskan. Akibatnya bukti matematis tidak hanya membuktikan/menyakinkan, melainkan juga menjelaskan. Karenanya penting mempertimbangkan implikasi bukti dalam kurikulum matematika di sekolah, serta perlunya menyajikan bab materi kepada mahasiswa pendidikan matematika tidak hanya bukti yang membuktikan, melainkan juga bukti yang menjelaskan.Proofs that Prove and Proofs that Explain in Mathematics ClassroomAbstractThe purpose of this study was to comprehensively describe the differences of the proofs that prove and proofs that explain based on the consideration of the implications of the two proofs as the basis for the construction reasoning and proofs in mathematics. The study was undertaken with the activity of describing the specific differences between the two and providing examples of cases of both proofs; and provide justification for the importance of introducing both proofs in mathematics classrooms. Both proofs are illustrated by the problem of the odd number sequence concept. Proofs that prove is only shown using mathematical induction, while proofs that explain shows with Gaussian proof, a geometric representation of point shape, and zigzag line. The difference between the two appears to be the reasoning that comes from the proof itself. The results of the study indicate that the role of proof in mathematics classes at the tertiary level is proving/convincing, at the senior secondary level it is proving and explaining, and at the junior and elementary school level its main role is explaining. As a result, mathematical proof does not only prove/convince, but also explain. It is therefore important to consider the implications of proof in the mathematics curriculum in schools, as well as the need to present chapter materials to mathematics education students not only proofs that prove but also proof that explain.

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Liu Hui Shares His Views with Young Students

Tsiapou

2018

Mathematics, Education and History

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Proof as a practice of mathematical pursuit in a cultural, socio-political and intellectual context

Cited by 8 publications

References 11 publications

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Bukti yang Membuktikan dan Bukti yang Menjelaskan dalam Kelas Matematika

Liu Hui Shares His Views with Young Students

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