Inductive and Intuitive in Proving the Identity Element of A Group: A Structure of Argumentation
Abstract
This research applies the Toulmin Argumentation Model in identifying the argumentation structure and proving the identity property of a group with an inductive and intuitive approach. This research is qualitative descriptive research, and the instrument is one problem of proving the identity property of a group. Data were collected from a cohort of 30 students who enrolled in the Introduction to Ring Theory course. All participants selected one Subject based on complete and correct answers for further analysis. The results showed that the Subject used his intuition to take one element, which would then be proven as the identity element of a group. Then, the Subject used an Inductive Warrant to prove it. The Subject only takes one element that fulfils the identity property. However, the Subject states that the conclusion applies in general, which makes the argument invalid because valid arguments are based on deductive. At the same time, students at the college level should use a deductive approach to proof. By using the Toulmin Argumentation Model, the subject's ability to formulate and construct arguments in a proof can be seen as structured and clear. This model allows a systematic explanation and strengthens confidence in the validity of the evidence. This research is expected to enrich the understanding of argumentation structure in inductive proofs of group identity properties and show the potential use of the Toulmin Argumentation Model in identifying more in-depth mathematical argumentation.
Penelitian ini menerapkan Model Argumentasi Toulmin dalam mengidentifikasi struktur argumentasi pada pembuktian sifat identitas suatu grup dengan pendekatan induktif dan intuitif. Penelitian ini termasuk penelitian dekriptif kualitatif, dan instrumen berupa satu soal pembuktian sifat identitas suatu grup. Data diperoleh dari 30 mahasiswa yang menempuh mata kuliah Pengantar Teori Gelanggang. Dari seluruh partisipan, satu subjek dipilih berdasarkan jawaban lengkap dan benar untuk dianalisis lebih lanjut. Hasil penelitian menunjukkan bahwa subjek menggunakan intuisinya dalam mengambil satu elemen yang kemudian akan dibuktikan sebagai elemen identitas suatu Grup. Kemudian Subjek menggunakan Warrant Induktif dalam membuktikannya. Subjek hanya mengambil satu elemen yang memenuhi sifat identitas, namun subjek menyatakan bahwa kesimpulan tersebut berlaku secara umum, yang menjadikan argumenya tidak valid. Karena argumen yang valid didasari pada deduktif. Padahal mahasiswa di tingkat perguruan tinggi seharusnya menggunakan pendekatan deduktif dalam pembuktian. Dengan menggunakan Model Argumentasi Toulmin, kemampuan Subjek dalam merumuskan mengonstruksi argumen dalam pembuktian dapat terlihat terstruktur dan jelas. Model ini memungkinkan penjelasan yang sistematis dan memperkuat kepercayaan terhadap validitas pembuktian. Penelitian ini juga menunjukkan kekuatan metode induktif dan intuitif dalam pembuktian matematika, menunjukkan bagaimana pendekatan ini dapat menghasilkan pemahaman yang lebih komprehensif tentang pembuktian matematika. Penelitian ini diharapkan dapat memperkaya pemahaman mengenai struktur argumentasi dalam pembuktian induktif sifat identitas grup dan menunjukkan potensi penggunaan Model Argumentasi Toulmin dalam mengidentifikasi argumentasi matematika yang lebih mendalam.
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