Prospective mathematics teachers’ argumentation structure when constructing a mathematical proof: The importance of backing - Christina Martha Laamena; Toto Nusantara (Universitas Islam Negeri (UIN) Mataram, 2019)
[English]: This qualitative study with phenomenology design aims to investigate the use of backing and its relation to rebuttal and qualifier in prospective mathematics teachers’ (PMTs) argumentation when constructing a mathematical proof about algebraic function. The data were collected through subjects' works on the proof, recorded think-aloud data, and in-depth interviews. Data analysis was guided by Toulmin’s argumentation scheme. The results show that the PMTs used three types of backing, i.e., backing in the form of definitions or theorems (reference backing), examples of numbers (numerical backing) and graphs of functions (graphical backing). The PMTs utilized the backings to strengthen deductive and inductive warrant. A numerical backing is used when a warrant cannot justify the truth of a claim. Graphical backing is used to convince oneself about the truth of the data that has been made while the reference backing is only clarification when students have understood or have knowledge of the statement given. Numerical and graphical backing relate directly to rebuttal and provide counter-examples and qualifier of the claim. A numerical backing makes students more confident about claims that are generated compared to reference backing. Keywords: Argumentation, Mathematical proof, Backing [Bahasa]: Penelitian kualitatif dengan desain fenomenologi ini bertujuan untuk menyelidiki penggunaan backing dan hubungannya dengan rebuttal dan qualifier dalam membangun bukti matematika terkait fungsi aljabar oleh calon guru matematika. Data dikumpulkan melalui hasil kerja siswa, rekaman think aloud, dan wawancara mendalam. Analisis data merujuk pada skema argumentasi Toulmin. Hasil penelitian menunjukkan bahwa backing yang digunakan siswa tidak hanya berbentuk teorema atau definisis (reference backing) tetapi juga contoh-contoh bilangan (numerical backing) dan grafik fungsi (graphical backing). Ketiga jenis backing tersebut untuk memperkuat warrant induktif maupun deduktif. Numerical backing digunakan ketika warrant tidak dapat menjustifikasi kebenaran klaim. Graphical backing digunakan untuk meyakinkan diri sendiri tentang kebenaran klaim yang telah dibuat sedangkan reference backing hanya bersifat klarifikasi karena siswa telah memahami pernyataan yang diberikan. Numerical backing dan graphical backing berhubungan langsung dengan rebuttal untuk memberikan contoh penyangkal dan jaminan kebenaran (qualifier) klaim. Numerical backing membuat siswa lebih percaya diri tentang klaim yang dihasilkan dibandingkan dengan reference backing. Kata kunci: Argumentasi, Bukti matematis, Backing