Obstacles in Constructing Geometrical Proofs of Mathematics-Teacher-Students Based on Boero’s Proving Model

Abstract

This study aimed at identifying the obstacles of mathematics-teacher-students based on Boero’s proving model. This study was conducted using a mix method by applying sequential explanatory strategy. The stages of the research were carried out by taking the quantitative data and revealing the qualitative data using semi-structured interviews. In the result of this study, it was found that most of mathematics-teacher-students had difficulties in constructing geometrical proofs of each Boero’s proving model. Even in the phase of writing formal proof, there were only 6.67% of students could write fully in the cases of indirect proving. There were 13.33% of students in the cases of direct proving. This study concluded several obstacles which students faced in constructing the geometrical proofs formally in each phase of Boero’ proving model. The obstacles included: the difficulty in making a diagrammatic sketch of conjecture which was completely made with the correct geometrical notation; the difficulty in knowing of cause-effect of geometrical problems to be proved, if it involved some conditional sentences; inability to write a conjecture made in the form of geometrical symbols, formulas and axiomatic deduction; the difficulty in selecting a valid statement of the conjecture made and the difficulty in writing formal proof.

Kemampuan Mengkonstruksi Bukti Geometri Mahasiswa Calon Guru Matematika Pada Perkuliahan Geometri

“…Instrumen pada penelitian ini menggunakan tes kemampuan mengkonstruksi bukti geometri. Indikator yang digunakan dalam penyusunan intrumen tersebut mengacu pada: 1) kemampuan membuat sketsa diagram (gambar) dan label geometri dari pernyataan yang akan dibuktikan; 2) kemampuan memanfaatkan konjektur yang telah dikonstruksi 3) kemampuan menentukan langkah awal pembuktian; 4) kemampuan menyusun alur berpikir yang logis; 5) kemampuan menuliskan argumen untuk membuktikan pernyataan; 6) kemampuan memahami dan memanfatkan teorema atau konsep geometri dalam menyusun bukti (Mariotti & eISSN: 2442-4226 Pedemonte, 2019; Arnawa, Sumarno, Kartasasmita, & Baskoro, 2007;Isnarto, 2014;Bieda, Ji, Drwencke, & Picard, 2014;Sommerhoff & Ufer, 2019;Maarif, Perbowo, Noto & Harisman, 2019). Berikut tes mengkonstruksi bukti geometri yang diberikan kepada mahasiswa dengan mengacu pada keenam indikator yang tidak terpisah.…”

“…Pemilihan terhadap postulat dan teorema yang akan digunakan dalam menyusun bukti akan menentukan kebenaran bukti yang diajukan (Magro, 2019). Pemahaman terhadap postulat, teorema dan prinsip-prinsip geometri sangat dibutuhkan dalam kegiatan mengkonstruksi bukti geometri (Maarif, Perbowo, Noto & Harisman, 2019).…”

Penerapan Model Guided Discovery Learning dalam Mengembangkan Kemampuan Mengkonstruksi Bukti Geometri

“…Pembuktian menjadi indikator utama bagi seorang mahasiswa dalam mengembangkan kematangan bermatematik (Otten, Gilbertson, Males, & Clark, 2014;Maarif, Perbowo, Noto, & Harisman, 2019). Sehingga para praktisi di bidang pendidikan matematika mencurahkan pemikiranya untuk melakukan penelitian dalam upaya mengembangkan kemampuan pembuktian bagi para mahasiswa.…”

Depicting Epistemological Obstacles in Understanding the Concept of Sequence and Series

“…On the other hand, students found it challenging to understand the concept of sequence and series (Hardiyanti, 2017;Nopriana et al, 2016). The difficulties mostly due to a lack of understanding of the concepts that are related to daily activities or realistic mathematical problems (Maarif et al, 2019;Ningrum, 2013;Widyatari, 2017). The impact of errors that occur to students is that students cannot understand the intent, direction, and purpose of the questions so that students' answers feel inconsequential in solving problems Widodo et al, 2019.…”