Students’ Geometric Thinking Based on Van Hiele’s Theory

Abstract

The current study aims to identify the development level of students' geometric thinking in mathematics education department, Universitas Ahmad Dahlan based on van Hiele's theory. This is a descriptive qualitative research with the respondents as many as 129 students. In addition to researchers, the instrument used in this study is a test consisting of 25 items multiple choice questions. The data is analyzed by using Milles and Huberman model. The result shows that there were 30,65% of students in pre-visualization level, 21,51% of students in visualizes level, and 29,03% of students in analyze level, 16,67% of students in informal deduction level, 2,15% of students in deduction level, and 0,00% of student in rigor level. Furthermore, findings indicated a transition level among development levels of geometric thinking in pre-analyze, pre-informal deduction, pre-deduction, and pre-rigor that were 20%; 13,44%; 6,45%; 1,08% respectively. The other findings were 40,32% of students were difficult to determine and 4,3% of students cannot be identified. AbstrakPenelitian ini bertujuan untuk mengidentifikasi level perkembangan berpikir geometri mahasiswa prodi pendidikan matematika UAD berdasarkan teori van Hiele. Pendekatan penelitian yang digunakan adalah deskriptif kualitatif dengan jumlah responden sebanyak 129 siswa. Selain peneliti, isntrumen yang digunakan dalam penelitian ini adalah tes yang terdiri dari 25 butir soal pilihan ganda. Analisis data menggunakan model Milles dan Huberman. Hasil penelitian menunjukkan bahwa terdapat 30,65% mahasiswa pada level pravisualisasi, 21,51% mahasiswa pada level visualisasi, 29,03% mahasiswa pada level analisis, 16,67% mahasiswa berada pada level deduksi informal, 2,15% mahasiswa pada level deduksi, dan 0,00% mahasiswa pada level rigor. Selain itu, ditemukan terdapat level transisi di antara level perkembangan berpikir geometri berturut-turut dari pra analisis, pra deduksi informal, pra deduksi dan pra rigor yaitu 17,20%; 13,44%; 6,45%; 1,08%. Temuan lainnya lagi adalah sebanyak 40,32% mahasiswa sulit diklasifikasikan dan 4,3% mahasiswa tidak bisa diklasifikasikan.

Effect of Two-Dimensional Geometry Learning on Geometric Thinking of Undergraduate Students During the COVID-19 Pandemic

“…Seeing the distribution of geometric thinking levels, students were from level 0 to level 3. However, as in previous studies, reaching level 4 is still uncommon at the student level, if not impossible (Bulut & Bulut, 2012;Fitriyani et al, 2018). Students struggle to reach level 3 (deduction) because they have difficulty thinking and logically organizing evidence.…”

“…Students should understand the importance of deduction and use it to construct geometric theories based on axioms and proofs (Ngirishi & Bansilal, 2019). This is supported by several studies explaining that the undergraduate students' achievement of geometric thinking is at level 3 or formal deductive thinking formal (Bulut & Bulut, 2012;Fitriyani et al, 2018) and infrequently happens to reach the highest level.…”

“…Geometry has great pedagogical value as it can cultivate students' cognitive skills and directly connect mathematics with the real world (Voskoglou, 2017) as well as other fields of science. In addition, learning geometry can train students' logical, systematic, and creative thinking skills (Fitriyani et al, 2018). These skills are indispensable for studying other branches of mathematics and solving everyday life's problems.…”

A Systematic Review on Geometric Thinking: A Review Research Between 2017-2021

“…However, some previous research results showed that many teachers or pre-service teachers have not achieved deductive reasoning (Decano, 2017;Denizli & Erdoğan, 2018). Some research results on geometric thinking level with mathematics preservice teachers as the subject revealed that the majority of them are at level 3 (Bulut & Bulut, 2012;Fitriyani et al, 2018), with level 4 being extremely rare and difficult to achieve. Van Hiele (Van de Walle, 2018) Research on geometry skills of students of Pendidikan Guru Sekolah Dasar (PGSD)/Elementary School Teacher Education Degree Program, Faculty of Education, Universitas Negeri Semarang, showed that the students' characteristics on the types of spatial ability and geometric thinking level are essential to induce the geometry lecture strategy.…”

Anxiety of Students in Visualization, Analysis, and Informal Deduction Levels to Solve Geometry Problems

“…Van Hiele's five geometric thinking levels are as follows (Armah, Cofie, & Okpoti, 2018;Fitriyani & Widodo, 2018;Walle, Folk, Karp, & Williams, 2013;Yudianto et al, 2018): Level 0: Visualization. Students know and name shapes based on the area characteristics and appearance of those shapes will form an embodiment approach.…”