BETWEEN FORMAL AND INFORMAL THINKING: THE USE OF ALGEBRA FOR SOLVING GEOMETRY PROBLEMS FROM THE PERSPECTIVE OF VAN HIELE THEORY
DOI:
https://doi.org/10.18269/jpmipa.v21i2.44254Keywords:
algebra, geometry, formal and informal thinking, Van Hiele theory, aljabar, geometri, berpikir formal dan informal, teori Van HieleAbstract
This study investigated primary education master program students’ problem solving strategies and their formal and informal thinking ability when dealing with geometry problems that require the use of algebra in its solution processes. In order to do so, an explorative study through individual written test, observation, and field notes, involving 47 primary education master program students was carried out. The perspective of Van Hiele theory on the development of geometric thought was used to interpret student formal and informal thinking strategy when dealing with geometry problems. The results showed that more than half of the students used informal rather than formal algebraic strategies in solving geometry problems; when students used algebraic strategies, their work were imperfect as they still made mistakes in applying the strategies. In the light of Van Hiele theory, it can be concluded that students’ level of thinking are still in between formal and informal thinking when dealing with geometry problems.
Penelitian ini menyelidiki strategi pemecahan masalah mahasiswa program magister pendidikan dasar serta kemampuan berpikir formal dan informal mereka ketika menyelesaikan soal geometri yang memerlukan penggunaan aljabar dalam proses penyelesaiannya. Untuk mencapai tujuan ini, studi eksploratif melalui tes individu tertulis, observasi dan catatan lapangan dilakukan dengan melibatkan 47 mahasiswa program magister pendidikan dasar. Teori Van Hiele digunakan untuk menginterpretasi kemampuan berpikir formal dan informal mahasiswa dalam menyelesaikan soal-soal geometri. Hasil penelitian menunjukkan bahwa lebih dari separuh mahasiswa menggunakan strategi-strategi informal ketimbang strategi-strategi aljabar formal dalam proses penyelesaian soal-soal geometri; ketika mahasiswa menggunakan strategi-strategi aljabar, proses penyelesaian yang mereka lakukan tidak sempurna dan masih melakukan kekeliruan-kekeliruan dalam menerapkan strategi tersebut. Berdasarkan tinjauan teori Van Hiele, dapat disimpulkan bahwa kemampuan berpikir mahasiswa masih berada pada kemampuan antara formal dan informal ketika menyelesaikan soal-soal geometri.
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