Strategi Analogi-Abstraksi untuk Membangun Literasi Matematis pada Eksistensi Elemen Identitas dan Elemen Invers pada Materi Grup

Abstract

Abstrak

Fokus dari penelitian ini menerapkan strategi analogi-abstraksi sebagai salah satu strategi untuk  menumbuhkan literasi matematis yakni kemampunan menganalisis, penalaran, memecahkan masalah, dan menafsirkan. Tujuan penelitian ini untuk mendeskripsikan kemampuan literasi matematis mahasiswa pada eksistensi elemen identitas  dan elemen invers pada materi grup dengan melalui strategi analogi-abstraksi. Penelitian ini menggunakan pendekatan kualitatif deskriptif berbasis perkuliahan dan tugas, dengan teknik pengumpulan data melalui tes, lembar pengamatan dengan member check dan wawancara. Proses pengumpulan data secara blended learning  yang dilakukan secara luring dan daring melalui google meet kepada 24 mahasiswa selama 5 pertemuan. Subjek dipilih dari 24 mahasiswa berdasarkan kategori respon selama diskusi dan tanya jawab di setiap pertemuan.   Jumlah subjek yang banyak merespon selama 5 pertemuan diperoleh sebanyak 3 mahasiswa, yang cukup merespon sebanyak 4 mahasiswa, dan yang kurang konsisten 4 mahasiswa, serta yang tidak merespon sama sekali sebanyak 13 mahasiswa. Selanjutnya subjek dipilih berdasarkan perbandingan tetap masing-masing kategori 2 subjek dari tiga kategori merespon.  Hasil tugas dan tes  dari 6 subjek dianalisis secara kualitatif dan kemudian dilakukan wawancara untuk pendalaman. Selanjutnya dilakukan triangulasi sumber dengan memilih pekerjaan yang sama dan kemudian triagulasi metode dilakukan dengan membandingkan hasil pekerjaan tugas dan hasil tes serta wawancara.  Hasil penelitian menunjukkan kemampuan literasi matematis pada subyek kategori sering respon cukup dapat menganalisis, cukup dapat bernalar, cukup dapat memecahkan masalah dan cukup dapat menafsirkan adanya elemen identitas dan elemen invers sebatas pada himpunan terbatas maupun himpunan sebarang dengan operasi biner baku dan non baku. Subyek kategori cukup respon mempunyai kecenderungan kurang dapat menganalisis, kurang dapat bernalar, kurang dapat memecahkan masalah, dan kurang dapat menafsirkan sebatas pada himpunan bilangan dengan operasi biner bentuk baku saja tanpa dapat memahami konsepnya. Subyek kategori jarang merespon mempunyai kecenderungan cukup dapat menganalisis, cukup dapat bernalar dan cukup dapat menafsirkan, namun kurang dapat memecahkan masalah secara baik pada himpunan bilangan dengan operasi biner bentuk baku saja.

Kata Kunci: Literasi Matematis, strategi analogi-abstraksi, elemen identitas dan elemen invers.

Abstract

The focus of this study was to apply analogy-abstraction strategy as one of the strategies to foster mathematical literacy, i.e., analyzing skills, reasoning skills, problem-solving skills, and interpreting skills. The purpose of this study was to describe students' mathematical literacy skills in the existence of identity elements and inverse elements on group topics /materials through analogy-abstraction strategy. This research uses a descriptive qualitative approach based on lectures and assignments, using data collection techniques through tests, observation sheets, member checks, and interviews. The data collection process was done in blended learning (offline and online) using google meet to 24 students for five meetings. Subjects were selected from 24 students based on the categories of responses given during discussions and Q&A at each meeting. The number of subjects who responded with high intensity during five meetings was three students; those who responded with sufficient intensity /moderate were four students, those who were less consistent in responding were four students, and those who did not respond at all were 13 students. Furthermore, the subjects were selected based on a fixed comparison of each category with two subjects from three categories that give the response. The results of the tasks and tests of the six subjects were analyzed qualitatively, and they were given an in-depth interview. Furthermore, the source triangulation was done by choosing the results of the same work /assignment, and then the triangulation method was done by comparing the results of the work /task and the results of tests and interviews. The results showed that mathematical literacy skills in subjects with high response category are that they are sufficiently analytical, sufficiently able to do reasoning, sufficiently able to solve problems, and sufficiently capable of interpreting the existence of identity elements and inverse elements but only to limited sets or sets with standard and non-standard binary operations. The subjects of sufficient/moderate response category tend to be less able to analyze, less able to do reasoning, less able to solve problems, and less able to interpret but only to the set of numbers with binary operations of the standard form without being able to understand the concept. The subjects with a rare response tend to be sufficiently competent to analyze, do reasoning adequately, and interpret adequately, but less able to solve problems well in the set of numbers with binary operations of the standard form only.

Keywords: Mathematical literacy, analogy-abstraction strategy, identity element and inverse element.