EKSPLORASI KEMAMPUAN FUNCTIONAL THINKING DAN LEARNING OBSTACLE DALAM MENYELESAIKAN MASALAH ALJABAR AWAL PADA SISWA SEKOLAH MENENGAH PERTAMA

Kemampuan functional thinking merupakan kemampuan individu untuk memahami hubungan antar variabel sebagaimana bekerja dengan fungsi. Memiliki kemampuan ini penting bagi siswa sebagai pengantar untuk memahami aljabar sebagai studi dari fungsi secara formal, mulai dari fungsi linear di SMP, fungsi non-linear di SMA, sampai kalkulus di perguruan tinggi. Meskipun begitu, penelitian terdahulu mengungkapkan berbagai kesulitan siswa dalam menghadapi masalah yang menuntut kemampuan functional thinking ini. Penelitian ini bertujuan untuk mendeskripsikan kemampuan functional thinking siswa dalam menyelesaikan masalah aljabar awal SMP dan bagaimana kemampuan tersebut diperolehnya melalui pengalaman belajar terdahulu. Melalui penelusuran pengalaman belajar, learning obstacle siswa dapat diidentifikasi. Untuk mencapai tujuan tersebut, penelitian kualitatif ini menggunakan desain fenomenologi hermeneutik. Partisipan pada penelitian ini adalah 39 siswa kelas IX SMP dan seorang guru matematika. Pengumpulan data dilakukan melalui triangulasi data yakni tes tertulis, wawancara, dan studi dokumen. Hasil penelitian ini menunjukkan bahwa mayoritas siswa tidak sampai pada level correspondence pada kemampuan functional thinking-nya. Mayoritas siswa hanya sampai level recursive patterns dan covariation, bahkan mengalami kesulitan dalam menyelesaikan masalah. Adapun cara siswa dalam menyelesaikan masalah dipengaruhi oleh pengalaman belajarnya pada konsep aljabar awal (fungsi) yang bersumber dari sajian materi guru dan sumber belajar lainnya seperti buku teks matematika. Oleh karena itu, penelitian ini menunjukkan bahwa siswa mengalami beberapa learning obstacles yaitu ontogenic obstacle (ketidakpahaman siswa pada konsep variabel dan soal cerita), didactical obstacle (guru hanya berfokus pada konsep operasional dari pada struktural fungsi), dan epistemological obstacle (terbatasnya pengetahuan siswa pada konsep variabel dan fungsi). Berdasarkan hasil penelitian, learning obstacles yang teridentifikasi dapat menjadi salah satu pertimbangan untuk membuat desain didaktis materi fungsi yang memfasilitasi siswa untuk mengembangkan kemampuan functional thinking-nya. The functional thinking ability is an individual ability that focuses on the relationship between co-varying quantities (variables) as it works in a function. Acquiring this ability is important for students as it performs as a bridge for them to understand algebra as the study of functions, starting from linear functions in middle school and non-linear functions in high school to calculus in higher education. However, recent studies have revealed multiple challenges that students encounter when solving problems that require functional thinking ability. This study aims to describe junior high school students' functional thinking ability in solving early algebra problems and how their abilities are developed through their previous learning experiences. By exploring students’ learning experiences, their learning obstacles can be identified. To reach this aim, qualitative research with a hermeneutic phenomenological design was conducted in this study. There were 39 ninth graders and a mathematics teacher as the participants in this study. The data were collected using the data triangulation: the written test, the interview, and the document study. According to the findings, the majority of students do not achieve the correspondence level in their functional thinking ability. Many of them are on the recursive patterns or covariation level and are having difficulty solving the problem. Furthermore, the way they solve the problem is influenced by their learning experiences with early algebra concepts, particularly functions, sourced from the task presented by their teacher and other learning sources such as mathematics textbook. As a result, this study reveals that students have some learning obstacles, including ontogenic obstacles (students' lack of comprehension of the concept of variables and in solving word problems), didactical obstacles (the teacher focuses solely on the operational rather than structural concept of a function), and epistemological obstacles (students' limited knowledge in the concept of variables and functions). Therefore, the identified learning obstacles can be one of the references when developing a didactical design in the concept of functions, allowing students to develop their functional thinking ability