ANALISIS LEVEL PEMAHAMAN SISWA SMA KELAS X
BERDASARKAN TEORI APOS TOPIK LOGARITMA
Kristiono Novisita Ratu Inawati Budiono
Program Studi S1 Pendidikan Matematika Fakultas Keguruan dan Ilmu Pendidikan Universitas Kristen Satya Wacana Jalan Diponegoro 52-60 Salatiga Jawa Tengah Indonesia
ABSTRACT
Logarithm is an important topic in mathematics because it has many uses in everyday life. Despite this, many students have difficulty in understanding this topic. Student difficulties in understanding logarithms can be anticipated by understanding how students construct this concept of logarithms on in their minds. APOS theory can be used to identify students' understanding of logarithms. In this theory, a mathematical concepts is constructed by the students through four levels of understanding, namely action, process, object and scheme. This study is a qualitative descriptive study in purpose to analyze level of understanding of High School students class X by APOS theory on the topic of logarithms. Subjects of this study consisted of six high school students of class X that has been studied logarithms. Through the activity of working on the problems logarithm given and interviews with each subject were obtained descriptions of abilities in logarithms. These abilities demonstrate the level of understanding possessed high school students in a class X. Each logarithm ability demonstrated by each of the subjects described in this study, in the table form and paragraph form. The results of this study indicate that student with action level of logartihms determine the result of logarithm by guessing and limited to determining the result of the simpel natural logarithm. Students with procces level can determine logarithms of 1 as a result of interioritation of guessing action. Students with object level able to add, subtract, divide and multiply logarithms, but have not a full understanding of the definition of logarithms. Student with scheme level can associate with other concepts exponents logarithms and concept equations involving variable x.
Keywords: Level of understanding, APOS Theory, Logarithms
ABSTRAK
logaritma. Kemampuan-kemampuan tersebut menunjukkan level pemahaman yang dimiliki siswa SMA kelas X. Setiap kemampuan dalam logaritma yang ditunjukkan oleh masing-masing subjek dideskripsikan dalam penelitian ini, baik dalam bentuk tabel, maupun dalam bentuk paragraf. Hasil penelitian ini menunjukkan bahwa pada siswa dengan level pemahaman aksi menentukan nilai logaritma dengan cara menerka dan terbatas pada menentukan nilai logaritma bilangan cacah yang sederhana saja. Siswa dengan level pemahaman proses dapat menentukan logaritma bilangan 1 sebagai hasil interiorisasi aksi menerka. Siswa dengan level pemahaman objek telah dapat menjumlahkan, mengurangkan, membagi dan mengalikan logaritma, akan tetapi belum memiliki pemahaman yang utuh tentang definisi logaritma. Siswa dengan level pemahaman skema dapat mengaitkan logaritma dengan konsep lain eksponen dan konsep persamaan yang melibatkan variabel �.
