Kurrotul Hasanah
Universitas Negeri Surabaya

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THE CONSTRUCTION PROCESS OF NEW CONCEPT BASED ON APOS THEORY: MALE VS FEMALE IN DIRECT PROPORTION Abdul Haris Rosyidi; Kurrotul Hasanah
AKSIOMA: Jurnal Program Studi Pendidikan Matematika Vol 11, No 4 (2022)
Publisher : UNIVERSITAS MUHAMMADIYAH METRO

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1248.195 KB) | DOI: 10.24127/ajpm.v11i4.5706

Abstract

The concept construction process makes students' mathematical knowledge develop better than before. It’s because the concept construction process involves the relationship of one concept to another. In constructing a mathematical concept, gender is influential in process. This qualitative research aims to describe the process of constructing new concept of male and female students. The subjects were two sixth grade elementary school students (one male, one female). The instruments were test and interview. The data analyzed using APOS theory (Action, Process, Object, Schema). At action stage, they can solve problems related to direct proportion concept. At process stage, they can interpret direct proportion problem into various representations and explain the characteristics. At object stage, they can provide other examples of direct proportion concept and identify a problem including direct proportion concept or not. At schema stage, they can define direct proportion but female student was clearer in defining it than male student. They can also conclude its relationship with some concepts. They can construct new concept well, although there are errors in the process. Female student is better than male student at conveying the results of her thoughts both in writing and verbally in the process of constructing new concept.Proses konstruksi konsep menjadikan pengetahuan matematika siswa berkembang lebih baik dari sebelumnya. Hal ini karena proses konstruksi konsep melibatkan hubungan antara satu konsep dengan konsep lainnya. Dalam membangun konsep matematika, jenis kelamin berpengaruh dalam prosesnya. Penelitian kualitatif ini bertujuan untuk mendeskripsikan proses konstruksi konsep baru siswa laki-laki dan perempuan. Subjek penelitian adalah dua siswa kelas VI SD (satu laki-laki, satu perempuan). Instrumen yang digunakan adalah tes dan wawancara. Data dianalisis menggunakan teori APOS (Aksi, Proses, Objek, Skema). Pada tahap aksi, mereka dapat memecahkan masalah yang berkaitan dengan konsep perbandingan senilai. Pada tahap proses, mereka dapat menginterpretasikan masalah perbandingan senilai ke dalam berbagai representasi dan menjelaskan karakteristiknya. Pada tahap objek, mereka dapat memberikan contoh lain dari konsep perbandingan senilai dan mengidentifikasi suatu masalah termasuk konsep perbandingan senilai atau bukan. Pada tahap skema, mereka dapat mendefinisikan perbandingan senilai tetapi siswa perempuan lebih jelas dalam mendefinisikannya daripada siswa laki-laki. Mereka juga dapat menyimpulkan hubungannya dengan beberapa konsep. Mereka dapat mengonstruksi konsep baru dengan baik, meskipun ada kesalahan dalam prosesnya. Siswa perempuan lebih baik daripada siswa laki-laki dalam menyampaikan hasil pemikirannya baik secara tertulis maupun lisan dalam proses mengonstruksi konsep baru.
The Process of System of Linear Equations in Three Variables Solving Procedure’s Construction Using Analogy: Individual VS Paired Kurrotul Hasanah; Abdul Haris Rosyidi
MATHEdunesa Vol 12 No 2 (2023): Jurnal Mathedunesa Volume 12 Nomor 2 Tahun 2023
Publisher : Program Studi S1 Matematika UNESA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathedunesa.v12n2.p534-556

Abstract

The process of knowledge construction can provide meaningful learning experiences for students. This is because students build new knowledge themselves by connecting one knowledge to another. The purpose of this qualitative research is to describe the process of new procedure’s construction using analogy. The subjects of the research consisted of three students of grade X high school (one student took the test individually, two students took the test in pair). Data analysis based on the APOS theory’s stage (Action, Process, Object, and Schema). At the action stage, both individual and paired students determine what is known and asked about the system of linear equations (SLE) in three variables problem based on analogy with the known things and asked about the SLE in two variables problem. They correctly determine the solution set of SLE in three variables. They also checked the correctness of the solution set of SLE in three variables correctly. At the process stage, they outline the steps of defining the solution set of SLE in three variables clearly. At the object stage, individual student cannot explain other methods of solving SLE in three variables, while paired students explain four other methods of solving SLE in three variables, that is the method of elimination, substitution, graphing, and matrix. At the schema stage, individual student cannot generalize some methods of solving SLE in three variables, whereas paired student generalize some methods of solving SLE in three variables. They also concluded the most effective method of solving SLE in three variables, that is the combined method. Individual student also explains that there is a SLE in three variables that has no solution, whereas paired students cannot explain it. They can construct new procedure well, despite errors in their process. In the process of new knowledge construction, the student's prior knowledge determines the quality of its construction process.