Profil Folding Back Siswa SMA dalam Menyelesaikan Masalah Matematika berdasarkan Jenis Kelamin

Folding Back Profile of High School Students in Solving Mathematical Problems by Gender

Patmaniar. 2022. Profil Folding Back Siswa SMA dalam Menyelesaikan Masalah Matematika berdasarkan Jenis Kelamin. Disertasi, Program Studi S3 Pendidikan Matematika, Pascasarjana, Universitas Negeri Surabaya. Pembimbing (I): Prof. Dr. Hj. Siti Maghfirotun Amin, M.Pd. dan (II) Dr. Raden Sulaiman, M.Si.

Kata-kata kunci: pemahaman, folding back, masalah matematika, jenis kelamin.

 Pirie & Kieren (1994) merepresentasikan pemahaman matematika sebagai proses pertumbuhan yang utuh, dinamis, berlapis tapi tidak linear, dan tidak pernah berakhir. Teori Pirie & Kieren mengemukakan delapan level pemahaman, yaitu: primitive knowing, image making, image having, property noticing, formalising, observing, structuring, dan inventising. Kunci utama teori pemahaman Pirie & Kieren adalah folding back yaitu kembali ke level pemahaman yang lebih dalam ketika dihadapkan dengan suatu masalah pada level pemahaman yang lebih luar.

Penelitian ini bertujuan untuk mendeskripsikan folding back siswa SMA dalam menyelesaikan masalah matematika berdasarkan jenis kelamin. Adapun tujuan secara spesifik penelitian ini, yaitu (1) mendeskripsikan profil folding back siswa laki-laki dalam menyelesaikan masalah matematika, dan (2) mendeskripsikan profil folding back siswa perempuan dalam menyelesaikan masalah matematika.

Penelitian ini merupakan penelitian deskriptif dengan pendekatan kualitatif. Penelitian ini dilaksanakan di SMAN 2 Bone. Dari enam kelas XI MIA SMA dipilih secara purposive kelas XI MIA 1 yang terdiri dari 12 siswa laki-laki dan 21 siswa perempuan yang diberikan Tes Kemampuan Matematika (TKM) untuk menetapkan calon subjek. Penetapan subjek menggunakan teknik purposive sampling yaitu berdasarkan kriteria, yaitu (1) nilai Tes Kemampuan Matematika (TKM), dan dokumen nilai matematika siswa pada Ujian Akhir Semester (UAS) dengan mempertimbangkan Kriteria Ketuntasan Minimal (KKM) pada mata pelajaran matematika di SMAN 2 Bone, yaitu 75. Pasangan subjek yang terpilih adalah satu siswa laki-laki dengan inisial MNAR dan satu siswa perempuan dengan inisial AWAR. Pasangan subjek yang terpilih diberikan soal Tes Pemecahan Masalah Matematika (TPMM) dan dilakukan wawancara berdasarkan jawaban Tes Pemecahan Masalah Matematika (TPMM).

Instrumen penelitian, yaitu peneiti sendiri sebagai instrumen utama dan instrumen pendukung yang divalidasi berupa Tes Kemampuan Matematika (TKM),  Tes Pemecahan Masalah Matematika (TPMM) dan pedoman wawancara. Teknik pengumpulan data adalah pemberian tes dan wawancara. Terdapat dua jenis tes yaitu yang digunakan untuk memilih calon subjek yang memenuhi kriteria dan Tes Pemecahan Masalah Matematika (TPMM) digunakan untuk mengetahui folding back siswa SMA dalam menyelesaikan masalah matematika. Data hasil Tes Pemecahan Masalah Matematika (TPMM) dilanjutkan dengan wawancara. Untuk mengecek kredibilitas, validitas, dan keabsahan data yang diperoleh, peneliti menggunakan teknik triangulasi waktu.

Hasil penelitian menunjukkan ada perbedaan folding back siswa dalam menyelesaikan masalah. Siswa laki-laki melakukan folding back sebanyak tiga kali, yaitu 1) pada level image having, siswa laki-laki melakukan folding back ke level primitive knowing; 2) pada level formalising, siswa laki-laki melakukan folding back ke level primitive knowing; dan 3) pada level stucturing, siswa laki-laki melakukan folding back ke level observing. Selanjutnya, siswa perempuan melakukan folding back sebanyak empat kali, yaitu 1) pada level image having, siswa perempuan melakukan folding back ke level primitive knowing; 2) pada level formalising, siswa perempuan melakukan folding back ke level image having; 3) pada level formalising, siswa perempuan melakukan folding back ke level primitive knowing; dan 4) pada level observing, siswa perempuan melakukan folding back ke level formalising.

Siswa laki-laki dan siswa perempuan mampu melakukan kegiatan pemahaman, antara lain menjelaskan informasi suatu masalah matematika, mendefinisikan konsep, memiliki gambaran umum tentang topik tertentu, mengidentifikasi persamaan dan perbedaan, mengabstraksikan konsep matematika, dan memahami ide-idenya sesuai dengan yang diberikan.

Patmaniar. 2022. Folding Back Profile of High School Students in Solving Mathematical Problems by Gender. Dissertation, Mathematics Education Study Program, Postgraduate, Surabaya State University. Supervised by (I): Prof. Dr. Hj. Siti Maghfirotun Amin, M.Pd, and (II) Dr. Raden Sulaiman, M.Si.

Keywords: understanding, folding back, mathematical problem, gender.

Pirie & Kieren (1994) represent the understanding of mathematics as a whole, dynamic, layered, but not linear, and never-ending growth process. Pirie & Kieren’s theory suggests eight levels of understanding, namely: primitive knowing, image making, image having, property noticing, formalising, observing, structuring, and inventising. A key of the Pirie-Kieren theory is folding back, namely returning to an inner level of understanding when faced with a problem at the outer layer.

This study aims to describe the folding back of high school students in solving math problems based on gender. The specific objectives of this study are (1) to describe the folding back profile of male student in solving math problems, and (2) to describe the folding back profile of female student in solving math problems.

This research was a descriptive research with a qualitative approach. This research was conducted at SMAN 2 Bone. Of the six class XI MIA SMA that were chosen purposively, class XI MIA 1 became the chosen class. This class consisted of 12 male students and 21 female students who were given a Mathematical Ability Test (TKM) to determine prospective subjects. Determination of the subject using a purposive sampling technique that was based on the criteria, namely (1) the value of the Mathematics Ability Test (TKM), and the student’s mathematical score document in the Final Semester Examination (UAS) by considering the Minimum Completeness Criteria (KKM) in mathematics subjects at SMAN 2 Bone , which was 75. The selected subjects pair were one male student with the initials MNAR and one female student with the initials AWAR. The selected subjects were given the Mathematical Problem Solving Test (TPMM) questions and an interview was conducted based on the answers to the Mathematical Problem Solving Test (TPMM).

In this study, the researcher acted as the main instrument and validated supporting instruments were in the form of a Mathematical Ability Test (TKM), Mathematical Problem Solving Test (TPMM) and interview guidelines. Data collection techniques were giving tests and interviews. There were two types of tests in this study, namely the test used to select prospective subjects who met the criteria and the Mathematical Problem Solving Test (TPMM) which was used to determine the folding back of high school students in solving math problems. The results of the Mathematics Problem Solving Test (TPMM) were followed by interviews. To check the credibility, validity, and validity of the data obtained, the researcher used a time triangulation technique.

The results showed that there were differences in students’ folding back profile in solving problems. Male student did folding back three times, namely 1) at the level of image having, male student did folding back to the level of primitive knowing; 2) at the formalising level, male student did folding back to the primitive knowledge level; and 3) at the structuring level, male student conducted folding back to the observing level. Furthermore, the female student did the folding back four times, namely 1) at the image having level, the female student did the folding back to the primitive knowing level; 2) at the level of formalizing, female student did folding back to the level of image having; 3) at the formalizing level, female student did folding back to the primitive knowing level; and 4) at the observing level, female student did folding back to the formalizing level.

Male student and female student were able to carry out understanding activities, including explaining information on a mathematical problem, defining concepts, having an overview of certain topics, identifying similarities and differences, abstracting mathematical concepts, and understanding ideas as given.