Surabaya memiliki Daerah Surabaya (PERDA) tentang Pengelolaan Sampah dan Kebersihan. Berdasarkan peraturan tersebut tidak hanya badan-badan pemerintah yang wajib melaksanakan pengurangan dan penenganan sampah, namun juga lembaga pendidikan mulai dari jenjang sekolah dasar harus memulai program sekolah berbasis lingkungan atau biasa disebut program adiwiyata. Salah satunya adalah SDN Jambangan I/413 Surabaya. Sekolah berlabel adiwiyata memiliki kurikulum berbasis lingkungan untuk mengintegrasikan mata pelajaran dengan pendidikan lingkungan hidup. Siswa dilibatkan secara aktif dalam pengambilan keputusan mengenai permasalahan sampah dan kegiatan peduli sampah.

                Tujuan penelitian ini adalah untuk mengetahui konsep-konsep Matematika dalam permasalahan sampah dan kegiatan peduli sampah, kemudian mendesain serangkaian aktivitas pembelajaran Matematika terkait dengan permasalahan sampah dan kegiatan peduli sampah yang dapat digunakan guru dengan pendekatan PMRI pada siswa kelas V SDN Jambangan I/413 Surabaya.

                Penelitian ini merupakan penelitian kualitatif yang menggabungkan dua jenis penelitian yaitu transformative research dan design research, dengan dua atau lebih paradigma yang digunakan. Teknik pengumpulan data yang digunakan pada transformative research yaitu narrative writing, observasi partisipan, wawancara, dan analisa dokumen. Sedangkan untuk design research teknik pengumpulan data yang digunakan yaitu observasi non partisipan, wawancara, dokumentasi, dan catatan lapangan. Data disajikan dalam bentuk narasi dan creative writing untuk transformative research. Sedangkan, data design research disajikan dalam bentuk uraian dan tabel untuk menggambarkan kesulitan dan strategi yang digunakan siswa di setiap aktivitas. Adapun teknik keabsahan data yang digunakan pada transformative research yaitu trustworthiness and authenticity, critical reflexivity, crystallization, praksis, dan verisimilitude. Sedangkan pada design research teknik keabsahan data yang digunakan yaitu validitas internal dan realibilitas. Pada design research, ada tiga siklus Hypothethical Learning Trajectory (HLT).

   Hasil penelitian transformative research adalah konsep-konsep Matematika yang ditemukan pada setiap cerita, dongeng, puisi dan gambar illustrasi, yaitu konsep pengolahan data, konsep operasi hitung dan konsep pengukuran (jarak dan berat). Dari situ, dipilih satu topik yang dominan muncul di setiap data, yaitu konsep pengolahan data. Sedangkan hasil dari design research adalah teori pembelajaran lokal yang terdiri dari empat desain aktivitas pembelajaran pada materi pengolahan data. Pada aktivitas 1, siswa mengelompokkan, mencatat, menyajikan data sampah yang dihasilkan kelompoknya dalam tabel frekuensi, membaca data, menyimpulkan bentuk penyajian data tabel frekuensi, mengaitkan data sampah kelompoknya dengan permasalahan sampah dan saling memberikan solusi untuk mengurangi sampah. Pada aktivitas 2, siswa diminta untuk mengelompokkan sampah plastik dan non plastik, menyajikan data dalam bentuk diagram gambar (piktogram), membaca data, menyimpulkan bentuk penyajian diagram gambar, mendaftar lama sampah terurai dan menjelaskan pentingnya memilah sampah. Pada aktivitas 3, siswa diminta untuk mengelompokkan sampah, menyusun sampah, menggambarkan susunan sampah sebagai representasi diagram batang, membaca data, menyimpulkan bentuk penyajian diagram batang dan mengaitkan data sampah temuan dengan data sampah kelompok. Pada aktivitas 4, siswa diminta untuk mencatat data sampah daur ulang dan tidak didaur ulang, menyajikan data dalam bentuk diagram lingkaran, membaca data, menyimpulkan bentuk penyajian diagram lingkaran dan menjelaskan manfaat kegiatan daur ulang sampah.

Kata Kunci: Permasalahan sampah, Penelitian multi paradigma, PMRI, Hypothetical Learning Trajectory

Surabaya has regional regulation concerning Waste and Hygiene Management. Based on the regulation, not only government agencies are obliged to carry out the reduction and handling of waste, but also educational institutions from elementary school level should establish an environment-based school program or commonly called the adiwiyata program. One of the schools is SDN Jambangan I/413 Surabaya. The adiwiyata labeled school has an environment-based curriculum to integrate subjects with environmental education. Students are actively involved in making decisions about waste problems and waste-caring activities.

The purposes of this study were to find out Mathematics concepts in waste problems and waste-caring activities, then design a set of mathematics learning activities related to garbage problems and waste-caring activities that can be used by the teacher with a PMRI approach for fifth-grade students of SDN Jambangan I/413 Surabaya.

                This research was qualitative research that combines two types of research, namely transformative research and design research, with two or more paradigms used. Data collection techniques used in transformative research were narrative writing, participant observation, interviews, and document analysis. While for design research, data collection techniques used were non-participant observation, interviews, documentation, and field notes. Data were presented in the forms of narratives and creative writing for transformative research. Meanwhile, design research data were presented in the forms of descriptions and tables to describe the difficulties and strategies used by students in each activity. The quality standards of the data used in transformative research were trustworthiness and authenticity, critical reflexivity, crystallization, praxis, and verisimilitude. While in the design research, the data validity techniques used were internal validity and reliability. In design research, there were three cycles of the Hypothetical Learning Trajectory (HLT).

The results of transformative research were Mathematical concepts found in every story, fairy tale, poetry and illustration images, namely the concept of data processing, the concept of counting operations and the concept of measurement (distance and weight). From those, one dominant topic appearing in every type of data was chosen for designing the set of mathematical activities,  namely the concept of data processing. Whilst, the result of design research was a local instructional theory consisting of four learning activities in the data processing. In the activity 1, students were grouping, recording, reading data, and concluding the form of table data presentation frequency, linking the group’s waste data with waste problems and providing each other with solutions to reduce waste. In the activity 2, students were asked to classify plastic and nonplastic waste, present data in the form of image diagram (pictogram), read the data, conclude the form of image diagram presentation, register the length of the waste decomposed and explain the importance of sorting waste. In the activity 3, students were asked to classify waste, arrange waste, describe the arrangement of waste as a bar chart representation, read the data, conclude the form of presentation of bar chart and associate the findings of waste data with group waste data. In the activity 4, students were asked to record the data of recycled waste and not recycled, present data in the form of a pie chart, read the data, conclude the form of presentation of a pie chart and explain the benefit of waste recycling activities.

Keyword: Waste problem, multi paradigmatic research, PMRI, Hypothetical Learning Trajectory