Learning place values from 2 digits to multi-digit requires various forms of representation. The representation will bring up a variety of Hypothetical Learning Trajectory (HLT) in the form of predictions of possible student responses, which will later produce the actual student learning trajectory. This study aims to find students' learning trajectory patterns and determine the factors that influence students' learning trajectory patterns in the 3-digit place value material. The research design uses qualitative research. The learning trajectory pattern was obtained through analysing student responses in the field based on the previously designed HLT. The subjects of this study were 50 students of grade II from three elementary schools in the Kebumen Regency. The research instrument is a written test and field notes. The written test contains four place value questions with a horizontal representation strategy. Field notes in the form of student responses by watching videos during the application of lesson design accompanied by making transcripts to further clarify the word for word that comes out as a form of response during learning so that the suitability of the response with HLT can be known. The results of this study indicate that the student's learning trajectory pattern takes place through the application of a didactic design consisting of 4 types of lesson designs that place the number 0 in different positions. The application of didactic design can also direct students to learn independently gradually. Meanwhile, the learning trajectory supporting factors consist of students' prerequisite abilities, planning and learning processes, and the use of learning resources.

Tujuan penelitian ini yaitu meningkatkan kemandirian belajar pada siswa kelas IIIB SDN Jogosimo tahun pelajaran 2020/2021 melalui model discovery learning. Penelitian Tindakan Kelas ini dilaksanakan dalam dua siklus, tiap siklus terdiri dua pertemuan. Hal ini dapat dibuktikan dengan peningkatan persentase sikap kemandirian belajar siswa yang berkriteria sangat tinggi siswa pada setiap siklus serta tercapainya indikator kinerja penelitian. Pada siklus I ketuntasan belajar siswa mencapai 28,57% dan meningkat menjadi 67,86%. Kemudian siklus II ketuntasan belajar siswa meningkat dari 71,43% menjadi 75%.; (3) Penggunaan model discovery learning dapat meningkatkan hasil belajar siswa seiring dengan meningkatnya kemandirian belajar siswa. Hal ini dibuktikan dengan peningkatan ketuntasan belajar siswa pada setiap siklus serta tercapainya indikator kinerja penelitian. Pada siklus I ketuntasan belajar siswa mencapai 28,57% dan meningkat menjadi 39,29%. Kemudian siklus II ketuntasan belajar siswa meningkat dari 46,43% menjadi 82,14%