Hermeneutics of mathematics learning in Yogyakarta state middle schools

This research aims to: (1) explore the interaction between teachers and Mathematics learning tools; and (2) identify the Mathematical Thinking of junior high school students. A qualitative research design was employed, using a hermeneutic phenomenological approach. The study was conducted in class VIII during the second semester of the 2023/2024 academic year at Yogyakarta State Middle School. The research subjects consisted of 32 eighth-grade students, with 4 students and 1 teacher selected as interview participants. Data were collected through observation, interviews, video recordings, and documentation studies. The validity of the data was ensured through credibility, transferability, and dependability. Data analysis included the following steps: (1) descriptive analysis, which involved compiling detailed research data from observations, interviews, and documentation; (2) interpretive analysis, which involved interpreting participants' experiences; (3) presenting findings; (4) building relationships between categories; and (5) testing the validity of the classifications developed based on the collected data. The conclusions of this research are as follows: (1) The teacher's interaction with Mathematics learning tools includes the use of a problem-based learning approach, a contextual approach, various learning media, and the teacher’s role as an agent of change. (2) Mathematical thinking is linked to Mathematical attitudes, which include: (a) striving to understand the problem, goal, or concept; (b) taking logical actions; (c) expressing problems clearly and concisely; and (d) seeking better solutions. (3) Mathematical thinking is related to Mathematical methods, including inductive, analogical, deductive, and abstract thinking. (4) Mathematical thinking is connected to the content of Mathematics, involving: (a) expressing propositions and formula relationships, and interpreting their meanings (formula ideas); (b) understanding the broader context of objects and operations and applying that understanding (approach ideas); and (c) focusing on basic rules and properties (fundamental property ideas).