Designing a Hypothetical Learning Trajectory Based on Students’ Learning Obstacles in the Transition from Arithmetic Thinking to Algebraic Thinking among Seventh-Grade Students

This study aims to identify students’ learning obstacles in the transition from arithmetic thinking to algebraic thinking and to design a Hypothetical Learning Trajectory based on these findings through a Didactical Design Research approach in the prospective analysis stage. This research employed an exploratory qualitative method involving 33 seventh-grade junior high school students selected through purposive sampling. Data were collected through diagnostic tests, teacher interviews, student interviews, and document analysis, and were analyzed using the Miles and Huberman model, consisting of data reduction, data display, and conclusion drawing. The findings reveal that students experience ontogenetic, epistemological, and didactical learning obstacles, particularly in understanding variables, coefficients, constants, algebraic term structures, and relationships among verbal, numerical, symbolic, and geometric representations. Based on these findings, a Hypothetical Learning Trajectory was developed, consisting of progressive learning stages from understanding the meaning of algebraic symbols, recognizing structural relationships among algebraic elements, connecting multiple representations, to performing substitution operations. In conclusion, the developed Hypothetical Learning Trajectory is anticipatory and grounded in students’ learning obstacles, providing a systematic and adaptive foundation for mathematics instructional design that supports the development of students’ algebraic thinking.