Many paths, one unknown: Uncovering the diverse minds behind algebraic thinking - Septiani Yugni Maudy (Universitas Sarjanawiyata Tamansiswa, 2025)
This qualitative study examines the diversity in algebraic thinking among high school students (Grades VII-IX) by considering algebraic activity models, reasoning types, and generalization layers. We used clinical interviews along with task-based assessments so that we could investigate students' problem-solving processes with just a hermeneutic phenomenological approach. Participants solved contextualized algebra problems using several solution strategies. These strategies included visual representations, arithmetic generalizations, proportional reasoning, and symbolic parameterization. The findings reveal three key conclusions: (1) students think algebraically and develop along a continuum from concrete representations to abstract symbolic reasoning; (2) cultural and instructional contexts influence their ability to transition between factual, contextual, and symbolic generalization layers quite greatly; and (3) multimodal approaches understand algebra better via accommodating diverse cognitive styles. This study contributes in two primary ways for mathematics education research: First, it analyzes semiotic progression within non-Western educational contexts through such culturally-situated framework, which then addresses a gap for current algebra research. Second, it offers design principles validated empirically for creating inclusive algebraic tasks. These tasks do support multiple entry points as well as solution pathways. The results do show that it is important for us to teach in an adaptive manner by both recognizing and then nurturing diverse mathematical styles of thinking in algebra education.