Analysis of Students' Problem-Solving Ability on Two-Variable Linear Inequalities Based on Polya's Steps

Abstract

Students in the Mandailing region continue to struggle with the concept of arithmetic sequences because instruction is generally delivered through abstract, decontextualized formulas that ignore learners' cultural surroundings. Although the Gordang Sambilan, a nine-drum ensemble whose playing pattern embodies a numerical sequence, offers a ready-made cultural context for teaching arithmetic sequences, no prior study has translated this instrument into a validated Hypothetical Learning Trajectory (HLT) for classroom use. This study therefore designed and empirically tested an HLT for arithmetic sequences based on the Gordang Sambilan context, using the Realistic Mathematics Education (RME) approach. A design research method comprising three phases, preliminary design, teaching experiment, and retrospective analysis, was carried out with 32 seventh-grade students at SMP Negeri 2 Satu Atap Pangkatan, North Sumatra, selected through purposive sampling across low, medium, and high socioeconomic status (SES) groups. Data were collected through learning outcome tests, participatory interviews, and classroom observations, and were analyzed descriptively-qualitatively by comparing the hypothesized learning steps with students' actual responses, supported by source and technique triangulation. The retrospective analysis showed that students' understanding progressed through the intended learning trajectory, from watching and identifying the Gordang Sambilan's playing pattern, to expressing that pattern informally, to formally defining and computing arithmetic sequences. Paired-samples t-tests indicated statistically significant gains from pre-test to post-test in all three SES groups (p < .001, Cohen's d > 1.80), while a one-way ANOVA found no significant difference in post-test achievement across SES groups, F(2, 29) = 0.93, p = .406, indicating that the trajectory supported comparable gains regardless of students' socioeconomic background. These findings contribute a validated, replicable local instructional theory that demonstrates how Mandailing cultural artifacts can be systematically embedded in RME-based instruction on arithmetic sequences.