DEVELOPMENT OF LEARNING TRAJECTORY-BASED INSTRUCTIONAL MATERIALS ON MAGIC POLYGON TO ENHANCE VOCATIONAL HIGH SCHOOL STUDENTS

Low mathematical logical reasoning and conceptual understanding among Vocational High School (SMK) students remain a major challenge in mathematics education, largely due to procedural instruction and limited exploration of discrete mathematical structures. This study aims to develop and evaluate the validity, practicality, and effectiveness of mathematics learning materials based on the Magic Polygon Learning Trajectory to enhance students' mathematical reasoning and problem-solving abilities. This Research and Development (R&D) study adapted the 4D model (Define, Design, Develop, Disseminate). The developed instructional materials consisted of Teaching Modules, Student Worksheets (LKM), and Student Progress Tests (TPM), structured across four progressive cognitive activity levels: informal, pre-formal, formal, and mastery. The subjects of the field trial were 31 Grade X students of SMKN 1 Seririt. Data were gathered using expert validation sheets, implementation observation sheets, student response questionnaires, and mathematical progress tests (pretest and posttest). The results demonstrated that: the learning materials were highly valid, achieving an average validation score of 3.754 (93%); the materials were highly practical, evidenced by an optimal instructional execution rate of 88% and a 93% positive student response rate; and the materials were effective in significantly enhancing students' achievement, as indicated by an increase in mean test scores from 54.00 to 69.84 (p < 0.05). Qualitative analysis confirmed that the Magic Polygon Learning Trajectory successfully transitioned students' reasoning from random trial-and-error to structured algebraic reasoning across decomposition, pattern recognition, abstraction, and algorithm design stages.