<![CDATA[The low capacity of Vocational High School (SMK) students in translating abstract mathematical ideas into structured programming command lines frequently leads to underachieved basic programming competencies. This quantitative investigation was carried out with the primary objective of evaluating the tangible impact of adopting mathematical vector concepts as spatial visualization tools to accelerate students' comprehension of multidimensional array architecture and graphical coordinate determination. A quantitative approach with a pre-experimental design utilizing the One-Group Pretest-Posttest Design model was implemented as the operational research framework. A single group of subjects involved in this experimentation comprised precisely 23 tenth-grade software engineering students. Quantitative data collection instruments were driven by cognitive objective tests administered during the pre-test and post-test phases, complemented by the distribution of closed-ended response questionnaires. Based on empirical data analysis, a convincing academic shift was proven through a sharp surge in the class average score from an initial pre-test score of 58.4 to 82.1 in the final post-test. The acquisition of a normalized gain index (N-Gain) of 0.57 confirms that the effectiveness rate of this interdisciplinary intervention falls into the "moderate" category. Through this convergence modeling, the utilization of geometric representation is significantly proven capable of guiding students' algorithmic reasoning while simultaneously truncating the duration of coding logic errors (debugging).]]>
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