Learning Independence as a Key to Mathematical Connections in Sequences and Series

The ability to make mathematical connections is a critical skill that enables students to relate various mathematical concepts and apply them in diverse contexts. However, many students continue to struggle with this skill, indicating a significant gap in mathematical understanding. This study aims to describe students’ mathematical connection ability through the lens of learning independence—an intersection that has received limited scholarly attention. Employing a qualitative descriptive method, the research involved 25 tenth-grade students, from whom six were selected based on stratified levels of mathematical connection ability (high, middle, and low). Data were collected through a written test focused on arithmetic sequences and series, guided by indicators of mathematical connection adopted from the national high school mathematics textbook. Complementary interviews were conducted to assess aspects of learning independence. The findings reveal that students with high learning independence demonstrated stronger mathematical connection ability, while those in the middle and low categories showed frequent conceptual errors and imprecise reasoning. The novelty of this study lies in its integrated analysis of cognitive and affective dimensions, offering new insights into how learning independence supports mathematical understanding.