BRIDGING OF ARITHMETIC AND ALGEBRA: A RELATIONAL LOCAL INSTRUCTIONAL THEORY
DOI:
https://doi.org/10.24127/ajpm.v15i2.14895Keywords:
Didactical design research, early algebra, equality, Local Instructional Theory, relational understandingAbstract
Bridging arithmetic and algebra remains a persistent challenge in mathematics education, largely due to students’ operational interpretations of the equal sign and fragmented coordination of representations. Existing instructional approaches often emphasize procedural fluency without systematically supporting the relational understanding required to connect these domains. This study aims to develop and examine a relational instructional trajectory that functions as a conceptual bridge between arithmetic and early algebra. Using a Didactical Design Research (DDR) approach, the study involved 29 fifth-grade students from an elementary school in East Java, including five students in a pilot experiment and twenty-four students in a teaching experiment. The “Jembatan Aritmatika (Arithmetic Bridge)” e-module was designed based on an initial analysis of students’ learning obstacles, particularly in understanding equality and symbolic representations. Data were collected through pre- and post-tests, questionnaires, classroom observations, and semi-structured interviews. Data analysis combined qualitative analysis of students’ reasoning patterns with quantitative comparisons of pre- and post-intervention performance. The findings indicate a shift from procedural and counting-based strategies toward relational reasoning. Students increasingly interpreted the equal sign as expressing equivalence and demonstrated improved coordination of symbolic and contextual representations in solving early algebraic tasks. This study contributes a relational Local Instructional Theory (LIT) that specifies a progressive learning trajectory—from contextual and visual representations to symbolic reasoning—and explicit didactical anticipations for bridging arithmetic and algebra, grounded in empirically identified learning obstacles.
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