Fostering understanding of infinite geometric series through a visual area model
a didactic design based on APOS theory
DOI:
https://doi.org/10.22633/rpge.v30iesp2.21364Keywords:
Infinite geometric series, APOS theory, Area model, Didactic engineering, Visual representationAbstract
This study investigates how a visual area model (iterative unit square subdivision) influences students’ construction of the sum of an infinite geometric series, and clarifies the cognitive mechanisms involved. Following a didactic engineering approach, 52 Grade 11 students completed a four-question worksheet. Data from worksheets and semi-structured interviews were analyzed using APOS-based coding. The visual model appeared to facilitate completion (36.5% of students correctly predicted the limit 1/3 before formal instruction) and encapsulation (61.5% reached the Object level). However, generalization to arbitrary ratios remained challenging (only 34.6% achieved Schema). The study extends APOS theory by demonstrating that visual totality alone can trigger completion and encapsulation, even without full algebraic mastery. It also offers a refinement of the genetic decomposition for infinite geometric series, highlighting the need for additional scaffolding in generalization. A ready‑to‑use instructional design is provided.
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