Calculating the Impossible: Student Suspension of Sense-making in an Overspecified and Contradictory Geometry Task

Abstract

Grounded in Brousseau’s theory of didactical situations, this study highlights epistemic validation, often neglected in geometry compared to arithmetic. Addressing the mechanism of "suspension of sense-making," we investigate how valid calculations can mask impossible objects. We analyzed 109 Indonesian students' reasoning regarding an overspecified task containing mutually exclusive side-angle properties. Results classify participants into "Pythagorean Pragmatists" (~80%) exhibiting metacognitive blindness to fulfill the contract, "Procedural Formalists" (~15%) experiencing dissonance, and rare "Critical Whistleblowers" (<5%) capable of validation. These findings frame errors as rational adaptations to school norms, advocating for diagnostic teaching to foster epistemic agency.

Keywords

sense-makingsuspension of sense-makinggeometryoverspecified and contradictory task

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