Abstract

This article develops a local theory for characterizing metric thinking in the measurement of spatial properties from a multilevel curricular perspective, understood as an analytic lens for scaling measurement processes across curricular complexity rather than as empirical evidence from all educational levels. The study adopts a qualitative, explanatory approach and articulates grounded theory with educational design research. The methodological process was organized into four broad moments, operationalized in five phases: an initial literature-based characterization; the design of learning activities involving length, area, volume, center of mass, and angular measure; implementation with engineering students enrolled in integral calculus; analysis of projected and emergent abilities through grounded performance levels; and refinement of the characterization. The findings propose a robust characterization of metric thinking composed of five cognitive processes: perceiving, recognizing, and distinguishing measurable properties; selecting, using comprehensively, and refining measurement instruments; formulating, operationalizing, and optimizing measurement strategies; applying measurement; and developing a critical perspective on measurement. These processes are interpreted as cyclic and mutually connected rather than hierarchical or linear. Within the university engineering tasks analyzed, they also show how measurement can mediate connections between advanced mathematical domains and STEM-related problem contexts. The article concludes by offering a definition of metric thinking that may guide research, curriculum design, and instruction while requiring further validation beyond the university context examined in this study.

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