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Understanding Before Executing: A Literature Review of Conceptual Fraction Instruction and Its Implications for Upper Elementary Students and Teachers
Ullrich, Toni
Ullrich, Toni
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Abstract
Fractions remain one of the most persistently challenging topics in upper elementary mathematics despite decades of curricular reform. This extended literature review examines the long-term benefits of teaching fractions conceptually before procedurally in upper elementary classrooms, with fraction division serving as the primary focal concept through which this argument is examined, synthesizing research from the 1990s through contemporary systematic reviews. Three interconnected theoretical frameworks guide this analysis: the Conceptual vs. Procedural Knowledge Framework, the Mathematics Achievement Prediction Framework, and the Proficiency Development Framework. Together, these frameworks demonstrate that conceptual-first instruction provides the cognitive foundation for meaningful fraction learning and fraction division understanding specifically, predicts sustained mathematical achievement, and supports knowledge transfer to ratios, proportional reasoning, and algebra. The review also addresses significant counterpoints, including the persistence of whole number bias, which is particularly consequential for fraction division where whole number intuitions about division are most directly contradicted, individual variation in development pathways, and limitations of traditional part-whole instructional approaches. These counterpoints refine rather than undermine the central argument, pointing toward a more nuanced position: procedural instruction alone is demonstrably insufficient, conceptual understanding must come first to initiate meaningful learning, and teachers must remain responsive to individual students as conceptual and procedural knowledge develop in tandem. A consistent finding across the literature is that effective conceptual instruction depends fundamentally on teachers' own conceptual understanding, as many elementary teachers lack the mathematical depth necessary to teach fractions meaningfully. The evidence affirms that improving fraction instruction requires not merely resequencing content, but transforming mathematical experiences through investment in teacher preparation and instructional practices that prioritize conceptual depth over procedural coverage.
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Date
2026-04-28
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University of Wyoming Libraries
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Keywords
Fractions,Conceptual Understanding,Upper Elementary Mathematics,Instruction,Mathematical Achievement,Teacher Preparation
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CC0 1.0 Universal