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Instructional design and its implementation: the case of the process of objectification of the rational number through measurement processes.

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Title: Instructional design and its implementation: the case of the process of objectification of the rational number through measurement processes.
Authors: Castro, Walter F.1 (AUTHOR) walter.castro@udea.edu.co, Cisneros, Jose Wilde2 (AUTHOR) jose.wilde@gmail.com, Vergel, Rodolfo3 (AUTHOR) rvergelc@udistrital.edu.co
Source: Discover Education. 6/23/2025, Vol. 4 Issue 1, p1-21. 21p.
Subject Terms: *Mathematics education, *Seventh grade (Education), *Instructional systems design, *Cognition, Rational numbers, Reification, Calibration, Mathematics
Abstract: Introduction: In this paper, we present how seventh-grade students become aware of rational numbers during mathematics instruction through the social process of objectification when comparing two magnitudes. Methods: Theoretical elements of the Theory of Objectification and the Onto-Semiotic Approach to Mathematical Instruction and Cognition guide the design of mathematical activities are presented. Both theoretical schemes allow and enable the articulation of mathematical knowledge that recognizes the role played by human activity and interaction processes in social practices, particularly historically and culturally constituted mathematical practices through which the subjects transform and position themselves. The design proposal used measurement to introduce meanings derived from fractions (such as proportion, part-whole relationship, and fraction as a quotient). Result: Students expressed the comparison relationship between two magnitudes to quantify the rational number. Conclusion: The analyses suggest that students made progress in objectifying rational numbers, in which measurement played an important role. [ABSTRACT FROM AUTHOR]
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Database: Education Research Complete
Description
Abstract:Introduction: In this paper, we present how seventh-grade students become aware of rational numbers during mathematics instruction through the social process of objectification when comparing two magnitudes. Methods: Theoretical elements of the Theory of Objectification and the Onto-Semiotic Approach to Mathematical Instruction and Cognition guide the design of mathematical activities are presented. Both theoretical schemes allow and enable the articulation of mathematical knowledge that recognizes the role played by human activity and interaction processes in social practices, particularly historically and culturally constituted mathematical practices through which the subjects transform and position themselves. The design proposal used measurement to introduce meanings derived from fractions (such as proportion, part-whole relationship, and fraction as a quotient). Result: Students expressed the comparison relationship between two magnitudes to quantify the rational number. Conclusion: The analyses suggest that students made progress in objectifying rational numbers, in which measurement played an important role. [ABSTRACT FROM AUTHOR]
ISSN:27315525
DOI:10.1007/s44217-025-00507-5