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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
Language: English
Authors: Walter F. Castro (ORCID 0000-0002-7890-681X), Jose Wilde Cisneros (ORCID 0000-0001-8281-6895), Rodolfo Vergel (ORCID 0000-0002-0925-3982)
Source: Discover Education. 2025 4.
Availability: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
Peer Reviewed: Y
Page Count: 21
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Junior High Schools
Middle Schools
Secondary Education
Elementary Education
Grade 7
Descriptors: Instructional Design, Program Implementation, Measurement, Number Concepts, Middle School Mathematics, Middle School Students, Grade 7, Mathematics Instruction, Semiotics, Fractions, Mathematics Skills
DOI: 10.1007/s44217-025-00507-5
ISSN: 2731-5525
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.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1475219
Database: ERIC
FullText Text:
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  Data: <searchLink fieldCode="AR" term="%22Walter+F%2E+Castro%22">Walter F. Castro</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-7890-681X">0000-0002-7890-681X</externalLink>)<br /><searchLink fieldCode="AR" term="%22Jose+Wilde+Cisneros%22">Jose Wilde Cisneros</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0001-8281-6895">0000-0001-8281-6895</externalLink>)<br /><searchLink fieldCode="AR" term="%22Rodolfo+Vergel%22">Rodolfo Vergel</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-0925-3982">0000-0002-0925-3982</externalLink>)
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  Data: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
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  Data: 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.
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