Instructional design and its implementation: the case of the process of objectification of the rational number through measurement processes - Walter F. Castro; Jose Wilde Cisneros; Rodolfo Vergel (Discover Education, 2025)
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.