CRA-Based Learning in the 21st Century: Empowering Learners Through Inquiry and Conceptual Reasoning in Mathematics in the Modern World

Diansuy, Aileen A.

CRA-Based Learning in the 21st Century: Empowering Learners Through Inquiry and Conceptual Reasoning in Mathematics in the Modern World

James Alexander Gordon on 30th October 2025

Author Information

Aileen A. Diansuy, Antipolo Institute of Technology, Philippines

Abstract

In traditional mathematics education, many students are trained to manipulate symbols without being able to relate these manipulations to actual mathematical concepts in life; this is often a result of the disconnection between theorem application and the real world. The study explored how implementing the CRA (Concrete–Representational–Abstract) instructional framework applied to the Mathematics in the Modern World (MMW) course at the Antipolo Institute of Technology (AiTECH) in the Philippines assisted students in bridging the gap between active learning and using mathematics in a real-world context. Through a qualitative inquiry method, undergraduate students completed four experiential tasks: measuring the architecture of campus buildings for the Golden Ratio; documenting examples of natural Fibonacci sequences; modelling the Four-Color Theorem onto a map of Rizal Province, Philippines; and modelling weighted graphs for the purpose of optimizing transportation within their communities. Information from instructor narratives and digital portfolios of the students showed evidence of successful transitions from conceptual reasoning to abstract. Grounded in physical/visual representation of mathematical objects, students found that they could transition more easily to symbolic representations of mathematics, particularly in the case of complex modelling tasks. Additionally, the inclusion of the digital documentation promoted ethical authorship and community engagement by supporting the students' use of mathematical inquiry within their local communities. This study concludes that using the CRA model for contextualized mathematics instruction fosters cognitive trust, digital fluency, and a framework for scalable mathematics education in diverse institutional settings.