Toward a Theoretical Model of Deep Mathematical Thinking: Integrating Deep Learning and Mathematical Reasoning Frameworks

Abstract

In the context of 21st-century education, deep mathematical thinking is key to developing higher-order cognitive abilities. However, current mathematics learning predominantly focuses on procedural skills rather than conceptual understanding and reflection, often hindering the optimal development of students' deep mathematical thinking. Therefore, this study aims to develop a theoretical Deep Mathematical Thinking model through the integration of deep learning pedagogical principles and the mathematical thinking framework. Employing a systematic theoretical synthesis approach, the developed model identifies and interconnects core elements of deep learning, such as conceptual connectivity, intrinsic motivation, and metacognition with components of mathematical thinking, including reasoning, generalization, representation, and abstraction. The outcome is a three levels hierarchical Deep Mathematical Thinking model: the foundational level, the applied cognitive level, and the integrative level. This model offers theoretical and practical implications for curriculum design, assessment, and instructional practices. While still conceptual and requiring further empirical validation, the model is flexible and adaptable across diverse educational levels and contexts, positioning it as a potentially robust conceptual framework for developing reflective and meaningful mathematics learning.