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

Yoga Tegar Santosa; Muhammad Noor Kholid; Naufal Ishartono; Munaaya Fitriyya; Iwan Junaedi

Authors

Yoga Tegar Santosa Universitas Muhammadiyah Surakarta
Indonesia https://orcid.org/0009-0004-6314-6688
Muhammad Noor Kholid Universitas Muhammadiyah Surakarta
Indonesia https://orcid.org/0000-0002-7215-3239
Naufal Ishartono Faculty of Teacher Training and Education, Universitas Muhammadiyah Surakarta
Indonesia
Munaaya Fitriyya Faculty of Health, Universitas Muhammadiyah PKU Surakarta
Indonesia
Iwan Junaedi Faculty of Mathematics and Natural Sciences, Universitas Negeri Semarang
Indonesia

Keywords:

deep learning, educational model, mathematical thinking, reasoning, creativity, higher-order thinking

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.

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