From Mathematical Thinking to Mathematics Teaching: Designing an Approach to Link Thinking Processes with Teaching Methods

Background and Objectives: The purpose of this theoretical-applied research is to elucidate the relationship between mathematical thinking processes and teaching methods, and to present an educational framework for reinforcing the five Process Standards of the National Council of Teachers of Mathematics (NCTM) in the classroom. Mathematical thinking in this article is defined based on the standards of Problem Solving, Connections, Reasoning & Proof, Communication, and Representation, which form the foundation for deep learning of the Content Standards. Methods: The present study employed documentary and content analysis to identify and match appropriate teaching methods with each standard. Findings: Based on the findings, the three approaches to problem solving (teaching about, via, and for problem solving) were proposed to strengthen the key Problem Solving standard. Additionally, Socratic Dialogue and Collabraitive Learning were identified as effective for the Reasoning and Proof and Communication standards, Concept Mapping and Advance Organizers for Connections, and Demonstration Teaching for effective Representation. Conclusion: The results show that the conscious selection of teaching methods not only reinforces each of these standards and processes individually but also, due to the inherent interconnectedness of these standards, leads to an overall enhancement of students' mathematical thinking and meaningful learning of mathematical content.