Changes in students’ perceptions of logical thinking through a mathematical logic-based instructional model in discrete mathematics

The purpose of this study is to apply a Mathematical Logic-Based Instructional Model (MLIM) consisting of 'Questioning, Mathematical Modeling, and Proof' to a discrete mathematics course to alleviate the cognitive barriers experienced by engineering students and to analyze the changes in learners' perception of logical thinking and their learning experiences.To this end, the model was applied to an actual university lecture for computer engineering majors, and surveys were conducted three times throughout the semester (beginning, middle, and end).The collected data were analyzed using a mixed-methods approach, performing both quantitative analysis of 5-point Likert scale items and qualitative analysis of descriptive responses.The quantitative results showed that learners reported positive changes in their perceptions of logical thinking through the class, and expressed high agreement on the necessity of understanding key units and recalling prerequisite concepts.In particular, positive perceptions of logical thinking significantly increased at the end of the semester compared to the beginning.The qualitative analysis revealed that Thought Elicitation through the instructor's questioning, Logical Structuring through visualization, and Formal Justification through stepwise reasoning, along with support for understanding through recalling prerequisite concepts, played important roles in the learning experience.Many learners responded that they came to perceive proofs and logical formulas not as objects of rote memorization but as a 'process of thinking' .Furthermore, they reported a sense of intellectual achievement, specifically citing a clearer conceptual understanding of major topics such as matrices and functions.These findings suggest that the MLIM is perceived by learners as effective in structuring the logical thinking process while alleviating the cognitive load of engineering students.This study demonstrates that discrete mathematics instruction can be transformed from calculationor procedure-centered learning to education that reflects on and justifies thinking processes.It is significant in presenting a logic-centered instructional model applicable to actual university lecture settings, and further research is suggested to verify its validity and effectiveness by extending its application to various majors and liberal arts courses.