Integrating Healthy Psychological Cognition into College Mathematics: Developing Innovative Biotechnological Teaching Models

Abstract

This study addresses the challenges posed by the inherent difficulties of public basic mathematics courses in colleges and universities, which often lead to psychological cognition issues among students. Recognizing the potential of integrating psychological principles into educational frameworks, this paper develops an innovative teaching model that incorporates healthy psychological cognition processes—from knowledge recognition to internalization—specifically tailored for mathematics learning. Utilizing biotechnological approaches, such as data analytics and cognitive modeling, the research establishes and validates a model of psychological characteristics essential for effective mathematics learning. This model was tested through questionnaires that assessed various cognitive dimensions. The findings informed the adjustment of the model's dimensions based on exploratory and confirmatory factor analysis. The practical application of this model is demonstrated through the redesign of course systems, with a specific focus on Probability Theory and Mathematical Statistics. A case teaching method was introduced to optimize learning outcomes, evidenced by a pilot study that showed significant improvements in students’ psychological engagement and academic performance. Prior to implementing the new teaching model, students achieving scores of 90 or above averaged 4.31 ± 0.34 in the "knowledge learning" dimension. Post-pilot, the same student cohort improved to 4.54 ± 0.18, indicating enhanced comprehension and interest levels. This innovative teaching model not only augments students' perceptions and appreciation of the mathematics curriculum but also leverages biotechnological tools to enhance educational practices. The integration of cognitive and psychological insights into the curriculum design represents a significant advancement in educational biotechnology, offering a robust framework for improving student outcomes in challenging academic subjects.