Research on the Path of Teachers' Professionalism Improvement Based on Principal Component Analysis under the Framework of Basic Theory of Education

Teachers' professional competence levels influence students' learning quality. This paper constructs an evaluation index system for professional competence within the framework of basic educational theory and systematically analyzes the requirements for the development of teachers' professional competence. Principal component analysis (PCA) is used to reduce the dimensionality of the evaluation data. For some non-linear data, kernel principal component analysis (KPCA) is introduced to complete the principal component calculation. By calculating the feature vector load matrix and T² statistic, the principal component factors are extracted, and teachers' professional competence is ranked. The study shows that the sum of the variance contribution rates of the first four principal components is 94.247%. The four principal components are defined as practical professional competence, innovative professional competence, ethical professional competence, and information professional competence. The comprehensive principal component scores of the eight teachers range from [0.015, 0.064]. Based on the principal component analysis results, four pathways for enhancing professional competence were proposed.