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Educational data classification has become an effective tool for exploring the hidden pattern or relationship in educational data and predicting students' performance or teachers' competency. This study proposes a new method based on machine learning algorithms to predict the technology-integrated competency of pre-service mathematics teachers. In this paper, we modified the inertial subgradient extragradient algorithm for pseudomonotone equilibrium and proved the weak convergence theorem under some suitable conditions in Hilbert spaces. We then applied to solve data classification by extreme learning machine using the dataset comprised of the technology-integrated competency of 954 pre-service mathematics teachers in a university in northern Thailand, longitudinally collected for five years. The flexibility of our algorithm was shown by comparisons of the choice of different parameters. The performance was calculated and compared with the existing algorithms to be implemented for prediction. The results show that the proposed method achieved a classification accuracy of 81.06%. The predictions were implemented using ten attributes, including demographic information, skills, and knowledge relating to technology developed throughout the teacher education program. Such data driven studies are significant for establishing a prospective teacher competency analysis framework in teacher education and contributing to decision-making for policy design. [ABSTRACT FROM AUTHOR]