The purpose of exploring output-oriented ways to develop the teaching ability of teacher-training students in mathematics is to help better them improve their teaching ability. Starting from big data analysis technology, this paper first introduces the principle of support vector machines and explains that many types of support vector machines are classified by solving the optimal objective function through the Lagrange multiplier method. Then, the principle of the particle swarm optimization algorithm is introduced, the steps and process of the PSO algorithm are given, and the PSO-SVM classification model is constructed by using the PSO algorithm to optimize the parameters of support vectors. Finally, the PSO-SVM model is used to construct and analyze the evaluation index system with the example of teacher-training students majoring in mathematics at YL University. From the indicators of professional foundation and instructional design, 40%, 39.32%, 14.31%, and 6.35% were evaluated at A, B, C, and D levels, respectively. From the indicators of teaching evaluation and reflective development, the four levels of A, B, C and D evaluations accounted for 40.84%, 24.77%, 15.98% and 18.41%, respectively. This indicates that in addition to theoretical and practical techniques, it is also necessary to train teacher trainees in teaching evaluation and reflective development to improve their teaching ability under the output-oriented approach.