Application of mathematical modeling in analyzing and optimizing English teaching methods in vocational education

In the era of big data, mathematical and scientific methods significantly contribute to educational reform, continuously revitalizing precision teaching. In this paper, we use the new Hawkes process to collect and vectorize data on how students learn. Then, we use the unique thermal coding method to combine the behavioral feature vector with the teaching feature vector. Finally, we classify the data and use the softmax function to predict the learning effect. Based on the prediction results, a mathematical model for precise teaching optimization of vocational education English has been established, and the decision function is used to solve the problem and optimize teaching methods. It was found that all the indicators of learning behavior characteristics of students in the experimental class applying the teaching method optimization model were significantly improved, and there was a significant difference at the level of 0.05 (P = 0.000<0.05). Furthermore, the students in the experimental class achieved higher academic performance in vocational education English than those in the control class under traditional teaching. This paper provides a scientific basis for teaching English to students in vocational education and provides methodological references and ideas for unfolding individualized and precise learning in classroom teaching.