In order to infer the cognitive state of students and provide teachers with the potential learning state of students, a diagnostic teaching model for preschool education in colleges and universities under the background of big data is proposed. By increasing students’ programming ability and modeling students’ theoretical and practical abilities at the same time, the cognitive diagnosis is introduced into the field of computer teaching, so as to make it applicable to computer classrooms and provide students’ cognitive information needed for teaching. The experimental results show that the advantages of the CDF-CSE approach gradually emerge as the training data become sparse (the proportion of training data decreases from 80% to 20%). In the combined questions of the three datasets, when the training set is 20% and MAE is used as the criterion, the CDF-CSE model improves by 47.8%, 65.8%, and 49.8%, respectively, compared with the other methods that perform best on the training set. When the number of questions is small, the CDF-CSE model improves by 37.8%, 42.5%, and 27.7% on RMSE on three datasets, respectively, compared with the best-performing other methods. When there are more questions, it has 32.3%, 36.5%, and 45.6% improvement, respectively. It is concluded that this model can accurately predict students’ performance in computer courses and provide detailed and rich cognitive reports.