This study investigated 42,643 eighth grade students from 762 secondary schools in 104 districts and counties in the Z province of mainland China and also test the mediating role of self-efficacy in teacher-student relationship prediction of academic achievement. The results show that there are certain gender differences and regional differences in teacher-student relationship, but they have no practical significance; teacher-student relationship and self-efficacy can significantly predict mathematics academic achievement and both have a positive effect; self-efficacy plays an intermediary role between teacher-student relationship and mathematics achievement, and the ratio of the mediating effect to the total effect is 68%.

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Both wrapper and hybrid methods in feature selection need the intervention of learning algorithm to train parameters. The preset parameters and dataset are used to construct several sub-optimal models, from which the final model is selected. The question is how to evaluate the performance of these sub-optimal models? What are the effects of different evaluation methods of sub-optimal model on the result of feature selection? Aiming at the evaluation problem of predictive models in feature selection, we chose a hybrid feature selection algorithm, FDHSFFS, and conducted comparative experiments on four UCI datasets with large differences in feature dimension and sample size by using five different cross-validation (CV) methods. The experimental results show that in the process of feature selection, twofold CV and leaveone-out-CV are more suitable for the model evaluation of low-dimensional and small sample datasets, tenfold nested CV and tenfold CV are more suitable for the model evaluation of high-dimensional datasets; tenfold nested CV is close to the unbiased estimation, and different optimal models may choose the same approximate optimal feature subset.

Online study collaboration is a recent professional development approach that goes beyond school and regional boundaries and even helps reach rural schools in China. In this study, we focused on a specific online study collaboration program to examine its potential benefits for improving participating teachers' expertise in instructional design. Data were collected from the online study collaboration organizers and four main participating schools. The results reveal the program's well-structured process and organization for planning and conducting the online study collaboration. Participating teachers benefited from their sharing and discussions with experts and other teachers. Their instructional designs show many important changes that are aligned with experts' comments. Selected teachers' expertise improvement includes their knowledge about the textbook and content, their perspectives about students' learning and instruction, and their learning of different instructional approaches to engage students in classroom instruction. The use of online study collaboration for improving teachers' expertise and the study's limitations are then discussed.

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