We investigate the behavior of the partial derivative approach to the change of scale formula and prove relationships among the analytic Wiener integral and the analytic Feynman integral of the partial derivative for the function space integral.

Computer and Smart Device-assisted Learning (CSDL) has gained increasing attention from educational researchers and practitioners in recent years. However, it remains controversial whether student can benefit from CSDL and what moderator could affect the impact of CSDL. Within the specific context of Korea, where the interest in digital education is steadily increasing, the number of empirical studies exploring the causal effect of CSDL remains relatively scarce. The primary objective of this empirical study was to investigate the impact of CSDL on students' academic achievement in Korea. To achieve this objective, a two-way fixed effect model was employed, utilizing a panel dataset spanning three years derived from the 'Korean Education Longitudinal Study 2013'. The findings revealed a significant positive impact of CSDL on students’ Mathematics achievement. Notably, higher income levels, increased availability of computer resources provided by schools, and the implementation of more individualized education were identified as factors that moderate the effect of CSDL on students' achievement levels in Korean and English subjects. These findings underscore the need for an approach that optimizes the educational benefits of CSDL by considering subject-specific characteristics. Furthermore, this study highlights the importance of allocating educational resources, such as computers and smart devices, and integrating individualized educational activities within the classroom environment.

This study investigated changes in the average BMI of 5th and 6th grade elementary school students in Korea and provided foundational data to suggest the role of physical education for student health and set future directions. The 2019–2021 Physical Activity Promotion System (PAPS) of the Korean Ministry of Education was used. Data corresponding to 5th and 6th grade students (124,693 from 2019, 126,226 from 2020, and 117,809 from 2021) in 1,208 elementary schools in Korea were collected. The BMI was obtained by dividing weight by the square of height (㎏/m2). Repeated measures ANOVA was conducted for data analysis, and confidence intervals were modified through the Bonferroni correction for multiple comparisons. The Greenhouse-Geisser correction was used for effects test. The study findings are: First, the average BMI of 5th and 6th grade elementary school students in Korea increased significantly in 2021 compared to 2019 and 2020. Second, changes in the yearly average BMI showed a significant difference depending on gender and grade. Obesity among 5th and 6th grade elementary school students in Korea increased steadily in 2019–2021, which may be due to a decrease in students’ physical activity. Male students showed a steeper increase, regardless of grade.