Digital handwriting acquisition enables the capture of detailed temporal and kinematic signals reflecting the motor processes underlying writing behavior. While handwriting analysis has been extensively explored in clinical or adult populations, its potential for studying developmental and educational characteristics in children remains less investigated. In this work, we examine whether handwriting dynamics encode information related to student characteristics using a large-scale online dataset collected from Japanese students from elementary school to junior high school. We systematically compare three families of handwriting-derived features: basic statistical descriptors of kinematic signals, entropy-based measures of variability, and parameters obtained from the sigma-lognormal model. Although the dataset contains dense stroke-level recordings, features are aggregated at the student level to enable a controlled comparison between representations. These features are evaluated across three prediction tasks: grade prediction, gender classification, and academic performance classification, using Linear or Logistic Regression and Random Forest models under consistent experimental settings. The results show that handwriting dynamics contain measurable signals related to developmental stage and individual differences, especially for the grade prediction task. These findings highlight the potential of kinematic handwriting analysis and confirm that through their development, children's handwriting evolves toward a lognormal motor organization.