Modern trends in the digitalization of education contribute to the active introduction of technology into the process of teaching writing, especially at the preschool stage. The article presents an intelligent system for analyzing the formation of graphomotor skills in preschool children based on mathematical modeling of errors when writing letters using touch devices. The purpose of the research is to develop and test a mathematical model for estimating graphomotor errors, which makes it possible to identify and analyze typical deviations from the standard when performing tasks in the Dexterous Fingers digital application. The model is based on comparing the user’s trajectory with the reference one, represented as piecewise linear functions. Smoothing using the Catmull-Rum spline is used to improve the accuracy of the analysis. A system of metrics is proposed: shape deviation, angular deviation, offset of the start/end points, and similarity metric (Frechet distance). These parameters form an integral assessment of the quality of the task. The app automatically generates progress reports and graphs for educators and parents, as well as provides recommendations for corrective actions. The developed interface visualizes errors, forms recommendations and records progress. This approach significantly expands the possibilities of diagnosing and correcting writing skills, complementing traditional methods of teacher supervision. Thus, the smart electronic application “Dexterous Fingers” is an effective tool for digital pedagogical diagnostics, contributing to the early detection of writing disorders and improving preschool children’s readiness for school education.