It is important to determine when and why stereotyped movements indicative of developmental disabilities occur in order to provide timely medical treatment. However, these behaviors are unpredictable, which renders their automatic detection very useful. In this paper, we propose a machine learning system that runs on a smartwatch and a smartphone to recognize stereotyped movements in children with developmental disabilities. We train a classifier by tagging data from an accelerometer and a gyroscope in a smartwatch to one of six stereotyped movements made by children and recognized by special educational needs teachers. This classifier can then recognize when a child wearing a smartwatch is making one of the stereotyped movements. These schemes were implemented as a suite of apps used by parents and caregivers. In tests on children and young people with developmental disabilities, the system achieved an average recognition accuracy of 91% when individual training data was used.