On-device training of DNNs allows models to adapt and fine-tune to newly collected data or changing domains while deployed on microcontroller units (MCUs). However, DNN training is a resource-intensive task, making the implementation and execution of DNN training algorithms on MCUs challenging due to low processor speeds, constrained throughput, limited floating-point support, and memory constraints. In this work, we explore on-device training of DNNs for Cortex-M MCUs. We present a method that enables efficient training of DNNs completely in place on the MCU using fully quantized training (FQT) and dynamic partial gradient updates. We demonstrate the feasibility of our approach on multiple vision and time-series datasets and provide insights into the tradeoff between training accuracy, memory overhead, energy, and latency on real hardware.