Assessing student answers and providing valuable feedback is crucial for effective learning, but it can be a time-consuming task. Traditional methods of automating student answer assessment through text classification often suffer from issues such as lack of trustworthiness, transparency, and the ability to provide a rationale for the automated assessment process. These limitations hinder their usefulness in practice. In this paper, we explore using ChatGPT, a cutting-edge large language model, for the concurrent tasks of student answer scoring and rationale generation under both the zero-shot and few-shot settings. We introduce a critic module which automatically filters incorrect outputs from ChatGPT and utilizes the remaining ChtaGPT outputs as noisy labelled data to fine-tune a smaller language model, enabling it to perform student answer scoring and rationale generation. Moreover, by drawing multiple samples from ChatGPT outputs, we are able to compute predictive confidence scores, which in turn can be used to identify corrupted data and human label errors in the training set. Our experimental results demonstrate that despite being a few orders of magnitude smaller than ChatGPT, the fine-tuned language model achieves better performance in student answer scoring. Furthermore, it generates more detailed and comprehensible assessments than traditional text classification methods. Our approach provides a viable solution to achieve explainable automated assessment in education.