Automatic spoken language assessment (SLA) is a challenging problem due to the large variations in learner speech combined with limited resources. These issues are even more problematic when considering children learning a language, with higher levels of acoustic and lexical variability, and of code-switching compared to adult data. This paper describes the ALTA system for the INTERSPEECH 2020 Shared Task on Automatic Speech Recognition for Non-Native Children’s Speech. The data for this task consists of examination recordings of Italian school children aged 9-16, ranging in ability from minimal, to basic, to limited but effective command of spoken English. A variety of systems were developed using the limited training data available, 49 hours. State-of-the-art acoustic models and language models were evaluated, including a diversity of lexical representations, handling code-switching and learner pronunciation errors, and grade specific models. The best single system achieved a word error rate (WER) of 16.9% on the evaluation data. By combining multiple diverse systems, including both grade independent and grade specific models, the error rate was reduced to 15.7%. This combined system was the best performing submission for both the closed and open tasks.