Converting source or unit test code to English has been shown to improve the maintainability, understandability, and analysis of software and tests. Code summarizers identify 'important' statements in the source/tests and convert them to easily understood English sentences using static analysis and NLP techniques. However, current test summarization approaches handle only a subset of the variation and customization allowed in the JUnit assert API (a critical component of test cases) which may affect the accuracy of conversions. In this paper, we present our work towards improving JUnit test summarization with a detailed process for converting a total of 45 unique JUnit assertions to English, including 37 previously-unhandled variations of the assertThat method. This process has also been implemented and released as the AssertConvert tool. Initial evaluations have shown that this tool generates English conversions that accurately represent a wide variety of assertion statements which could be used for code summarization or other NLP analyses.